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Prepare, Apply, Assess and Develop Employability Skills with MyLab Economics

86% of students said

MyLab Economics helped them earn higher grades

on homework, exams, or the course

*Source: 2017 Student Survey, n 13,862

MyLabTM Economics is an online homework, tutorial, and assessment program constructed to work with this text to engage students and improve results. It was designed to help students develop and assess the skills and applicable knowl- edge that they will need to succeed in their courses and their future careers.

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Dynamic Study Modules

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of students would tell their instructor to keep using

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For additional details visit: www.pearson.com/mylab/economics

See what more than 55,000 students had to say about MyLab Economics:

“MyLab Economics is the database for all ‘need to know’ information throughout the course. The major incentive is how much insight it gives when studying for a test.”

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Prepare, Apply, Assess and Develop Employability Skills with MyLab Economics

86% of students said

MyLab Economics helped them earn higher grades

on homework, exams, or the course

*Source: 2017 Student Survey, n 13,862

MyLabTM Economics is an online homework, tutorial, and assessment program constructed to work with this text to engage students and improve results. It was designed to help students develop and assess the skills and applicable knowl- edge that they will need to succeed in their courses and their future careers.

Digital Interactives are dynamic and engaging activities that use real-time data from the Federal Reserve’s Economic Data (FRED™) to promote critical thinking and application of key economic principles.

Question Help consists of homework and practice questions to give students unlimited opportunities to master concepts. Learning aids walk students through the problem—giving them assistance when they need it most.

Dynamic Study Modules use the latest developments in cognitive science and help students study chapter topics by adapting to their performance in real time.

% of students who found learning aids helpful

91% 90% 90%

eText Study Plan

Dynamic Study Modules

Pearson eText enhances student learning. Worked examples, videos, and interactive tutorials bring learning to life, while algorithmic practice and self-assessment opportunities test students’ understanding of the material.

The Gradebook offers an easy way for you and your students to see their performance in your course.

of students would tell their instructor to keep using

MyLab Economics

89%

For additional details visit: www.pearson.com/mylab/economics

See what more than 55,000 students had to say about MyLab Economics:

“MyLab Economics is the database for all ‘need to know’ information throughout the course. The major incentive is how much insight it gives when studying for a test.”

— Economics Student, Heaven Ferrel, ECPI University

“I love the ‘Help Me Solve This’ feature. It really helped me figure out what I was doing wrong and how to fix a problem rather than just saying ‘wrong’ or ‘right’.”

— Student, Illinois State University

CVR_PERL3786_03_SE_FEP.indd 3 19/12/2018 16:21

Symbols Used in This Book

∆ [capital delta] = a change in the following variable— for example, the change in p between Periods 1 and 2 is ∆p = p2 - p1, where pi is the price in Period i)

e [epsilon] = the price elasticity of demand

π [pi] = profit = revenue - total cost = R - C θ = proportion or probability or share

Abbreviations, Variables, and Function Names

AFC = average fixed cost = fixed cost divided by output = F>q

AVC = average variable cost = variable cost divided by output = VC>q

AC = average cost = total cost divided by output = C>q

APi = average product of input i—for example, APL is the average product of labor

C = total cost = variable cost + fixed cost = VC + F CS = consumer surplus

D = market demand curve

DWL = deadweight loss

F = fixed cost

i = interest rate

I = indifference curve

K = capital

L = labor

LR = long run

m = constant marginal cost

MC = marginal cost

MPi = marginal (physical) product of input i—for example, MPL is the marginal product of labor

MR = marginal revenue

MRS = marginal rate of substitution

MRTS = marginal rate of technical substitution

n = number of items such as firms in an industry

p = price

PS = producer surplus

Q = market (or monopoly) output

q = firm output

R = revenue = pq

r = price of capital services

s = per@unit subsidy

S = market supply curve

SR = short run

t = specific or unit tax

T = tax revenue (tQ)

TS = total surplus

U = utility

VC = variable cost

w = wage

Y = income or budget

CVR_PERL3786_03_SE_FEP.indd 4 19/12/2018 16:21

Managerial Economics and Strategy

THIRD EDITION

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Managerial Economics and Strategy

THIRD EDITION

Jeffrey M. Perloff University of California, Berkeley

James A. Brander Sauder School of Business, University of British Columbia

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FOR JACKIE, LISA, BARBARA, AND CATHY

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v

Brief Contents Preface xiii

Chapter 1 Introduction 1 Chapter 2 Supply and Demand 9 Chapter 3 Empirical Methods for Demand Analysis 44 Chapter 4 Consumer Choice 87 Chapter 5 Production 124 Chapter 6 Costs 153 Chapter 7 Firm Organization and Market Structure 191 Chapter 8 Competitive Firms and Markets 225 Chapter 9 Monopoly 266 Chapter 10 Pricing with Market Power 307 Chapter 11 Oligopoly and Monopolistic Competition 350 Chapter 12 Game Theory and Business Strategy 385 Chapter 13 Strategies Over Time 424 Chapter 14 Decision Making Under Uncertainty 462 Chapter 15 Asymmetric Information 500 Chapter 16 Government and Business 536 Chapter 17 Global Business 579 Answers to Selected Questions E-1

Definitions E-14

References E-19

Sources for Managerial Problems, Mini-Cases, and Managerial Implications E-27

Index E-38

Credits E-74

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Preface xiii

Chapter 1 Introduction 1

1.1 Managerial Decision Making 1 Profit 2 Trade-Offs 2 Other Decision Makers 2 Strategy 3

1.2 Economic Models 3 MINI-CASE Using an Income Threshold

Model in China 4 Simplifying Assumptions 4 Testing Theories 5 Positive and Normative Statements 6 New Theories 7

1.3 Using Economic Skills in Your Career 7 Summary 8

Chapter 2 Supply and Demand 9 MANAGERIAL PROBLEM Carbon Taxes 9

2.1 Demand 10 The Demand Curve 11 The Demand Function 14 USING CALCULUS Deriving the Slope

of a Demand Curve 16 Summing Demand Curves 16 MINI-CASE Summing Corn Demand Curves 16

2.2 Supply 17 The Supply Curve 18 The Supply Function 19 Summing Supply Curves 20

2.3 Market Equilibrium 20 Using a Graph to Determine the Equilibrium 20 Using Math to Determine the Equilibrium 20 Forces That Drive the Market to Equilibrium 22 MINI-CASE Speed of Adjustment

to New Information 23 2.4 Shocks to the Equilibrium 23

Effects of a Shift in the Demand Curve 23 Q&A 2.1 24 Effects of a Shift in the Supply Curve 25 MINI-CASE The Opioid Epidemic

Reduces Labor Market Participation 26 Q&A 2.2 26 MANAGERIAL IMPLICATION Taking

Advantage of Future Shocks 27

2.5 Effects of Government Interventions 27 Policies That Shift Curves 27 MINI-CASE Occupational Licensing 28 Price Controls 28 MINI-CASE Venezuelan Price Ceilings

and Shortages 30 Sales Taxes 33 Q&A 2.3 35 MANAGERIAL IMPLICATION Cost Pass-Through 36

2.6 When to Use the Supply-and- Demand Model 36 MANAGERIAL SOLUTION Carbon Taxes 37 Summary 39 ■  Questions 39

Chapter 3 Empirical Methods for Demand Analysis 44

MANAGERIAL PROBLEM Estimating the Effect of an iTunes Price Change 44

3.1 Elasticity 45 The Price Elasticity of Demand 45 MANAGERIAL IMPLICATION Changing

Prices to Calculate an Arc Elasticity 47 Q&A 3.1 47 MINI-CASE Demand Elasticities for

Google Play and Apple Apps 49 USING CALCULUS The Point Elasticity of Demand 49 Elasticity Along the Demand Curve 49 Q&A 3.2 51 Other Types of Demand Elasticities 53 MINI-CASE Anti-Smoking Policies May

Reduce Drunk Driving 53 Demand Elasticities over Time 54 Other Elasticities 54 Estimating Demand Elasticities 54

3.2 Regression Analysis 55 A Demand Function Example 55 MINI-CASE The Portland Fish Exchange 57 Multivariate Regression 62 Q&A 3.3 62 Goodness of Fit and the R2 Statistic 63 MANAGERIAL IMPLICATION Focus Groups 64

3.3 Properties and Statistical Significance of Estimated Coefficients 64 Repeated Samples 64 Desirable Properties for Estimated Coefficients 65 A Focus Group Example 65 Confidence Intervals 67 Hypothesis Testing and Statistical Significance 67

Contents

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3.4 Regression Specification 68 Selecting Explanatory Variables 69 MINI-CASE Determinants of CEO Compensation 69 Q&A 3.4 71 Functional Form 72 MANAGERIAL IMPLICATION Experiments 74

3.5 Forecasting 75 Extrapolation 75 Theory-Based Econometric Forecasting 78 MANAGERIAL SOLUTION Estimating

the Effect of an iTunes Price Change 79 Summary 81 ■  Questions 82

Appendix 3A The Identification Problem 85

Chapter 4 Consumer Choice 87 MANAGERIAL PROBLEM Paying Employees

to Relocate 87 4.1 Consumer Preferences 88

Properties of Consumer Preferences 89 MINI-CASE You Can’t Have Too Much Money 90 Preference Maps 90

4.2 Utility 97 Utility Functions 97 Ordinal and Cardinal Utility 98 Marginal Utility 98 USING CALCULUS Marginal Utility 99 Marginal Rates of Substitution 100

4.3 The Budget Constraint 100 Slope of the Budget Line 102 USING CALCULUS The Marginal Rate

of Transformation 102 Effects of a Change in Price on

the Opportunity Set 102 Effects of a Change in Income on

the Opportunity Set 103 Q&A 4.1 104 MINI-CASE Rationing 104 Q&A 4.2 105

4.4 Constrained Consumer Choice 105 The Consumer’s Optimal Bundle 105 Q&A 4.3 107 MINI-CASE Why Americans Buy More

E-Books Than Do Germans 108 Q&A 4.4 109 Promotions 109 MANAGERIAL IMPLICATION Designing

Promotions 111 4.5 Deriving Demand Curves 111 4.6 Behavioral Economics 113

Tests of Transitivity 114 Endowment Effects 114 MINI-CASE How You Ask the

Question Matters 115 Salience 115 MANAGERIAL IMPLICATION Simplifying

Consumer Choices 116

MANAGERIAL SOLUTION Paying Employees to Relocate 117

Summary 118 ■  Questions 119 Appendix 4A The Marginal Rate of Substitution 122 Appendix 4B The Consumer Optimum 123

Chapter 5 Production 124 MANAGERIAL PROBLEM Labor Productivity

During Recessions 124 5.1 Production Functions 125 5.2 Short-Run Production 126

The Total Product Function 127 The Marginal Product of Labor 128 USING CALCULUS Calculating the Marginal

Product of Labor 128 Q&A 5.1 129 The Average Product of Labor 129 Graphing the Product Curves 129 The Law of Diminishing Marginal Returns 132 MINI-CASE Malthus and the Green Revolution 133

5.3 Long-Run Production 134 Isoquants 134 MINI-CASE Self-Driving Trucks 137 Substituting Inputs 138 Q&A 5.2 139 USING CALCULUS Cobb-Douglas

Marginal Products 141 5.4 Returns to Scale 141

Constant, Increasing, and Decreasing Returns to Scale 141

Q&A 5.3 143 MINI-CASE Returns to Scale for Crocs 143 Varying Returns to Scale 144 MANAGERIAL IMPLICATION Small Is

Beautiful 145 5.5 Innovation 146

Process Innovation 146 MINI-CASE Robots and the Food You Eat 147 Organizational Innovation 147 MINI-CASE A Good Boss Raises Productivity 148 MANAGERIAL IMPLICATION Technical

Progress and Competitive Advantage 148 MANAGERIAL SOLUTION Labor

Productivity During Recessions 148 Summary 149 ■  Questions 149

Chapter 6 Costs 153 MANAGERIAL PROBLEM Technology

Choice at Home Versus Abroad 153 6.1 The Nature of Costs 154

Opportunity Costs 154 MINI-CASE The Opportunity Cost of an MBA 155 Q&A 6.1 156 Costs of Durable Inputs 156

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Sunk Costs 157 MANAGERIAL IMPLICATION Ignoring Sunk Costs 158

6.2 Short-Run Costs 158 MINI-CASE Costs of Building a Guitar 158 Common Measures of Cost 159 USING CALCULUS Calculating Marginal Cost 161 Cost Curves 161 Q&A 6.2 163 Production Functions and the Shapes

of Cost Curves 164 Short-Run Cost Summary 167

6.3 Long-Run Costs 168 MINI-CASE Short Run Versus Long Run

in the Sharing Economy 168 Input Choice 169 MANAGERIAL IMPLICATION Cost Minimization

by Trial and Error 174 MINI-CASE The Internet and Outsourcing 175 Q&A 6.3 176 The Shapes of Long-Run Cost Curves 176 MINI-CASE Economies of Scale at Google 178 Q&A 6.4 179

6.4 The Learning Curve 179 MINI-CASE Solar Power Learning Curves 180

6.5 The Costs of Producing Multiple Goods 181 MINI-CASE Medical Economies of Scope 182 MANAGERIAL SOLUTION Technology

Choice at Home Versus Abroad 182 Summary 184 ■  Questions 184

Appendix 6A Calculating Cost Curves 189 Appendix 6B Long-Run Cost Minimization 190

Chapter 7 Firm Organization and Market Structure 191

MANAGERIAL PROBLEM Amazon’s Delivery Services 191

7.1 Ownership and Governance of Firms 192 Private, Public, and Nonprofit Firms 192 MINI-CASE Chinese State-Owned Enterprises 193 Ownership of For-Profit Firms 194 Firm Governance 196

7.2 Profit Maximization 196 Profit 196 Two Steps to Maximizing Profit 197 USING CALCULUS Maximizing Profit 199 Q&A 7.1 200 MANAGERIAL IMPLICATION Marginal

Decision Making 200 Social Responsibility 202 MINI-CASE Trends in Social Responsibility 203 Forcing Firms to Maximize Profit:

The Survivor Principle and Competition for Corporate Control 204

7.3 Profits Over Time 206 Interest Rates 206

Investing and Profit Maximizing Over Time 208 Q&A 7.2 208 MANAGERIAL IMPLICATION Stock Prices

Versus Profit 209 7.4 The Make or Buy Decision 210

Stages of Production 210 Vertical Integration 210 Profitability and the Supply Chain Decision 213 MINI-CASE Netflix 214 MINI-CASE The Gig Economy 215 Market Size and the Life Cycle of a Firm 216

7.5 Market Structure 217 The Four Main Market Structures 217 Comparison of Market Structures 219 Disruptive Innovations and the Evolution

of Market Structure 220 Road Map to the Rest of the Book 220 MANAGERIAL SOLUTION Amazon’s

Delivery Services 221 Summary 221 ■  Questions 222

Chapter 8 Competitive Firms and Markets 225

MANAGERIAL PROBLEM The Rising Cost of Keeping On Truckin’ 225

8.1 Perfect Competition 226 Characteristics of a Perfectly

Competitive Market 226 Deviations from Perfect Competition 228

8.2 Competition in the Short Run 228 How Much to Produce 229 Q&A 8.1 231 USING CALCULUS Profit Maximization

with a Specific Tax 232 Whether to Produce 233 MINI-CASE Fracking and Shutdowns 235 Q&A 8.2 236 MANAGERIAL IMPLICATION Sunk Costs

and the Shutdown Decision 237 The Short-Run Firm Supply Curve 237 The Short-Run Market Supply Curve 238 Short-Run Competitive Equilibrium 240

8.3 Competition in the Long Run 241 Long-Run Competitive Profit

Maximization 241 The Long-Run Firm Supply Curve 242 MINI-CASE The Size of Ethanol

Processing Plants 242 The Long-Run Market Supply Curve 242 MINI-CASE Industries with High Entry and

Exit Rates 243 MINI-CASE An Upward-Sloping Long-Run

Supply Curve for Cotton 246 Long-Run Competitive Equilibrium 246 Q&A 8.3 247 Zero Long-Run Profit with Free Entry 247

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8.4 Competition Maximizes Economic Well-Being 247 Consumer Surplus 248 MANAGERIAL IMPLICATION Willingness to

Pay on eBay 250 MINI-CASE Digital Surplus 251 Producer Surplus 252 Q&A 8.4 254 Q&A 8.5 254 Competition Maximizes Total Surplus 255 MINI-CASE The Deadweight Loss of

Holiday Gifts 257 Effects of Government Intervention 258 Q&A 8.6 258 MANAGERIAL SOLUTION The Rising Cost

of Keeping On Truckin’ 260 Summary 261 ■  Questions 262

Chapter 9 Monopoly 266 MANAGERIAL PROBLEM Brand-Name

and Generic Drugs 266 9.1 Monopoly Profit Maximization 268

Marginal Revenue 268 USING CALCULUS Deriving a Monopoly’s

Marginal Revenue Function 271 Q&A 9.1 271 Choosing Price or Quantity 273 Two Steps to Maximizing Profit 274 USING CALCULUS Solving for the

Profit-Maximizing Output 275 MINI-CASE Apple’s iPad 276 Q&A 9.2 276 Effects of a Shift of the Demand Curve 277 Q&A 9.3 279 MINI-CASE Taylor Swift Concert Pricing 280 Q&A 9.4 280

9.2 Market Power 281 Market Power and the Shape of the

Demand Curve 281 MANAGERIAL IMPLICATION Checking

Whether the Firm Is Maximizing Profit 282 The Lerner Index 283 Q&A 9.5 283 Sources of Market Power 284

9.3 Market Failure Due to Monopoly Pricing 284 Q&A 9.6 286

9.4 Causes of Monopoly 287 Cost-Based Monopoly 288 Q&A 9.7 289 Government Creation of Monopoly 289 MINI-CASE The Canadian Medical

Marijuana Market 290 MINI-CASE Botox 291

9.5 Advertising 293 Deciding Whether to Advertise 293 How Much to Advertise 295

USING CALCULUS Optimal Advertising 295 Q&A 9.8 296 MINI-CASE Super Bowl Commercials 296

9.6 Internet Monopolies: Network Effects and Scale Economies 297 Network Externalities 297 MANAGERIAL IMPLICATION

Introductory Prices 298 Behavioral Network Externalities 298 Two-Sided Markets 299 Natural Monopoly on the Internet 299 MINI-CASE Critical Mass and eBay 300 Disruptive Technologies 300 MANAGERIAL SOLUTION Brand-Name

and Generic Drugs 301 Summary 302 ■  Questions 302

Chapter 10 Pricing with Market Power 307 MANAGERIAL PROBLEM Sale Prices 307

10.1 Conditions for Price Discrimination 309 Why Price Discrimination Pays 309 MINI-CASE Disneyland Pricing 311 Which Firms Can Price Discriminate 311 MANAGERIAL IMPLICATION Preventing Resale 312 MINI-CASE Preventing Resale of Designer Bags 312 Not All Price Differences Are Price

Discrimination 313 Types of Price Discrimination 313

10.2 Perfect Price Discrimination 313 How a Firm Perfectly Price Discriminates 314 Perfect Price Discrimination Is

Efficient but Harms Some Consumers 315 MINI-CASE Botox Revisited 317 Q&A 10.1 318 Individual Price Discrimination 318 MINI-CASE Google Uses Bidding for

Ads to Price Discriminate 319 10.3 Group Price Discrimination 320

Group Price Discrimination with Two Groups 320

USING CALCULUS Maximizing Profit for a Group Discriminating Monopoly 321

MINI-CASE Age Discrimination 323 Q&A 10.2 323 Identifying Groups 325 MANAGERIAL IMPLICATION Discounts 325 Effects of Group Price Discrimination

on Total Surplus 326 10.4 Nonlinear Price Discrimination 327 10.5 Two-Part Pricing 329

Two-Part Pricing with Identical Consumers 330 Two-Part Pricing with Differing

Consumers 331 MINI-CASE Available for a Song 333

10.6 Bundling 334 Pure Bundling 334

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Mixed Bundling 336 Q&A 10.3 337 Requirement Tie-In Sales 338 MANAGERIAL IMPLICATION Ties That Bind 339

10.7 Peak-Load Pricing 339 MINI-CASE Downhill Pricing 340 Peak-Load Pricing with a Capacity Constraint 340 Dynamic Pricing 341 Q&A 10.4 342 MANAGERIAL SOLUTION Sale Prices 343 Summary 344 ■  Questions 345

Chapter 11 Oligopoly and Monopolistic Competition 350

MANAGERIAL PROBLEM Gaining an Edge from Government Aircraft Subsidies 350

11.1 Cartels 352 Why Cartels Succeed or Fail 352 MINI-CASE Employer “No-Poaching” Cartels 354 Maintaining Cartels 355 MINI-CASE Cheating on the Maple

Syrup Cartel 356 11.2 Cournot Oligopoly 357

Airlines 359 USING CALCULUS Deriving the Cournot

Equilibrium 362 The Number of Firms 363 MINI-CASE Mobile Phone Number

Portability 364 Nonidentical Firms 365 Q&A 11.1 366 Q&A 11.2 368 Mergers 369 MINI-CASE Airline Mergers 370

11.3 Bertrand Oligopoly 370 Identical Products 370 Differentiated Products 372 MANAGERIAL IMPLICATION Differentiating

a Product Through Marketing 373 MINI-CASE Rising Market Power 374

11.4 Monopolistic Competition 374 MANAGERIAL IMPLICATION Managing in

the Monopolistically Competitive Food Truck Market 375

Equilibrium 376 Q&A 11.3 377 Profitable Monopolistically

Competitive Firms 377 MINI-CASE Subsidizing the Entry Cost

of Dentists 378 MANAGERIAL SOLUTION Gaining an Edge

from Government Aircraft Subsidies 378 Summary 380 ■  Questions 380

Appendix 11A Nash-Bertrand Equilibrium 384

Chapter 12 Game Theory and Business Strategy 385

MANAGERIAL PROBLEM Dying to Work 385 12.1 Oligopoly Games 388

Dominant Strategies 388 Best Responses 390 Failure to Maximize Joint Profits 392 MINI-CASE Strategic Advertising 394 Q&A 12.1 395 Pricing Games in Two-Sided Markets 396

12.2 Types of Nash Equilibria 397 Multiple Equilibria 397 MINI-CASE Cheap Talk in eBay’s Best

Offer Market 399 MINI-CASE Timing Radio Ads 400 Mixed-Strategy Equilibria 400 MINI-CASE Competing E-Book Formats 404 Q&A 12.2 404

12.3 Information and Rationality 405 Incomplete Information 406 MANAGERIAL IMPLICATION Solving

Coordination Problems 407 Rationality 407 MANAGERIAL IMPLICATION Using Game

Theory to Make Business Decisions 408 12.4 Bargaining 409

Bargaining Games 409 The Nash Bargaining Solution 409 Q&A 12.3 411 USING CALCULUS Maximizing the

Nash Product 411 MINI-CASE Nash Bargaining over Coffee 412 Inefficiency in Bargaining 412

12.5 Auctions 413 Elements of Auctions 413 Bidding Strategies in Private-Value Auctions 414 MINI-CASE Experienced Bidders 415 The Winner’s Curse 416 MANAGERIAL IMPLICATION Auction Design 417 MANAGERIAL SOLUTION Dying to Work 417 Summary 418 ■  Questions 419

Chapter 13 Strategies Over Time 424 MANAGERIAL PROBLEM Intel and AMD’s

Advertising Strategies 424 13.1 Repeated Games 426

Strategies and Actions in Dynamic Games 426 Cooperation in a Repeated

Prisoners’ Dilemma Game 426 MINI-CASE Tit-for-Tat Strategies in

Trench Warfare 429 Implicit Versus Explicit Collusion 430 MINI-CASE Signaling Drug Price Increases 430 Finitely Repeated Games 430

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13.2 Sequential Games 431 Stackelberg Oligopoly 432 Q&A 13.1 435 Credible Threats 436 Q&A 13.2 436

13.3 Deterring Entry 437 Exclusion Contracts 438 MINI-CASE Pay-for-Delay Agreements 439 Limit Pricing 440 MINI-CASE Pfizer Uses Limit Pricing

to Slow Entry 440 Q&A 13.3 441 Entry Deterrence in a Repeated Game 442

13.4 Cost and Innovation Strategies 443 Investing to Lower Marginal Cost 443 Learning by Doing 445 Raising Rivals’ Costs 445 Q&A 13.4 445 MINI-CASE Auto Union Negotiations 446

13.5 Disadvantages of Moving First 447 The Holdup Problem 447 MINI-CASE Venezuelan Nationalization 448 MANAGERIAL IMPLICATION Avoiding

Holdups 449 Too-Early Product Innovation 450 MINI-CASE Advantages and

Disadvantages of Moving First 450 13.6 Behavioral Game Theory 451

Ultimatum Games 451 MINI-CASE GM’s Ultimatum 451 Levels of Reasoning 453 MANAGERIAL IMPLICATION Taking

Advantage of Limited Strategic Thinking 454 MANAGERIAL SOLUTION Intel and AMD’s

Advertising Strategies 454 Summary 455 ■  Questions 456

Appendix 13A A Mathematical Approach to Stackelberg Oligopoly 461

Chapter 14 Decision Making Under Uncertainty 462

MANAGERIAL PROBLEM BP’s Risk and Limited Liability 462

14.1 Assessing Risk 464 Probability 464 MINI-CASE Risk of a Cyberattack 465 Expected Value 466 Q&A 14.1 467 Variance and Standard Deviation 467 MANAGERIAL IMPLICATION Summarizing Risk 469

14.2 Attitudes Toward Risk 469 Expected Utility 469 Risk Aversion 470 Q&A 14.2 472

USING CALCULUS Diminishing Marginal Utility of Wealth 472

MINI-CASE Stocks’ Risk Premium 473 Risk Neutrality 473 Risk Preference 474 MINI-CASE Gambling 474 Risk Attitudes of Managers 476 Q&A 14.3 476

14.3 Reducing Risk 477 Obtaining Information 478 MINI-CASE Bond Ratings 478 Diversification 479 MANAGERIAL IMPLICATION Diversify Your

Savings 481 Insurance 482 Q&A 14.4 483 MINI-CASE Flooded by Insurance Claims 484

14.4 Investing Under Uncertainty 485 Risk-Neutral Investing 485 Risk-Averse Investing 486 Q&A 14.5 487 Oligopolistic R&D Investments Under

Uncertainty 487 14.5 Behavioral Economics and Uncertainty 488

Biased Assessment of Probabilities 488 MINI-CASE Biased Estimates 489 Violations of Expected Utility Theory 490 Prospect Theory 491 MANAGERIAL IMPLICATION Loss Aversion

Contracts 493 MANAGERIAL SOLUTION BP’s Risk and

Limited Liability 493 Summary 494 ■  Questions 495

Chapter 15 Asymmetric Information 500 MANAGERIAL PROBLEM Clawing Back

Bonuses 500 15.1 Adverse Selection 502

Adverse Selection in Insurance Markets 502 Products of Unknown Quality 503 Q&A 15.1 505 Q&A 15.2 506 MINI-CASE Reducing Consumers’ Information 506

15.2 Reducing Adverse Selection 507 Restricting Opportunistic Behavior 507 Equalizing Information 508 MANAGERIAL IMPLICATION Using Brand

Names and Warranties as Signals 509 MINI-CASE Discounts for Data 510 MINI-CASE Adverse Selection and

Remanufactured Goods 511 15.3 Moral Hazard 512

Moral Hazard in Insurance Markets 512 Moral Hazard in Principal-Agent

Relationships 513

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MINI-CASE Honest Cabbies? 513 The Owner-Manager Relationship 514 MINI-CASE Company Jets 514 Q&A 15.3 518

15.4 Using Contracts to Reduce Moral Hazard 519 Fixed-Fee Contracts 519 Contingent Contracts 520 Q&A 15.4 521 MINI-CASE Sing for Your Supper 523 Q&A 15.5 524

15.5 Using Monitoring to Reduce Moral Hazard 525 Hostages 526 MINI-CASE Capping Oil and Gas Bankruptcies 527 MANAGERIAL IMPLICATION Efficiency Wages 527 After-the-Fact Monitoring 528 MANAGERIAL SOLUTION Clawing Back Bonuses 528 Summary 529 ■  Questions 530

Chapter 16 Government and Business 536 MANAGERIAL PROBLEM Licensing Inventions 536

16.1 Market Failure and Government Policy 537 The Pareto Principle 537 Cost-Benefit Analysis 538

16.2 Regulation of Imperfectly Competitive Markets 539 Regulating to Correct a Market Failure 539 Q&A 16.1 541 MINI-CASE Natural Gas Regulation 543 Regulatory Capture 544 Applying the Cost-Benefit Principle

to Regulation 544 16.3 Antitrust Law and Competition Policy 545

Mergers 547 MINI-CASE Are Monopoly Mergers Harmful? 548 Q&A 16.2 548 Predatory Actions 549 Vertical Relationships 550 MINI-CASE Piping Up About Exclusive Dealing 551

16.4 Externalities 552 MANAGERIAL IMPLICATION Disney

Internalizes an Externality 552 The Inefficiency of Competition with

Externalities 553 Reducing Externalities 555 MINI-CASE Pulp and Paper Mill Pollution

and Regulation 557 Q&A 16.3 558 MINI-CASE Why Tax Drivers 559 The Coase Theorem 560 MANAGERIAL IMPLICATION Buying a Town 562

16.5 Open-Access, Club, and Public Goods 562 Open-Access Common Property 563 MINI-CASE Spam 564 Club Goods 565 MINI-CASE Piracy 565 Public Goods 565

16.6 Intellectual Property 568 Patents 568 Q&A 16.4 569 MANAGERIAL IMPLICATION Trade Secrets 570 Copyright Protection 571 MANAGERIAL SOLUTION Licensing Inventions 571 Summary 573 ■  Questions 574

Chapter 17 Global Business 579 MANAGERIAL PROBLEM Responding to

Exchange Rates 579 17.1 Reasons for International Trade 581

Comparative Advantage 581 Q&A 17.1 583 MANAGERIAL IMPLICATION Brian May’s

Comparative Advantage 584 Increasing Returns to Scale 584 MINI-CASE Barbie Doll Varieties 585

17.2 Exchange Rates 586 Determining the Exchange Rate 586 Exchange Rates and the Pattern of Trade 587 MANAGERIAL IMPLICATION Limiting

Arbitrage and Gray Markets 587 Managing Exchange Rate Risk 588

17.3 International Trade Policies 589 Quotas and Tariffs in Competitive Markets 589 MINI-CASE Russian Food Ban 591 Q&A 17.2 594 Rent Seeking 595 Noncompetitive Reasons for Trade Policy 596 MINI-CASE Protection of U.S. Steel,

Aluminum, and Washing Machines 598 Trade Liberalization and the World

Trading System 599 Trade Liberalization Problems 600

17.4 Multinational Enterprises 601 Becoming a Multinational 601 MINI-CASE What’s an American Car? 602 International Transfer Pricing 602 Q&A 17.3 604 MINI-CASE Profit Repatriation 606

17.5 Outsourcing 606 MANAGERIAL SOLUTION Responding

to Exchange Rates 608 Summary 609 ■  Questions 610

Answers to Selected Questions E-1

Definitions E-14

References E-19

Sources for Managerial Problems, Mini-Cases, and Managerial Implications E-27

Index E-38

Credits E-74

Contents

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Preface

What’s New in the Third Edition We have substantially revised the third edition based in large part on the very help- ful suggestions of instructors and students who used the second edition. We have updated and revised every chapter. Key revisions include:

 ● Spreadsheet-based Q&A Exercises are a new feature in Chapters 3, 6–10, and 12–16. This major innovation helps students learn how to address real-world busi- ness problems using spreadsheets, which is an increasingly important skill in today's business world.

 ● Chapters 1, 5, 6, 7, 9, and 14 have a new theme on disruptive innovations: innova- tions, such as online retailing, 3D printing, and social media, that dramatically change consumer options or the way an industry is structured, possibly creating new industries and destroying old ones.

 ● A new feature is the 21 Common Confusions, which explain why a widely held belief is incorrect.

 ● Over three-quarters of the Mini-Cases (brief applications of the theory) are new (22) or revised (48).

 ● Of the 655 end-of-chapter questions, 150 are new or revised.  ● Nearly a quarter of the Managerial Implications (brief discussions of how to

use economic theory to improve managerial decisions) are new or substantially revised.

 ● This edition is even more user-friendly. It drops some of the more technical mate- rial from Chapters 2, 4, 6, 7, 8, and 11, and adds more emphasis on current mana- gerial issues in both the main text and the features.

 ● Because instructors and students enjoyed the cartoons in the second edition, this edition has 45% more cartoons. In addition to providing entertainment, these cartoons convey important economic points in a memorable way.

The Managerial Economics Program This book differs from other managerial economics books in three main ways:

1. Modern Theories. We place greater emphasis than other texts on modern theories that are increasingly useful to managers. These include: • Modern contract theory to show students how to write contracts to avoid or

minimize problems • Behavioral economics to explain why people deviate from rational behavior

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• Game theory to help students think about business strategies and choose strate- gies that maximize profits

• Analysis of real-world pricing tools. 2. Real-world Examples. We make more extensive use of real-world business exam-

ples to illustrate how to use economic theory in making business decisions. To illustrate important economic concepts, we use calculations, graphs, and spread- sheets based on actual markets and real data.

3. Problem-based Learning. We employ a problem-based learning approach to dem- onstrate how to apply economic theory to specific business decisions. In each chapter, we solve problems using a step-by-step approach to model good problem- solving techniques, and each end of chapter section includes an extensive set of questions.

These innovative hallmarks are woven throughout the text. To improve student results, we recommend pairing the text content with MyLab

Economics, which is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and will help students learn and retain key course concepts while developing skills that future employers are seeking in their candidates. MyLab Economics allows professors increased flex- ibility in designing and teaching their courses. Learn more at www.pearson.com/ mylab/economics.

Solving Teaching and Learning Challenges As teachers, we understand the challenges of managerial economics courses. Our experience teaching managerial economics at the Wharton School (University of Pennsylvania) and the Sauder School of Business (University of British Columbia) as well as teaching a wide variety of students at the Massachusetts Institute of Technol- ogy; Queen’s University; and the University of California, Berkeley, has convinced us that students do best with an emphasis on problem solving and real-world issues and examples from actual markets. In the features of the book and MyLab Economics, we show how to apply economic theory to managerial decisions using actual busi- ness examples and real data.

We demonstrate that economics is practical and useful to managers by examining real markets and actual business decisions. Successful managers make extensive use of economic tools to reduce the cost of production, to choose pricing structures or output levels to maximize profit, and to make many other managerial decisions. We highlight applications of these tools in the Managerial Problems, Mini-Cases, Managerial Implications, and Q&As throughout the book, and the videos in MyLab Economics.

Managerial Problems After the introductory chapter, each chapter starts with a Managerial Problem that motivates the chapter by posing a real-world managerial question. At the end of each chapter, we answer this question in the Managerial Solution using the economic

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principles discussed in that chapter. Thus, each Managerial Problem–Managerial Solution pair combines the essence of a Mini-Case and a Q&A.

Mini-Cases The Mini-Cases apply economic theory to interesting and important managerial prob- lems. For example, Mini-Cases demonstrate how price increases on iTunes affect music downloads using actual data, how to estimate Crocs’ production function for shoes using real-world data, why top-end designers limit the number of designer bags customers can buy, the effect of cyberattacks, how Pfizer used limit pricing to slow the entry of rivals, why advertisers pay so much for Super Bowl commercials, and how managers of auto manufacturing firms organize production and trade to avoid taxes and tariffs.

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Managerial Implications The Managerial Implications feature provides bottom-line statements of economic principles that managers can use to make key managerial decisions. For example, we describe how managers can assess whether they are maximizing profit. We also show how they can structure discounts to maximize profits, promote customer loy- alty, design auctions, prevent gray markets, and use important insights from game theory to make good managerial decisions.

Q&As and End-of-Chapter Questions The largest challenge facing students is learning how to apply economics concepts to solve problems. To help them learn this crucial skill, we provide three to five Q&As (Questions & Answers) in each chapter after the introductory chapter. Each Q&A poses a qualitative or quantitative problem and then uses a step-by-step approach to solve the problem. The Q&As focus on important managerial issues such as how a cost-minimizing firm should adjust to changing factor prices, how a manager prices bundles of goods to maximize profits, how to determine Intel’s and AMD’s profit- maximizing quantities and prices using their estimated demand curves and marginal costs, and how to allocate production across plants internationally.

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At the end of the book, we provide solutions to selected end-of-chapter questions. In addition, detailed answers to all the end-of-chapter questions are provided in MyLab Economics so that students can confirm their understanding without having to contact a professor and also be better prepared for exams.

MyLab Economics Videos Today's students learn best when they analyze and discuss topics in the text outside of class. To further students’ understanding of what they are reading and discussing in the classroom, we provide a set of videos in MyLab Economics. In these videos, Tony Lima presents key figures, tables, Excel applications and concepts in step-by- step animations with audio explanations that discuss the economics behind each step. For example, some of these show students how to use Excel to run regressions, analyze different pricing strategies, cover applications of game theory, address risk and diversification, and choose contracts that reduce moral hazard in principal-agent relationships.

Using Calculus Sections and Calculus Exercises Some students learn economics best using verbal or graphical explanations. How- ever, others find mathematical explanations clearer. Consequently, some managerial economics courses use calculus while others do not. Both types of course can use this book effectively due to the optional Using Calculus sections in the text. Non-calculus courses can omit these short sections with no loss of continuity. For courses that require calculus, Using Calculus sections reinforce the graphical, verbal, and algebraic treatment of major topics.

In contrast, many other books relegate calculus to appendices, mix calculus in with other material where it cannot easily be skipped, or avoid calculus entirely. Our approach has proven effective in courses that use no calculus and have very limited mathematical prerequisites, and in courses with significant calculus content. End- of-chapter questions that require calculus are clearly indicated.

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Developing Career Skills You may be asking yourself, why study economics if I want to manage a business or work as a consultant, as a financial analyst, as an investment banker, in human resources, or in marketing? The reason is that employers know that you need eco- nomic skills to perform well. To get a great job upon graduation and have a success- ful career, you need a range of economic skills and need to know how to apply these skills to solve traditional and new managerial challenges.

How to Use Economic Reasoning on the Job This book starts by illustrating how to use economic reasoning to analyze and solve a variety of problems. It trains you to use logical analysis based on empirical evidence. You will learn how to apply a variety of techniques that firms value such as how to work with spreadsheets to solve decision problems, conduct regression analyses and interpret the results, use game trees to map strategic decisions, and analyze the effects of pricing decisions.

The book shows you how to approach problems that you are likely to encoun- ter on the job. These applications include using basic economic tools to predict the effects of input price changes or government actions on a market. But they also include using modern economic theories to address new managerial challenges such as

 ● developing strategies to compete in oligopolistic markets,  ● structuring stock options to motivate executives,  ● using online platforms (two-sided markets) that bring buyers and sellers together,

such as eBay,  ● responding to cyberattacks and to potentially disruptive innovations such as 3D

printing.

Spreadsheet Exercises In contrast to other managerial economics textbooks, a major feature of this book helps you develop a facility in using spreadsheets and shows how to use them to solve real-world managerial problems.

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Managers increasingly rely on spreadsheets. Spreadsheets make it easier than ever to apply economic principles to managerial decisions. Earlier editions of this book included spreadsheet-based end-of-chapter questions. In this edition, we've added 11 spreadsheet Q&As, which train you by taking you step-by-step through spread- sheets to solve a managerial problem. These Q&As show how to use spreadsheets to calculate elasticities, determine the effect of price changes on revenue and profit, calculate present values, assess the benefits of dynamic pricing, simplify decision- making under uncertainty, and analyze other important questions.

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In addition to these Q&As, each chapter except the first has three end-of-chapter spreadsheet exercises addressing topics such as choosing the profit-maximizing level of advertising and designing compensation contracts to motivate employees. All spreadsheet exercises are available in MyLab Economics as static exercises, and select exercises (marked with an in the text) are available in an auto-graded for- mat. Using proven, field-tested technology, auto-graded Excel Projects let profes- sors seamlessly integrate Microsoft® Excel® content into the course without having to manually grade spreadsheets. Students can practice important skills in Excel, helping you master key concepts and gain proficiency with the program. Simply download a spreadsheet, work live on a problem in Excel, and then upload that file back to MyLab Economics. Within minutes, you will receive a report that provides personalized, detailed feedback and, if necessary, pinpoints where you went astray in the problem. This feedback helps nurture your understanding of the key topics in the course while building confidence in your Excel skills, preparing you for success in class and in your career.

Table of Contents Overview Because instructors differ in the order in which they cover material and in the range of topics they choose to teach, this text allows for flexibility. The most common approach to teaching managerial economics is to follow the sequence of the chapters in order. However, many variations are possible. For example, some instructors choose to address empirical methods (Chapter 3) first.

Instructors may skip consumer theory (Chapter 4) without causing problems in later chapters. Or, they may cover consumer theory after the chapters on production and cost (Chapters 5 and 6).

Chapter 7, “Firm Organization and Market Structure,” provides an overview of the key issues that are discussed in later chapters, such as types of firms, profit

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maximization and its alternatives, and the structure of markets. We think that pre- senting this material early in the course is ideal, but an instructor can cover all of this material except for the section on profit maximization later.

An instructor may teach pricing with market power (Chapter 10) at any point after discussing monopoly (Chapter 9). Because game theory is introduced in two chap- ters (Chapters 12 and 13), instructors can conveniently choose how much game theory to present. Although Chapter 11 on oligopoly and monopolistic competition precedes the game theory chapters, a course could cover the game theory chapters first.

A common variant is to present Chapter 14 on uncertainty earlier in the course. A course could present asymmetric information (Chapter 15) at any point after the uncertainty chapter. Thus, a course could cover both the uncertainty and informa- tion chapters early.

Chapter 16 on government and business discusses market failures, government regulation, externalities, public goods, and intellectual property. A course could cover this material earlier. For example, the regulation and intellectual property material could follow monopoly. The externality and public good treatment could be presented at any point after Chapter 8 on competitive firms and markets.

The final chapter, Global Business (Chapter 17), is valuable in a course that stresses international issues. An instructor could cover this chapter at any point after the competition and monopoly chapters.

Instructor Teaching Resources This book has a full range of supplementary materials that support teaching and learning. This program comes with the following teaching resources:

Supplements available to instructors at www.pearsonhighered.com Features of the Supplement

Instructor’s Manual Authored by Matt Roelofs of Western Washington University

• Chapter Outlines include key terminology, teaching notes, and lecture suggestions.

• Teaching Tips and Additional Discussion Questions provide tips for alter- native ways to cover the material and brief reminders on additional help to provide students.

• Solutions are provided for all problems in the book.

Test Bank Authored by Todd Fitch of the University of California, Berkeley

• Multiple-choice problems of varying levels of complexity, suitable for homework assignments and exams

• Many of these draw on current news and events

Computerized TestGen TestGen allows instructors to: • Customize, save, and generate classroom tests • Edit, add, or delete questions from the Test Item Files • Analyze test results • Organize a database of tests and student results.

PowerPoints Authored by Nelson Altamirano of National University

• Slides include all the graphs, tables, and equations in the textbook, as well as lecture notes.

• PowerPoints meet accessibility standards for students with disabilities. Features include, but not limited to: • Keyboard and Screen Reader access • Alternative text for images • High color contrast between background and foreground colors

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Acknowledgments Our greatest debt is to our very patient students at MIT; the University of British Columbia; the University of California, Berkeley; and the University of Pennsylvania for tolerantly dealing with our various approaches to teaching them economics. We appreciate their many helpful (and usually polite) suggestions.

We also owe a great debt to our editors for the first edition, Adrienne D’Ambrosio and Jane Tufts. Adrienne D’Ambrosio, Editorial Director, was involved in every stage in designing the book, writing the book, testing it, and developing supplemental materials. Jane Tufts, our developmental editor, reviewed each chapter of this book for content, pedagogy, and presentation. By showing us how to present the material as clearly and thoroughly as possible, she greatly strengthened this text. For the sec- ond edition, we thank Christina Masturzo for guiding us as our Portfolio Manager on the print and digital resources.

We are also grateful to Satyajit Ghosh, University of Scranton, for doing most of the work on the end-of-chapter spreadsheet exercises in the first two editions and in MyLab Economics. We benefitted greatly from his creative ideas about using spreadsheets to teach managerial economics. Our other major debt is to Tony Lima for his outstanding work creating MyLab Economics videos and for valuable com- ments on the text.

We thank our teaching colleagues who provided many helpful comments and from whom we have shamelessly borrowed ideas. We particularly thank Tom Davidoff, Isaac Holloway, Stephen Meyer, Nate Schiff, Ratna Shrestha, Mariano Tappata, James Vercammen, and Lanny Zrill for using earlier versions of the textbook and for mak- ing a wide range of helpful contributions. We are also grateful to our colleagues Jen Baggs, Michael Brar, Dennis Carlton, Jean-Etienne de Bettignies, Keith Head, Larry Karp, John Ries, Juliana Rogo, Tom Ross, Leo Simon, Scott Templeton, Chloe Tergiman, and Ralph Winter for many helpful comments. We thank Sophie Endl, Evan Flater, Kai Rong Gan, Albina Gibadullina, Guojun He, Joyce Lam, WeiYi Shen, Yihang Xu, Louisa Yeung, and Maddison Zapach for their valuable work as research assistants on the book.

We are very grateful to the many reviewers who spent untold hours reading and commenting on our original proposal and several versions of each chapter. Many of the best ideas in this book are due to them.

We’d especially like to thank Matthew Roelofs for carefully reviewing the accu- racy of the entire manuscript for the first two editions and for many contributions to the end-of-chapter questions in this edition, along with other helpful comments. We also thank Gordon Lenjosek for checking the accuracy of this edition and sug- gesting useful changes.

We also thank the following reviewers and others, who provided valuable com- ments at various stages:

Laurel Adams, Northern Illinois University

James C. W. Ahiakpor, California State University, East Bay

Nelson Altamirano, National University

Ariel Belasen, Southern Illinois University, Edwardsville

Bruce C. Brown, California State Polytechnic University, Pomona

Donald Bumpass, Sam Houston State University

James H. Cardon, Brigham Young University

Jihui Chen, Illinois State University

Ron Cheung, Oberlin College

Abdur Chowdhury, Marquette University

George Clarke, Texas A&M International University

Kristen Collett-Schmitt, Notre Dame University

Douglas Davis, Virginia Commonwealth University

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xxiiiPreface

Christopher S. Decker, University of Nebraska, Omaha

Craig A. Depken, II, University of North Carolina, Charlotte

Jed DeVaro, California State University, East Bay

Casey DiRienzo, Elon University

David Ely, San Diego State University

Asim Erdilek, Case Western Reserve University

John Fizel, Penn State University

Satyajit Ghosh, University of Scranton

Rajeev Goel, Illinois State University

Abbas P. Grammy, California State University, Bakersfield

Clifford Hawley, West Virginia University

Cary Heath, University of Louisiana

Matthew John Higgins, Georgia Institute of Technology

Jack Hou, California State University, Long Beach

Andrew Hussey, University of Memphis

Timothy James, Arizona State University

Charles Johnston, Baker College

Michael Jones, University of Cincinnati

Peter Daniel Jubinski, St. Joseph’s University

Chulho Jung, Ohio University

David E. Kalist, Shippensburg University

Barry Keating, University of Notre Dame

Daniel Lee, Shippensburg University

Tom K. Lee, California State University, Northridge

Dale Lehman, Alaska Pacific University

Tony Lima, California State University, East Bay

Albert Loh, University of North Florida

Vincent J. Marra Jr., University of Delaware

Scott McGann,. San Diego State University

Sheila J. Moore, California Lutheran University

Thomas Patrick, The College of New Jersey

Anita Alves Pena, Colorado State University

Troy Quast, Sam Houston State University

Jack Reardon,. Hamline University

Barry Ritchey, Anderson University

Matthew Roelofs, Western Washington University

Charles Sebuharara, Binghampton University

Amit Sen, Xavier University

Stephanie Shayne, Husson University

Maura Shelton, University of Washington

Nancy Sowers, Berea College

Caroline Swartz, University of North Carolina, Charlotte

Scott Templeton, Clemson University

Xiahua (Ken) Wei, University of Washington

Keith Willett, Oklahoma State University

Douglas Wills, University of Washington, Tacoma

Mark L. Wilson, Troy University

David Wong, California State University, Fullerton

It was a pleasure to work with the highly skilled people at Pearson and Pearson CSC, who were incredibly helpful in producing this book. Carolyn Philips, Kathy Smith, and Nicole Suddeth did a wonderful job of supervising the production process, assembling the extended publishing team, and managing the schedule. We also want to acknowl- edge, with appreciation, the efforts of Melissa Honig, Courtney Kamauf, and Noel Lotz, in developing the MyLab Economics online assessment and tutorial system for the book.

Finally, we thank our wives, Jackie Persons and Barbara Spencer, for their great patience and support during the nearly endless writing process. We apologize for misusing their names—and those of our other relatives and friends—in the book!

J. M. P. J. A. B.

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1

If all the food, clothing, entertainment, and other goods and services we wanted were freely available, no one would study economics, and we would not need managers. However, most of the good things in life are scarce. We cannot have everything we want. Consumers cannot consume everything but must make choices about what to purchase. Similarly, managers of firms cannot produce everything and must make careful choices about what to produce, how much to produce, and how to produce it. Studying such choices is the main subject matter of economics. Eco- nomics is the study of decision making in the presence of scarcity.1

Managerial economics is the application of economic analysis to managerial deci- sion making. It focuses on how managers make economic decisions by allocating the scarce resources at their disposal. To make good decisions, a manager must under- stand the behavior of other decision makers, such as consumers, workers, other managers, and governments. In this book, we examine decision making by such participants in the economy, and we show how managers can use this understand- ing to be successful.

1Many dictionaries define economics as the study of the production, distribution, and consump- tion of goods and services. However, professional economists think of economics as applying more broadly, including any decisions made subject to scarcity.

1Introduction An Economist’s Theory of Reincarnation: If you’re good, you come back on a higher level. Cats come back as dogs, dogs come back as horses, and people— if they’ve been very good like George Washington—come back as money.

Learning Objectives

1. Describe the major business decisions managers face.

2. Explain how economic models are useful in managerial decision making.

3. Illustrate how a knowledge of economics can help your career.

1.1 Managerial Decision Making A firm’s managers allocate the limited resources available to them to achieve the firm’s objectives. The objectives vary for different managers within a firm but each managerial task is constrained by resource scarcity. At any moment in time, a pro- duction manager has to use the existing factory and a marketing manager has a limited marketing budget. Such resource limitations can change over time, but man- agers always face constraints.

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2 CHAPTER 1 Introduction

Profit The main objective of most private-sector firms is to maximize profit, which is the difference between revenue and cost. Senior managers of a firm might have other concerns as well, including social responsibility and personal career objectives. How- ever, the primary responsibility of senior managers to the owners of the firm is to focus on the bottom line: maximizing profit.

Managers have a variety of roles in the profit maximization process. The produc- tion manager seeks to minimize the cost of producing a particular good or service. The market research manager determines how many units of any particular product can be sold at a given price, which helps to determine how much output to produce and what price to charge. The research and development (R&D) manager supervises the development of new products that will be attractive to consumers. The most senior manager, usually called the chief executive officer (CEO), coordinates the firm’s managerial functions and sets its overall strategy.

Trade-Offs People and firms face trade-offs because they can’t have everything. Managers must focus on the trade-offs that directly or indirectly affect profits. Evaluating trade- offs often involves marginal reasoning: considering the effect of a small change. Key trade-offs include:

●● How to produce: To produce a given level of output, a firm trades off inputs, deciding whether to use more of one and less of another. Car manufacturers choose between metal and plastic for many parts, which affects the car’s weight, cost, and safety.

●● What prices to charge: Some firms, such as farms, have little or no control over the prices at which their goods are sold and must sell at the price determined in the market. However, many other firms set their prices. When a manager of such a firm sets the price of a product, the manager must consider whether raising the price by a dollar increases the profit margin on each unit sold by enough to offset the loss from selling fewer units. Consumers, given their limited budgets, buy fewer units of a product when its price rises. Thus, ultimately, the man- ager’s pricing decision is constrained by the scarcity under which consumers make decisions.

●● Whether to innovate: One of the major trade-offs facing managers is whether to maximize profit in the short run or in the long run. For example, a forward- looking firm may invest substantially in innovation—designing new products and better production methods—which lowers profit in the short run, but may raise profit in the long run.

Other Decision Makers It is important for managers of a firm to understand how the decisions made by consumers, workers, managers of other firms, and governments constrain their

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firm. Consumers purchase products subject to their limited budgets. Workers decide on which jobs to take and how much to work given their scarce time and limits on their abilities. Rivals may introduce new, superior products or cut the prices of existing products. Governments around the world may tax, subsidize, or regulate products.

Interactions between economic decision makers take place primarily in mar- kets. A market is an exchange mechanism that allows buyers to trade with sellers. A  market may be a town square where people go to trade food and clothing, or it may be an international telecommunications network over which people buy and sell financial securities. When we talk about a single market, we refer to trade in a single good or group of goods that are closely related, such as soft drinks, movies, novels, or automobiles. The primary participants in a market are firms that supply the product and consumers who buy it, but government policies such as taxes also play an important role in the operation of markets.

Strategy When competing with a small number of rival firms, senior managers consider how their firm’s products are positioned relative to those of its rivals. The firm uses a strategy—a battle plan that specifies the actions or moves that the firm will make to maximize profit. A strategy might involve choosing the level of output, the price, or the type of advertising now and possibly in the future. For example, in setting its pro- duction levels and prices, Pepsi’s managers must consider what choices Coca-Cola’s managers will make. One tool that is helpful in understanding and developing such strategies is game theory, which we use in several chapters.

1.2 Economic Models Economists use economic models to explain how managers and other decision mak- ers make decisions and to interpret the resulting market outcomes. A model is a description of the relationship between two or more variables. Models are used in many fields. For example, astronomers use models to describe and predict the movement of comets and meteors, medical researchers use models to describe and predict the effect of medications on diseases, and meteorologists use models to pre- dict weather.

Business economists construct models dealing with economic variables and use such models to describe and predict how a change in one variable will affect another variable. Such models are useful to managers in predicting the effects of their decisions and in understanding the decisions of others. Models allow managers to consider hypothetical situations—to use a what-if analysis—such as “What would happen if we raised our prices by 10%?” or “Would profit rise if we phased out one of our product lines?” Models help managers predict answers to what-if questions and to use those answers to make good decisions.

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Simplifying Assumptions Everything should be made as simple as possible, but not simpler. —Albert Einstein

A model is a simplification of reality. The objective in building a model is to include the essential issues, while leaving aside the many complications that might distract us or disguise those essential elements. For example, the income threshold model focuses on only the relationship between income and purchases of durable goods. Prices, multiple car purchases by a single consumer, and other factors that might affect durable goods purchases are left out of the model. Despite these simplifica- tions, the model—if correct—gives managers a good general idea of how the auto- mobile market is likely to evolve in countries such as China.

We have described the income threshold model in words, but we could have presented it using graphs or mathematics. Representing economic models using mathematical formulas in spreadsheets has become very important in managerial decision making. Regardless of how the model is described, an economic model is a simplification of reality that contains only its most important features. Without sim- plifications, it is difficult to make predictions because the real world is too complex to analyze fully.

Mini-Case According to the income threshold model, people whose incomes are below a threshold do not buy a particular consumer durable, while many people whose income exceeds that threshold buy it.

If this theory is correct, we predict that, as most people’s incomes rise above the threshold in lower-income countries, consumer durable purchases will increase from near zero to large numbers virtually overnight. This prediction is consistent with evidence from Malaysia, where the income threshold for buy- ing a car is about $4,000.

In China, incomes have risen rapidly and now exceed the threshold levels for many types of durable goods. In response to higher incomes, Chinese car purchases have taken off.

For example, Li Rifu, a 46-year-old Chinese farmer and watch repairman, thought that buying a car would improve the odds that his 22- and 24-year- old sons would find girlfriends, marry, and produce grandchildren. Soon after Mr. Li purchased his Geely King Kong for the equivalent of $9,000, both sons met girlfriends, and his older son got married.

Given the rapid increase in Chinese incomes in the past couple of decades, four-fifths of all new cars sold in China are bought by first-time customers. An influx of first-time buyers was responsible for Chinese car sales increasing by a factor of nearly 18 between 2000 and 2017. In 2005, China produced fewer than half as many cars as the United States. In 2017, China was by far the largest producer of cars in the world. It produced nearly three times as many cars as the United States—the second largest producer—as well as 39% more than the entire European Union. One out of every three cars in the world is produced in China.2

2The sources for Mini-Cases are available at the back of the book.

Using an Income Threshold Model in China

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51.2 Economic Models

Economists make many assumptions to simplify their models. When using the income threshold model to explain car purchasing behavior in China, we assume that factors other than income, such as the color of cars, do not have an important effect on the decision to buy cars. Therefore, we ignore the color of cars that are sold in China in describing the relationship between income and the number of cars consumers want. If this assumption is correct, by ignoring color, we make our analysis of the auto market simpler without losing important details. If we’re wrong and these ignored issues are important, our predictions may be inaccurate. Part of the skill in using economic models lies in selecting a model that is appropriate for the task at hand.

Testing Theories Blore’s Razor: When given a choice between two theories, take the one that is funnier.

Economic theory refers to the development and use of a model to formulate hypotheses, which are proposed explanations for some phenomenon. A useful theory or hypothesis is one that leads to clear, testable predic- tions. A theory that says “If the price of a product rises, the quantity demanded of that product falls” provides a clear prediction. A theory that says “Human behavior depends on tastes, and tastes change randomly at random intervals” is not very useful because it does not lead to testable predictions.

Economists test theories by checking whether the theo- ry’s predictions are correct. If a prediction does not come true, they might reject the theory—or at least reduce their confidence in the theory. Economists use a model until it is refuted by evidence or until a better model is developed for a particular use.

A good model makes sharp, clear predictions that are consistent with reality. Some very simple models make sharp or precise predictions that are incorrect. Some more realistic and therefore more complex models make ambig- uous predictions, allowing for any possible outcome, so they are untestable. Neither incorrect models nor untest- able models are helpful. The skill in model building lies in developing a model that is simple enough to make clear predictions but realistic enough to be accurate. Any model is only an approximation of reality. A good model is one that is a close enough approximation to be useful.

Although economists agree on the methods they use to develop and apply testable models, they often disagree on the specific content of those models. One model might present a logically consistent argument that prices will go up next quarter. Another, using a different but equally logical theory, may contend that prices will fall next quar- ter. If the economists are reasonable, they will agree that pure logic alone cannot resolve their dispute. Indeed, they

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6 CHAPTER 1 Introduction

will agree that they’ll have to use empirical evidence—facts about the real world—to find out which prediction is correct. One goal of this book is to teach managers how to think like economists so that they can build, apply, and test economic models to deal with important managerial problems.

Positive and Normative Statements Economic analysis sometimes leads to predictions that seem undesirable or cynical. For instance, an economist doing market research for a producer of soft drinks might predict that “if we double the amount of sugar in this soft drink we will significantly increase sales to children.” An economist making such a statement is not seeking to undermine the health of children by inducing them to consume excessive amounts of sugar. The economist is only making a scientific prediction about the relationship between cause and effect: More sugar in soft drinks is appealing to children.

Such a scientific prediction is known as a positive statement: a testable hypothesis about matters of fact such as cause-and-effect relationships. Positive does not mean that we are certain about the truth of our statement; It indicates only that we can test the truth of the statement.

An economist may test the hypothesis that the quantity of soft drinks demanded decreases as the price increases. Some may conclude from that study that “The gov- ernment should tax soft drinks so that people will not consume so much sugar.” Such a statement is a value judgment. It may be based on the view that people should be protected from their own unwise choices, so the government should intervene.

This judgment is not a scientific prediction. It is a normative statement: a belief about whether something is good or bad. A normative statement cannot be tested because a value judgment cannot be refuted by evidence. A normative statement concerns what somebody believes should happen; a positive statement concerns what is or what will happen. Normative statements are sometimes called prescriptive state- ments because they prescribe a course of action, while positive statements are some- times called descriptive statements because they describe reality. Although a normative conclusion can be drawn without first conducting a positive analysis, a policy debate will be better informed if a positive analysis is conducted first.3

Good economists and managers emphasize positive analysis. This emphasis has implications for what we study and even for our use of language. For example, many economists stress that they study people’s wants rather than their needs. Although people need certain minimum levels of food, shelter, and clothing to survive, most people in developed economies have enough money to buy goods well in excess of the minimum levels necessary to maintain life. Consequently, in wealthy countries, calling something a “need” is often a value judgment. You almost certainly have been told by someone that “you need a college education.” That person was probably making a value judgment—“you should go to college”—rather than a scientific pre- diction that you will suffer terrible economic deprivation if you do not go to college. We can’t test such value judgments, but we can test a (positive) hypothesis such as “Graduating from college or university increases lifetime income.”

3Some argue that, as (social) scientists, we economists should present only positive analyses. Others argue that we shouldn’t give up our right to make value judgments just like the next person (who happens to be biased, prejudiced, and pigheaded, unlike us).

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71.3 Using Economic Skills in Your Career

New Theories One of the strengths of economics is that it is continually evolving, for two reasons. First, economists—like physicists, biologists, and other scientists—are always trying to improve their understanding of the world around them.

For example, traditional managerial textbooks presented theories based on the assumption that decision makers always optimize: They do the best they can with their limited resources. While we cover these traditional theories, we also present another recently developed approach referred to as behavioral economics, which is the study of how psychological biases and cognitive limits can prevent managers and others from optimizing.4

Second, economic theory evolves out of necessity. Unlike physical and biological scientists, economists and managers also have to develop new ways to think about disruptive innovations. Although most innovations are incremental, some are suffi- ciently disruptive to dramatically change the way an industry is structured—or even to create new industries and destroy old ones.

The internet is an example of a disruptive innovation. Internet-based online retail- ing has displaced much traditional brick-and-mortar retailing, online payment sys- tems have largely replaced cash and checks, and online media, especially social media, have changed the way most people acquire and transmit information.

To analyze the economic effects of the internet and other disruptive innovations, economists have extended established theories and developed new ones. For exam- ple, the internet has given rise to many services that allow two groups of users to interact—such as auction services, dating sites, job matching services, and payment services. In response, economists have developed the theory of such two-sided mar- kets, which has been important to the ongoing evolution of these markets and to government policy toward them.5 This book describes economic theories of the inter- net and of two-sided markets, along with other recent developments in economics.

1.3 Using Economic Skills in Your Career This book will help you develop skills in economic analysis that are crucial in busi- ness decision-making. Some readers will get jobs that use economic analysis inten- sively, as in assessing financial investment options for financial institutions. Others may work in setting prices or planning other actions based on formal analyses, such as spreadsheet-based economic modeling. Other students will get jobs that empha- size different skills, but economic decisions come up everywhere in business.

All readers will benefit from familiarity with the applications of economics pre- sented in this book. Many managers as well as concerned citizens regularly use these skills to predict the likely outcomes from government actions and other events. Read- ers will also find that much of the analysis in the book is relevant to their own per- sonal decisions, such as investment or educational choices.

4The 2017 Nobel Prize in Economic Sciences was awarded to Richard H. Thaler “for his contribu- tions to behavioral economics.” 5For example, economist Hal Varian used two-sided market theory to help Google develop its auction-based approach to selling ads. Courts have relied on economic analyses of two-sided mar- kets in credit card, merger, and other cases.

5For example, economist Hal Varian used two-sided market theory to help Google develop its auction-based approach to selling ads. Courts have relied on economic analyses of two-sided mar- kets in credit card, merger, and other cases.

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8 CHAPTER 1 Introduction

SUMMARY

1. Managerial Decision Making. Economic analy- sis helps managers develop strategies to pursue their objectives effectively in the presence of scarcity. Various managers within a firm face different objectives and different constraints, but the overriding objective in most private-sector firms is to maximize profits. Mak- ing decisions subject to constraints implies making trade-offs. To make good managerial decisions, man- agers must understand how consumers, workers, other managers, and governments will act. Economic theo- ries normally (but not always) assume that all decision makers attempt to maximize their well-being given the constraints they face.

2. Economic Models. Managers use models based on economic theories to help make predictions and

decisions, which they use to run their firms. A good model is simple to use and makes clear, testable predic- tions that are supported by evidence. Economists use models to construct positive hypotheses such as causal statements linking changes in one variable, such as income, to its effects, such as purchases of automobiles. These positive propositions can be tested. In contrast, normative statements, which are value judgments, can- not be tested.

3. Using Economic Skills in Your Career. A knowl- edge of economics will be valuable to you in a career in management, economics, or other fields. It will also be useful in your everyday life.

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9

2Supply and Demand Talk is cheap because supply exceeds demand.

Burning fossil fuels such as gasoline, coal, and heating oil releases gases containing carbon into the air.1 These “greenhouse” gases are widely believed to contribute to global warming. To reduce this problem and raise tax revenues, many environ- mentalists and political leaders have proposed levying a carbon tax on the carbon content in fossil fuels.2

When governments impose carbon taxes on gasoline, managers of firms that sell gasoline need to think about how much of the tax they have to absorb and how much they can pass through to firms and consumers who buy gasoline. Similarly, managers of firms that purchase gasoline must consider how any pass-through charges will affect their costs of shipping, air travel, heating, and production. This pass-through analysis is critical in making managerial decisions concerning how much to produce, how to set prices, whether to undertake long-run capital invest- ments, and whether to operate or shut down.

Finland and Sweden implemented the first broad-based carbon taxes on fuels containing carbon (such as gasoline) in the early 1990s. Various other countries followed suit, including Ireland and India in 2010 and the United Kingdom in 2013. However, strong opposition to carbon taxes has limited adoption in other parts of the world.

The first North American carbon tax was introduced in 2006 in Boulder, Colorado (where it was applied to only electricity generation), and this tax was renewed in 2012. In 2007 and 2008, the Canadian provinces of Quebec and British Columbia became the first provinces or states in North America to impose a broad-based car-

bon tax. Canada is set to impose a national carbon tax in 2018. Such carbon taxes harm some industries and help others. The

tax hurts owners and managers of gasoline retailing firms, who need to consider whether they can stay in business in the face of a significant carbon tax. Shippers and manufacturers that use substantial amounts of fuel in production, as well as other firms, would also see their operating costs rise.

In contrast, a carbon tax creates opportunities for other firms and industries. For example, wind and solar power, which are alternatives to fossil fuels in generating electricity, would become

1Starting with this chapter, each chapter begins with a Managerial Problem that contains a specific question, which is answered at the end of the chapter using the theories presented in the chapter. Sources for the Managerial Problems, Mini-Cases, and Managerial Implications appear at the back of the book. 2Their political opponents object, claiming that fears about global warming are exaggerated and warning of large price increases from such taxes.

Carbon Taxes

Managerial Problem

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10 CHAPTER 2 Supply and Demand

To analyze the effects of carbon taxes on gasoline prices and other variables, man-agers use an economic tool called the supply-and-demand model. Managers who use this model to anticipate the effects of events make more profitable decisions. The supply-and-demand model provides a good description of many markets and

applies particularly well to those with many buyers and many sellers, as in most agricultural markets, much of the construction industry, many retail markets (such as gasoline retailing), and several other major sectors of the economy. In markets where this model is applicable, it allows us to make clear, testable predictions about the effects of new taxes or other shocks on prices and additional market outcomes.

2.1 Demand Consumers decide whether to buy a particular good or service and, if so, how much to buy based on its price and on other factors, including their incomes, the prices of other goods, their tastes, and the information they have about the product. Govern- ment regulations and other policies also affect buying decisions. Before concentrat- ing on the role of price in determining quantity demanded, let’s look briefly at some other factors.

much more attractive. Anticipating greater opportunities in this market in the future, PacifiCorp, a utility owned by Warren Buffett, announced a plan in 2017 to spend $3.5 billion over three years to bring hundreds of new wind turbines online. It also plans to greatly expand its use of solar power. In 2018, the Solar Corporation of India (SECI) called for bids (“tenders”) to build two large solar power projects.

Managers in the motor vehicle industry would need to consider whether to change their product mix in response to a carbon tax, perhaps focusing more on fuel-efficient vehicles. Even without a carbon tax, when gas prices rise, many con- sumers switch from sports utility vehicles (SUVs) to smaller cars. A carbon tax would favor fuel-efficient vehicles even more.

At the end of this chapter, we will return to this topic and answer a question of critical importance to managers in the motor vehicle industry and in other industries affected by gasoline prices: What would be the effect of imposing a carbon tax on the price of gasoline?

Learning Objectives

1. Explain how the quantity of a good or service that consumers want depends on its price and other factors.

2. Describe how the quantity of a good or service that firms want to sell depends on its price and other factors.

3. Show how the interaction between consumers’ demand curve and producers’ supply curve deter- mines the market price and quantity of a good or service.

4. Predict how an event that affects consumers or firms changes the market price and quantity.

5. Analyze the market effects of government policy using the supply-and-demand model.

6. Discuss when to use the supply-and-demand model.

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112.1 Demand

Income plays a major role in determining what and how much to purchase. People who suddenly inherit great wealth might be more likely to purchase expensive Rolex watches or other luxury items and would probably be less likely to buy inexpensive Timex watches and various items targeted toward lower-income consumers. More broadly, when a con- sumer’s income rises, that consumer will often buy more of many goods.

The price of a related good might also affect consumers’ buying decisions. Related goods can be either substitutes or complements. Substitutes are a pair of goods or ser- vices for which an increase in the price of one causes a consumer to demand a larger quantity of the other. Before deciding to go to a movie theater, a consumer considers the price of a substitute, such as streaming a movie online. The more expensive a trip to a movie theater is, the more likely that the consumer purchases a streamed movie to watch at home instead. Different brands of a good are often close substitutes. Before buying a pair of Levi’s jeans, a customer might check the prices of other brands and substitute one of those brands for Levi’s if its price is sufficiently attractive.

Complements are a pair of goods or services for which an increase in the price of one causes a consumer to demand a smaller quantity of the other. Smartphones, such as the iPhone and Samsung Galaxy, and music purchased online and downloaded to the smartphone are complements. A decline in the price of smartphones increases the demand for online music.

Consumers’ tastes are important in determining their demand for a good or ser- vice. Consumers do not purchase foods they dislike or clothes they view as unfash- ionable or uncomfortable. The importance of fashion illustrates how changing tastes affect consumer demand. Clothing items that have gone out of fashion often languish in discount sections of clothing stores even though they commanded high prices a couple of years (or even a few weeks) earlier when they were in fashion. Firms devote significant resources to trying to change consumer tastes through advertising.

Similarly, information about the effects of a good has an impact on consumer deci- sions. In recent years, positive health outcomes linked to various food items have created greater demand for these healthy foods (such as soy products and high-fiber breads) when the information became well known.

Government rules and regulations affect demand. If a city government bans the use of skateboards on its streets, demand for skateboards in that city falls. Governments might also restrict sales to particular groups of consumers. For example, many politi- cal jurisdictions do not allow children to buy tobacco products, which reduces the quantity of cigarettes consumed.

Other factors might also affect the demand for specific goods. For example, con- sumers are more likely to use Facebook if most of their friends use Facebook. This network effect arises from the benefits of being part of a network and from the poten- tial costs of being outside the network.

Although many factors influence demand, economists focus most on how a good’s own price affects the quantity demanded. The relationship between price and quantity demanded plays a critical role in determining the market price and quan- tity in supply-and-demand analysis. To determine how a change in price affects the quantity demanded, economists ask what happens to quantity when price changes and other factors affecting demand, such as income and tastes, are held constant.

The Demand Curve The amount of a good that consumers are willing to buy at a given price, holding constant the other factors that influence purchases, is the quantity demanded. The quantity demanded of a good or service can exceed the quantity actually sold. For

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12 CHAPTER 2 Supply and Demand

example, as a promotion, a local store might sell Ghirardelli dark chocolate bars for $1 each today only. At that low price, you might want to buy 10 chocolate bars, but because the store has only 5 remaining, you can buy at most 5 chocolate bars at this price. The quantity you demand at this price is 10 chocolate bars—it’s the amount you want—even though the amount you actually buy is only 5.

Using a diagram, we can show the relationship between price and the quantity demanded. A demand curve shows the quantity demanded at each possible price, holding constant the other factors that influence purchases. Figure 2.1 shows the estimated annual world demand curve, D1, for coffee, which is one of the world’s most valuable traded commodities. The inter- nationally traded commodity is unroasted (“green”) coffee beans. These unroasted beans are sold to Starbucks, Folgers, Maxwell House, and other firms that roast and sell coffee to retail consumers.3 In this section, we ana- lyze the market for unroasted coffee beans, which we call coffee. Although

this demand curve is a straight line, demand curves may also be smooth curves or wavy lines. By convention, the vertical axis of the graph measures the price, p, per unit of the good. We measure the price of coffee in dollars per pound (abbreviated lb). The horizontal axis measures the quantity, Q, of the good, which is usually a physical measure per time period. This figure measures the quantity of coffee in millions of tons (2,000 lb) per year.

The demand curve hits the vertical axis at $12, indicating that the quantity demanded is zero when the price is $12 per lb or higher. The demand curve hits the horizontal (quantity) axis at 12 tons, the quantity of coffee buyers would want each year if the price were zero. To find out how much consumers demand at a price between zero and $12, say, $6, we draw a horizontal line from that price on the ver- tical axis until we hit the demand curve, and then we draw a vertical line down to the horizontal quantity axis. As the figure shows, the quantity demanded at a price of $6 per lb is 6 million tons per year.

3We estimated the demand curve using data from the Food and Agriculture Organization, Com- modity Review and Outlook and the International Coffee Organization, www.ico.org, and World Bank, World Development Indicators. We rounded the numbers for simplicity.

FIGURE 2.1 A Demand Curve

The estimated global demand curve, D1, for coffee shows the relationship between the quantity demanded per year in millions of tons and the price per lb. The downward slope of the demand curve shows that, holding other factors that influence demand constant, consumers demand a smaller quantity of a good when its price is high and a larger quantity when the price is low. A change in price causes a movement along the demand curve. For example, an increase in the price of coffee causes consumers to demand a smaller quantity of coffee.

p, $

p er

lb

6 8 10

Coffee demand curve, D1

12

Q, Million tons of coffee per year

0

4.00

2.00

6.00

12.00

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132.1 Demand

One of the most important things to know about a demand curve is what it does not show. All relevant economic variables that the demand curve graph does not explicitly display—income, prices of related goods (such as tea or sugar), tastes, information, and so on—are held constant. Thus, the demand curve shows how quantity varies with price but not how quantity varies with income, the prices of related goods, tastes, information, or other variables.

Effects of a Price Change on the Quantity Demanded. One of the most important results in economics is the Law of Demand: Consumers demand more of a good if its price is lower, holding constant income, the prices of other goods, tastes, and other factors that influence the amount they want to consume. According to the Law of Demand, demand curves slope downward, as in Figure 2.1.

A downward-sloping demand curve illustrates that consumers demand a larger quantity of this good when its price is low and a smaller quantity when its price is high. What happens to the quantity of coffee demanded if the price of coffee drops and all other variables remain constant? If the price falls from $6 per lb to $4 per lb in Figure 2.1, the annual quantity buyers want to purchase increases from 6 million tons to 8 million tons per year. Similarly, if the price drops from $4 to $2 per lb, the quantity buyers demand increases from 8 to 10 million tons.4

These changes in the quantity demanded in response to changes in price are movements along the demand curve. Thus, the demand curve is a concise summary of the answer to the question “What happens to the quantity demanded as the price changes, when all other factors are held constant?”

Although we generally expect demand curves to have a clear downward slope, as the coffee demand curve does, a vertical or horizontal demand curve is possible. We can think of horizontal and vertical demand curves as being extreme cases of downward-sloping demand. The Law of Demand rules out demand curves that have an upward slope.

The Law of Demand is an empirical claim—a claim about what actually happens. It is not a claim about general theoretical principles. It is theoretically possible that a demand curve could slope upward. However, the available empirical evidence strongly supports the Law of Demand.

Effects of Other Factors on Demand. If a demand curve shows how a price change affects the quantity demanded, holding constant all other factors that affect demand, how can we use demand curves to show the effects of a change in one of these other factors, such as income? One approach is to draw the demand curve in a three-dimensional diagram with the price of coffee on one axis, income on a second axis, and the quantity of coffee on the third axis. But just thinking about drawing such a diagram probably makes your head hurt.

Economists use a simpler approach to show the effect of factors other than a good’s own price on demand. A change in any relevant factor other than the price of the good causes a shift of the demand curve rather than a movement along the demand curve. We illustrate such a shift in Figure 2.2. This figure shows that the coffee demand curve shifts to the right from the original demand curve D1 to a new demand curve D2 if average annual household income in high-income countries, which consume most of the world’s coffee, increases by $15,000, from $35,000 to $50,000. On the new

4From now on, we will not state the physical and time period measures unless they are particularly relevant. Thus, we say that the price is $2 (with the “per lb” understood) and the quantity is 10 (with the “million tons per year” understood).

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14 CHAPTER 2 Supply and Demand

demand curve, D2, consumers demand more coffee at any given price than on D1 because income has risen, encouraging consumers to buy more coffee. At a price of $2 per lb, the quantity of coffee demanded goes from 10 million tons on D1, before the increase in income, to 11.5 million tons on D2, after the increase.

The prices of related goods—substitutes and complements—also affect the quan- tity of coffee demanded. Consumers who view tea and coffee as substitutes demand more coffee at any given price of coffee as the price of tea rises. That is, their demand curve for coffee shifts to the right.

Complements have the opposite effect. Consumers who view sugar and coffee as complements demand less coffee at any given price of coffee as the price of sugar rises. That is, their demand curve for coffee shifts to the left.

In addition, changes in other factors that affect demand, such as information, can shift a demand curve. Reinstein and Snyder (2005) found that movie reviews affect the demand for some types of movies, but not others. Holding price constant, they deter- mined that if a film received “two-thumbs-up” reviews on a popular movie-review television program, the opening weekend demand curve shifted to the right by 25% for a drama, but the demand curve did not significantly shift for an action film or a comedy.

To properly analyze the effects of a change in some variable on the quantity demanded, we must distinguish between a movement along a demand curve and a shift of a demand curve. A change in the good’s own price causes a movement along a demand curve. A change in any other relevant factor besides the good’s own price causes a shift of the demand curve.

The Demand Function The demand curve shows the relationship between the quantity demanded and a good’s own price, holding other relevant factors constant at some particular levels. We illustrate the effect of a change in one of these other relevant factors by shift- ing the demand curve. We can also represent the same information—information about how price, income, and other variables affect quantity demanded—using a

FIGURE 2.2 A Shift of the Demand Curve

The global demand curve for coffee shifts to the right from D1 to D2 as average annual household income in high-income countries rises by $15,000, from $35,000 to $50,000. As a result of the increase in income, more coffee is demanded at any given price.

Effect of a $15,000 increase in the average incomep

, $ p

er p

ou nd

10 11.5

Q, Million tons of coffee per year

0

2.00

D2, average income is $50,000

D1, average income is $35,000

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152.1 Demand

mathematical relationship called the demand function. This function shows the effect of a good’s own price and other relevant factors on the quantity demanded. Any factors not explicitly listed in the demand function are assumed to be irrelevant or held constant. For example, we could specify the demand for coffee as a function of the price of coffee, income, the price of tea, the price of sugar, the prices of other related goods, and possibly other factors as well. However, if we hold constant all potentially relevant factors except the price of coffee, p, the price of sugar, ps, and income, Y, the demand function is

Q = D(p, ps, Y), (2.1)

where Q is the quantity of coffee demanded, D is the demand function, p is the price of coffee, and Y is income. This expression shows how the quantity of coffee demanded varies with the price of coffee and the income of consumers.

Equation 2.1 is a general functional form—it does not specify a particular form for the relationship between quantity, Q, and the explanatory variables, p and Y. The estimated demand function that corresponds to the demand curve D1 in Figures 2.1 and 2.2 has the specific (linear) form

Q = 8.56 - p - 0.3ps + 0.1Y, (2.2)

where Q is the quantity of coffee in millions of tons per year, p is the price of coffee in dollars per lb, ps is the price of sugar in dollars per lb, and Y is the average annual household income in high-income countries in thousands of dollars.

When we draw the demand curve D1 in Figures 2.1 and 2.2, we set ps and Y at specific values, ps = $0.20 per lb and Y = $35 thousand per year. By substituting these values for ps and Y in Equation 2.2, we can express the quantity demanded as a function of only the price of coffee:

Q = 8.56 - p - 0.3ps + 0.1Y = 8.56 - p - (0.3 * 0.2) + (0.1 * 35)

= 12 - p. (2.3)

The demand function in Equation 2.3 corresponds to the straight-line demand curve D1 in Figure 2.1 with Y = 35. The constant term, 12, in Equation 2.3 is the quan- tity demanded (in millions of tons per year) if the price is zero. Setting the price equal to zero in Equation 2.3, we find that the quantity demanded is Q = 12 - 0 = 12. Figure 2.1 shows that Q = 12 where D1 hits the quantity axis—where price is zero.

Equation 2.3 also shows us how quantity demanded varies with a change in price: a movement along the demand curve. If the price falls from p1 to p2, the change in price, ∆p, equals p2 - p1. (The ∆ symbol, the Greek letter delta, means “change in” the variable following the delta, so ∆p is the “change in the price.”) If the price of coffee falls from p1 = $4 to p2 = $2, then ∆p = $2 - $4 = - $2. Quan- tity demanded changes from Q1 = 8 at a price of $4 to Q2 = 10 at a price of $2, so ∆Q = Q2 - Q1 = 10 - 8 = 2 million tons per year, as Figure 2.1 shows.

More generally, the quantity demanded at p1 is Q1 = D(p1), and the quantity demanded at p2 is Q2 = D(p2). The change in the quantity demanded, ∆Q = Q2 - Q1, in response to the price change (using Equation 2.3) is

∆Q = Q2 - Q1 = D(p2) - D(p1) = (12 - p2) - (12 - p1) = -(p2 - p1) = - ∆p.

Thus, the change in the quantity demanded, ∆Q, is - ∆p in this case.

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16 CHAPTER 2 Supply and Demand

For example, if ∆p = - $2, then ∆Q = -1∆p = -1(-2) = 2. That is, a $2 decrease in price causes the quantity demanded to rise by 2 million tons per year. The change in quantity demanded is positive—the quantity demanded increases—when the price falls. This effect is consistent with the Law of Demand. Similarly, raising the price would cause the quantity demanded to fall.

Summing Demand Curves The overall demand for coffee is composed of the demand of many individual con- sumers. If we know the demand curve for each of two consumers, how do we deter- mine the total demand curve for the two consumers combined? The total quantity demanded at a given price is the sum of the quantity each consumer demands at that price.

We can use individual demand functions to determine the total demand of several consumers. Suppose that the demand function for Consumer 1 is

Q1 = D1(p)

and the demand function for Consumer 2 is

Q2 = D2(p).

At price p, Consumer 1 demands Q1 units, Consumer 2 demands Q2 units, and the total quantity demanded by both consumers is the sum of these two quantities:

Q = Q1 + Q2 = D1(p) + D2(p).

We can generalize this approach to look at the total demand for three, four, or more consumers, or we can apply it to groups of consumers rather than just to indi- viduals. It makes sense to add the quantities demanded only when all consumers face the same price. Adding the quantity Consumer 1 demands at one price to the quantity Consumer 2 demands at another price would not be meaningful for this purpose—the result would not show us a point on the combined demand curve.

Deriving the Slope of a Demand Curve

Using Calculus We can use calculus to determine how the quantity changes as the price increases. Given the demand function for coffee of Q = 12 - p, the derivative of the demand function with respect to price is dQ>dp = -1. Therefore, the slope of the demand curve in Figure 2.1, which is dp>dQ = 1>(dQ>dp), is also -1. More generally, the Law of Demand states that the derivative of the demand function with respect to price is negative, dQ>dp 6 0.

Mini-Case We illustrate how to sum individual demand curves to get a summed or com- bined demand curve graphically, using estimated demand curves for corn (McPhail & Babcock, 2012). The figure shows the U.S. feed demand (the use of corn to feed animals) curve, the U.S. food demand curve, and the summed demand curve from these two sources.5

5For graphical simplicity, we do not show the other major sources of U.S. demand for corn: export, storage, and use in biofuels (ethanol). Thus, this summed demand curve is not the total demand curve for corn.

Summing Corn Demand Curves

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172.2 Supply

2.2 Supply Knowing how much consumers want to buy at any given price is not enough by itself to tell us the market price and quantity. We also need to know how much firms want to supply at any given price. Firms determine how much of a good to supply given the price of that good and other factors, including the costs of producing the good. Usually, we expect firms to supply more at a higher price. Before concen- trating on the role of price in determining supply, we describe the role of some other factors.

Costs of production (how much the firm pays for factors of production such as labor, fuel, and machinery) affect how much of a product firms want to sell. As a firm’s cost falls, it is usually willing to supply more, holding price and other factors constant. Conversely, a cost increase will often reduce a firm’s willingness to pro- duce. If the firm’s cost exceeds what it can earn from selling the good, the firm will produce nothing. Thus, factors that affect costs also affect supply. If a technological advance allows a firm to produce its good at lower cost, the firm supplies more of that good at any given price, holding other factors constant.

Government rules and regulations can also affect supply directly without working through costs. For example, in some parts of the world, retailers may not sell most goods and services on particular days of religious significance. Supply on those days is constrained by government policy to be zero.

To derive the sum of the quantity demanded for these two uses at a given price, we add the quantities from the individual demand curves at that price. That is, we add the demand curves horizontally. At a price for corn of $7.40, the quantity demanded for food is 1.3 billion bushels per year and the quantity demanded for feed is 4.6 billion bushels. Thus, the summed quantity demanded at that price is Q = 1.3 + 4.6 = 5.9 billion bushels.

When the price of corn exceeds $27.56 per bushel, farmers stop using corn for animal feed, so the quantity demanded for this use equals zero. As a result, the summed demand curve is the same as the food demand curve at prices above $27.56.

p, $

p er

b us

he l

4.61.3

Food demand

5.9

Q, Billion bushels of corn per year

0

7.40

27.56

Feed demand

Aggregate demand

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18 CHAPTER 2 Supply and Demand

The Supply Curve The quantity supplied is the amount of a good that firms want to sell at a given price, holding constant other factors that influence firms’ supply decisions, such as costs and government actions. We can show graphically the relationship between price and the quantity supplied. A supply curve displays the quantity supplied at each possible price, holding constant the other factors that influence firms’ supply  decisions. Figure 2.3 shows the estimated supply curve, S1, for coffee. As with the demand curve, the price on the vertical axis is measured in dollars per physical unit (dollars per lb), and the quantity on the horizontal axis is measured in physical units per period (millions of tons per year). Because we hold fixed other variables that may affect supply, the supply curve concisely answers the question “What happens to the quantity supplied as the price changes, holding all other rel- evant factors constant?”

Effects of Price on Supply. We illustrate how price affects the quantity sup- plied using the supply curve for coffee in Figure 2.3. The supply curve is upward sloping. As the price increases, firms supply more. If the price is $2 per lb, the quan- tity supplied by the market is 10 million tons per year. If the price rises to $4, the quantity supplied rises to 11 million tons. An increase in the price of coffee causes a movement along the supply curve: firms supply more coffee.

Although the Law of Demand states that the demand curve slope downward, no corresponding “Law of Supply” states that the supply curve must slope in a particular way. We observe supply curves that are vertical, horizontal, or downward sloping in particular situations. However, supply curves are commonly upward sloping. Accordingly, if we lack specific information about the slope, we usually draw upward-sloping supply curves. Along an upward-sloping supply curve, the higher the price, the larger the quantity that firms supply, holding other factors constant.

Effects of Other Variables on Supply. A change in a relevant variable other than the good’s own price causes the entire supply curve to shift. One such variable is the price of cocoa (which is a major component in chocolate). The land

FIGURE 2.3 A Supply Curve

The estimated supply curve, S1, for coffee shows the relation- ship between the quantity sup- plied per year and the price per lb, holding constant cost and other factors that influence supply. The upward slope of this supply curve indicates that firms supply more coffee when its price is high and less when the price is low. An increase in the price of coffee causes firms to supply a larger quantity of coffee; any change in price results in a movement along the supply curve.

p, $

p er

lb

10

Coffee supply curve, S1

11

Q, Million tons of coffee per year

0

2.00

4.00

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192.2 Supply

on which coffee is grown can also grow cocoa. When the price of cocoa rises, many coffee farmers switch to producing cocoa. Therefore, when the price of cocoa rises, the amount of coffee produced at any given price for coffee falls.

In Figure 2.4, when the cocoa price increases from $3 per lb to $6 per lb, the sup- ply curve for coffee shifts leftward from S1 to S2. At a price of $2 per lb for coffee, the quantity supplied falls from 10 million tons on S1 to 9.4 million tons on S2.

It is important to distinguish between a movement along a supply curve and a shift of the supply curve. When the price of coffee changes, the change in the quantity supplied reflects a movement along the supply curve. When the price of cocoa or other variables that affect supply change, the entire supply curve shifts.

The Supply Function We can write the relationship between the quantity supplied and price and other factors as a mathematical relationship called the supply function. Using a general functional form, we can write the coffee supply function, S, as

Q = S(p, pc), (2.4)

where Q is the quantity of coffee supplied, p is the price of coffee, and pc is the price of cocoa. The supply function, Equation 2.4, might also incorporate other factors such as wages, transportation costs, and the state of technology, but by leaving them out, we are implicitly holding them constant.

Our estimated supply function for coffee is

Q = 9.6 + 0.5p - 0.2pc, (2.5)

where Q is the quantity in millions of tons per year, p is the price of coffee in dollars per lb, and pc is the price of cocoa in dollars per lb. If we hold the cocoa price fixed at $3 per lb, we can rewrite the supply function in Equation 2.5 as solely a function of the coffee price. Substituting pc = $3 into Equation 2.5, we find that

Q = 9.6 + 0.5p - (0.2 * 3) = 9 + 0.5p. (2.6)

FIGURE 2.4 A Shift of a Supply Curve

A $3 per lb increase in the price of cocoa, which farmers can grow instead of coffee, causes the supply curve for coffee to shift leftward from S1 to S2. At a coffee price of $2 per lb, the quantity supplied falls from 10 on S1 to 9.4 on S2. p

, $ p

er p

ou nd

10

S1, Cocoa $3 per lb

9.4

Q, Million tons of coffee per year

0

2.00

Effect of a $3 increase in the price of cocoa

S2, Cocoa $6 per lb

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20 CHAPTER 2 Supply and Demand

What happens to the quantity supplied if the price of coffee increases by ∆p = p2 - p1? As the price increases from p1 to p2, the quantity supplied goes from Q1 to Q2, so the change in quantity supplied is

∆Q = Q2 - Q1 = (9 + 0.5p2) - (9 + 0.5p1) = 0.5 (p2 - p1) = 0.5∆p.

Thus, a $1 increase in price (∆p = 1) causes the quantity supplied to increase by ∆Q = 0.5 million tons per year. This change in the quantity of coffee supplied as p increases is a movement along the supply curve.

Summing Supply Curves The total supply curve shows the total quantity produced by all suppliers at each possible price. The overall amount of coffee supplied at any given price is the sum of the quantity supplied by Brazilian, Vietnamese, Colombian, and other producers in various countries.

2.3 Market Equilibrium The supply and demand curves jointly determine the price and quantity at which a good or service is bought and sold. The demand curve shows the quantities consumers want to buy at various prices, and the supply curve shows the quan- tities firms want to sell at various prices. Unless firms set the price so that con- sumers want to buy exactly the same amount that suppliers want to sell, some consumers cannot buy as much as they want or some sellers cannot sell as much as they want.

When all market participants are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. A price at which consumers can buy as much as they want and sellers can sell as much as they want is the equilibrium price. At this price, the quantity demanded equals the quantity supplied. This quantity is the equilibrium quantity. Thus, if the government does not intervene in the market, the supply-and-demand model is in equilibrium when the market clears in the sense that buyers and sellers are both able to buy or sell as much as they want at the market price—no one is frustrated and all goods that are supplied to the market are sold.

Using a Graph to Determine the Equilibrium To illustrate how supply and demand curves determine the equilibrium price and quantity, we use the coffee example. Figure 2.5 shows the supply curve, S1, and demand curve, D1, for coffee. The supply and demand curves intersect at point e, the market equilibrium. The equilibrium price is $2 per lb, and the equilibrium quantity is 10 million tons per year, which is the quantity firms want to sell and the quantity consumers want to buy.

Using Math to Determine the Equilibrium We can determine the coffee equilibrium mathematically, using supply and demand functions that correspond to the supply and demand curves. We use these two

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212.3 Market Equilibrium

equations to solve for the equilibrium price at which the quantity demanded equals the quantity supplied (the equilibrium quantity). The demand function, Equation 2.3, is the relationship between the quantity demanded, Qd, and the price:6

Qd = 12 - p.

The supply function, Equation 2.6, is the relationship between the quantity supplied, Qs, and the price:

Qs = 9 + 0.5p.

We want to find the equilibrium price, p, at which Qd = Qs = Q. Thus, we set the right sides of these two equations equal,

12 - p = 9 + 0.5p,

and solve for the price. Adding p to both sides of this expression and subtracting 9 from both sides, we

find that 3 = 1.5p. Dividing both sides of this last expression by 1.5, we learn that the equilibrium price is p = $2. We can determine the equilibrium quantity by substitut- ing this p into either the supply function or the demand function. Using the demand function, we find that the equilibrium quantity is

Q = 12 - 2 = 10

million tons per year. We can obtain the same quantity by using the supply function:

Q = 9 + (0.5 * 2) = 10.

6Usually, we use Q to represent both the quantity demanded and the quantity supplied. However, for clarity in this discussion, we use Qd and Qs.

Q = 9 + 10.5 * 2) = 10.

FIGURE 2.5 Market Equilibrium

The intersection of the supply curve, S1, and the demand curve, D1, for coffee determines the mar- ket equilibrium point, e, where p = $2 per lb and Q = 10 million tons per year. At the lower price of p = $1, the quantity demanded is 11, but the quantity supplied is only 9.5, so the excess demand is 1.5. At p = $3 the price exceeds the equilibrium price. As a result, the market has an excess sup- ply of 1.5 because the quantity demanded, 9, is less than the quantity supplied, 10.5. With either excess demand or excess supply, market forces drive the price back to the equilibrium price of $2.

p, $

p er

lb 10.0

D1

S1

11.010.59.0 9.5

Q, Million tons of coffee per year

0

3.00

2.00

1.00

Excess supply = 1.5

Market equilibrium, e

Excess demand = 1.5

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22 CHAPTER 2 Supply and Demand

Forces That Drive the Market to Equilibrium A market equilibrium is not just an abstract concept or a theoretical possibility.7 Economic forces cause markets to adjust to the equilibrium. At the equilibrium, price and quantity remain stable until some new event occurs that shifts the demand or supply curve.

Remarkably, an equilibrium occurs without any explicit coordination between consumers and firms. In a competitive market such as that for most agricultural products, millions of consumers and thousands of firms make their buying and selling decisions independently. Yet each firm can sell the quantity it wants at the market price and each consumer can buy the quantity he or she wants at that price. It is as though an unseen market force like an invisible hand (a phrase coined by Adam Smith in 1776) directs people and firms to coordinate their activities to achieve equilibrium.

What forces cause the market to move to equilibrium? If the price is not at the equilibrium level, consumers or firms have an incentive to change their behavior in a way that will drive the price to the equilibrium level, as we now illustrate.

If the price were initially lower than the equilibrium price, consumers would want to buy more than suppliers want to sell. If the price of coffee is $1 in Figure 2.5, firms are willing to supply 9.5 million tons per year but consumers demand 11 million tons. At this price, the market is in disequilibrium: the quantity demanded is not equal to the quantity supplied. This market has excess demand—the amount by which the quantity demanded exceeds the quantity supplied at a specified price. If the price is $1 per lb, the market has an excess demand of 11- 9.5 = 1.5 million tons per year.

Some consumers are lucky enough to buy the coffee at $1 per lb. Other consumers cannot find anyone who is willing to sell them coffee at that price. What can they do? Some frustrated consumers may offer to pay suppliers more than $1 per lb.

Alternatively, suppliers, noticing these disappointed consumers, might raise their prices. Such actions by consumers and producers cause the market price to rise. As the price rises, the quantity that firms want to supply increases and the quantity that consumers want to buy decreases. This upward pressure on price continues until it reaches the equilibrium price, $2, which eliminates the excess demand.

If, instead, the price is initially above the equilibrium level, suppliers want to sell more than consumers want to buy. For example, at a price of $3, suppliers want to sell 10.5 million tons per year but consumers want to buy only 9 million tons, as Figure 2.5 shows. This market has an excess supply—the amount by which the quan- tity supplied exceeds the quantity demanded at a specified price—of 1.5 (= 10.5 - 9) million tons at a price of $3. Not all firms can sell as much as they want. Rather than allow their unsold coffee to get stale, firms lower the price to attract additional cus- tomers. As long as the price remains above the equilibrium price, some firms cannot sell as much coffee as they want, so they lower the price further. The price falls until it reaches the equilibrium level, $2, which eliminates the excess supply and hence removes the pressure to lower the price further.

Not all markets reach equilibrium through the independent actions of many buy- ers or sellers. In institutionalized or formal markets, such as the Chicago Mercantile Exchange—where coffee and other agricultural commodities, financial instruments,

7MyLab Economics has games (called experiments) for the Managerial Economics and Strategy course. These online games allow you to play against the computer. The Market Experiment illus- trates the operation of the supply-and-demand model, allowing you to participate in a simulated market. To play, go to MyLab Economics Multimedia Library, Single Player Experiment, and set the Chapter field to “All Chapters.”

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232.4 Shocks to the Equilibrium

energy, and metals are traded—buyers and sellers meet at a single location (or on a single website). Often in these markets certain individuals or firms, sometimes referred to as market makers, act to adjust the price and bring the market into equi- librium very quickly.

In summary, at any price other than the equilibrium price, either consumers or suppliers are unable to trade as much as they want. These disappointed market par- ticipants act to change the price, driving the price to the equilibrium level. The equilib- rium price is called the market clearing price because no buyers or sellers are frustrated at this price—the market eliminates or clears any excess demand or excess supply.

2.4 Shocks to the Equilibrium Once a market achieves equilibrium, the equilibrium can persist indefinitely because no one applies pressure to alter the price. The equilibrium changes only if a shock occurs that shifts the demand curve or the supply curve. These curves shift if one of the variables we were holding constant changes. If tastes, income, government poli- cies, or costs of production change, the demand curve or the supply curve or both shift, and the equilibrium changes.

Effects of a Shift in the Demand Curve Suppose that the average income in high-income countries increases by $15,000, from $35,000 to $50,000. As a result, consumers purchase more coffee at any given price. Reflecting this change, the demand curve for coffee shifts to the right from D1 to D2 in panel a of Figure 2.6. At the initial equilibrium price of $2, consumers now want to purchase 11.5 million tons of coffee per year. However, at that price, suppliers want to sell only 10 million tons, so the market has an excess demand of 11.5 - 10 = 1.5 million tons.

Mini-Case Most markets adjust quickly, especially formal markets, such as the Chicago Board of Trade corn futures market. Corn futures are contracts to deliver a fixed amount of corn at a specified future date. The price in this market is the futures price and the quantity is the number of contracts.

The U.S. Department of Agriculture (USDA) provides information about the corn market, which influences sellers and buyers, shifting the market supply and demand curves. The most important types of information that the USDA announces are its forecasts about corn pro- duction, changes in conditions that affect the crop while it is growing, and estimates of world supply and demand quantities.

The USDA made its announcements electronically two hours before the start of trading on a given day. Lehecka, Wang, and Garcia (2014) studied how these announcements affect futures prices and the num- ber of contracts minute by minute. They found that the price changed rapidly in the first minute after trading started compared to the last minute of the previous day. The price adjustments diminished with each subsequent minute and died out within 10 minutes. Thus, this market adjusts very quickly.

Speed of Adjustment to New Information

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24 CHAPTER 2 Supply and Demand

This excess demand creates market pressure, which drives the price up until it reaches a new equilibrium price of $3. At that price, firms want to sell 10.5 million tons and consumers want to buy 10.5 million tons, the new equilibrium quantity. The increase in income causes a shift of the demand curve, which in turn causes a movement along the supply curve from e1 to e2.

FIGURE 2.6 Equilibrium Effects of a Shift of a Demand or Supply Curve

(a) A $15,000 increase in average annual household income causes the demand curve for coffee to shift to the right from D1 to D2. At the original equilibrium (e1) price of $2, initially the market has excess demand of 1.5 million tons per year. Market pressures drive up the price. The equilibrium moves along the supply curve to e2, where the new equilibrium price is $3.

(b) A $3 per pound increase in the price of cocoa causes some producers to shift from coffee produc- tion to cocoa production, reducing the quantity of coffee supplied at every price. The supply curve shifts to the left from S1 to S2, causing the market equilibrium to move from e1 to e2, where the new equilibrium price is $2.40.

p, $

p er

p ou

nd

10

S1

11.510.5

Q, Million tons of coffee per year

0

3.00

2.00

D1

D2

e2

e1 p,

$ p

er p

ou nd

109.4 9.6

Q, Million tons of coffee per year

0

2.40

2.00

D1

S2

e2

e1

S1

(a) Effect of a $15,000 Increase in Income (b) Effect of a $3 Increase in the Price of Cocoa

Excess demand = 0.6Excess demand = 1.5

Q&A 2.1 The estimated global supply function for coffee is Q = 9 + 0.5p. The esti- mated demand function is Q = 8.56 - p - 0.3ps + 0.1Y, where ps is the price in dollars per lb of sugar, and Y is the average income in high-income countries in  thousands of dollars. The initial price of sugar is $0.20 per lb. The ini- tial income is Y = 35 ($35,000). Using algebra, determine the initial equilibrium price and quantity of coffee, and then determine how price and quantity change if the average income increases by 15 to Y = 50 and the price of sugar remains constant.

Answer 1. Substitute the initial value of Y into the demand function to obtain quantity demanded

purely as a function of p. As we derived in Equation 2.3, if Y = 35, then

Q = 8.56 - p - 0.3ps + 0.1Y = 8.56 - p - (0.3 * 0.2) + (0.1 * 35) = 12 - p.

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252.4 Shocks to the Equilibrium

Effects of a Shift in the Supply Curve We now consider how a shift in the supply curve affects the coffee market equilib- rium. Assume that income remains at its original level of $35,000 but the price of cocoa rises from $3 per lb to $6 per lb. This increase in the price of cocoa causes some coffee producers to switch to cocoa production. As a result, the supply curve for cof-

fee shifts to the left from S1 to S2 in panel b of Figure 2.6. At any given price, producers want to supply less coffee than they did before the price of cocoa increased. At the original equilibrium price of coffee of $2 per lb, consumers still want 10 million tons, but producers are now willing to supply only 9.4 million tons, so the market’s excess demand is 0.6 million tons. Market pressure forces the price of coffee up until the market reaches a new equilibrium at e2, where the equilibrium price is $2.40 and the equilibrium quantity is 9.6. Here, a shift of the supply curve results in a movement along the demand curve.

In summary, a change in an underlying factor, such as income, the price of a related good, land use, or the cost of production, shifts the demand curve or the supply curve. As a result, the equilibrium changes. To describe the effect of this change, we compare the original equilibrium price and quantity to the new equilibrium values.

2. Equate the supply and demand functions to determine the initial equilibrium. The equilibrium price is determined by equating the right sides of these supply and demand functions:

9 + 0.5p = 12 - p.

Solving this equation for p, we find that 1.5p = 3, or p = $2. We calcu- late the equilibrium quantity by substituting this price into the supply or demand  function: Q = 9 + (0.5 * 2) = 10 or Q = 12 - 2 = 10 million tons per year.

3. Repeat steps 1 and 2 using Y = 50 instead of Y = 35. The new demand function is

Q = 8.56 - p - 0.3ps + 0.1Y = 8.56 - p - (0.3 * 0.2) + (0.1 * 50) = 13.5 - p.

Equating this expression to the right-hand side of the supply function, we obtain 9 + 0.5p = 13.5 - p. Solving for p, we find that 1.5p = 4.5 or p = $3. We  calculate the equilibrium quantity by substituting this price into the supply or demand function: Q = 9 + (0.5 * 3) = 10.5 or Q = 13.5 - (1 * 3) = 10.5.

4. Show how the equilibrium price and quantity of coffee change by subtract- ing the original values from the new ones. The change in the equilibrium price is ∆p = $3 - $2 = $1. The change in the equilibrium quantity is ∆Q = 10.5 - 10 = 0.5 million tons per year. Panel a of Figure 2.6 illustrates these changes in the equilibrium price and quantity.

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26 CHAPTER 2 Supply and Demand

Mini-Case Opioids are drugs that act on the nervous system to relieve pain. They include heroin, fentanyl, and pain relievers that are available legally by prescrip- tion, such as oxycodone (OxyContin), hydrocodone (Vicodin), codeine, and morphine.

Although patients can safely use opioid pain relievers for a short period, many patients continue to use them for longer periods because these drugs pro- duce euphoria in addition to pain relief. Unfortunately, continued use can result in dependence, and excessive use can cause death. Every day, 90  Americans die from opioid overdoses.

Opioid prescriptions per capita rose 350% nationwide between 1999 and 2015. The use and abuse of opioids are responsible for fewer people working due to premature deaths, an inability to pass a job-drug test, or an unwilling- ness to work due to sedation and other effects of the drug.

The labor-force participation rate of men—the ratio of employed working-age men to all working-age men—was 3.2 percentage points lower during 2014–2016 than during 1999–2001. According to Krueger (2017), labor-force participation fell more in areas where doctors prescribe relatively more opioid pain medica- tion. He calculated that 0.6 percentage points of the decline for men, a fifth of the total, was due to opioid prescriptions. Similarly, the study estimated that about one-quarter of the decline in women’s labor-force participation was attributable to the growth in opioid prescriptions.

The Opioid Epidemic Reduces Labor Market Participation

Q&A 2.2 As the preceding Mini-Case discusses, opioid use reduces labor-force participa- tion. Use a supply-and-demand diagram to show the effects of opioid use on the labor market equilibrium quantity, which is the number of workers, L, and the equilibrium price, which is the wage, w.

Answer 1. Determine the original labor market equilibrium before the epidemic. The intersec-

tion of the labor demand curve, D, and the original labor supply curve, S1, determines the original equilibrium, e1, where the quantity is L1 and the wage is w1.

2. Show how the opioid epidemic affects the labor supply curve. The opioid epidemic does not affect the labor demand curve, but it causes the labor supply curve to shift to the left from S1 to S2. At any given wage, fewer people are willing to work.

3. Determine the new labor market equilibrium. The new equilibrium occurs where the demand curve, D, intersects the new supply curve, S2, at e2. The new equilibrium quantity is L2, and the new equilibrium wage is w1.

4. Discuss the effect of the epidemic on the labor market. The equilibrium quantity falls from L1 to L2. The equilibrium wage rises from w1 to w2 for workers who remain employed.

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272.5 Effects of Government Interventions

2.5 Effects of Government Interventions Often governments are responsible for changes in market equilibrium. We examine three types of government policies. First, some government actions shift the supply curve, the demand curve, or both curves, which causes the equilibrium to change. Second, the government may use price controls that cause the quantity demanded to differ from the quantity supplied. Third, the government may tax or subsidize a good, which results in a gap between the price consumers pay and the amount sellers receive.

Policies That Shift Curves Government policies may cause demand or supply curves to shift. Governments often limit who can buy goods. For example, many governments forbid selling alco- hol to young people, which decreases the quantity demanded at each price and thereby shifts the demand curve to the left. Similarly, a government may restrict the amounts of foreign products that can be imported, which decreases the quantity

Managers can use the supply-and-demand model to anticipate how shocks to supply or demand will affect future business conditions and can take advantage of that knowledge. For example, Mars, one of the world’s largest producers of chocolate products, is often among the first companies to learn about events that affect cocoa production, most of which occurs in Africa. Using their cocoa supply- and-demand model, Mars managers (called Martians) predict how much prices will change in the near future. If they expect prices to increase substantially, they immediately buy a great deal of cocoa at relatively low prices directly from sup- pliers in Africa. Alternatively, if they expect prices to fall, they may hold off buy- ing now and then buy later at a lower price from organized markets such as ICE Futures U.S. or the London International Financial Futures and Options Exchange.

Taking Advantage of Future Shocks

Managerial Implication

D

e2

w , $

p er

h ou

r

S1

L, Workers per year

S2

e1 w1

w2

L1L2

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28 CHAPTER 2 Supply and Demand

supplied of imported goods at each price and shifts the importing country’s supply curve to the left. Or, the government could start buying a good, which increases the quantity demanded at each price for the good and shifts the demand curve to the right.

Price Controls Government policies that directly control the price of a good may alter the market outcome even though they do not affect the demand or supply curves of the good. Such a policy may lead to excess supply or excess demand if the price the govern- ment sets differs from the unregulated equilibrium price. We illustrate this result with two types of price control programs. When the government sets a price ceiling at p, no goods may be sold at a price higher than p. When it sets a price floor at p, no goods may be sold at a price below p.8

Price Ceilings. Price ceilings have no effect if they are set above the equilibrium price that would be observed in the absence of price controls. If the government says

8MyLab Economics has a Price Floors Experiment and a Price Ceilings Experiment that illustrate the operation of price controls. To participate go to the MyLab Economics Multimedia Library, Single Player Experiment, and set the Chapter field to “All Chapters.”

Mini-Case In the United States, in many occupations, working without a license is ille- gal. More than 800 occupations require licensing at the local, state, or federal level, including animal trainers, dietitians and nutritionists, doctors, electricians, embalmers, funeral directors, hairdressers, librarians, nurses, psychologists, real estate brokers, respiratory therapists, and teachers (but not economists).

During the early 1950s, fewer than 5% of U.S. workers were in occupations covered by licensing laws at the state level. Since then, the share of licensed workers has grown, reaching nearly 18% by the 1980s, at least 20% in 2000, and 26% in 2015. Licensing is more common in occupations that require extensive education: More than 40% of workers with post-college education are required to have a license compared to only 15% of those with less than a high school education.

A worker must pass a test to obtain a license in some occupations. Frequently, licensed members of the occupation design these tests. By making the exam dif- ficult, current workers can limit entry. For example, only 50% of people taking the California State Bar Examination in July 2017 passed it and only 27% passed the February 2018 exam, although all of them had law degrees.

To the degree that testing is objective, licensing may raise the average quality of the workforce. However, it restricts the number of workers in an occupa- tion, which affects wages. To analyze the wage effect of licensing, we can use a graph similar to panel b of Figure 2.6, where the wage is on the vertical axis and the number of workers per year is on the horizontal axis. Licensing shifts the occupational supply curve to the left, reducing the equilibrium quantity of workers and raising the wage.

On average, licensing raises occupational wages by 11% in the United States (Kleiner and Vorotnikov, 2017) and 4% in the European Union (Koumenta and Pagliero, 2018). Kleiner (2015) estimates that occupational licensing costs con- sumers $203 billion annually.

Occupational Licensing

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that firms may charge no more than p = $6 per gallon of gas and firms are actually charging p = $4, the government’s price control policy is irrelevant. However, if the unregulated equilibrium price, p, were above the price ceiling p, the price that is actually observed in the market is the price ceiling. For example, if the equilibrium price of gas were $4 and a price ceiling of $3 is imposed, then the ceiling price of $3 is charged.

Currently, Canada and many European countries set price ceilings on pharmaceuticals. The United States used price ceilings on many goods during both world wars, the Korean War, and in 1971–1973 during the Nixon administration, among other times. Hawaii limited the price of wholesale gasoline from 2005 to 2006. New Jersey has a state law that pro- hibits raising prices on essential goods by more than 10% within 30 days of a declared state of emergency. In the aftermath of Hurricane Sandy in 2012, many businesses received fines as a result of this law.

The U.S. experience with gasoline illustrates the effects of price con- trols. In the 1970s, the Organization of Petroleum Exporting Countries (OPEC) reduced supplies of crude oil (which is converted into gasoline)

to Western countries. As a result, the total supply curve for gasoline in the United States shifted to the left from S1 to S2 in Figure 2.7. Because of this shift, the equilib- rium price of gasoline would have risen substantially, from p1 to p2. In an attempt to protect consumers by keeping gasoline prices from rising, the U.S. government set price ceilings on gasoline in 1973 and 1979.

The government told gas stations that they could charge no more than p1 = p. Figure 2.7 shows the price ceiling as a solid horizontal line extending from the price axis at p. The price control is binding because p2 7 p. The observed price is the price ceiling. At p, consumers want to buy Qd = Q1 gallons of gasoline, which is the equilibrium quantity they bought before OPEC acted. However, firms supply only Qs, which is determined by the intersection of the price control line with S2. The binding price control resulted in excess demand of Qd - Qs.

Were it not for the price controls, market forces would drive up the market price to p2, the price at which the excess demand would be eliminated. The government

FIGURE 2.7 A Price Ceiling on Gasoline

Reduced crude oil production (the major input in producing gasoline) causes the supply curve of gasoline to shift from S1 to S2. In an unregu- lated market, the equilibrium price would increase to p2 and the equi- librium quantity would fall to Q2. Suppose the government imposes a price control so that gasoline stations may not charge a price above the price ceiling, p1 = p. At this price, producers are willing to supply only Qs, which is less than the amount Q1 = Qd that consumers want to buy. The result is excessive demand, or a shortage of gasoline of Qd - Qs.

p, $

p er

g al

lo n

Qs Q2 Q1 = Qd

Price ceiling

S1

D

S2

Q, Gallons of gasoline per month

Shortage (Excess demand)

p2

e2

e1 p1 = p

–

Reduced crude oil production

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30 CHAPTER 2 Supply and Demand

price ceiling prevents this adjustment. As a result, an enforced price ceiling causes a shortage: a persistent excess demand.

At the time of the controls, some government officials argued that the shortages resulted from OPEC’s cutting off its supply of oil to the United States, but that’s not true. Without the price controls, the new equilibrium would be e2. In this equi- librium, the price, p2, is much higher than before, p1, but it eliminates the shortage. Moreover, without controls, the quantity sold, Q2, is greater than the quantity sold under the control program, Qs.

With a binding price ceiling, the supply-and-demand model predicts an equilib- rium with a shortage. In this equilibrium, the quantity demanded does not equal the quantity supplied. The reason that we call this situation an equilibrium, even though a shortage exists, is that buyers and sellers who abide by the law do not change their behavior. Without the price controls, consumers facing a shortage would try to get more output by offering to pay more, or firms would raise prices. With effective government price controls, both firms and consumers know that they can’t drive up the price, so they live with the shortage.

What happens? Some lucky consumers get to buy Qs units at the low price of p. Other potential customers are disappointed: They would like to buy at that price, but they cannot find anyone willing to sell gas to them. In addition, consumers spend a lot of time waiting in line—a pure waste that adds considerably to the cost of such government interventions.

What determines which consumers are lucky enough to find goods to buy at the low price with price controls? With enforced price controls, sellers use criteria other than price to allocate the scarce commodity. Firms may supply their friends, long- term customers, or people of a certain race, gender, age, or religion. They may sell their goods on a first-come, first-served basis. Or they may limit everyone to only a few gallons.

Another possibility is that firms and customers will try to evade the price controls. A consumer could go to a gas station owner and say, “Let’s not tell anyone, but I’ll pay you twice the price the government sets if you’ll sell me as much gas as I want.” If enough customers and gas station owners behaved that way, no shortage would occur. However, in cities such as Chicago, Hartford, New York, Portland, and Tucson, potential customers waited in line at the pump for an hour or more.9 Deacon and Sonstelie (1989) estimated that for every dollar consumers saved due to the 1979 gasoline price controls, they lost $1.16 in waiting time and other factors.

9See MyLab Economics Chapter Resources, Chapter 2, “Gas Lines,” for a discussion of the effects of the 1973 and 1979 gasoline price controls.

Mini-Case Venezuela was one of the richest countries in Latin America. A leading oil producer, it also has many other agricultural and nonagricultural industries.

So why do people start lining up to buy groceries in Venezuela at 4 a.m., when shops open at 8 a.m.? Strict price ceilings on food and other goods create shortages throughout the country.

According to a university study in 2018, one-quarter of Venezuelans eat two or fewer meals a day, 60% reported waking up hungry, and people reported losing 24 lb of weight on average during the previous year. Venezuelans also suffer from condom, birth control pill, and toilet paper shortages.

Venezuelan Price Ceilings and Shortages

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Price Floors. Governments also commonly use price floors. One of the most important examples of a price floor is a minimum wage in a labor market. A mini- mum wage law forbids employers from paying less than the minimum wage, w.

Minimum wage laws date from 1894 in New Zealand, 1909 in the United King- dom, and 1912 in Massachusetts. The Fair Labor Standards Act of 1938 set a federal U.S. minimum wage of 25¢ per hour. The U.S. federal minimum hourly wage rose to $7.25 in 2009 and remained at that level through early 2018, but 29 states and a num- ber of cities set higher minimum wages.10 As of 2019, the highest minimum wage is in Washington, D.C. ($14.00), followed by Washington State ($11.50), California ($12.00 for large firms),11 and Massachusetts ($11.00). The minimum wage in Canada differs across provinces, ranging from C$14.00 to C$10.96 (where C$ stands for Cana- dian dollars) in 2018. If the minimum wage is binding—that is, if it exceeds the equi- librium wage, w*—it creates unemployment: a persistent excess supply of labor.

10See www.dol.gov for U.S. state and federal minimum wages. See www.fedee.com/pay-job - evaluation/minimum-wage-rates/ for minimum wages in European countries. 11According to California government website the minimum wage for large employers (> 25 employees) is $11.00 and for small companies is $10.50. See www.dir.ca.gov/dlse/faq_minimum- wage.htm. It is scheduled to go to $12 and $11 as of January 2019. According to www.ncsl.org/ research/labor-and-employment/state-minimum-wage-chart.aspx, the current Washington D.C. minimum wage is $13.25 and is scheduled to go to $14 on July 1, 2019.

Because Venezuela regulates the prices of many goods such as gasoline and corn flour, while Colombia, its direct neighbor to the west, does not, smuggling occurs. Given that gaso- line sells for about 4¢ a gallon in Venezuela, and the price is over $3 a gallon in most of Colombia, the temptation to smuggle is great. Venezuela’s Táchira state is adjacent to the Colombian border. Its government says that as much as 40% of the food sent to Táchira is smuggled into Colombia. Why sell corn flour at an artificially low price in Venezuela if you can sell it at a higher, market price in Colombia?

Venezuela’s populist President Hugo Chávez and his handpicked successor, Nico-

lás Maduro, imposed strict price ceilings, purportedly to rein in inflation and make the goods more affordable for the poor. Do the ceilings help the poor?

For many Venezuelans, the answer is “No!” As Nery Reyes, a restaurant worker, said, “Venezuela is too rich a country to have this. I’m wasting my day here standing in line to buy one chicken and some rice.”

Demonstrators have taken to the streets to protest persistent economic and social problems, including shortages. Many have died in these violent clashes with the National Guard. Hundreds of thousands of people have left Venezuela, and more than half of those between the ages of 15 and 29 say they want to leave the country.

The ultimate irony is that President Nicolás Maduro has advised Venezu- elans to consume less to alleviate the shortages.

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32 CHAPTER 2 Supply and Demand

We illustrate the effect of a minimum wage law in a labor market in which every- one is paid the same wage. Figure 2.8 shows the supply and demand curves for labor services (hours worked). Firms buy hours of labor service by hiring workers. The horizontal axis shows the quantity of hours worked per year, and the vertical axis shows the hourly wage, which is the price of labor hours.

With no government intervention, the market equilibrium is e, where the wage is w* and the number of hours worked is L*. The minimum wage creates a price floor, a horizontal line, at w. At that wage, the quantity demanded falls to Ld and the quantity supplied rises to Ls. As a result, the market has an excess supply of labor of Ls - Ld. The minimum wage prevents market forces from eliminating this excess supply, so it leads to an equilibrium with unemployment.

The original 1938 U.S. minimum wage law, which was set much higher than the equilibrium wage in Puerto Rico, created substantial unemployment there. It is ironic that a law designed to help workers by raising their wages may harm some of them by causing them to lose their jobs. A minimum wage law benefits only those workers who remain employed.12

Why Supply Need Not Equal Demand. The price ceiling and price floor examples show that the quantity supplied does not necessarily equal the quantity demanded in a supply-and-demand model. The quantity supplied need not equal the quantity demanded because of the way we define these two concepts. The quantity supplied is the amount sellers want to sell at a given price, holding other factors that affect supply, such as the price of inputs, constant. The quantity demanded is the quantity that buyers want to buy at a given price, if other factors that affect demand are held constant. The quantity that sellers want to sell and the quantity that buyers want to buy at a given price need not equal the actual quantity that is bought and sold.

When the government imposes a binding price ceiling of p on gasoline, the quantity demanded is greater than the quantity supplied. Despite the lack of equality between

12The minimum wage could raise the wage enough that total wage payments, wL, rise despite the fall in demand for labor services. If the workers could share the unemployment—everybody works fewer hours than he or she wants—all workers could benefit from the minimum wage. Card and Krueger (1995) have argued, based on alternatives to the simple supply-and-demand model, that minimum wage laws raise wages in some markets (such as fast foods) without significantly reducing employ- ment. In contrast, Neumark and Wascher (2008) conclude, based on an extensive review of minimum wage research, that increases in the minimum wage often have negative effects on employment.

FIGURE 2.8 The Minimum Wage: A Price Floor

In the absence of a minimum wage, the equilibrium wage is w* and the equilibrium number of hours worked is L*. A minimum wage, w, set above w*, leads to unemployment—persistent excess supply—because the quantity demanded, Ld, is less than the quan- tity supplied, Ls.

w , W

ag e

pe r

ho ur

Ld L* Ls

Minimum wage, price floor

S

D

L, Hours worked per year

Unemployment (Excess Supply)

e w*

w—

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332.5 Effects of Government Interventions

the quantity supplied and the quantity demanded, the supply-and-demand model is useful in analyzing this market because it predicts the excess demand that is observed.

We could have defined the quantity supplied and the quantity demanded so that they must be equal. If we were to define the quantity supplied as the amount firms actually sell at a given price and the quantity demanded as the amount consum- ers actually buy, supply must equal demand in all markets because the quantity demanded and the quantity supplied are defined to be the same quantity.

This distinction is important because many people, including politicians and news- paper reporters, are confused on this point. Someone who insists that “demand must equal supply” must be defining supply and demand as the actual quantities sold.

Because we define the quantities supplied and demanded in terms of people’s wants and not actual quantities bought and sold, we view the statement “supply equals demand” as a theory, not a definition. This theory says that the intersection of the supply curve and the demand curve determines the price and quantity in a market, and the market clears if the government does not intervene. However, the theory also tells us that government intervention can prevent market clearing. For example, the supply-and-demand model predicts that excess demand will arise if the govern- ment imposes a price ceiling below the market clearing price or excess supply will result if the government imposes a price floor above the market clearing price.

Sales Taxes New Jersey’s decision to eliminate the tax on Botox has users elated. At least we think they’re elated—we can’t really tell.

Governments frequently impose sales taxes on goods, such as the carbon tax dis- cussed at the beginning of the chapter.13 Sales taxes typically raise the price that consumers pay for a good and lower the price that firms receive for it.

One type of sales tax is a specific tax, in which the government collects a specified dollar amount, t, per unit of output. For example, the federal government collects t = 18.4¢ on each gallon of gas sold in the United States.14

In this section, we examine two questions about the effects of a specific tax:

1. What effect does a specific tax have on the equilibrium price and quantity? 2. Is it true, as many people claim, that firms pass the entire tax through to their

customers—the price that consumers pay rises by the full amount of the tax?

Equilibrium Effects of a Specific Tax. To answer these two questions, we must extend the standard supply-and-demand analysis to take account of taxes. We can illustrate the effect of a specific tax—our first question—using estimated supply and demand functions for the U.S. corn market.15

Many nutritionists argue that to fight obesity, we should reduce the amount of corn syrup (sugar) we consume. One way to do that would be to tax corn. Suppose that the government collects a specific tax of t = $2.40 per bushel of corn from sellers (farms). If a customer pays p to a firm, the government takes t = $2.40, so the firm keeps p - t = p - $2.40.

13MyLab Economics has a Taxes Experiment that illustrates the effect of sales taxes. To participate go to the MyLab Economics Multimedia Library, Single Player Experiment, and set the Chapter field to “All Chapters.” 14The other major type of sales tax is an ad valorem tax, in which the government collects a percentage of the price that consumers pay. The analysis of ad valorem taxes is similar to the analysis of specific taxes. 15Our linear curves are based on Roberts and Schlenker (2013).

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34 CHAPTER 2 Supply and Demand

Before the tax, the intersection of the before-tax corn demand curve D1 and the before-tax corn supply curve S1 in Figure 2.9 determines the before-tax equilib- rium, e1, where the equilibrium price is p1 = $7.20, and the equilibrium quantity is Q1 = 12 billion bushels of corn per year.

The tax causes the supply curve to shift. Before the tax, firms were willing to supply 11.6 billion bushels of corn per year at a price of $5.60 per bushel, as the pre- tax supply curve S1 shows. After the tax, if customers pay $5.60, firms keep only $5.60 - $2.40 = $3.20, so they are not willing to supply as much corn as before the tax. For firms to be willing to sell 11.6 units after the tax, customers must pay $8.00 so that the firms receive $8.00 - $2.40 = $5.60 after paying the tax. As a result, the after-tax supply curve, S2, is t = $2.40 above the original supply curve S1 at every quantity, as the figure shows.

The intersection of S2 and the demand curve D1 determines the after-tax equilib- rium e2, where consumers pay p2 = $8.00, firms receive p2 - t = p2 - $2.40 = $5.60, and Q2 = 11.6. Thus, the answer to our first question is that the specific tax causes the equilibrium price consumers pay to rise, the net price that firms receive (after paying the tax) to fall, and the equilibrium quantity to fall.

Although customers pay a higher price and producers receive less because of the tax, the government acquires new tax revenue of T = tQ2 = $2.40 per bushel * 11.6 billion bushels per year = $27.84 billion per year. The length of the shaded rect- angle is Q2 = 11.6 billion per year, and its height is t = $2.40 per bushel, so the area of the rectangle equals the tax revenue.

Pass-Through. Our second question concerns whether customers bear the entire burden of a tax, as many politicians and news stories assert.

FIGURE 2.9 Effect of a $2.40 Specific Tax on Corn Collected from Producers

The specific tax of t = $2.40 per bushel of corn collected from producers shifts the pre- tax corn supply curve, S1, up to the post-tax supply curve, S2. The tax causes the equilibrium to shift from e1 (determined by the intersection of S1 and D1) to e2 (intersection of S

2 with D1). The equilibrium price—the price consumers pay—increases from p1 = $7.20 to p2 = $8.00. The government collects tax reve- nues of T = tQ2 = $27.84 billion per year.

p, $

p er

b us

he l

Q2 = 11.6 Q1 = 12

T = $27.84 billion

Q, Billion bushels of corn per year

0

p2 = 8.00

p1 = 7.20

p2 – t = 5.60

t = $2.40

S2

e1

e2

S1

D1

Common Confusion Businesses pass through any sales tax to consumers, so that the price that consumers pay increases by the amount of the tax.

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352.5 Effects of Government Interventions

This belief is not accurate in general. Full pass-through can occur, but partial pass- through is more common.

As we just showed for the corn market in Figure 2.9, the price consumers pay rises from $7.20 to $8.00 after a $2.40 specific tax is imposed on firms. Thus, the firms shift only $0.80 of the $2.40 tax to consumers. The firms absorb $1.60 of the tax, because the price that firms receive falls from $7.20 to $5.60. Thus, the fraction of the tax that consumers pay is $0.80>$2.40 = 13 and the fraction that firms absorb is $1.60>$2.40 = 23.

However, in one special case, firms do pass the full amount of the tax to consum- ers, as the following Q&A shows.

Q&A 2.3 If the supply curve is horizontal and the demand curve is linear and downward sloping, what is the effect of a $1 specific tax collected from producers on equi- librium price and quantity, and what share of the tax do consumers pay? Why?

Answer 1. Determine the equilibrium in the absence of a tax. Before the tax, the perfectly elas-

tic supply curve, S1 in the graph, is horizontal at p1. The downward-sloping linear demand curve, D, intersects S1 at the pre-tax equilibrium, e1, where the price is p1 and the quantity is Q1.

2. Show how the tax shifts the supply curve and determine the new equilibrium. A spe- cific tax of $1 shifts the pre-tax supply curve, S1, upward by $1 to S2, which is horizontal at p1 + 1. The intersection of D and S2 determines the after-tax equilibrium, e2, where the price consumers pay is p2 = p1 + 1, the price firms receive is p2 - 1 = p1, and the quantity is Q2.

3. Compare the before- and after-tax equilibria. The specific tax causes the equilib- rium quantity to fall from Q1 to Q2, the price firms receive to remain at p1, and the equilibrium price consumers pay to rise from p1 to p2 = p1 + 1. Thus, the firms pass the entire tax, $1, on to consumers.

4. Explain why. The reason consumers must absorb the entire tax is that firms will not supply the good at a price that is any lower than they received before the tax, p1. Thus, the price must rise enough that the price suppliers receive after tax is unchanged. As consumers do not want to consume as much at a higher price, the equilibrium quantity falls.

p, P

ric e

pe r

un it

Q, Quantity per time period

Q1Q2

p1

p2 = p1 + 1

S1

S2

e1

e2

D

t = $1

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36 CHAPTER 2 Supply and Demand

2.6 When to Use the Supply-and-Demand Model As we have seen, the supply-and-demand model can help us to understand and predict real-world events in many markets. As with many models, the supply-and- demand model need not be perfect to be useful. It is much like a map. A map can leave out many details and still be valuable—indeed, maps are useful in large part because they simplify reality. Similarly, the supply-and-demand model gains much of its power from its simplicity. The main practical question concerns whether the model is close enough to reality to yield useful predictions and conclusions. We have learned that the supply-and-demand model provides a very good description of actual events in highly competitive markets. It is precisely accurate in perfectly competitive markets, which are markets in which all firms and consumers are price takers: no market participant can affect the market price.

Perfectly competitive markets have five characteristics that result in price tak- ing by firms: (1) many buyers and sellers transact in a market, (2) all firms produce identical products, (3) all market participants have full information about price and product characteristics, (4) transaction costs are negligible, and (5) firms can easily enter and exit the market over time.

In a market with a very large number of sellers, no single producer or consumer is a large enough part of the market to affect the price. The more firms in a market, the less any one firm’s output affects total market output and hence the market price. If one of the many thousands of wheat farmers stops selling wheat, the price of wheat will not change. Similarly, no individual buyer of wheat can cause price to change through a change in buying patterns.

If consumers believe all firms produce identical products, consumers do not pre- fer one firm’s good to another’s. Thus, if one firm raised its price, consumers would all buy from the other firm.

If consumers know the prices that all firms charge and one firm raises its price, that firm’s customers will buy from other firms. If consumers have less information about product quality than a firm, the firm can take advantage of consumers by selling them inferior-quality goods or by charging a much higher price than that charged by other firms. In such a market, the observed price may be higher than that predicted by the supply-and-demand model, the market may not exist at all (consumers and firms cannot reach agreements), or different firms may charge dif- ferent prices for the same good.

If it is cheap and easy for a buyer to find a seller and make a trade, and if one firm raises its price, consumers can easily arrange to buy from another firm. That is, per- fectly competitive markets typically have very low transaction costs: the expenses, over and above the price of the product, of finding a trading partner and making a trade for the product. These costs include the time and money spent gathering information on quality and finding someone with whom to trade. The costs of trav- eling and the value of the consumer’s time are transaction costs. Other transaction

Managers should use pass-through analysis to predict the effect on their price and quantity from not just a new tax but from any per unit increase in costs. Suppose that the cost of producing corn rises $2.40 per bushel because of an increase in the cost of labor or other factors of production, rather than because of a tax. Then, the same analysis as in Figure 2.9 would apply, so a manager would know that only 80¢ of this cost increase could be passed through to consumers.

Cost Pass-Through

Managerial Implication

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372.6 When to Use the Supply-and-Demand Model

costs may include the costs of writing and enforcing a contract, such as the cost of a lawyer’s time. If transaction costs are very high, no trades at all might occur. In less extreme cases individual trades may occur, but at a variety of prices.

The ability of firms to enter and exit a market freely leads to a large number of firms in a market and promotes price taking. Suppose a firm could raise its price and make a higher profit. If other firms could not enter the market, this firm would not be a price taker. However, if other firms can enter the market, the higher profit will encourage entry until the price reverts to the original level.

In markets without these characteristics, firms may not be price takers. For exam- ple, in a market with only one seller of a good or service—a monopoly—the seller is a price setter and can affect the market price. Because demand curves slope down- ward, a monopoly can increase the price it receives by reducing the amount of a good it supplies. Firms are also price setters in an oligopoly—a market with only a small number of firms. In markets with price setters, the market price is usually higher than that predicted by the supply-and-demand model. That does not make the model wrong. It means only that the supply-and-demand model might not be the right tool to analyze markets with a small number of buyers and/or sellers. In such markets, we use other models.

As a practical matter, it is rare to find a market that fully and completely satisfies all the conditions needed for perfect competition. The practical issue concerns whether the market is “competitive enough” for the supply-and-demand model to be useful in the sense that it accurately describes the market and predicts the effects of changes to the equilibrium. Experience has shown that the supply-and-demand model is reli- able in a wide range of markets, such as those for agriculture, financial products, labor, construction, many services, real estate, wholesale trade, and retail trade.

Carbon Taxes

Managerial Solut ion

We conclude our analysis of the supply-and-demand model by returning to the managerial problem posed in the introduction of this chapter: What will be the effect of imposing a carbon tax on the price of gasoline?

The primary targets of carbon taxes are fossil fuels such as oil, natural gas, and coal. These fuels release carbon-based pollutants—including greenhouse gases that contribute to global warming—into the environment. Typically, a carbon tax is a specific tax on the amount of carbon produced by consuming fuels or other products. Currently, the carbon tax in Sweden is about $150 per ton of carbon. Because the amount of carbon in a gallon or liter of gasoline is fixed, effectively, a carbon tax is a specific tax on gasoline. Consequently, we can analyze the impact of a carbon tax on gasoline in the same way that we analyzed the effect of a specific tax on corn.

A good manager considers the short-run and long-run price effects of a tax, which are likely to differ. As we’ve already seen, the degree to which a tax is passed through to consumers depends on the shapes of the demand and supply curves. Typically, short-run supply and demand curves differ from the long-run curves.

In particular, the long-run supply curve of gasoline differs substantially from the short-run curve. In the long run, the supply curve is upward sloping, as in our typical figure. However, the U.S. short-run supply curve of gasoline is very close to vertical. The U.S. refinery capacity has fallen over the past few decades. Currently, the 141 U.S. refineries can process a maximum of only 18.3 million barrels of crude oil per day, compared to 1981, when 324 refineries could process 18.6 million barrels per day. Refineries operate at almost full capacity during the

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38 CHAPTER 2 Supply and Demand

summer, when the gasoline demand curve shifts to the right because families take long car trips during vacation. Consequently, refineries cannot increase their output in the short run, and the supply curve for gasoline is nearly vertical at the maximum capacity, Q. That is, even if the price of gasoline rises, producers sell no more gasoline than Q.

From empirical studies, we know that the U.S. federal gasoline specific tax of t = 18.4¢ per gallon is shared roughly equally between gasoline companies and consumers in the long run. However, we expect most of the tax to fall on firms that sell gasoline in the short run.

We contrast the long-run and short-run effects of a carbon tax in the figure. In both panels, the carbon tax is equivalent to a specific gasoline tax of t per gal- lon. If the government collects this tax from consumers, the before-tax demand curve D1 shifts down by t to the after-tax demand curve D2. Also, in both panels, the equilibrium shifts from e1—the intersection of D1 and the relevant supply curve—to e2—the intersection of D2 and the relevant supply curve (though these equilibrium points are not the same across the two panels).

Panel a shows the effect of the tax in the long run, where the long-run supply curve is upward sloping. The price that firms receive falls from p1 to p2, and the price that consumers pay rises from p1 to p2 + t. As the figure illustrates, the tax is shared roughly equally by consumers and firms in the long run.

In the short run in panel b, the upward-sloping short-run supply curve becomes vertical at full capacity, Q. The price that consumers pay, p1, is the same before the tax and after the tax. That is, the price that gasoline firms receive, p2, falls by the full amount of the tax.

Manufacturing and other firms that ship goods are consumers of gasoline. They can expect to absorb relatively little of a carbon tax when it is first imposed, but half of the tax in the long run.16

16An alternative approach to using a carbon tax to control pollution is for the government to restrict emissions directly. The government gives each firm a fixed number of emission permits, each of which allows the owner to release a given quantity of emissions. A market-based variant allows firms to buy or sell these emission permits in a market. The resulting price of an emission permit acts much like a tax on emissions. See Chapter 16.

(b) Short-Run Gasoline Market

p, ¢

p er

g al

lo n

Q, Gallons of gasoline per day

p2 + t = p1

p2

e1

e2

D1

D 2

Q

SLR

SSR

(a) Long-Run Gasoline Market

p, ¢

p er

g al

lo n

Q, Gallons of gasoline per day

p2 + t

p2 e2

D1

D 2

Q

SLR

e1p1

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39Questions

QUESTIONS All exercises are available on MyLab Economics; * = answer at the back of this book; = this exercise is available in Excel Grader in MyLab Economics.

1. Demand *1.1 Does an increase in average income cause a shift of

the demand curve for coffee or a movement along the demand curve? Explain briefly.

1.2 Given the estimated demand function, Equation 2.2, for coffee, Q = 8.56 - p - 0.3ps + 0.1Y, use algebra (or calculus) to show how the demand curve shifts as per capita income, Y, increases by $10,000 a year. Illustrate this shift in a diagram.

1.3 Using the coffee demand function, Q = 8.56 - p - 0.3ps + 0.1Y, show that sugar is a complement for

coffee. You can use a numerical example, algebra, or calculus.

1.4 Assume that both the U.S. and Canadian demand curves for lumber are linear. The Canadian demand curve lies inside the U.S. curve (the Canadian demand curve hits the axes at a lower price and a lower quantity than the U.S. curve). Draw the indi- vidual country demand curves and the combined (summed) demand curve for the two countries. Explain the relationship between the country and summed demand curves in words. (Hint: See the Mini-Case “Summing Corn Demand Curves.”)

SUMMARY

1. Demand. The quantity of a good or service demanded by consumers depends on the price of a good, the price of goods that are substitutes and complements, con- sumers’ incomes, the information they have about the good, their tastes, government regulations, and other factors. The Law of Demand—which is based on observa- tion—says that demand curves slope downward: the higher the price, the less quantity of the good demanded, hold- ing constant other factors that affect demand. A change in price causes a movement along the demand curve. A change in income, tastes, or another factor that affects demand other than price causes a shift of the demand curve. To get a total demand curve, we horizontally sum the demand curves of individuals or other subgroups of consumers. That is, we add the quantities demanded by each individual at a given price to get the total quan- tity demanded.

2. Supply. The quantity of a good or service supplied by firms depends on the price, costs of inputs, the state of technology, government regulations, and other fac- tors. The market supply curve usually, but not always, slopes upward. A change in price causes a movement along the supply curve. A change in the price of an input or in technology causes a shift of the supply curve. The total supply curve is the horizontal sum of the supply curves for individual firms.

3. Market Equilibrium. Equilibrium arises when no mar- ket participant has an incentive to change its behavior. In an unregulated supply-and-demand model, the mar- ket equilibrium is a point: a price and a quantity. The intersection of the supply curve and the demand curve determines the market equilibrium. At the equilibrium price, the market for the good clears in the sense that the quantity of the good demanded by consumers exactly equals the quantity of the good that suppliers

supply to the market, which is the equilibrium quantity. The actions of buyers and sellers put pressure on price and quantity to move toward equilibrium levels if the market price is initially too low or too high.

4. Shocks to the Equilibrium. A change in an underlying factor other than a good’s own price causes a shift of the supply curve or the demand curve, which alters the equilibrium. For example, if the price of coffee rises, we would expect the demand for tea, a substitute, to shift outward, putting upward pressure on the price of tea and leading to an increase in the quantity of tea sold.

5. Effects of Government Interventions. Some govern- ment policies—such as restrictions on who can buy a product—cause a shift in the supply or demand curves, thereby altering the equilibrium. Other government policies, such as price controls, can cause the quan- tity supplied to be greater or less than the quantity demanded, leading to persistent excesses or shortages. A specific tax, a type of sales tax, typically lowers the equilibrium quantity, raises the price paid by consum- ers, and lowers the price received by sellers, so firms are unable to pass the entire tax through to consumers.

6. When to Use the Supply-and-Demand Model. The supply-and-demand model is a powerful tool used to explain what happens in a market and to make predic- tions about what will happen if an underlying factor changes. This model accurately predicts what occurs in some markets but not others. The supply-and-demand model performs best in explaining and predicting the behavior of markets with many buyers and sellers, with identical or at least very similar products provided by different producers, with free entry and exit by produc- ers, with full information about price and other market characteristics, and with low transaction costs.

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40 CHAPTER 2 Supply and Demand

*1.5 The demand function for a truckload of firewood for college students in a small town is Qc = 400 - p. It is sometimes convenient to rewrite a demand func- tion with price on the left side. We refer to such a relationship as the inverse demand function. Therefore, the inverse demand function for college students is p = 400 - Qc. The demand function for other town residents is Qr = 400 - 2p.

a. What is the inverse demand function for other town residents?

b. At a price of $300, will college students buy any firewood? What about other town residents? At what price is the quantity demanded by other town residents zero?

c. Draw the total demand curve, which sums the demand curves for college students and other residents. (Hint: See the Mini-Case “Summing Corn Demand Curves.”)

2. Supply 2.1 The estimated supply function for avocados is

Q = 58 + 15p - 20pf, where pf is the price of fer- tilizer. Determine how much the supply curve for avocados shifts if the price of fertilizer rises by $1.10 per lb. Illustrate this shift in a diagram.

*2.2 Explain why a change in the price of fertilizer causes a shift in the supply curve for avocados rather than a movement along the supply curve for avocados.

*2.3 Holding the price of fertilizer constant, by how much would the price of avocados need to rise to cause an increase of 60 million lb per month in the quantity of avocados supplied?

2.4 Assume that the total U.S. supply curve for frozen orange juice is the sum of the supply curve from Florida and the imported supply curve from Brazil. In a diagram, show the relationship between these three supply curves and explain it in words.

3. Market Equilibrium *3.1 A large number of firms are capable of producing

chocolate-covered cockroaches. The linear, upward- sloping supply curve starts on the price axis at $6 per box. A few hardy consumers are willing to buy this product (possibly to use as gag gifts). Their lin- ear, downward-sloping demand curve hits the price axis at $4 per box. Draw the supply and demand curves. Does an equilibrium occur at a positive price and quantity? Explain your answer.

3.2 The demand function is Q = 5,000 - 10p, and the supply function is Q = 200 + 6p. Determine the equilibrium price and quantity.

3.3 Using the demand function, Equation 2.2, Q = 8.56 - p - 0.3ps + 0.1Y, and the supply function,

Equation 2.5, Q = 9.6 + 0.5p - 0.2pc, for coffee, determine the  equilibrium price and quantity of coffee if Y = $55,000, ps = 0.20, and pc = $5. Draw the demand and supply curves and illustrate this equilibrium in a diagram.

*3.4 Using the demand function Q = 8.56 - p - 0.3ps + 0.1Y and supply function Q = 9.6 + 0.5p - 0.2pc, determine the amount of any excess demand or excess supply at a price of $4 and explain the mech- anism that would cause the equilibrium price to be reached.

4. Shocks to the Equilibrium 4.1 Using supply-and-demand diagrams, illustrate and

explain the effect of an outward shift in the demand curve on price and quantity if

a. The supply curve is horizontal.

b. The supply curve is vertical.

c. The supply curve is upward sloping.

4.2 Use supply-and-demand diagrams to illustrate the qualitative effect of the following possible shocks on the world coffee market.

a. A new study shows significant health benefits from drinking coffee.

b. An important new use for cocoa is discovered.

c. A recession causes a decline in per capita income.

d. A new coffee plant that allows for much greater output or yield without increasing cost is intro- duced into the market.

*4.3 The United States is increasingly outsourcing jobs to India: having the work done in India rather than in the United States. For example, the Indian firm Tata Consultancy Services, which provides informa- tion technology services, increased its workforce by 70,000 workers in 2010 (“Outsourcing Firm Hiring 60,000 Workers in India,” San Francisco Chronicle, June 16, 2011). As a result of increased outsourc- ing, wages of some groups of Indian skilled work- ers have increased substantially over the years. Use a supply-and-demand diagram to explain this outcome.

4.4 The estimated monthly U.S. demand function for avocados is Q = 144 - 40p + 20pt where p is the price of avocados and pt is the price of tomatoes, a substitute for avocados. The estimated supply func- tion is given in Question 2.1, where the price of fertilizer, pf, is $0.40, so the supply function can be written as Q = 50 + 15p. The initial price of toma- toes is 80¢ per lb. Using algebra, determine the ini- tial equilibrium price and quantity of avocados, and then determine how price and quantity change if the

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41Questions

price of tomatoes increases by 55¢ to $1.35. (Hint: See Q&A 2.1.)

4.5 President Trump introduced several policy mea- sures designed to curb immigration. Use a supply- and-demand diagram to illustrate the effect of such policies on wages and employment if the policies shift the labor supply curve to the left but have no effect on the labor demand curve.

*4.6 Given that the U.S. supply of frozen orange juice comes mainly from Florida and Brazil, what effect would a freeze that damages oranges in Florida have on the price and quantity of frozen orange juice sold in the United States? What effect would the freeze have on the price of grapefruit juice? Use supply-and-demand diagrams in your answer.

4.7 Ethanol, a fuel, is made from corn. Ethanol produc- tion in 2014 was approximately 17 times what it was in 1990 (www.ethanolrfa.org, June 2015). What effect did this increased use of corn for producing ethanol have on the price of corn and the consump- tion of corn as food? Illustrate using a supply-and- demand diagram.

4.8 The major BP oil spill in the Gulf of Mexico sub- stantially reduced the harvest of shrimp and other seafood in the Gulf, but had limited impact on the prices that U.S. consumers paid in 2010 (Emmeline Zhao, “Impact on Seafood Prices Is Limited,” Wall Street Journal, June 20, 2010). The reason was that the United States imports about 83% of its seafood and only 2% of domestic supplies come from the Gulf. Use a supply-and-demand diagram to illus- trate what happened.

4.9 For years, Chinese parents bought imported baby formula because of their concerns about the safety of domestic formula. However, in 2013, a major for- eign producer announced that its concentrate might contain botulism. In 2014, the Chinese government yanked production permits for a third of the coun- try’s infant formula manufacturers due to safety concerns. Many worried parents stopped buying any formula. The price of formula rose from 350 to 450 yuan (the Chinese currency). Use a supply- and-demand diagram to explain why the price rose. Show the effect on equilibrium quantity.

* 4.10 Increases in the price of petroleum affect the demand curve for aluminum. Petroleum-based chemicals (petrochemicals) are the main raw material used for plastic. Manufacturers use plastics to make many products, including beverage containers, auto parts, and construction materials. An alternative to plastic in these (and other) uses is aluminum. Thus, plas- tic and aluminum are substitutes. An increase in petroleum prices increases the cost of petrochemi- cals. Petroleum prices also affect the supply curve

for aluminum. Increases in petroleum prices tend to raise energy prices, including electricity prices. Elec- tricity is a very important input in producing alu- minum. Therefore, increasing petroleum prices tend to increase the cost of electricity. In a supply-and- demand diagram, show how an increase in petro- leum prices affects the demand curve and supply curve for aluminum. If the price of petroleum rises, would the price of aluminum rise, fall, or remain unchanged, or is the result indeterminate? Would the quantity of aluminum sold rise, fall, or remain unchanged, or is the result indeterminate? Explain your answers.

4.11 Use a figure to explain the fisher’s comment about the effect of a large catch on the market price in the cartoon in this chapter about catching lobsters. What is the supply shock?

4.12 Bentonite clay, which consists of ancient volcanic ash, has many uses, including manufacturing kitty litter and clarifying wine. A major use is for drilling mud, a material pumped down oil and gas wells during drilling to keep the drilling bit cool. When oil drilling decreases, less bentonite is demanded at any given price. The price of crude oil was about $50 a barrel in 2016–2017. However, by 2018, it was over $70, causing drilling to increase. Use a supply-and- demand diagram to show the effect on the bentonite market and explain in words what happened.

5. Effects of Government Interventions 5.1 New York City has licensed street vendors for more

than a century. It currently provides only a small number of general vending licenses. The waiting list is very long and, aside from military veterans, some- one trying to get a license today has no chance. One popular item for street vendors is handbags. Use a supply-and-demand model to show how this licens- ing affects the market price and quantity of handbags sold by New York street vendors. (Hint: See the Mini- Case on “Occupational Licensing” and Q&A 2.2.)

*5.2 After Katrina, a major hurricane, damaged many U.S. gasoline refineries in 2005, the price of gaso- line shot up around the country. The Federal Trade Commission announced that it would investigate price gouging—charging “too much”—and several members of Congress called for price controls on gasoline. What would have been the likely effect of such a law had it been passed?

5.3 Usury laws place a ceiling on interest rates that lend- ers such as banks can charge borrowers. Why would we expect low-income households in states with usury laws to have significantly lower levels of con- sumer credit (loans) than comparable households in states without usury laws? (Hint: The interest rate is

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42 CHAPTER 2 Supply and Demand

the price of a loan, and the amount of the loan is the quantity measure.)

5.4 Some cities impose rent control laws, which are price controls or limits on the price of rental accommoda- tions (apartments, houses, and mobile homes). As of 2015, New York City alone had approximately one million apartments under rent control. Show the effect of a rent control law on the equilibrium rental price and the quantity of New York City apartments. Show the amount of excess demand on your supply- and-demand diagram.

5.5 If the minimum wage raises the market wage, w, but hours worked, L, fall as a result, total wage pay- ments, wL, may rise or fall. Use supply and demand curves to show that either outcome is possible depending on the shapes (slopes) of the supply and demand curves. (Hint: With the wage on the ver- tical axis and hours worked, L, on the horizontal axis, wage payments equal the area of the box with a height of the equilibrium wage and length of the equilibrium hours worked.)

5.6 Use the demand function and the supply function for the avocado market (given in Question 4.4) to determine how the equilibrium price and quantity change when a 55¢ per lb specific tax is imposed on this market. (Hint: See Figure 2.9.)

5.7 If the government collects a $1 specific tax, what share of the tax is paid by consumers and firms in each of the following cases? Explain why. (Hint: See Q&A 2.3.)

a. The demand curve is vertical at quantity Q and the supply curve is upward sloping.

b. The demand curve is horizontal at price p and the supply curve is upward sloping.

c. The demand curve is downward sloping and the supply curve is horizontal at price p.

5.8 In Figure 2.9, the government imposes a specific tax on sellers, which causes the supply curve to shift up. At any given price paid by consumers, sellers supply less than before. Now suppose that the tax is imposed on buyers. Illustrate this effect by shift- ing the demand curve inward. Is the resulting equi- librium quantity the same as in Q&A 2.3? Explain briefly.

5.9 In 2012, voters in the state of Washington approved a ballot measure legalizing the recreational use of marijuana. The measure required that consumers pay a 37% tax on sales of recreational marijuana. For what slopes of the supply or demand curves will

this tax substantially reduce the equilibrium quan- tity of marijuana?

5.10 Since 2014, Quebec, Canada, has offered a per-child subsidy (which is a negative tax) on day care for young children that lowers the price to $7 per child.

a. What is the effect of this subsidy on the equilib- rium price and quantity?

b. Show the incidence of the subsidy on day care providers and parents using a supply-and- demand diagram.

6. When to Use the Supply-and-Demand Model 6.1 List as many industries as you can for which

the supply-and-demand model is likely to be appropriate.

7. Managerial Problem 7.1 During the spring and summer of 2008, when gasoline

prices were rising quickly, politicians in several coun- tries proposed a moratorium on some or all gasoline taxes to help consumers. In the United States, John McCain, the Republican candidate for president, pro- posed suspending the federal gasoline tax of 18.4¢ for the summer, when demand tends to be high. (Hillary Clinton, while an active candidate for the Democratic nomination for president, also pushed this plan.) In the United Kingdom, Prime Minister Gordon Brown proposed delaying a two pence per liter rise in a fuel tax until the fall. How would these short-run poli- cies have affected the prices consumers would pay in these countries if the policies had been enacted?

8. MyLab Economics Spreadsheet Exercises17

8.1 Suppose that the market for video games is competi- tive with demand function Qd = 130 - 4p + 2Y + 3pm - 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that an average consumer has available for entertainment, pm is the aver- age price of a movie, and pc is the price of a controller that is required to play these games.

a. Given that Y = $100, pm = $30, and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Use Excel’s charting tool to draw the demand curve.

b. Now, Y increases to $120. Recalculate the demand schedule in part a. Use Excel’s chart- ing tool to draw the new demand curve in the same diagram.

c. Let Y = $100 and pc = $30 again, but let pm increase to $40. Recalculate the demand

17The spreadsheet exercises in this chapter are based on the work of Satyajit Ghosh in cooperation with the authors. The answers are available on MyLab Economics.

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43Questions

schedule in part a. Use Excel’s charting tool to draw the graph of the new demand curve.

d. Let Y = $100, pm = $30, and pc increase to $40. Recalculate the demand schedule in part a and use Excel to draw the new demand curve.

8.2 In Smalltown, Pennsylvania, the demand function for men’s haircuts is Qd = 500 - 30p + 0.08Y, where Qd is quantity demanded per month, p the price of a haircut, and Y the average monthly income in the town. The supply function for men’s haircuts is Qs = 100 + 20p - 20w, where Qs is the quantity supplied and w the average hourly wage of barbers.

a. If Y = $5,000 and w = $10, use Excel to calcu- late quantity demanded and quantity supplied for p = $5, $10, $15, $20, $25, and $30. Calcu- late excess demand for each price. (Note that an excess supply is negative excess demand.) Determine the equilibrium price and quantity. Use Excel’s charting tool to draw the demand and supply curves.

b. Assume that Y increases to $6,875 and w increases to $15. Use Excel to recalculate quan- tity demanded, quantity supplied, and excess demand for p = $5, $10, $15, $20, $25, and $30. Determine the new equilibrium price and

quantity. Use Excel to draw the new demand and supply curves. How can you explain the change in equilibrium?

8.3 The demand and supply functions for oil in a small isolated country are Qd = 210 - 1.5p and Qs = -140 + 2p, where p is the price per barrel and quantities are in millions of barrels per year.

a. Use Excel to calculate the quantity demanded and quantity supplied for p = $70, $75, $80, . . . , $140 (in $5 increments). Determine the equilibrium price and quantity.

b. Use Excel’s charting tool to draw the demand and supply curves you derived in part a and graphically determine the equilibrium calcu- lated in part a.

c. Now, assume that the government imposes a price ceiling of $80 per barrel. Use the spread- sheet from part a to determine the amount of any excess demand or excess supply. How much oil is sold?

d. The government abandons the price ceiling described in part c and imposes a price floor of $110 per barrel instead. Use your spreadsheet to determine any excess demand or excess supply now. How much oil is sold?

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44

3 Empirical Methods for Demand Analysis 98% of all statistics are made up.

Managers commonly use data to estimate economic relationships, such as that between price and quantity shown by a demand curve, or to examine whether a particular economic theory applies in their markets. Data-based analysis of economic relationships is often referred to as empirical analysis. This chap- ter discusses empirical methods that can be used to analyze economic relationships, emphasizing particularly the empirical analysis of demand.

In Chapter 2, we focused on market demand curves in highly competitive mar- kets, such as most agricultural markets. In highly competitive markets with many firms selling identical products, each individual firm is a price taker. In such markets, no one firm can significantly influence the market price. Any firm that tried to raise its price above the market equilibrium price would lose all of its sales. However, many firms, such as Apple, operate in markets that are not as competitive. Such firms are price setters that can raise their prices without losing all their sales. In the market for music downloads, Apple is a price setter.

When Apple launched iTunes, it charged 99¢ for each song on its U.S. site. Later, Apple reconsidered its pricing strategy. Music producers wanted Apple to charge more, but price competition from rivals such as Amazon created pressure on Apple to lower its price. In April 2009, Apple switched to a new U.S. pricing scheme: 69¢ a song for the older catalog, 99¢ for most new songs, and $1.29 for the most popular tracks.

In June 2015, Apple introduced a streaming audio service, Apple Music, which allows customers to play as many songs as they want as often as they want for $9.99 per month. This service competes with traditional music downloads, but

Apple decided not to change the price of those downloads, keeping a price of $1.29 for hit songs, and that price remains in force.

Before Apple managers change an iTunes price, they predict the likely effect of the price change on sales. Rather than run a potentially costly experiment of trying different possible prices to see how the quantity demanded changes, iTunes managers could ask a focus group consisting of a random sample of music buyers how they would react to a price hike. After collecting their responses, the managers could analyze the data to predict the likely effects of a price change. How could the managers use the data to estimate the demand curve facing iTunes? How could the managers determine if a price increase would be likely to raise rev- enue, even though the quantity demanded would fall?

Estimating the Effect of an iTunes Price Change

Managerial Problem

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453.1 Elasticity

A price-setting firm is concerned about the demand curve facing the firm rather than a market demand curve. In particular, the manager of a price-setting firm often wants to know how responsive its quantity demanded is to changes in its price or in other variables that affect demand. For example, in deciding whether to raise the price of iTunes songs by 30¢, an Apple manager would want to know how the number of iTunes downloads would fall in response to a 30¢ increase in price. This responsiveness can be measured empirically using the price elasticity of demand.

A manager might also wish to estimate the entire demand function to decide how to set the firm’s profit-maximizing price, plan an advertising campaign, or choose how large a plant to build. In Chapter 2, we used estimated demand (and supply) functions to determine the equilibrium price and to analyze the effects of government policies on the market. This chapter describes how to estimate demand functions using regression analysis, which is an empirical method used to estimate a mathemati- cal relationship between a dependent variable, such as quantity demanded, and explanatory variables, such as price and income.

Further, managers often wish to use data to forecast the future value of an impor- tant economic quantity such as future sales. This chapter describes major forecasting methods, focusing particularly on the role of regression analysis in forecasting.

3.1 Elasticity Managers commonly summarize the responsiveness of one variable—such as the quantity demanded—to a change in another—such as price—using a measure called an elasticity, which is the percentage change in one variable divided by the associ- ated percentage change in the other variable. In particular, a manager can use the elasticity of demand to determine how the quantity demanded varies with price.

The Price Elasticity of Demand In making critical decisions about pricing, a manager needs to know how a change in price affects the quantity sold. The price elasticity of demand (or simply the elasticity of demand or the demand elasticity) is the percentage change in quantity demanded, Q, divided by the percentage change in price, p. That is, the price elasticity of demand (which we represent by e, the Greek letter epsilon) is

e = percentage change in quantity demanded

percentage change in price =

∆Q > Q ∆p > p . (3.1)

The symbol ∆ (the Greek letter delta) indicates a change, so ∆Q is the change in the quantity demanded; ∆Q>Q is the percentage change in the quantity demanded;

Learning Objectives

1. Calculate elasticities and apply them to managerial problems.

2. Use regression analysis to estimate business relationships.

3. Determine the confidence we can place in a regression analysis.

4. Explain how to choose an appropriate regression specification.

5. Forecast important business variables using regression analysis.

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46 CHAPTER 3 Empirical Methods for Demand Analysis

∆p is the change in price; and ∆p>p is the percentage change in price. According to Equation 3.1, if a 1% increase in the price of a product results in a 3% decrease in the quantity demanded of that product, the elasticity of demand is e = -3%>1% = -3.

The elasticity of demand is a pure number: It is not measured in any particular units like dollars or tons. A useful way to think about elasticity is to consider the effect of a 1% change. If the price elasticity of demand is -2, a 1% decrease in price would cause quantity demanded to increase by 2%.

Arc Elasticity. Very often, a manager has observed the quantity demanded at two different prices. The manager can use this information to calculate an arc price elasticity of demand, which is a price elasticity of demand calculated using two distinct price-quantity pairs.1

Suppose a manager observes that when the price of coffee rises from p1 = $1.80 to p2 = $2.20, the global quantity of coffee demanded falls from q1 = 10.2 million tons to q2 = 9.8 million tons per year. To use Equation 3.1, the manager must deter- mine the percentage change in the quantity, ∆Q>Q, and the percentage change in price, ∆p>p.

The change in the quantity demanded as the price falls is ∆Q = q2 - q1 = 9.8 - 10.2 = -0.4 million tons. To determine the percentage change in quantity, the man- ager needs to divide this change by a quantity, Q. Should the manager use the initial quantity, 10.2, the final quantity, 9.8, or something else? When calculating a per- centage change, this choice of the base quantity makes a difference. If the man- ager uses the initial quantity as the base, then the percentage change in quantity is -0.4>10.2 ≈ -3.9% (where≈means “approximately equal to”). If the manager uses the final quantity as the base, the percentage change is -0.4>9.8 ≈ -4.1%.

Another approach is to use the average quantity as the base. The average quantity is (9.8 + 10.2) >2 = 10, so the associated percentage change is -0.4>10 = -4.0%. Many analysts use the average quantity because the elasticity is the same regardless of whether we start at a quantity of 10.2 and move to 9.8 or start at 9.8 and move to 10.2. If, instead, the manager consistently uses the initial quantity as the base, or consistently uses the final quantity as the base, then the percentage change would vary depending on the direction of movement.

The percentage change in price can also be calculated by using the average price as the base. The price change is ∆p = p2 - p1 = $2.20 - $1.80 = $0.40. The aver- age price is ( $1.80 + $2.20) >2 = $2.00. Thus, the percentage change in price is $0.40>$2.00 = 20%.

An arc price elasticity is an elasticity that uses the average price and average quantity as the denominator for percentage calculations.2 Using Equation 3.1, the arc price elasticity is

e = percentage change in quantity demanded

percentage change in price =

∆Q > Q ∆p > p , (3.2)

where the bars over Q and p indicate average values. In our example, the arc price elasticity is - (∆Q>Q) > (∆p>p) = -4%>20% = -0.2.

1In mathematics an arc is any segment of a smooth curve, so the arc price elasticity of demand is the elasticity along some segment of the demand curve. 2Because the arc elasticity of demand uses the average price and quantity as the base for percentage calculations it is sometimes called the midpoint elasticity.

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473.1 Elasticity

Point Elasticity. An arc elasticity is based on a discrete change between two dis- tinct price-quantity combinations on a demand curve. If we let the distance between these two points become infinitesimally small, we are effectively evaluating the elas- ticity at a single point. We call an elasticity evaluated at a specific price-quantity combination a point elasticity.

If a manager knows only two specific price-quantity points on a demand curve, then the manager’s best summary of how quantity demanded responds to price changes is the arc elasticity of demand for the movement between these two points. If, in contrast, the manager has information about the entire demand curve, it is pos- sible to calculate the point elasticity of demand at any point on the demand curve.

One of the easiest and most straightforward ways for a manager to determine the elasticity of demand for a firm’s product is to conduct an experiment. If the firm is a price setter and can vary the price of its product—as Apple, Toyota, Kraft Foods, and many other firms can—the manager can change the price and observe how the quantity sold varies. Armed with two observations—the quantity sold at the original price and the quantity sold at the new price—the manager can calculate an arc elasticity. Depending on the size of the calculated elasticity, the manager may continue to sell at the new price or revert to the original price. It is often possible to obtain useful information from an experiment in a few markets or even just one small submarket—in one country, in one city, or even in one supermarket. Managers of price-setting firms should consider using such experi- ments to assess the effect of price changes on quantity sold.

Changing Prices to Calculate an Arc Elasticity

Managerial Implication

Q&A 3.1 In 2018, Amazon raised the annual subscription fee for its Prime membership service, which provides free two-day shipping on many goods and other bene- fits, from $99 to $119. Piper Jaffray, an investment bank, estimated that before the price increase, Prime had 77 million U.S. subscribers.3 The bank speculated that the number of members would fall to about 62 million. If so, what is the arc elasticity of demand for a Prime membership?

Answer Use Equation 3.2 to calculate the arc elasticity. The change in the price is ∆p = $119 - $99 = $20, and the change in quantity is ∆Q = 62 - 77 = -15. The average price is p = ( $99 + $119) >2 = $109, and the average quantity is Q = (77 + 62) >2 = 69.5 million. Plugging these values into Equation 3.2, we find that the arc price elasticity of demand for Prime memberships is

e = ∆Q>Q ∆p>p =

-15>69.5 20>109 ≈ -

0.216 0.183

≈ -1.18.

When price rose by 18.3%, the quantity demanded was estimated to fall by 21.6%, so the arc elasticity of demand is e = -1.18. Based on this elasticity, a 1% rise in price would cause the quantity demanded to fall by 1.18 percent.

3Jaclyn Cosgrove and Abha Bhattarai, “Amazon Prime’s Price Is Jumping to $119 a Year,” Los Angeles Times, April 27, 2018.

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48 CHAPTER 3 Empirical Methods for Demand Analysis

The point elasticity indicates the effect on the quantity demanded arising from a very small change in price.

To calculate a point elasticity, we first rewrite the price elasticity formula, Equa- tion 3.1, as

e = ∆Q>Q ∆p>p =

∆Q ∆p

p Q

(3.3)

where we are evaluating the elasticity at the point (Q, p) and ∆Q>∆p is the ratio of the change in quantity to the change in price.

Holding other variables that affect demand fixed, we can use Equation 3.3 to cal- culate the elasticity of demand for a general linear demand curve. The mathematical function corresponding to a linear demand curve is

Q = a + bp, (3.4)

where a and b are parameters or coefficients. We assume that a is a positive constant and b is a negative constant. The parameter a is the quantity demanded if the price is zero. The parameter b shows how much the quantity demanded falls if the price is increased by one unit (such as a dollar). As we showed in Chapter 2, if the price changes from p1 to p2, then

∆Q = Q2 - Q1 = (a + bp2) - (a + bp1) = b(p2 - p1) = b∆p, (3.5)

so if ∆p = 1, the change in the quantity demanded, ∆Q = b, is negative. Rearranging Equation 3.5, we see that ∆Q>∆p = b. Thus, the elasticity of demand

for a linear demand curve is

e = ∆Q ∆p

p Q

= b p Q

. (3.6)

As we discussed in Chapter 2, our estimated linear demand function for coffee is

Q = 12 - p,

where Q is the quantity of coffee in millions of tons and p is the price in dollars per lb. For this specific linear demand function, a = 12 and b = -1. Substituting these values into Equation 3.6, we find that the point elasticity of demand for coffee is

e = -1 p Q

. (3.7)

Equation 3.7 allows us to determine the elasticity of demand at any point (any price-quantity combination) on the demand curve. In particular, we can find the point elasticity of demand at p = $2.20, where the quantity demanded is Q = 12 - (1 * 2.20) = 9.8, by substituting these values into Equation 3.7:

e = -b p Q

= - 2.20 9.8

≈ -0.22.

We previously used the estimated demand function for coffee to calculate the arc elasticity of demand for a price change from $2.20 to $1.80. That elasticity was -0.2, which is different from the point elasticity of -0.22 just calculated. Although these two elasticities are different, neither is incorrect. Both are appropriate measures— they are just measuring different elasticities. The arc elasticity correctly measures the elasticity associated with a discrete change from a price of $2.20 to a price of $1.80,

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493.1 Elasticity

while the point elasticity correctly measures the elasticity at a price of $2.20 for an infinitesimal change in the price. Both elasticity measures are useful. To keep our discussion as short and clear as possible, the subsequent analysis will deal just with point elasticities unless explicitly stated otherwise.

Elasticity Along the Demand Curve The elasticity of demand is different at every point along a downward-sloping linear demand curve. However, horizontal and vertical demand curves, which are extreme cases of a linear demand curve, have the same elasticity at every point.

Downward-Sloping Linear Demand Curves. The elasticity of demand is different at every point along a downward-sloping linear demand curve. According to Equation 3.6, the elasticity of demand on a linear demand curve is e = b(p>Q). Although b is a constant, the price-quantity ratio, p>Q, varies as we move along the demand curve, so the elasticity must also vary. The higher the price, the lower the quantity, so the ratio p>Q is a more negative number, and the elasticity must be more negative. A 1% increase in price causes a larger percentage fall in quantity near the top (left) of the demand curve than near the bottom (right).

We use the linear coffee demand curve in Figure 3.1 to illustrate how the elasticity varies with price. At the lower right corner of Figure 3.1, where the coffee demand curve hits the quantity axis (p = 0 and Q = 12), the elasticity of demand for coffee, Equation 3.7, is e = -1(p>Q) = -1(0>12) = 0. At a point where the elasticity of demand is zero, we say that the demand curve is perfectly inelastic.

For quantities between the midpoint of the linear demand curve and the lower end where p = 0, the demand elasticity lies between zero and negative one: 0 7 e 7 -1.

Mini-Case The Apple App Store (iOS) had about 2.1 million apps (mobile applications for smartphones and tablets) available as of 2018. Google Play (Android) had even more, about 3.7 million. How price sensitive are consumers of apps (mobile applications)? Are Apple aficionados more or less price sensitive than people who use Android devices?

Ghose and Han (2014) estimated the demand for an app in the Apple App Store as -2.0. That is, a 1% increase in price causes a 2% drop in the quantity demanded for an Apple app. Thus, demand is elastic in the Apple App Store. The estimated demand elasticity for an app in Google Play is -3.7. Thus, the demand elasticity of a typical Android app is nearly twice that of an Apple app. Google Play consumers are more price sensitive than are Apple App consumers.

Demand Elasticities for Google Play and Apple Apps

The Point Elasticity of Demand

Using Calculus As the change in price becomes very small, ∆p S 0, the ratio ∆Q>∆p converges to the derivative dQ>dp. Thus, the point elasticity of demand in Equation 3.3 may be written as

e = dQ dp

p Q

. (3.8)

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50 CHAPTER 3 Empirical Methods for Demand Analysis

A point along the demand curve where the elasticity is between 0 and -1 is inelastic (but not perfectly inelastic): a 1% increase in price leads to a fall in quantity of less than 1%. For example, when the coffee price is $3 and the quantity demanded is 9, the elasticity of demand is e = - (3>9) = -13, so a 1% increase in price causes quantity to fall by one-third of a percent.

Rearranging the elasticity formula in Equation 3.1, the percentage change in Q is e times the percentage change in price: ∆Q>Q = e ( ∆p>p). If the elasticity e lies between 0 and -1, the percentage change in quantity is smaller than the per- centage change in price. Thus, demand is inelastic in the sense that it changes little in response to a price change. As a physical analogy, if you try to stretch a rope, it stretches only slightly. The change in price is the force pulling at demand, just as your effort provides the force pulling at the rope. If the quantity demanded does not change much in response to this force, we say that the demand curve is inelastic.

At the midpoint of the linear demand curve, a 1% increase in price causes a 1% fall in quantity, so the elasticity equals -1, which we refer to as unitary elasticity.4 At prices higher than at the midpoint of the demand curve ($6 on the coffee demand curve), the elasticity of demand is less than negative one, e 6 - 1. That is, the elasticity is a more negative number because it is larger in absolute value. In this range, the demand curve is elastic. A physical analogy is a rubber band that stretches substantially when you pull on it. A 1% increase in price causes a more than 1% fall in quantity. Figure 3.1 shows that the coffee demand elasticity is -3 where the price is $9 and 3 million tons are demanded: a 1% increase in price causes a 3% drop in quantity.

Where the demand curve hits the price axis at p = $12 and Q = 0, the elasticity of demand is e = - (12>0), which is not defined. As Q approaches zero, the elastic- ity becomes a larger and larger negative number that approaches negative infinity, - ∞ . The demand curve is perfectly elastic at the point where Q = 0. Because quantity is zero at p = 12, if we lower the price even slightly so that the quantity demanded becomes positive, the percentage increase in quantity demanded is infinite.

4At the midpoint of a general linear demand curve, Q = a>2 and p = -a> (2b), so, using Equation 3.6, e = bp>Q = -b (a>[2b]) > (a>2) = -1.

p, $

p er

lb

63

D

129

Q, Million tons of coffee per year

0

9

12

3

6

Elastic: e < –1

e = –3

Unitary: e = –1

1 3e =

Inelastic: 0 > e > –1

Perfectly inelastic

Perfectly elastic

–

FIGURE 3.1 The Elasticity of Demand Varies Along the Linear Coffee Demand Curve

With a linear demand curve, such as the coffee demand curve, the higher the price, the more elastic the demand curve (e is larger in absolute value: it becomes a more negative number as we move up the demand curve). The demand curve is perfectly inelastic (e = 0) where the demand curve hits the horizontal axis, is perfectly elastic where the demand curve hits the ver- tical axis, and has unitary elasticity at the midpoint of the demand curve.

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513.1 Elasticity

Horizontal Demand Curves. Horizontal demand curves have constant elas- ticity (as do vertical demand curves). The demand curve that is horizontal at p* in panel a of Figure 3.2 implies that people are willing to buy as much as firms want to sell at any price less than or equal to p*. If the price increases even slightly above p*,

Q&A 3.2 An estimated linear equation for the U.S. corn demand function is 5

Q = 15.6 - 0.5p,

where p is the price in dollars per bushel and Q is the quantity demanded in billion bushels per year. Use Excel to calculate the price elasticity of demand for every price between $2 and $10 in one-dollar increments. Round the elasticity to three digits after the decimal point. Is the demand curve more elastic or less elastic at higher prices?

Answer 1. Open an Excel spreadsheet; put titles “Price,” “Quantity,” and “Elasticity” in cells A1,

B1, and C1; and put prices 2 through 10 in one-dollar increments in cells A2 through A10. 2. Use the corn demand function to fill in quantities in column B. Enter

“=15.6-0.5*A2” in cell B2. Then copy cell B2 and paste it into cells B3 through B10. The quantity associated with each price in column A should appear in column B.

3. Use the elasticity formula for a linear demand function given by Equation 3.6 to fill in column C. Using Equation 3.6, e = bp>Q = -0.5p>Q, because b = -0.5 in the corn demand function. Therefore, enter “= -0.5*A2>B2” in cell C2. Copy cell C2 and paste it into cells C3 through C10. The elasticity associated with each price in column A should appear in column B. Use Excel’s format feature to round to three digits after the decimal point.

4. The spreadsheet shows that higher prices are associated with elasticities that are “more negative” (negative numbers that are larger in absolute value).

5This demand curve is a linearized version of the estimated demand curve in Roberts and Schlenker (2013).

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52 CHAPTER 3 Empirical Methods for Demand Analysis

however, demand falls to zero. Thus, a small increase in price causes an infinite drop in quantity, so the demand curve is perfectly elastic.6

A horizontal demand curve is an extreme case of a linear demand curve: it is the flattest possible linear demand curve. Unlike downward-sloping linear demand curves, a horizontal demand curve does not have the property that the elasticity changes along the demand curve. For a horizontal demand curve, the elasticity is negative infinity at every point.

Why would a good’s demand curve be horizontal? One reason is that consumers view this good as identical to another good and do not care which one they buy. If consumers regard Gala apples grown in Washington and Gala apples grown in Oregon as identical, they won’t buy Washington apples if these sell at a higher price than those from Oregon. Similarly, they won’t buy Oregon apples if their price is higher than that of Washington apples. If the two prices are equal, consumers do not care which type of Gala apple they buy. Thus, the demand curve for Oregon apples is horizontal at the price of Washington apples.

Vertical Demand Curves. A vertical demand curve, as in panel b in Figure 3.2, is perfectly inelastic everywhere. Such a demand curve is an extreme case of a linear demand curve—the opposite extreme from the horizontal demand curve. A vertical demand curve has an infinite (vertical) slope. A vertical demand function is also a special case of the constant-elasticity demand function. If e takes on the value 0, then the demand function is Q = Ap0 = A, so the demand curve is a verti- cal line at quantity A. If the price goes up, the quantity demanded is unchanged, so ∆Q = 0. The elasticity of demand as given by Equation 3.1 must be zero: (∆Q>∆p) (p>Q) = (0>∆p) (p>Q) = 0.

A demand curve is vertical for essential goods—goods that people feel they must have and will pay anything to get. Because Jerry has diabetes, his demand curve for insulin could be vertical at a day’s dose, Q*. Panel c of Figure 3.2 assumes that the maximum feasible price is p* and illustrates that the quantity demanded is unchanged at Q* for all possible prices less than p*.

6Using the constant-elasticity demand function, as e becomes a very large negative number, the demand curve becomes increasingly flat and approaches a horizontal line.

FIGURE 3.2 Vertical and Horizontal Demand Curves

(a) A horizontal demand curve is perfectly elastic at p*. (b) A vertical demand curve is perfectly inelastic at every price.

(c) The demand curve for insulin of an individual with diabetes is perfectly inelastic below p* and perfectly elastic at p*, which is the maximum price the individual can afford to pay.

p, P

ric e

pe r

un it

(a) Perfectly Elastic Demand

Q, Units per time period

p*

(b) Perfectly Inelastic Demand

p, P

ric e

pe r

un it

Q* Q, Units per time period

(c) Individual’s Demand for Insulin

p*

p, P

ric e

of in

su lin

d os

e

Q* Q, Insulin doses per day

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533.1 Elasticity

Other Types of Demand Elasticities In addition to the price elasticity of demand, we can also use elasticities to summa- rize how quantity demanded changes in response to changes in variables other than the good’s price. Two such elasticities are the income elasticity of demand and the cross-price elasticity of demand.

The income elasticity of demand is the percentage change in the quantity deman ded divided by the percentage change in income, Y:

percentage change in quantity demanded

percentage change in income =

∆Q > Q ∆Y > Y =

∆Q ∆Y

Y Q

.

We say a good is a normal good if the quantity demanded increases as income rises. That is, a normal good has a positive income elasticity of demand. Goods like cof- fee or music downloads are normal goods: people buy more of them when their incomes rise. Conversely, a good is an inferior good if the quantity demanded falls as income rises. Inferior goods have negative income elasticities. For many college students, Kraft Macaroni & Cheese (food in a box) is an inferior good—they buy it when their incomes are low but switch to more appealing and expensive foods when their incomes rise.

The cross-price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price of another good, po:

percentage change in quantity demanded

percentage change in other price =

∆Q > Q ∆po > po =

∆Q ∆po

po Q

.

The cross-price elasticity of demand determines whether goods are complements, sub- stitutes, or unrelated goods. When the cross-price elasticity is negative, people buy less of the good if the price of the other good rises. Such goods are complements. For example, if some people insist on having sugar in their coffee, then, as the price of sugar rises, they consume less coffee. The cross-price elasticity of coffee demanded with respect to the price of sugar is therefore negative and coffee and sugar are complements.

If, alternatively, the cross-price elasticity is positive, the goods are substitutes. As the price of one good rises, people buy more of the substitute good. For example, cot- ton and wool are substitutes, and so the quantity of cotton demanded increases if the price of wool rises. If the cross-price elasticity is zero, then the goods are unrelated. Coffee and wool are unrelated goods. An increase in the price of wool has no effect on the quantity of coffee demanded (see Chapter 2).

Mini-Case Anyone who has seen bar scenes in old movies will know that smoking and drinking apparently go together: they’re complements. Recent research has examined this relationship more rigorously, showing clearly that cigarettes and alcohol are complements. When the price of cigarettes rises or when smoking becomes more difficult (due to smoking bans, for example) people smoke less and drink less. The cross-elasticity of demand for alcohol with respect to cigarette prices is substantial. Krauss et al. (2014) found that a 1% increase in the price of cigarettes gives rise to almost a 1% decline in alcohol consumption. That is, the cross-price elasticity between alcoholic beverages and cigarettes is almost -1.

Over the past two decades, smoking bans in workplaces, restaurants, bars, and other public places have become increasingly common. In 1995, California

Anti-Smoking Policies May Reduce Drunk Driving

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54 CHAPTER 3 Empirical Methods for Demand Analysis

Demand Elasticities over Time The shape of a demand curve depends on the period under consideration. Often consumers substitute between products in the long run but not in the short run. The price of U.S. gasoline in May 2018 was nearly one-third higher than in the previous year. However, most consumers did not change their consumption demand very much in the short run. Someone who drives 27 miles to and from work every day in a Ford Explorer did not suddenly start using less gasoline. However, if gas prices were to remain high in the long run, people would reduce their consumption of gasoline. Many people would buy smaller, more fuel-efficient cars; some would take jobs closer to home; and some would even move closer to their work or to convenient public transportation.

Liddle (2012) estimated the gasoline demand elasticities across many countries and found that the short-run elasticity for gasoline was -0.16 and the long-run elas- ticity was -0.43. Thus, a 1% increase in price lowers the quantity demanded by only 0.16% in the short run but by more than twice as much, 0.43%, in the long run.

Other Elasticities We can summarize the relationship between any two related variables using an elasticity. In addition to the various demand elasticities that we’ve mentioned, oth- ers are also important. For example, just as we might measure the price elasticity of demand, we might also measure the price elasticity of supply, which is the percent- age change in quantity supplied divided by the percentage change in price. It shows the percentage increase in quantity supplied arising from a 1% increase in price. A manager might be interested in the elasticity of cost with respect to output, which shows the percentage increase in cost arising from a 1% increase in output. Or, dur- ing labor negotiations, a manager might cite the elasticity of output with respect to labor, which would show the percentage increase in output arising from a 1% increase in labor input, holding other inputs constant.

Estimating Demand Elasticities Price, income, and cross-price demand elasticities are important managerial tools. With these tools, managers can predict how the quantity demanded will respond to changes in consumer income, the product’s own price, or the price of a related

introduced one of the United States’ first statewide bans on smoking in public places, including bars and restaurants. Many other states followed suit, mostly about a decade later, although some, such as Texas and Alaska, still do not have statewide bans on smoking in public places. Smoking bans are common in much of the world, including in Australia, Canada, and most of Europe. China introduced a nationwide ban on smoking in enclosed public spaces in 2011, although enforcement is apparently very inconsistent. The Netherlands banned separate smoking rooms in hospitality facilities in 2018.

The complementarity between smoking and drinking implies that tobacco taxes (which raise the price of cigarettes) and restrictions on smoking have two health benefits. First, the tax reduces the negative health effects of smoking. Second, the tax reduces the negative effects of excessive drinking, including the very serious health risks created by drunk driving.

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553.2 Regression Analysis

good. Managers use this information to set prices, as in the iTunes example, and in many other ways.

Managers use data to calculate or estimate elasticities. For example, Q&A 3.1 shows how a manager can observe the quantity effect of a change in price to deter- mine the elasticity of demand for Amazon Prime memberships. Such a before-and- after price change calculation uses data from before the price change and after the price change to calculate an arc elasticity. By comparing quantities just before and just after a price change, managers can be reasonably sure that other variables that might affect the quantity demanded, such as income, have not changed appreciably.

Managers at iTunes could do such calculations for many songs and obtain an estimate of how the iTunes price change affected overall sales. They could then use this information to make other decisions about iTunes—such as how quickly to expand and upgrade server capacity or whether to charge different prices for vari- ous songs.

However, it may not always be feasible or desirable for a manager to calculate a before-and-after arc elasticity. To avoid a potentially expensive mistake, a manager often wants an estimate of the demand elasticity before actually making a price change. Similarly, a manager may fear a reaction by a rival firm in response to a pric- ing experiment. A manager wants to know the effect on demand of many possible price changes rather than focusing on just one price change. Such information enables the manager to select the best possible price rather than simply choosing between two particular prices. In effect, the manager would like an estimate of the entire demand curve. Regression analysis is an empirical technique that managers can use to estimate an entire demand curve or other important economic relationships.

3.2 Regression Analysis Regression analysis is a statistical technique used to estimate the mathematical rela- tionship between a dependent variable, such as quantity demanded, and one or more explanatory variables, such as price and income. The dependent variable is the vari- able whose variation is to be explained. The explanatory variables are those factors thought to affect the value of the dependent variable.

We focus on using regression analysis to estimate demand functions. However, regression analysis is a powerful tool that managers can also use to estimate many other important relationships, such as between cost and output or between wages and productivity. The use of regression analysis and related statistical methods in economics and business is called econometrics.

A Demand Function Example To illustrate the use of regression, we estimate a demand function, where the depen- dent variable is the quantity demanded. In general, a demand function may include a number of explanatory variables. However, we initially focus on the case with only one explanatory variable, the price. We assume that other factors possibly affecting the quantity demanded, such as income and prices of related goods, remain constant during the relevant period. A demand function with price as the only explanatory variable defines a demand curve.

We also assume initially that the demand function is linear. That is, the demand curve is a straight line, as in Figure 3.1.

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56 CHAPTER 3 Empirical Methods for Demand Analysis

The Demand Function and the Inverse Demand Function. We can write the relationship between the quantity demanded and the price in two ways. Quantity is a function of price in a demand function, whereas price is a function of quantity in an inverse demand function.

An example of a linear demand function with only one explanatory variable is Equation 3.4: Q = a + bp. We can use algebra to rearrange this linear demand equation so that the price is on the left side and the quantity is on the right side. By subtracting a from both sides to obtain Q - a = bp, dividing both sides of the equa- tion by b to obtain (1>b)Q - a>b = p, and rearranging the terms in the equation, we obtain

p = - a b

+ 1 b

Q = g + hQ, (3.9)

where g = -a>b 7 0 and h = 1>b 6 0, because b is negative. This equation, with p on the left side, is the inverse demand function. If a demand function is a linear function of p, as in Equation 3.4, then the inverse demand function, Equation 3.9, is a linear function of Q with constant coefficients g and h.

The inverse demand function and the demand function contain exactly the same information. Both versions of the demand relationship yield the same straight line when plotted on a diagram, and analysts commonly use both versions. Indeed, many people ignore the distinction between the inverse and direct forms and use the term demand function to describe both.

However, when doing regression analysis it is necessary to be clear about which version of the demand function we are estimating. In regression analysis, we put the dependent variable on the left side of the equation and the explanatory variable on the right side.

For example, suppose that Bill, the manager of the only lawn care firm in town, surveys customers about how many lawn treatments they will buy at various prices. He views the price as the explanatory variable and the quantity as the dependent variable, so he uses the survey to estimate a demand function. If instead his survey asked how much customers were willing to pay for various numbers of lawn treat- ments, he would estimate the inverse demand function.

Random Errors. For illustrative purposes, we have so far treated the estimated coffee demand function, Q = 12 - p, as if it were precisely accurate. This demand function tells us that if price is $2, then the quantity demanded is 10 (million tons), and if price rises to $3, then quantity demanded falls to 9. The real world is not that precise. When we look at actual data, we might see that in a year when price was $2, quantity demanded was slightly less than 10, while in a year when price was $3, quantity demanded was slightly more than 9. In practical terms, an estimated demand function is only an approximation; it does not necessarily match actual data perfectly. The imperfection in our estimate arises because we can never hold constant all the possible non-price factors that affect demand.

For example, if a new study reporting that coffee has previously unknown health benefits appeared during the period covered by our data, it might have caused the quantity demanded to increase for reasons unrelated to price. Conversely, another study suggesting negative health effects might have had the opposite effect. Many other factors, including random changes in consumer tastes, might also play a role. Or the data may contain errors. For instance, one year someone may have failed to record a large coffee shipment, so that it never showed up in the official data. Thus,

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573.2 Regression Analysis

the quantity demanded from year to year may vary in the data for many reasons aside from price changes.

If these other factors that affect demand are observed, such as consumers’ income, we can include these variables as explanatory variables when we estimate our demand function. However, some relevant factors are not observable, and hence we cannot include them. When we estimate a demand function using regression analysis, we capture the effect of these unobserved variables by adding a random error term, e, to the demand equation:

Q = a + bp + e. (3.10)

The random error term captures the effects of unobserved influences on the depen- dent variable that are not included as explanatory variables. The error is called random because these factors that might affect demand are unpredictable or even unknowable from the manager’s point of view.

Regression analysis seeks to estimate the underlying straight line showing the true effect of price on the quantity demanded by estimating a and b in Equation 3.4 while taking account of the random error term. If we could somehow hold e constant at zero, we could obtain various combinations of Q and p and trace out the straight line given by Equation 3.4, Q = a + bp. However, if e does not equal zero, then the observed Q is not on this line. For example, if e takes on a positive value for one year, corresponding to some positive random effect on demand, then the actual Q is larger than the value implied by the linear demand curve Q = a + bp.

Mini-Case We use data from the Portland Fish Exchange of Portland, Maine, to illustrate how to estimate a demand function using regression analysis. At the Exchange, fishing boats unload thousands of pounds of cod and many other types of fish on a daily basis. The fish are weighed and put on display in the Exchange’s 22,000-square-foot refrigerated warehouse. Buyers inspect the quality of the

day’s catch. At noon, an auction takes place in a room overlooking the fish in the warehouse. Fleece-clad buyers representing fish dealers and restaurants sit facing a screen, an auction- eer, and representatives of the sellers. A screen at the front of the room shows bid information. Thousands of pounds of fish sell rapidly.

The quantity of fish delivered each day, Q, varies due to fluctuations in weather and other factors. Because fish spoils rapidly, all the fish must sell immediately. Therefore, the daily auc- tion price for cod adjusts to induce buyers to demand the amount of cod available on that particular day. The price-quantity combination for cod on any particular day represents a point on the cod demand curve.

For each day it operates, the Portland Fish Exchange reports the quantity (in pounds) of each particular type of fish sold and the price for that type of fish. For example, on June 8, 2015, 2,946 lb of large white hake sold for $0.97 per lb. A collection of such observations provides a data set that can be used for demand analysis using regression.

The Portland Fish Exchange

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58 CHAPTER 3 Empirical Methods for Demand Analysis

Regression Analysis Using Microsoft Excel. We illustrate how to estimate a linear regression based on data for cod from the Portland Fish Exchange, using Microsoft Excel. Table 3.1 shows a data set (or sample) based on reports published online by the Portland Fish Exchange. Each data point is a pair of numbers: the price (dollars per pound) and the quantity of cod (thousands of pounds) bought on a particular day. Our analysis uses eight daily observations. We have ordered the data from the smallest quantity to the largest to make the table easy to read.

Figure 3.3 shows the data points in this sample. Estimating this linear regression is equivalent to drawing a straight line through these data points such that the data points are as close as possible to the line. To fit this line through the quantity-price observations for cod, we estimate the linear inverse demand function, Equation 3.9, with an error term attached:

p = g + hQ + e. (3.11)

The error term, e, captures random fluctuations in factors other than quantity that affect the price on a given day, such as random variations in the number of buyers who show up from day to day.7 We expect that the error term averages zero in large samples.8

7The cod supply curve each day is vertical at Q and largely determined by weather and government regulations on fishing. Because the quantity is determined independent of the price, it is said to be exogenous. As a result, we can use quantity to help explain the movement of the dependent variable, price, in our regression equation. Where the supply curve intersects the demand curve determines the equilibrium price for that day. Thus, fluctuations in the quantity—shifts in the vertical sup- ply curve—trace out the demand curve. The dependent variable, price, is endogenous: it is deter- mined inside the system by quantity and by the unobserved variables incorporated into the error term. If quantity and price are simultaneously determined—that is, both are endogenous variables— the demand curve should be estimated using different techniques than those we discuss here. 8We use a small data set in this and later examples to keep the presentation short and clear. In prac- tice, regression analysis would normally involve many more observations. Although some studies use only 30 or 40 observations, most regression studies would normally involve hundreds or even thousands of observations, depending on the availability of data.

Price, dollars per pound Quantity, thousand pounds per day

1.90 1.5

1.35 2.2

1.25 4.4

1.20 5.9

0.95 6.5

0.85 7.0

0.73 8.8

0.25 10.1

TABLE 3.1 Data Used to Estimate the Cod Demand Curve at the Portland Fish Exchange

Here, quantity is the explanatory variable. Whatever quantity comes to mar- ket sells that day. Price adjusts to ensure that the amount of fish available meets the buyers’ demand. As the quantity brought to market “explains” the price, we estimate an inverse demand curve.

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593.2 Regression Analysis

In Equation 3.11, g and h are the true coefficients, which describe the actual rela- tionship between price and quantity along the cod inverse demand function. The regression provides us with estimates of these coefficients, gn and hn, which we can use to predict the expected price, pn, for a given quantity:

pn = gn + hnQ. (3.12)

One way to estimate gn and hn is to use the Microsoft Excel Trendline option for scatterplots.9

1. Enter the quantity data in column A and the price data in column B. 2. Select the data, click on the Insert tab, and select the “Insert Scatter (X, Y) or Bubble

Chart” option in the Chart area of the toolbar. A menu of scatterplot types will appear, as the following screenshot shows.

9The following screenshots and detailed instructions are for the Windows version of Excel 2016. The Macintosh versions and other Windows versions of Excel are similar. Helpful instructions can be found in the Excel Help facility. Or search online for “Help Excel Trendline.”

FIGURE 3.3 Observed Price-Quantity Data Points for the Portland Fish Exchange

Each dot indicates a particular price and the quantity of cod demanded at that price on a particular day at the Portland Fish Exchange.

108642.20

Q, Thousand lb of cod per day

0.25

1.00

p, $

p er

p ou

nd

1.35

1.63

1.90

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60 CHAPTER 3 Empirical Methods for Demand Analysis

3. Click on the first scatterplot type, which is “Scatter.” A chart appears in the spreadsheet.

4. Click on the plus sign that appears just outside the upper right corner to obtain the dropdown menu titled Chart Elements.

5. Place the cursor over the Trendline option in the Chart Elements menu. An arrow appears beside the Trendline option. Click on this arrow. An additional menu drops down. Click on More Options in this menu. A Format Trendline dialog box opens at the right of the screen.

6. In the Format Trendline dialog box select the options “Linear,” “Display Equation on chart,” and “Display R-squared value on chart,” as the following screenshot shows. The estimated regression line appears in the diagram.

By default, Excel refers to the variable on the vertical axis as y (which is our p) and the variable on the horizontal axis as x (which is our Q). Rounding the coef- ficient estimates to two decimal places, we obtain the estimated inverse demand function

pn = 1.96 - 0.15Q, (3.13)

where gn = 1.96 and hn = -0.15 are the estimated coefficients. The estimated inverse function implies a demand curve that hits the price axis

at gn = 1.96, where the price is high enough to drive the quantity demanded to zero. The estimated coefficient hn = -0.15 is the slope of the demand curve. As the quantity increases by one unit (that is, by 1,000 pounds), the estimated change in price needed to induce buyers to purchase this larger quantity is hn = - $0.15 = -15¢.10

Ordinary Least Squares Regression. How does the regression routine in Excel estimate the parameters gn and hn? The objective of the regression procedure is to select a regression line that fits the data well in the sense that the line is as close as possible to all the observed points.

10The price is pn1 = gn + hnQ when quantity is Q and pn2 = gn + hn (Q + 1) when quantity is Q + 1. Thus, the change in price is p2 - p1 = (gn + hn[Q + 1]) - (gn + hnQ) = hn. Similarly, using calculus, dpn >dQ = hn.

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613.2 Regression Analysis

As Figure 3.4 shows, it would be impossible to draw a single straight line that fits the data perfectly by going through all eight points. Figure 3.4 shows that the actual prices and the prices predicted by the regression line differ. The second data point from the left (p = $1.35 and Q = 2.2) has the largest gap between the actual and predicted prices. The predicted price, given by Equation 3.13, for Q = 2.2 is pn = 1.96 - 0.15Q = 1.96 - (0.15 * 2.2) = 1.63.

The gap between the actual value of the dependent variable (price) and the predicted value is called a residual. For this observation, the residual is $1.35 - $1.63 = - $0.28, indicating that the actual price is 28¢ below the estimated price.

The objective of a regression method is to fit the line to the data such that the residuals are collectively small in some sense. However, different criteria might be used to measure the quality of the fit, leading to different regression methods.

The most commonly used regression method is ordinary least squares (OLS). Excel uses this method in its scatterplot Trendline option. The OLS regression method fits the line to minimize the sum of the squared residuals. If en1 is the residual for the first data point, en2 is the residual for the second data point, and so on, then OLS minimizes the sum e n 21 + e n 22 + c + e n 28.11

11If we have a regression equation of the form Y = a + bX + e, the formulas used by spreadsheets and statistical programs to determine the OLS parameters are

bn = a n

i = 1 (Xi - X) (Yi - Y)

a n

i = 1 (Xi - X)2

, and an = Y - bnX,

where the observations are indexed by i, the data set has n observations, a bar above a variable

indicates the average value of that variable, and the symbol a n

i = 1 indicates that the following expres-

sion should be summed from observation 1 through observation n.

FIGURE 3.4 An Estimated Demand Curve for Cod at the Portland Fish Exchange

The dots show the actual quantity-price pair data points. The line is the estimated regression line of the linear relationship between the price and the quantity: pn = gn + hnQ = 1.96 - 0.15Q. The gap between the actual price, p, at a given quantity and the estimated price, pn , is the residual for Day i, en i = pi - pn i. The figure shows the residual for the sec- ond day, where Q = 2.2, the observed price is p2 = $1.35, and the estimated price is pn 2 = $1.63, so the residual is en2 = - $0.28 = $1.35 - $1.63.

108642.20

Q, Thousand lb of cod per day

0.25

1.00

p, $

p er

p ou

nd

1.35

1.63

1.90

Estimated regression line, p = g + hQ e1

e4

e8

e7

e2

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62 CHAPTER 3 Empirical Methods for Demand Analysis

Multivariate Regression We call a regression with two or more explanatory variables a multivariate regres- sion or multiple regression. In our cod example, if the price consumers are willing to pay for a given quantity increases with income, Y, then we would estimate an inverse demand function that incorporates both quantity and income as explana- tory variables as

p = g + hQ + iY + e, (3.14)

where g, h, and i are coefficients to be estimated, and e is a random error. Using OLS, we would estimate the regression line:

pn = gn + hnQ + inY,

where gn, hn, and in are the estimated coefficients and pn is the predicted value of p for any given levels of Q and Y. The objective of an OLS multivariate regression is to fit the data so that the sum of squared residuals is as small as possible, where the residual for any data point is the difference between actual price, p, and predicted price, pn.

A multivariate regression is able to isolate the effects of each explanatory variable, holding the other explanatory variables constant. We estimated a linear demand function for the U.S. avocado market, using the price of avocados and income as explanatory variables:

Qn = 120 - 40p + 0.01Y, (3.15)

where quantity is measured in millions of lb per month, price is measured in dol- lars per lb, and Y is the average monthly household income in dollars. According to this estimated equation, if average income rises by $200 per month and the price of avocados stays constant, then the estimated quantity would rise by 0.01 * 200 = 2 million lb per month. The regression equation allows us to estimate the effect of changing only one variable, like income, while holding other explanatory vari- ables constant. Similarly, if income remains constant and the price increases by $0.05 ( = 5¢) per lb, then the estimated quantity demanded changes by -40 * 0.05 = -2 million lb per month.

Q&A 3.3 The manager of a trucking company that specializes in avocado transport uses the estimated demand function, Equation 3.15, to predict the quantity of avocados demanded at a price of $2.70 and a monthly income level of $6,000. What is the predicted quantity? If the actual quantity turns out to be 76 (million lb) what is the residual? Why would the predicted quantity differ from the actual quantity?

Answer 1. Use the estimated demand function, Equation 3.15, to predict the quantity of avocados

demanded. Substitute the price of $2.70 and the income of $6,000 into the esti- mated demand function to obtain the predicted quantity demanded:

Qn = 120 - 40(2.70) + 0.01(6,000) = 72. 2. Take the difference between the actual and the predicted quantity demanded to

determine the residual. Given that the actual quantity is 76, the residual is 76 - 72 = 4. The actual quantity differs from the predicted quantity because of the random error reflecting other variables not explicitly included in the regression equation.

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633.2 Regression Analysis

Goodness of Fit and the R2 Statistic Because an estimated regression line rarely goes through all the data points, manag- ers want some measure of how well the estimated regression line fits the data. One measure of the goodness of fit of the regression line to the data is the R2 (R-squared) sta- tistic. The R2 statistic is the share of the dependent variable’s variation that is “explained by the regression”—that is, accounted for by the explanatory variables in the esti- mated regression equation. The highest possible value for R2 is 1, which indicates that 100% of the variation in the dependent variable is explained by the regression. Such an outcome occurs if the dependent variable lies on the regression line for every observation.

If some observations do not lie on the regression line, as in Figure 3.4, then the R2 is less than 1. The variation in the dependent variable that is not explained by the regression line is due to the error term in the regression. The lowest possible value for R2 is zero, where the estimated regression explains none of the variation in the dependent variable. The R2 is zero if we try to fit a line through a cloud of points with no slope. Thus, the R2 statistic must lie between 0 and 1.

For example, Mai owns bakeries in two different small towns, where she faces no competition. She wants to know how many fewer pies she will sell if she raises her price, so she runs experiments in each town. At each bakery, she sets a new price each week for 14 consecutive weeks, so that she observes 14 weekly price-quantity com- binations for each town. She then runs a regression to estimate the weekly demand function, Q = a + bp, Equation 3.4, in each town, where we expect that a is positive and b is negative.

Figure 3.5 illustrates these two regressions based on different data sets. In panel a, all the data points are very close to the estimated demand curve. That is, almost all variation in the number of pies demanded is explained by the regression. The R2 sta- tistic is 0.98, which is close to 1, indicating that the regression line provides very good

FIGURE 3.5 Two Estimated Apple Pie Demand Curves with Different R2 Statistics

Mai, a bakery owner, changes the price of apple pie every Friday for 14 weeks to determine the weekly demand curve for apple pie. The observed price-quantity data points lie close to the estimated

demand curve in panel a, where R2 = 0.98. In panel b, where R2 = 0.54, the data points are more widely scattered around the estimated demand curve.

(a) R2 = 0.98

15

10

5

0 10 20 30 40

Q, Thousands of pies per month

p, $

p er

p ie

(b) R2 = 0.54

15

10

5

0 10 20 30 40

Q, Thousands of pies per month

p, $

p er

p ie

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64 CHAPTER 3 Empirical Methods for Demand Analysis

predictions of the amount demanded at any given price. (As the Portland cod regres- sion screenshot illustrates, Excel’s Trendline includes an option to calculate the R2.)

In contrast, the regression line in panel b does not fit the data as well. This panel shows some large divergences between data points and the predicted values on the regression line due to large random errors, and the R2 statistic is only 0.54. Thus, Mai is more confident that she can predict the effect of a price change in the first town than in the second.

3.3 Properties and Statistical Significance of Estimated Coefficients

Mai is particularly concerned about how close the estimated coefficients of the demand function Equation 3.4, an and bn, are to the true values. She cares because she wants to know how reliably she can predict the reduction in the number of pies she sells if she raises her price.

We now discuss the properties of these estimated coefficients and describe sta- tistics that indicate the degree of confidence we can place in these estimated coef- ficients. These statistics can be obtained using most regression software, including the regression tools in Excel.

Repeated Samples The intuition underlying statistical measures of confidence and significance rests on repeated samples. For example, Mai could use another focus group to generate an additional sample of data. She could then run a new regression and compare the regression for the first sample to that from this new focus group. If the results from the second sample were similar to those from the first, she would be more confi- dent in the results. However, if the results of the second sample were very different from those of the first, she might have serious doubts about whether the estimated demand parameters an and bn from either focus group were close to the true values.

A recent survey of North American males found 41% were overweight, 32% were critically obese, and 7% ate the survey. —Banksy

Managers interested in estimating market demand curves often can obtain data from published sources, as in our Portland Fish Exchange example. However, if Mai, the baker, wants to estimate the demand function for her firm, she must collect the relevant data herself. To estimate her firm’s demand curve, she needs information about how many units customers would demand at various prices.

To obtain this information, Mai can hire a specialized marketing firm to recruit and question a focus group, which consists of a number of her actual or potential consumers. The marketing firm asks members of the group how many pies per week they would want to buy at various prices. Alternatively, the marketing firm might conduct an online or written survey of potential customers designed to elicit similar information, which can be used to estimate a demand curve. Mai should use a focus group if it’s the least costly method of learning about the demand curve she faces.

Focus Groups

Managerial Implication

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653.3 Properties and Statistical Significance of Estimated Coefficients

Often it is costly, difficult, or impossible to gather repeated samples to assess the reliability of regression estimates. However, we can do something similar—we can divide a large data set into two subsamples and treat each subsample like a separate experiment. We can use each subsample to calculate regression parameter estimates. For that matter, we can take many random subsamples of the data set and generate estimates for each one. We can then assess whether the different parameter estimates for the different subsamples tend to be similar or widely dispersed.

Although analysts sometimes run regressions on random subsets of the data and use them to construct a set of parameter estimates, it may be unnecessary. Given cer- tain (usually reasonable) assumptions, we can use statistical formulas to determine how much we would expect the parameter estimates to vary across samples. The nature of this potential variation allows us to assess how much confidence to place in particular regression results.

Desirable Properties for Estimated Coefficients We would like our regression estimation method to have two properties. First, we would like the estimation technique to be unbiased in the sense that the estimated coefficients are not systematically lower or systematically higher than the true coef- ficients. An estimation method is unbiased if it produces an estimated coefficient, bn, that equals the true coefficient, b, on average. The ordinary least squares regression method is unbiased under mild conditions.12

The second property we would like an estimation technique to have is that the estimates should not vary greatly if we repeat the analysis many times using other samples. If we have two proposed unbiased estimation methods, we prefer the method that yields estimates that are consistently closer to the true values rather than a method that produces widely dispersed estimates in repeated samples. An important theoretical result in statistics is that under a wide range of conditions, the ordinary least squares estimation method produces estimates that vary less than other relevant unbiased estimation methods.

For each estimated coefficient, the regression program calculates a standard error. The standard error is a measure of how much each estimated coefficient would vary if we re-estimated the same underlying true demand relation with many different random samples of observations. The smaller the standard error of an estimated coefficient, the smaller the expected variation in the estimates obtained from differ- ent samples. A small standard error means that the various estimated coefficients would be tightly bunched around the true coefficient. If the standard error is large, the estimated coefficients are imprecise indicators of the true values.

A Focus Group Example Consumers are statistics. Customers are people. —Stanley Marcus (early president of Neiman Marcus)

To illustrate these ideas, suppose that Toyota has asked us to conduct a focus group to predict how the number of Toyota Camry vehicles demanded would change if the

12One important condition for OLS estimation to be unbiased is that the equation be properly speci- fied so that all relevant explanatory variables are included and the functional form is appropriate.

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66 CHAPTER 3 Empirical Methods for Demand Analysis

price changes. We arrange a focus group of 50 prospective car buyers to illustrate how Toyota could answer this question. We ask members of the group if they would be willing to buy a Camry at various prices. As a result, for each of eight prices rang- ing from $5,000 to $40,000, we have information on how many Camry vehicles this group would demand.

We estimate a linear demand function of the form Q = a + bp + e and obtain standard errors to assess the reliability of the estimated parameters. The Excel Trend- line does not provide standard errors. However, Excel’s Regression tool provides them.13 We demonstrate how to use this tool in an Excel Screenshot and correspond- ing step-by-step instructions.

13The Regression tool uses ordinary least squares to estimate the regression line and can accom- modate multiple explanatory variables. This tool is available in all Windows versions of Excel and in Excel for the Mac as of the 2016 version. See Excel Help for information.

1. Enter the data in an Excel spreadsheet, as shown in the screenshot. Title the col- umns Quantity and Price and put the quantities in cells A2 through A9 and the prices (in thousands of dollars) in cells B2 through B9.

2. Click on the Data tab, then on the Data Analysis icon at the upper right of the spreadsheet.14 The Data Analysis dialog box displays as shown. Select the Regres- sion tool and click OK.

3. In the Regression dialog that displays, fill in the Input Y Range field (the dependent variable) by selecting cells A2 through A9 or by typing A2:A9 into the box.

4. Fill in the Input X Range field (the explanatory variable) by selecting the cells containing the prices or by typing B2:B9.

5. Click the Output Range button, enter A12 in the associated box, and then click OK.

Excel displays the regression results. The coefficients indicate that the estimated regression line is Q = 53.857 - 1.438p. We can use this estimated demand function to predict the quantity demanded at any given price. According to our estimated demand function, if the price is 27( $27,000), we expect the focus group consum- ers to buy Qn = 53.857 - 1.438p = 15.03 Camrys. We would round this estimate to 15 cars, given that cars are sold in discrete units. However, if this focus group

14If you do not see the Data Analysis icon, the Analysis Toolpak is not installed in your version of Excel. See Excel Help for installation instructions. (Select the File tab, then click on the question mark in the upper right corner to reach Help.)

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673.3 Properties and Statistical Significance of Estimated Coefficients

represented a large group, perhaps a thousand times larger (50,000 consumers), our estimate of quantity demanded would be 15,030 vehicles.

The Regression tool also displays other regression output. The R2 statistic (called R Square by Excel) is 0.977, which is close to the maximum possible value. This high R2 indicates that the regression line explains almost all the variation in the observed quantity. Excel also displays standard errors and confidence intervals.

Confidence Intervals We know that an estimated coefficient is not likely to equal the true value exactly. Therefore, it is useful to construct a confidence interval, which provides a range of likely values for the true value of a coefficient, centered on the estimated coefficient. For example, a 95% confidence interval is a range of coefficient values constructed using a method such that the true value of the coefficient would lie in the specified interval 95% of the time in repeated samples.

The length of a confidence interval depends on the estimated standard error of the coefficient and the number of degrees of freedom, which is the sample size (number of observations) minus the number of coefficients estimated. In our Camry example, we have eight observations and estimate two coefficients, so we have six degrees of freedom.

In regressions with a large sample size, the lower end of a 95% confidence interval is (approximately) the estimated coefficient minus twice its estimated standard error, and the upper end of the interval is the estimated coefficient plus twice its estimated standard error.

With smaller sample sizes, the confidence interval is larger.15 With the six degrees of freedom of the Camry demand function regression, the confidence inter- val is the estimated coefficient plus or minus 2.447 times the standard error. In this regression, the slope coefficient, bn, on the price is -1.438 and its standard error is 0.090. Therefore, the 95% confidence interval for bn is centered on -1.438 and goes approximately from -1.658( = -1.438 - [2.447 * 0.090]) to -1.218( = -1.438 + [2.447 * 0.090]).

If the confidence interval is small, then we are reasonably sure that the true parameter lies close to the estimated coefficient. If the confidence interval is large, then we believe that parameter is not very precisely estimated. Typically, the more observations we have, the smaller the estimated standard errors and the tighter the confidence interval. Thus, having a larger data set tends to increase our confidence in our results.

Hypothesis Testing and Statistical Significance There are two possible outcomes: if the result confirms the hypothesis, then you’ve made a measurement. If the result is contrary to the hypothesis, then you’ve made a discovery. —Enrico Fermi

A manager can use estimated coefficients and standard errors to test important hypotheses. Very often, the crucial issue for a manager is to determine whether a cer- tain variable really influences another. For example, suppose a firm’s manager runs a regression where the demand for the firm’s product is a function of the product’s

15The relevant number can be found in a t-statistic distribution table.

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68 CHAPTER 3 Empirical Methods for Demand Analysis

price and the prices charged by several possible rivals. If the true coefficient on a rival’s price is zero, then the potential rival’s product is not in the same market as the manager’s product, and the manager can ignore that firm when making deci- sions. Thus, the manager wants to formally test the null hypothesis that the rival’s coefficient is equal to zero.

One approach is to determine whether the 95% confidence interval for that coefficient includes zero. If the entire confidence interval for the coefficient on a rival’s price contains only positive values, the manager can be confident that the explanatory variable has a positive effect: the higher the rival’s prices, the greater the demand for the manager’s product.

Equivalently, the manager can test the null hypothesis that the coefficient is zero using a t-statistic. Such a test is called a t-test. The Excel Regression tool reports t-statistics automatically. The t-statistic equals the estimated coefficient divided by its estimated standard error. That is, the t-statistic measures whether the estimated coefficient is large relative to the standard error. In the Camry example, the t-statistic for the constant or intercept coefficient is 53.857>2.260 ≈ 23.8, and the t-statistic on the price coefficient is -1.438>0.0895 ≈ -16.1.

If the absolute value of the t-statistic is larger than a critical value, then we know that the confidence interval does not include zero, so our t-test tells us to reject the null hypothesis that the coefficient is zero. For large samples, this critical value is about 2, while in our Camry example it is 2.447.

That is, our rule is that we reject the null hypothesis at a 95% level of confidence if the absolute value of the t-statistic exceeds the critical value. An equivalent state- ment is that, given a t-statistic with a magnitude exceeding the critical value, we will be wrong less than 5% of the time if we reject the hypothesis that the explanatory variable has no effect. The chance that we are wrong when we use a test statistic to reject the null hypothesis is often referred to as the significance level of the hypoth- esis test. Thus, in a large sample, if the (absolute value of the) t-statistic is greater than about 2, we reject the null hypothesis that the proposed explanatory variable has no effect at the 5% significance level or 95% confidence level. Rather than use this somewhat convoluted formal statement, many analysts say simply that the explanatory variable is “statistically significant” or “statistically significantly dif- ferent from zero.”

3.4 Regression Specification Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise. —John Tukey

The first step in a regression analysis is to select a regression equation. We must determine the regression specification, which includes the choice of the dependent variable, the explanatory variables, and the functional relationship between them (such as linear, quadratic, or exponential). For example, in the Camry demand function regression, the dependent variable is the quantity of Camrys demanded; the only explanatory variable is price, measured in thou- sands of dollars; and the functional relationship between the variables is linear: Q = a + bp + e.

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693.4 Regression Specification

A regression analysis is valid only if the regression equation is correctly specified. In particular, the specification should include the appropriate explanatory variables, it must closely approximate the true functional form, and the underlying assump- tions about its error term should be correct.

Selecting Explanatory Variables When selecting variables to include in a regression, we must take care in choosing which explanatory variables to include. We should use all the observable variables that are likely to have a meaningful effect on the dependent variable. We use our understanding of causal relationships, including those that derive from economic theory, to select explanatory variables. In the Camry focus group example, we used our knowledge of demand theory to conclude that the price was likely to affect the quantity demanded.

Mini-Case It is unfortunate we can’t buy many business executives for what they are worth and sell them for what they think they are worth. —Malcolm Forbes

Human resources managers often use regression studies to determine if their employees are paid comparably to individuals in similar positions in other firms.16 The very high compensation that chief executive officers (CEOs) of many major corporations receive is a source of much controversy, and many large corporations are under pressure to provide evidence to justify their payments. We use multivariate regression to analyze the determinants of CEO compensa- tion. We use economic theory and previous studies to choose the variables that we believe are important determinants of CEO compensation. Then, we test whether these variables belong in the equation.

In our regression analysis, we use data on CEO compensation from Standard & Poor’s Execucomp database for the 1992–2017 period for corporations in the S&P 500, which is Standard & Poor’s list of 500 large corporations whose shares are traded on the two major U.S. stock exchanges, the New York Stock Exchange (NYSE) and the NASDAQ. We have more than 9,300 observations in our data set, where the dependent variable in each observation is the CEO’s annual compensation in a particular S&P 500 corporation in a particular year, along with the values of the proposed explanatory variables. Well over half of this compensation was in the form of stock options, which give the holder the right to buy stock in the company, typically at an attractive price far below the market value. The rest consisted primarily of salary and bonuses.

In our multivariate regression, the dependent variable, Y, is CEO compensa- tion in thousands of dollars. We expect the compensation to be greater for CEOs who manage large firms because that requires more work and responsibility. We use two measures of firm size: assets, A (in $ billions), which are related to the firm’s capital input, and employees, L (thousands of workers). Presum- ably, a CEO receives more pay when the company does well. One measure of

16Another use is in union negotiations. A large firm retained one of us to perform a regression analy- sis to determine how its unionized employees’ wages compared to wages of comparable unionized and nonunionized workers in other firms. The firm used this study to bargain with its union.

Determinants of CEO Compensation

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a company’s success is shareholders’ average return over the previous three years, S (in percentage points per year). This return includes dividends, which are direct payments to shareholders, and capital gains, which are increases in the value of the shares of the shareholders. A CEO may also be worth more to a firm as the CEO’s experience, X (the number of years that the CEO has held this job), rises.

We use ordinary least squares to estimate a multivariate regression equation that relates a CEO’s salary to these explanatory variables:

Y = a + bA + cL + dS + f X + e,

where a is a constant and the other coefficients show how much a one-unit increase in the corresponding explanatory variable affects CEO compensation. For example, one extra unit of employees (1,000 employees) raises the CEO salary by c. The estimated compensation as a function of the explanatory vari- ables is Yn = 7,063.7 + 10.2A + 12.6L + 35.7S + 73.9X, as the following table of regression results shows.

CEO Compensation Regression Results Explanatory Variable Coefficient Standard Error t-Statistic

Constant 7,063.7 217.0 32.6*

Assets ($billions), A 10.2 0.9 11.3*

Employees (000s), L 12.6 1.3 9.5*

Shareholder return, S 35.7 5.9 6.1*

Experience (years), X 73.9 19.9 3.7*

*indicates that we can reject the null hypothesis that the coefficient is zero at the 5% signifi- cance level.

Based on these t-statistics, we reject the null hypothesis that the coefficients on our four variables are zero at the 5% significance level. Each of these four t-statistics is larger than 2. For example, the t-statistic on the total assets coef- ficient is 11.3, which is substantially larger than 2. Thus, we conclude that these variables belong in our specification.

The estimated effect of increasing total assets by $1 billion is to raise the CEO’s compensation by $10,200 ($10.2 thousand). If the average annual share- holder return over three years increases by one percentage point (say, rising from 6% to 7% per year), we estimate that a CEO’s annual compensation is higher by $35.7 thousand.

Although these variables are statistically significantly different than zero, not all of them are economically significant. That is, they do not have a large impact on CEO compensation. For example, the effect of the company’s financial per- formance—shareholders’ average return—on CEO salary is relatively small. Most S&P 500 companies have equity values of several billion dollars or more. An increase in shareholder return of one percentage point would apply to the overall equity value and would therefore imply additional returns to sharehold- ers of tens of millions of dollars. However, the difference in CEO salary would be about $36,000 per year. Although $36,000 is a significant amount to most of us, CEOs of S&P 500 companies have annual compensation well into the mil- lions of dollars. Thus, although the shareholder return variable is statistically significant, it has only a modest effect on a CEO’s compensation.

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713.4 Regression Specification

Correlation and Causation. When selecting explanatory variables, it is important to distinguish between correlation and causation. We say that two vari- ables, X and Y, are correlated if they move together. The quantity demanded and price are negatively correlated: when price goes up, quantity goes down. This correlation is causal, as changes in price directly affect the quantity demanded.

However, correlation does not necessarily imply causation. For example, monthly sales of gasoline and the monthly incidence of sunburn have a strong positive correlation in U.S. data. Both are rela- tively high in the summer months of July and August and low in winter months.

Does this correlation mean that a sunburn somehow increases a consumer’s demand for gasoline? Should we use the incidence of sunburn as an explanatory variable for gasoline demand? The answer to both these questions is no. A third variable—sunshine—is the main cause of the correlation between gasoline sales and sun- burn. During sunny summer months people drive more, in part because they take more vacations that involve driving. They also spend more time in the sun and are therefore more likely to get sun- burned. If our gasoline demand regression equation included the incidence of sunburn as an explanatory variable, we would find a high R2 statistic and a s tatistically significant positive coefficient on sunburn. However, these results would be spurious. Any interpreta- tion that getting sunburned increases the demand for gasoline would be incorrect.

Thus, it is critical that we do not include explanatory variables that have only a spurious relationship to the dependent variable in a regression equation. In estimating gasoline demand we would include price and income as explanatory variables, and we might include sunshine hours or temperature, but we would not include sunburn incidence as an explanatory variable.

Correlation does not imply causation. Correlations often result when two variables are both caused by a third variable, as when sunshine makes people more likely to get sunburn and more likely to go for long drives.

Q&A 3.4 In the preceding Mini-Case, what is the estimated effect of more employees on CEO compensation? Is this effect statistically significant?

Answer 1. Use the regression coefficient in the estimated CEO compensation function to identify

the estimated effect of more employees. The regression table in the CEO compensa- tion Mini-Case shows that if a firm’s workforce increases by 1,000 employees, the CEO’s compensation is estimated to rise by about $12,600 per year.

2. Use the t-statistic in the regression table to assess statistical significance. The t- statistic for the employees coefficient is 9.47. The asterisk in the table indicates that this coefficient is significantly different from zero at the 5% significance level, which is the normal standard applied to infer that a coefficient is statisti- cally significant. Thus, we can say that the number of employees is estimated to have a statistically significant effect on CEO compensation.

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72 CHAPTER 3 Empirical Methods for Demand Analysis

If two variables have a causal relationship, we should treat the causal variable as the explanatory variable. Suppose that a store selling umbrellas collects weekly data on rainfall and on umbrella sales. It would be incorrect to run a regression with umbrella sales as the explanatory variable and rainfall as the dependent variable. Although such a regression would likely yield a statistically significant coefficient on umbrella sales, it makes no sense to think of umbrella sales as affecting rainfall.17 Because rainfall increases the demand for umbrellas, rainfall should be the explanatory variable and the demand for umbrellas should be the dependent variable.

Omitted Variables. Often, a manager has an otherwise appropriately specified regression but lacks information about one or more potential explanatory variables. Because these variables are not included in the regression specification, they are called omitted variables. If a key explanatory variable is missing, then the resulting coefficient estimates and hypothesis tests may be unreliable.

Suppose Jacob and Santiago are managers in the same firm. Jacob wants to esti- mate the effect of price on quantity demanded and therefore experiments with the price over some time interval, starting with a low price and trying successively higher prices as time proceeds. However, Santiago is interested in the effect of adver- tising on demand and—without telling Jacob—varies the advertising level over the same time interval, starting with a low advertising level and moving to a high level as time passes. As the higher prices offset the increased advertising activity, the quantity demanded stays fairly stable.

Because Jacob does not know about the advertising experiment, after he regresses quantity on price, he is amazed to discover that price increases have no effect on demand. Clearly, a regression of quantity demanded on price alone would be highly misleading in this situation, steering Jacob to an incorrect conclusion about the firm’s demand function. If only the price increase occurred, the quantity demanded would have fallen. In this example, it is important to include both price and advertising as explanatory variables.

Functional Form If at first it doesn’t fit, fit, fit again. —John McPhee

So far, we have assumed that our regression equations were linear. However, we cannot assume that demand functions or other economic relationships are always linear.

Choosing the correct functional form may be difficult. One useful step, especially with a regression involving only one explanatory variable, is to plot the data and the estimated regression line for each functional form under consideration. We illustrate this approach with an advertising example. A large food manufacturing firm sells its products in many cities throughout the country. To determine the importance of

17Of course, many people believe that the failure to carry an umbrella causes rain.

Common Confusion If two variables move together, one of the variables must have a causal effect on the other.

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733.4 Regression Specification

advertising, it holds its price constant across cities but varies the number of com- mercials per week on local television in each city.18

Figure 3.6 shows the relationship between the quantity demanded and advertis- ing, holding price and other relevant explanatory variables constant. Both panels contain the same data points. The vertical axis shows the quantity demanded per family per week, and the horizontal axis is the number of commercials per week on local television.

The two panels have different estimated regression lines based on different func- tional form specifications. Panel a shows an estimated linear regression, which is based on the assumption that the relationship between the quantity demanded and advertising is linear: Q = a + bA + e, where Q is quantity demanded, A is a mea- sure of the amount of advertising, e is a random error term, and a and b are the parameters to be estimated.

Panel b shows an estimate based on a quadratic regression specification:

Q = a + bA + cA2 + e.

The only difference between this specification and the linear specification is that we have added an extra term, the coefficient c times the advertising index squared: cA2. If c ≠ 0, the plot of the relationship between Q and A is curved. If c = 0, this extra quadratic term drops out and the equation reverts to a linear form. Therefore, the test of whether c is statistically significantly different from zero can be used as a test of whether the quadratic form is better than the linear form.

Table 3.2 shows OLS estimates of both the linear and quadratic specifications. The estimation of the linear specification does not look bad when considered by itself. The coefficient on advertising is statistically significantly different from zero, and the R2 is 0.85, which implies that the line “explains” most of the variation in quan- tity. However, the data points in panel a of Figure 3.6 are not randomly distributed

18For example, Campbell Soup Company has conducted these types of experiments (Eastlack and Rao, 1989).

FIGURE 3.6 The Effect of Advertising on Demand

The linear regression line in panel a does not fit the data points as well as does the quadratic curve in panel b.

(a) Linear regression line

15

10

5

0 2 4 6 8 10 12 14 16 18

A, Commercials per week

Q , P

er w

ee k

(b) Quadratic regression

15

10

5

0 2 4 6 8 10 12 14 16 18

A, Commercials per week

Q , P

er w

ee k

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74 CHAPTER 3 Empirical Methods for Demand Analysis

around the regression line. Instead, they are first below the line, then above the line, and then below the line again. This pattern of residuals signals that the linear model is not the proper specification.

The estimated quadratic specification fits the data much better than the linear model: R2 = 0.99. All the coefficients are statistically significantly different from zero. In particular, cn, the estimated coefficient on A2, is statistically significant, so we reject the linear specification.

The data points appear randomly distributed around the quadratic regression curve in panel b of Figure 3.6, as they should for an appropriate specification. Because the quadratic functional form allows for a curved relationship between quantity and advertising, it captures two important phenomena that the linear specification misses. First, at high levels of advertising intensity, it becomes increasingly difficult to generate more demand, as virtually all potential consumers have purchased the product. The market becomes saturated: No more consumers can be convinced to buy the product. This saturation effect is captured by the declining slope of the regression line in panel b. The linear specification misses this effect.

Second, the linear form overstates the amount of demand that would occur at very low levels of advertising. If advertising activity is very low, small increases have a large payoff—an effect that is captured by the quadratic functional form but not by the linear functional form. A manager using the linear form to assess what would happen at either very high levels or very low levels of advertising would make a serious mistake. And even at intermediate levels of advertising, the linear regres- sion model would consistently understate demand, albeit by only a modest amount.

Although we have focused on linear and quadratic functional forms, many other functional forms are available. Selecting among possible functional forms is an impor- tant part of regression analysis. In this example, we were able to formally test whether to use a quadratic functional form or a linear functional form in the regression specifica- tion. However, it is not always possible to compare functional forms in this way, and it may be necessary to use advanced statistical techniques that are covered in statistics or econometrics courses to assist in making decisions about functional form specification.

Linear Specification Quadratic Specification

Coefficient Standard Error t-Statistic Coefficient Standard Error t-Statistic

Constant 5.43 0.54 10.05* 3.95 0.30 13.18*

Adverting, A 0.53 0.06 8.47* 1.20 0.10 12.18*

Advertising, A2

-0.04 0.01 -7.05*

*indicates that we can reject the null hypothesis that the coefficient is zero at the 5% significance level.

TABLE 3.2 Regressions of Quantity on Advertising

If you need a statistician to interpret your results, you haven’t designed your experiment properly.

Given the challenges in obtaining data and producing a regression that is prop- erly specified, many firms use controlled experiments. For example, a firm can vary its price and observe how consumers react. Unfortunately, firms cannot con- trol all important elements of an experiment as is done in a chemistry or physics

Experiments

Managerial Implication

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753.5 Forecasting

3.5 Forecasting We often refer to predictions about the future as forecasts. Managers frequently seek forecasts of important variables related to demand, such as sales or revenues. Large banks and other financial institutions commonly make forecasts regarding macro- economic variables such as interest rates, gross domestic product, unemployment, and inflation. Governments make forecasts of revenues, expenditures, and budget balances, among other things, and we are all familiar with weather forecasts.

Managers use many different methods to forecast. We concentrate on two com- monly used regression-based methods of forecasting: extrapolation and theory- based econometric forecasting.20

Extrapolation Extrapolation seeks to forecast a variable of interest, like revenue or sales, as a func- tion of time. Extrapolation starts with a series of observations collected over time, referred to as a time series. For example, a firm might have monthly sales data for

20An alternative approach is to rely on subjective judgments. One judgment-based approach is the Delphi technique. A group of experts make initial forecasts, which are then made known to the group, who discuss the reasoning behind them. The experts then make new forecasts, and the pro- cess repeats until broad consensus is reached or until the differences in opinion have converged as much as reasonably possible. The resulting forecasts reflect the collective judgment of the group.

lab. As a result, firms often use regressions to hold constant some variables that they could not control explicitly and to analyze their results.

Harrah’s Entertainment relies on randomized tests of various hypotheses to design its marketing. It might send an attractive hotel offer for a Tuesday night to a randomly selected group of customers and compare the responses of that test group to those of other customers who received the usual offer and who serve as a control group.

In 1994, the credit card company Capital One was founded with the plan to apply experimental methods to all aspects of its business. For example, if the company wanted to know whether a credit card solicitation would be more suc- cessful if mailed in a blue envelope or in a white one, it ran an experiment. By 2017, Capital One was running tens of thousands of experiments per year.

Other companies such as Amazon, Facebook, Google, and Netflix also use experiments. These companies run many experiments on the internet, which allows them to conduct very low-cost experiments involving tens of thousands of customers.

Google shows on its website how a firm can run randomized experiments on the effectiveness of advertising while controlling for geographic or other differ- ences. In an associated article, Google illustrates one such experiment and the linear regression models to analyze it and conduct hypothesis tests.19 These examples show that managers can benefit from running experiments, particu- larly if they can make use of low-cost internet experiments.

19See http://services.google.com/fh/files/blogs/geo_experiments_final_version.pdf.

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76 CHAPTER 3 Empirical Methods for Demand Analysis

a new product for several years and be interested in projecting future sales based on these historical data. In extrapolation, the time series is smoothed in some way to reveal the underlying pattern, and this pattern is then extended or extrapolated into the future to forecast future sales. This type of forecasting is called pure time-series analysis because it seeks to forecast future values of some variable, like sales, purely on the basis of past values of that variable and the passage of time.

Trends. Most of us automatically use our eyes to fit a trend line when we look at a plot of data points over time. Instead, a manager can use a regression technique to plot such a trend line more reliably.

Figure 3.7 shows quarterly revenue (= price times quantity) for Nike, a leading producer of athletic footwear and clothing.21 Nike’s quarters are December–February, March–May, June–August, and September–November, corresponding to winter, spring, summer, and fall in the Northern Hemisphere, where the vast majority of Nike sales occur. The first quarter in the figure is December 2008–February 2009 (the “winter of 2009”). The figure labels the winter, spring, summer, and fall quarters q1, q2, q3, and q4, respectively.

Nike could estimate its worldwide revenue (in billions of dollars) as a linear function of time, t, which equals 1 in the first quarter (winter 2009), 2 in the spring of 2009, and so on, up to 37 for the winter quarter of 2018, which is the final period in our sample. The linear regression equation is Revenue = a + bt + e, where e is the error term and a and b are the coeffi- cients to be estimated. The estimated trend line is Revenue = 4.189 + 0.134t, and the coefficient on the time trend is statistically significant at the 0.05 level. This line is plotted in Figure 3.7. Based on this regression, Nike

21The data are from Nike annual reports provided by Compustat. These data refer to worldwide revenues, about half of which come from North America.

FIGURE 3.7 Nike’s Quarterly Revenue: 2009–2018

Each point shows Nike’s worldwide revenue in bil- lions of dollars for a particular quarter. A regression is used to fit a trend line through these points. The

dashed portion of the line indicates a forecast. The red point at the end of the trend line shows the forecast revenue for the third quarter of 2020.

20 09

q 1 q2 q3 q4

20 10

q 1 q2 q3 q4

20 11

q 1 q2 q3 q4

20 12

q 1 q2 q3 q4

20 13

q 1 q2 q3 q4

20 14

q 1 q2 q3 q4

20 15

q 1 q2 q3 q4

20 16

q 1 q2 q3 q4

20 17

q 1 q2 q3 q4

20 18

q 1 q2 q3 q4

20 19

q 1 q2 q3 q4

20 20

q 1 q2 q3 q4

4

5

6

7

8

11

9

10

R ev

en ue

, $ b

ill io

ns

Quarter

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773.5 Forecasting

could forecast its sales in the summer quarter of 2020, which is quarter 47, as 4.189 + (0.134 * 47) = $10.5 billion, which is the red point at the right end of the trend line. Of course, the further into the future we forecast, the less reliable is the forecast.

Seasonal Variation. If we look at the trend line through the data in Figure 3.7, we notice a distinct pattern of the observations around the trend line. If this varia- tion were purely random, we could not do much about it except to note that our forecasts have potential random errors associated with them. However, because this pattern looks systematic, we may be able to adjust for it. Revenue in virtually every spring and summer quarter is above the trend line, while revenue in almost every fall and winter quarter is below the trend line. Thus, it appears that the demand for Nike products varies seasonally. This pattern is not surprising, as we expect higher athletic footwear and clothing sales in the spring and summer than in the fall or winter.

In making forecasts, we should adjust for these seasonal effects. We can add vari- ables to our regression that capture the seasonal effects. These variables, often called seasonal dummy variables, equal one in the relevant season and zero otherwise. For example, the winter dummy variable equals one in the winter quarter of the year and zero in all other quarters. We include these indicator variables only for winter, spring, and summer quarters. The fall quarter is then interpreted as the base case, and the coefficient on each of the other quarters shows us the difference between that quarter and the base case.

We estimate Revenue = a + bt + c1W + c2S + c3M + e, where W, S, and M are quarterly dummy variables for winter, spring, and summer, respectively, and a, b, c1, c2, and c3 are the coefficients we want to estimate. The new estimated equation is Revenue = 3.847 + 0.135t + 0.179W + 0.452S + 0.675M, and all the coefficients are statistically significant.

Our failure to include the seasonal dummy variables in our original regres- sion may have led to a biased estimate. Based on this new regression model, the forecast value for the summer quarter of 2020 is 3.820 + (0.135 * 47) + (0.179 * 0) + (0.452 * 0) + (0.675 * 1) = $10.84 billion. This adjusted forecast is $340 million (about 3.2%) more than our previous forecast that ignored seasonal effects. Properly incorporating seasonal effects allows us to adjust for the fact that revenues tend to be relatively high in the summer quarter.

Nonlinear Trends. Although Nike’s revenue follows a linear trend, not all time trends are linear. In particular, the revenue growth of new products is often non- linear. After a new product first reaches the market, its market share often grows slowly, as consumers need some time to become familiar with the product. At some point, a successful product takes off and sales grow very rapidly. Then, when the product eventually approaches market saturation, sales grow slowly in line with underlying population or real income growth. Ultimately, if other products displace this product, its sales will fall sharply. For example, the revenue of early genera- tion mobile phones experienced exponential growth until smartphones began to dominate the market.

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78 CHAPTER 3 Empirical Methods for Demand Analysis

Theory-Based Econometric Forecasting The consumers’ demand function determines revenue. We know that variables such as income, population, and advertising affect the quantity demanded. Yet our fore- cast based on extrapolation (pure time-series analysis) ignored these variables. The role of such variables may be implicit in an extrapolation. For example, one rea- son why revenue may have grown smoothly over some period is that population increased smoothly over that period.

As a first approximation, extrapolation often proves useful, especially if we have properly addressed seasonal effects. However, the problem with such forecasts is that they are not based on an understanding of how other variables cause or determine the variable of interest. As a result, it is difficult for the forecaster to understand the underlying causal relationship that determines revenue and to anticipate the effects of changes in causal variables such as income or population. If we are interested in underlying economic structure, we need to use a different approach.

An alternative forecasting approach uses economic theory, such as a demand framework, to derive the causal relationships between economic variables. For exam- ple, in forecasting Nike’s sales or revenue, we could estimate the effect of changes in income on demand for Nike’s products and then take the expected pattern of income growth into account in forecasting sales.

Forecasting using a regression specification that incorporates underlying causal explanatory variables is called causal econometric forecasting or theory-based econo- metric forecasting. Such forecasting methods incorporate both extrapolation and estimation of causal or explanatory economic relationships. Thus, to forecast sales, we might use both previous values of sales and time as explanatory variables, and we would also use causal variables such as income. That is, with theory-based (causal) econometric forecasting, we predict the dependent variable based on the underlying causal factors—not just on the time-series pattern of the dependent variable.

We use these estimates to make conditional forecasts, where we base our forecast on specified values for the explanatory variables. For example, a manager might make one conditional forecast of sales based on the assumption that income will be 5% higher next year than this year and another conditional forecast based on the assumption that income next year will be the same as this year.

In our extrapolation analysis, we assumed that Nike’s revenue would grow steadily over time. However, it is possible that underlying causal or structural factors affect its revenue. We would expect Nike’s revenue to deviate from the trend line if a rival entered the business, if Nike added a new major product to its product line or acquired another large company, if the cost of transportation changed dramatically, or if a major recession occurred. Nike could regress its revenue on these economic factors. It could then use that regression to make forecasts that are conditional on how it expects these other factors to evolve over time.

Forecasting using theory-based econometric modeling is more difficult than using extrapolation. However, it often provides a better chance of identifying sudden devi- ations from a simple trend line, and it may contribute more to a firm’s understanding of the underlying business interactions.

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793.5 Forecasting

Estimating the Effect of an iTunes Price Change

Managerial Solut ion

How could Apple use a focus group to estimate the demand function for iTunes to determine if raising its price would raise or lower its revenue? To answer this question, we asked a focus group of 20 Canadian college students how many popular tracks they would download from iTunes at various prices, assum- ing that their incomes and the prices of other goods remained constant. The responses were

Price, $ per song Quantity, Songs per year

1.49 441

1.29 493

1.19 502

1.09 536

0.99 615

0.89 643

0.79 740

0.69 757

0.49 810

The iTunes managers would first estimate a linear demand function of song downloads on price, obtaining demand coefficient estimates, the R2 statistic, and standard errors, and then calculate the t-statistics (dividing each coefficient by its standard error).

Based on these results, the estimated linear demand function is Qn = 1,024 - 413p, where Qn is our estimate of the number of downloads per year, and price p is the price in dollars per song. The price coefficient is -413, which means that a $1 increase in price would reduce estimated quantity demanded by 413 downloads. Converting this result to cents, a 1¢ increase in price would reduce estimated quantity demanded by 4.13 downloads per year. The t-statistic is -12.6, so this coefficient is significantly different from zero. The R2 statistic is 0.96, indicating that the regression line fits the data closely.

Apple’s manager could use such an estimated demand function to determine how revenue, R, which is price times quantity (R = p * Q), varies with price. Panel a of Figure 3.8 shows the estimated iTunes demand curve. At p = 99¢, 615 songs were downloaded by the focus group according to this estimated demand curve. The corresponding revenue is the rectangle consisting of areas A + B. The height of this rectangle is the price, p = 99¢. The length of the rectangle is the quantity of songs downloaded, Q = 615, so the area of the rectangle equals R = p * Q = $0.99 * 615 ≈ $609.

If the price were increased to $1.24, the quantity demanded would drop to 512. The corresponding revenue would be the rectangle = A + C, where the height is $1.24 and the length is 512. According to the focus group’s responses, Apple would lose revenue equal to area B but gain the revenue equal to area C. Area B shows how much Apple loses from selling 103 ( = 615 - 512) fewer units at the original price. Area C is the extra amount it makes on the 512 units it sells, because it sells each song for $0.25 ( = $1.24 - $0.99) more than it did originally.

An increase in price has two offsetting effects on revenue. Revenue tends to fall because the price increase causes fewer units to be sold. However, revenue

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80 CHAPTER 3 Empirical Methods for Demand Analysis

tends to rise because a higher price is collected on every unit that is sold. Because these two effects have opposite effects on revenue, management would not know in general whether a particular price increase would raise or lower revenue.

FIGURE 3.8 iTunes Focus Group Demand and Revenue Curves

Based on a focus group’s responses, we estimate the iTunes demand curve and calculate a revenue ( = price * quantity) curve. (a) Accord- ing to the estimated demand curve, if the price were 99¢, the focus group would download 615 songs per year and revenue would be areas A + B = $507 + $102 = $609 = p * Q = $0.99 * 615. At a price of $1.24, the songs demanded would fall to 512, and the revenue would be areas A + C = $507 + $128 = $635 = p * Q = $1.24 * 512. (b) According to the corresponding revenue curve, revenue is greatest for this focus group at p = $1.24, where R = $635.

Q, Songs per year

Q, Songs per year

1,024

1,024

512

0.99

Demand

Revenue

615

635

512 615

609

1.24

A = $507

C = $128

B = $102

e1

e2

0

0

(a) Demand Curve

(b) Revenue Curve

R , R

ev en

ue , $

p er

y ea

r p,

$ p

er s

on g

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81Summary

SUMMARY

1. Elasticity. An elasticity shows how responsive one variable is to changes in another variable. The price elasticity of demand, e, summarizes how much the quantity demanded changes when the price changes. The responsiveness of quantity is related to the shape of a demand curve at a particular point or over a particu- lar interval. Specifically, the price elasticity of demand is the percentage change in the quantity demanded divided by an associated percentage change in price. For example, a 1% increase in price causes the quantity demanded to fall by e %. Downward-sloping demand curves have a negative elasticity.

The demand curve is perfectly inelastic if e = 0, is ine- lastic if e is between 0 and -1, has unitary elasticity if e = -1, is elastic if e 6 -1, and becomes perfectly elastic as e approaches negative infinity. The quantity demanded varies less than in proportion to a 1% change in the price if the demand curve is inelastic, but varies more than in proportion if the demand curve is elastic. The elasticity of demand varies along a downward-sloping linear demand curve. A vertical demand curve is perfectly inelastic, and a horizontal demand curve is perfectly elastic.

2. Regression Analysis. Regression analysis fits an economic relationship to data. It explains variations in a dependent variable, such as the quantity demanded, using explanatory variables, such as price and income. A linear regression with just one explanatory variable corresponds to putting the dependent variable on the

vertical axis and the explanatory variable on the hori- zontal axis, plotting the data points, and drawing the “best possible” straight line through these points. One method for finding a suitable estimated relationship is ordinary least squares (OLS), which chooses parameter estimates or “draws the regression line” such that the sum of squared deviations of the data points from the regression line is as small as possible. To help assess the fit of the regression line to the data, statistical pack- ages report the R2 statistic, which is the fraction of the actual variation in the dependent variable explained by the estimated regression equation.

3. Properties and Statistical Significance of Esti- mated Coefficients. A good estimation method should yield coefficient estimates that are unbiased—that would average out to the true value in repeated samples. It is also desirable that an estimation method not produce very different coefficient estimates in different random samples. Regression software produces statistics that can be used to assess how much confidence to place in regression coefficient estimates. Standard errors tell us how much we might expect coefficient estimates to differ from their true values. We use a t-test to assess whether an estimated regression coefficient is different from zero. We obtain a t-statistic for each coefficient by dividing the coefficient by its standard error. If the t-statistic exceeds a critical value that is approximately equal to 2, we can be confident that the coefficient differs from zero.

However, because we have estimated the demand curve, we can calculate the size of these two effects and determine the net effect of a price increase on iTunes’s revenue. The lost revenue from fewer sales is area B, which is $102. The revenue gain due to the higher price on the units sold is area C, which is $128. Therefore, revenue increases by $26 ( = $128 - $102).

Panel b corresponds to panel a. Its horizontal axis measures quantity as in panel a, but its vertical axis measures revenue (rather than price as in panel a). Panel b shows the revenue curve, which relates revenue to the quantity sold.22 At the original price of 99¢, where Q = 615, the revenue curve shows that reve- nue is $609, consistent with panel a. This curve shows that the revenue curve reaches its maximum where Q = 512 and p = $1.24.

Given that the cost to Apple of selling an extra song is probably very close to zero, it seems that Apple would like to maximize its revenue. If the general popu- lation shares similar tastes with the focus group, then Apple’s revenue would increase if it raised its price to $1.24 per song.23

22Because the estimated demand function is Q = 1,024 - 413p, the corresponding inverse demand function is p ≈ 2.48 - 0.00242Q. Thus, the revenue function is R = p * Q ≈ 2.48Q - 0.00242Q2. 23See the Mini-Case “Available for a Song” in Chapter 10 for a larger-scale, more detailed study of Apple’s pricing.

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82 CHAPTER 3 Empirical Methods for Demand Analysis

4. Regression Specification. Regression analysis is reliable only if the equation to be estimated is prop- erly specified. One important aspect of specifica- tion is that the equation should include all relevant explanatory variables. A second specification issue is that a regression equation must have an appropriate functional form. Excluding relevant explanatory vari- ables, including inappropriate explanatory variables, or using the wrong functional form can lead to misleading results.

5. Forecasting. One method of forecasting is to extrap- olate a time series into the future. As a first step in

extrapolation, a manager can regress the variable to be forecast, such as sales, on a time-trend variable. Next, using the estimated trend line, a manager can forecast the future value by substituting future times into the estimated regression equation. When extrapolating, it is often necessary to adjust for seasonal or other patterns. A second method of forecasting uses causal economic relationships, where the manager includes economic variables as explanatory variables instead of or in addi- tion to a time trend. Here, forecasting the dependent variable may require the manager to use expected val- ues of the explanatory variables.

QUESTIONS

1. Elasticity 1.1 The U.S. Tobacco Settlement between the major

tobacco companies and 46 states caused the price of cigarettes to jump 45¢ (21%) in November 1998. Levy and Meara (2005) found only a 2.65% drop in prenatal smoking 15 months later. What is the elas- ticity of demand for this group?

1.2 When Apple raised the price of iTunes from 99¢ to $1.29, GS Boyz’s “Stanky Legg” sales dropped from 22,686 units to 19,692 units (Glenn Peoples, “iTunes Price Change: Sales Down, Revenue Up in Week 1,” Billboard, April 15, 2009). What was the song’s arc elasticity of demand? (Hint: See Q&A 3.1.)

*1.3 The demand function for a good is Q = 100 - 2p. What is the elasticity at the point p = 10 and Q = 80?

*1.4 The only type of downward-sloping demand curve that has the same elasticity at every price is given by the constant elasticity functional form Q = Ape, where A and e are constants. Show, by differentiating this demand function with respect to p, that the elasticity of demand is e in this case. C

1.5 The demand curve for a good is Q = 500 - 4p2. What is the elasticity at the point p = 5 and Q = 400? Is the demand curve elastic or inelastic at this point? C

1.6 Which section of a straight-line demand curve is elastic? Which section is inelastic?

*1.7 According to Duffy-Deno (2003), when the price of broadband access capacity (the amount of infor- mation one can send over an Internet connection) increases 10%, commercial customers buy about 3.8% less capacity. What is the elasticity of demand for broadband access capacity for these firms? Is demand at the current price inelastic?

1.8 Suppose that the demand curve for wheat in each of six countries is perfectly inelastic up to some “choke”

price p*—a price so high that nothing is bought— so that the demand curve is vertical at Q* at prices below p* and horizontal at p*. If p* and Q* vary across countries, what does the world’s demand curve look like? Discuss how the elasticity of demand varies with price along the world’s demand curve.

*1.9 Calculate the price and cross-price elasticities of demand for coconut oil. The coconut oil demand function (Buschena and Perloff, 1991) is

Q = 1,200 - 9.5p + 16.2pp + 0.2Y,

where Q is the quantity of coconut oil demanded in thousands of metric tons per year, p is the price of coco- nut oil in cents per pound, pp is the price of palm oil in cents per pound, and Y is the income of consumers. Assume that p is initially 45¢ per pound, pp is 31¢ per pound, and Q is 1,275 thousand metric tons per year.

1.10 Using the coconut oil demand function from Ques- tion 1.9, calculate the income elasticity of demand for coconut oil at the prices and quantity given. Is coconut oil a normal good at that price and quantity combination?

1.11 The Mini-Case “Anti-Smoking Policies May Reduce Drunk Driving” describes how the equilibrium changed in the market for alcoholic beverages when tobacco taxes rose. Use a supply-and-demand dia- gram to illustrate what happened.

1.12 Ghose and Han (2014) found that the elasticity of demand for Google Play apps is -3.7. (See the Mini-Case “Demand Elasticities for Google Play and Apple Apps.”) This elasticity applies to a small college town where consumers buy approximately 1,000 apps per month. If price rises by 5%, what would be the effect on quantity demanded? Would revenue rise or fall? What is the percentage change in revenue ( = price * quantity)?

All exercises are available on MyLab Economics; * = answer at the back of this book; C = use of calculus may be necessary; = this exercise is available in Excel Grader in MyLab Economics.

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83Questions

2. Regression Analysis 2.1 At the Portland Fish Exchange, each day fishers

deliver some amount of cod to market. Supply is perfectly inelastic at that amount. The quantity of cod caught and brought to market varies day to day. Assuming the demand curve does not vary over time, use the supply-demand framework to illustrate how the price is determined on different days. Explain how this process allows us to identify different points on the demand curve.

2.2 Suppose that a restaurant uses a focus group of regular customers to determine how many custom- ers would buy a proposed new menu item at vari- ous prices. Can this information be used to estimate an inverse demand function? A demand function? Explain briefly. Would it be possible to use a focus group to generate data that could be used to esti- mate a demand function that includes both price and income as explanatory variables?

*2.3 The estimated demand function for popsicles on a particular beach on a sunny summer day is given by Q = 130 - $3.5 p, where p is measured in dol- lars. What is the predicted quantity if p = $2.00? If the actual quantity demanded is 129, what is the residual? Suggest at least two unobserved vari- ables incorporated into the random error. (Hint: See Q&A 3.3.)

2.4 A producer of outdoor clothing used a focus group to obtain information about the demand for fleece jackets with built-in, battery-operated warming pan- els. At prices of $100, $90, $80, $70, $60, and $50, the focus group demanded 23, 31, 40, 44, 48, and 60 jack- ets, respectively. Use the Excel Trendline option to estimate a linear demand function and to determine the associated R2 statistic. (Hint: Put price in the first column. Price will appear on the horizontal axis in this case.)

2.5 Purdue University provides monthly data on Florida electricity consumption online (https://engineering. purdue.edu/LASCI/research-data/energy). We can use these data to estimate monthly residential electricity demand as a function of price and the average monthly temperature. Using a linear regres- sion equation, the estimated demand function is E = 2400 - 25p + 84F where E is residential energy consumption in gigawatt hours (GWH), p is price in cents per kilowatt hour (KWH), and F is temperature in Fahrenheit degrees.

a. What is the estimated residential electricity demand if the price is 8¢ per KWH and the average monthly temperature is 80 degrees?

b. What has a larger estimated effect on quan- tity demanded, a one-cent decline in price or a

one-degree fall in temperature? Explain, using calculations.

c. In Florida, electricity use rises with temperature because air conditioning is a very important source of demand. What sign would you expect on the temperature variable in Canada and the northern U.S. states? Explain briefly.

2.6 In Figure 3.5 two estimated demand curves are shown. These demand curves result from regres- sion equations in which Mai estimates quantity demanded as a function of price and no other vari- ables. However, Mai recognized that other vari- ables, such as sunshine or temperature, may affect the demand for pie. Collecting this data requires effort. In which town should collecting such data be a higher priority for Mai if she is trying to improve her ability to predict pie demand? Explain.

3. Properties and Statistical Significance of Esti- mated Coefficients

3.1 Using the data in Table 3.1, estimate the cod demand function if we use only the first seven observations.

3.2 How sensitive are your regression results in Ques- tion 3.1 to small changes in the data? In particular, how do your regression results change if

a. The quantity in the first row of Table 3.1 were 2.0 instead of 1.5?

b. The quantity in the second row of Table 3.1 were 2.7 instead of 2.2?

*3.3 In the Camry focus group analysis in this chapter, we use a regression to estimate the demand for Camrys. Using that equation, how many fewer Camrys would the focus group buy if the price were increased by $1,000? How many Camrys would we expect the focus group to purchase if the price is $20,000? What is the elasticity of demand if the price is $20,000?

3.4 Using the data in Question 2.4, determine the stand- ard error and t-statistic for the price coefficient. Is price statistically significantly different from zero at the 0.05 level of significance? (Hint: Use Excel’s Regression tool.)

4. Regression Specification 4.1 According to the regression results for CEO com-

pensation, is the effect of experience on CEO com- pensation statistically significant? Is it economically significant? Explain. (Hint: See Q&A 3.4.)

4.2 Suppose that you believe the demand function has a constant-elasticity: Q = Ape,where A is a positive constant and e is the constant elasticity of demand. You have some data and want to estimate the constant-elasticity demand function Q = Apeu,

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84 CHAPTER 3 Empirical Methods for Demand Analysis

where A is a positive constant, e is the constant elasticity of demand, and u is an error term. Take logarithms of both sides of this equation and show that you get an equation that is linear in logarithmic terms (called a log-linear equation). Explain how you can estimate this equation in Excel or other programs using the OLS techniques that we have discussed.

*4.3 You work for a firm producing fitness equipment. The firm tells you that the demand curve for the firm’s main product—a multi-station home gym— is linear. You have in hand price and quantity data obtained from focus groups and instructions to run a regression of revenue on price. Should you use a linear functional form—with revenue as a linear function of price—or something else? Explain.

4.4 A medical clinic that surveys patients with a his- tory of heavy drinking is likely to find that patients who have started to experience serious liver prob- lems are more likely to cut back their drinking than others with a history of heavy drinking. An enthusiastic doctor uses data from this population and regresses current liver function, L, on current alcohol consumption, A. The regression specifica- tion is L = a + bA. The doctor is likely to get a posi- tive estimate for b: Within the population of people with a history of heavy drinking, those who drink more currently tend to have healthier livers. What is wrong with this specification? (Hint: Think about factors that affect the demand for alcohol in this population.)

5. Forecasting 5.1 Heinz makes most of its money from ketchup and

other prepared, packaged foods that are substitutes for fresh foods. Its revenue tends to be low in the summer quarter and high in the winter quarter. Can you provide a possible reason for this pattern? (Hint: Fresh fruits and vegetables are substitutes for many of Heinz’s prepared foods.)

5.2 As reported in the text, we estimated Nike’s quarterly revenue (in billions of dollars) function as Revenue = 3.847 + 0.135t + 0.179W + 0.452S + 0.675M. What does this estimated equation tell us about Nike’s spring quarter revenues compared to the revenue in other quarters? (The spring quarter dummy variable is represented by S in the estimated regression equation.)

5.3 Recessions (when consumers’ incomes fall) strongly affect FedEx’s revenue, but have less of an effect on Heinz’s revenue. Both firms’ revenues vary

seasonally. What regression specifications would you suggest using to forecast revenue for FedEx and for Heinz? Why might these specifications differ?

5.4 Here are annual revenue data in billions of dol- lars for the 10-year period 2008–2017 for two well- known retailers:

Amazon: 19.1; 24.5; 32.4; 48.1; 61.1; 74.5; 89.0; 107.9; 136.0; 177.9.

Walmart: 402.2; 406.1; 420.0; 445.0; 467.2; 474.5; 483.5; 480.0; 482.2; 496.8.

a. For each company, use linear extrapolation in Excel to forecast revenue in the year 2021. (Hint: Use either the Trendline option or the Regres- sion tool.)

b. Based on these extrapolations, when would Amazon be predicted to equal Walmart in revenue?

c. Why has Amazon been growing faster than Walmart? Is the slow growth of Walmart related to the rapid growth of Amazon?

6. Managerial Problem 6.1 In the Managerial Solution, we estimated a focus

group’s demand function for iTunes downloads. The estimated coefficient on price is -413, and the t-statistic is -12.6.

a. Using these values, what is the standard error of this estimated coefficient?

b. Suppose we had another focus group sample, ran a regression on that sample, and obtained the same coefficient on price but with a stand- ard error 10 times as large. What can you say about the statistical significance of the price coefficient in this second sample?

*6.2 Using Excel or another program, estimate the lin- ear OLS demand regression for the iTunes focus group data in the Managerial Solution. What is the R2? What are the coefficient estimates, the stand- ard errors, and the t-statistics for each coefficient? Using a 95% confidence criterion, would you reject the hypothesis that the price coefficient is zero? (You can compare most of your answers to those in the Managerial Solution.)

7. MyLab Economics Spreadsheet Exercises24

7.1 The marketing department of Acme Inc. has esti- mated the following demand function for its popu- lar carpet deodorizer, Freshbreeze: Q = 100 - 5p, where Q is the quantity of an 8-ounce box (sold in thousand units) and p the price of an 8-ounce box. Using Excel, calculate the point price elasticity of

24The spreadsheet exercises in this chapter are based on the work of Satyajit Ghosh in cooperation with the authors. The answers are available on MyLab Economics.

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85Appendix 3A The Identification Problem

demand, e, for price, p = 1, 2, 3, . . . , 19. Describe the pattern of price elasticity of demand that you have calculated along the demand curve.

7.2 The ice cream store Cool Stuff sells exotic ice creams, including Tropical Cream and Green Mango. Cool Stuff has been varying the prices of these two flavors over the past 12 weeks and has recorded the sales data. The table shows the quantity sold of Tropical Cream, Q, given the price of a half-gallon of Tropi- cal Cream, p, and the price of the other flavor, Green Mango, po. Use these data to estimate the demand function for Tropical Cream. Are the coefficients on the two prices statistically significantly different from zero at the 5% significance level? What is the R2?

community and seek his services. However, Bob’s income is subject to seasonal fluctuations. Dividing the year into four seasons, the following data show Bob’s seasonal income in thousands of dollars for the past three years.

Bob’s Income (in thousands of dollars)

Year Jan–Mar Apr–Jun Jul–Sep Oct–Dec Total

1 22 20 25 13 80

2 24 21 24 16 85

3 30 22 22 17 91

Bob is still happy to take on more work. Assuming his prices remain unchanged and his community continues to grow, use Excel’s Regression tool to forecast Bob’s income in the four seasons of the next year and his total income for the year. Use seasonal dummy variables in your analysis.

7.3 Bob Kehoe runs a small business clearing snow in the winter and cutting grass in the other seasons. For the past three years he has kept his prices con- stant but has experienced an upward trend in his income as new households move into his growing

Q 84 82 85 83 82 84 87 81 82 79 82 78

p 8.50 9.00 8.75 9.25 9.50 9.25 8.25 10.00 10.00 10.50 9.50 10.25

po 5.25 6.00 6.00 6.50 6.25 6.25 5.25 7.00 7.25 7.25 6.75 7.25

Excercise 7.2

APPENDIX 3A The Identification Problem

Managers often want to know how much the quantity demanded will fall if they raise the price. That is, the manager wants a reliable estimate of the price coefficient in a demand function regression. Unfortunately, it is not always possible to estimate a demand function in which the price coefficient is identified. An identification problem arises if it is not possible to obtain a unique estimate of a particular parameter.

Two Examples To illustrate the nature of the identification problem, we consider two examples. A manager can identify the price coefficient in the first example and cannot do so in the second example.

In both examples, the manager of the market research division of a large retail bakery chain wants to estimate how the quantity demanded of hard red winter wheat changes as the price rises. The manager has data on the price and quantity of the wheat, which change from week to week.

We say that the manager can identify the demand function if all the coefficients are identified. Whether the manager can identify the demand function—and, in particular, the price coeffi- cient—depends on what causes the prices and quantities to vary over time. In any given week, the intersection of the demand and supply curves determines the observed price-quantity equilibrium pair. Shifts in either the demand or supply curve cause the price-quantity pair to change over time.

In our first example, we suppose that the factors other than price that affect the demand curve, such as income, remain constant, so that the demand curve does not shift. However, weather, which affects the supply curve, changes over time. Therefore, the supply curve shifts repeatedly.

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86 CHAPTER 3 Empirical Methods for Demand Analysis

S3

S2

S1

D3

D2

D1

p, $

p er

b us

he l

Q3 Q2 Q1

Q, Bushels of wheat per week

p1

p2

p3

(b) Identification Problem

X

p, $

p er

b us

he l

Q3 Q2 Q1

Q, Bushels of wheat per week

(a) Identification

p1

p2

p3

S3

S2

S1

D

In panel a of the figure, the supply curve shifts from S1 to S2 to S3 over time. The resulting price-quantity equilibrium pairs—(p1, Q1), (p2, Q2), and (p3, Q3)—lie on the demand curve, D. That is, the shifting supply curve traces out the demand curve. The demand function’s price coefficient is identified: Because the observed price-quantity pairs lie on the demand curve, they show how the quantity demanded changes as the price changes.

In our second example, panel b of the figure, the manager cannot identify the price coef- ficient. The identification problem arises because both weather and income change over time, so that both the supply curve and the demand curve shift. The resulting equilibrium price- quantity pairs—(p1, Q1), (p2, Q2), and (p3, Q3)—do not lie on either a demand curve or a sup- ply curve. Indeed, the line through them, labeled X, has no economic meaning. Interpreting the slope of X as the slope of the actual demand curve would be a mistake. Here, the manager cannot identify the demand function’s price coefficient.

Avoiding the Identification Problem If we knew that the demand curve was stable and that shifts in the supply curve generated the changes in price and quantity, then the observed data would trace out the demand curve and the price coefficient would be identified as in panel a. Our earlier estimate of the Portland Fish Exchange demand function was identified for this reason.

There are other possible ways to avoid the identification problem. One approach is to use a focus group, as in the Camry example. We could ask potential buyers about their buying intentions at particular prices. This process does not involve a supply curve. Respondents report points on their demand curves. The process traces out the demand curve, and there is no identification problem.

Another way to avoid an identification problem is to use an experiment, as in Mai’s pie shop example. Mai generated data by running experiments: changing the price of her pies and seeing how many pies she sold. Again, this approach involves no supply curve. The experi- menter exogenously determines the price and observes changes in quantity demanded, and is able to trace out the demand curve for each bakery.

Additional information may also be helpful. If we have data about factors that shift the supply and demand curves, managers can use more sophisticated regression techniques to separately identify and estimate the supply and demand functions.

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87

E conomists use the theory of consumer choice to analyze consumers’ decisions and to derive demand curves. To answer questions about individual consumer choice (or any kind of individual decision making) we need a model of indi- vidual behavior. The standard economic model of consumer behavior makes the following assumptions.

●● Individual tastes or preferences determine the pleasure or satisfaction people derive from the goods and services they consume.

●● Consumers face constraints or limits on their choices, particularly because their budgets limit how much they can buy.

●● Consumers seek to maximize the level of satisfaction they obtain from consump- tion, subject to the constraints they face. People seek to “do the best they can with what they have.”

4Consumer Choice If this is coffee, please bring me some tea; but if this is tea, please bring me some coffee.

When Google wants to transfer an employee from its Washington, D.C., office to its London branch, it must decide how much compensation to offer the worker to move. International firms are increasingly relocating workers throughout their home countries and internationally.

As you might expect, workers are not always enthusiastic about being relo- cated. In a survey by Runzheimer International, 79% of firms’ relocation managers responded that they experienced resistance from employees who were asked to relocate to high-cost locations. A survey of some of their employees found that 81% objected to moving because of fear of a lowered standard of living.

One possible approach to enticing employees to relo- cate is for the firm to determine the goods and services consumed by employees in the original location and then pay those employees enough to allow them to consume essentially the same items in the new location. According to a survey by Mercer, 79% of international firms reported that they provided their workers with enough income abroad to maintain their home lifestyle.

However, economists who advise on compensation packages point out that such an approach will typically overcompensate employees by paying them more than they need to obtain the same level of economic well-being they have in the original city. How can a firm’s human resources (HR) manager use consumer theory to optimally compensate employees who are transferred to other cities?

Paying Employees to Relocate

Managerial Problem

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88 CHAPTER 4 Consumer Choice

Consumers spend their money on the bundles of products that give them the most pleasure or satisfaction. Someone who likes music and does not have much of a sweet tooth might spend a lot of money on concerts and relatively little on sweet desserts. By contrast, a consumer who loves chocolate and has little interest in music might spend a significant amount on gourmet chocolate and never go to a concert.

Consumers must make choices about which goods to buy. Limits on the amount they can spend (called “budget constraints”) prevent them from buying everything that catches their fancy. Other constraints, such as legal restrictions on items like alcohol and recreational drugs, may also restrain their choices. Therefore, consumers buy the bundles of goods they like best, subject both to their budget constraints and to legal or other relevant constraints.

In economic analysis designed to explain behavior, economists assume that the consumer is the boss (sometimes referred to as consumer sovereignty). If Jason derives pleasure from smoking, an economist does not confuse the economic analysis of Jason’s choices by interjecting his or her own personal judgment that smoking is undesirable. Economists accept the consumer’s tastes and seek to predict the result- ing behavior. Accepting each consumer’s tastes is not the same as condoning the resulting behaviors. An economist might reasonably believe that consumers should avoid smoking. However, if the economist wants to know whether Jason will smoke more next year if the price of cigarettes decreases by 10%, any prediction is unlikely to be correct if the economist says, “He should not smoke; therefore, we predict he will stop smoking next year.” A prediction based on Jason’s actual tastes is more likely to be correct: “Given that Jason likes cigarettes, he is likely to smoke more next year if the price of cigarettes falls.”

This chapter provides an analysis of consumer choice, focusing on how consumer tastes or preferences give rise to consumer demand.

4.1 Consumer Preferences I have forced myself to contradict myself in order to avoid conforming to my own taste. —Marcel Duchamp, Dada artist

We start our analysis of consumer behavior by examining consumer preferences. Once we know about these, we will combine that knowledge with information about the constraints consumers face so that we can answer many questions such as the managerial problem posed at the beginning of this chapter.

A consumer faces choices involving many goods. Does the consumer prefer to buy ice cream or cake? Is it better to rent a large apartment or rent a single room and use

Learning Objectives

1. Predict consumer choices using underlying properties of consumer preferences.

2. Summarize a consumer’s preferences using a utility function.

3. Explain how prices and income limit what a consumer can purchase.

4. Show how consumers maximize their utility given prices and limited income.

5. Derive demand curves from underlying consumer preferences.

6. Discuss the role of behavioral biases in consumer choice.

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894.1 Consumer Preferences

the savings to pay for trips and concerts? A consumer must allocate his or her budget to buy a bundle (also called a market basket or combination) of goods.

How do consumers choose the bundles of goods they buy? One possibility is that consumers behave randomly and blindly choose one good or another without any thought. However, consumers appear to make systematic choices. For example, most consumers buy very similar items each time they visit a grocery store. A consumer typically ignores most items and buys a few specific items repeatedly. A consumer who likes apple juice and dislikes orange juice buys apple juice on a regular basis and rarely, if ever, buys orange juice. In contrast, a consumer who chose randomly would be as likely to buy apple juice as orange juice. By observing a consumer’s con- sistent purchase of apple juice rather than orange juice, we can reject the hypothesis of random choices.

To explain consumer behavior, economists assume that consumers have a set of tastes or preferences they use to guide them in choosing between goods. These tastes differ substantially among individuals. Let’s start by specifying the underlying assumptions in the economist’s model of consumer behavior.

Properties of Consumer Preferences Do not do unto others as you would that they should do unto you. Their tastes may not be the same. —George Bernard Shaw

Economists make three critical assumptions about the properties of consumers’ pref- erences. For brevity, they refer to these properties as completeness, transitivity, and more is better (or nonsatiation).

Completeness. The completeness property holds that, when facing a choice between any two bundles of goods, a consumer can rank them so that one and only one of the following three relationships is true.

1. The consumer prefers the first bundle to the second. 2. The consumer prefers the second bundle to the first. 3. The consumer likes the two bundles equally and therefore is indifferent between

the two bundles.

The completeness property rules out the possibility that the consumer cannot rank the bundles. Indifference is allowed, but indecision is not.

Transitivity. We assume that preferences are transitive. More specifically, we say that if a consumer weakly prefers Bundle a to Bundle b—likes a at least as much as b— and weakly prefers Bundle b to Bundle c, the consumer also weakly prefers Bundle a to Bundle c.

Transitivity of weak preference implies that indifference is also transitive: if a consumer is indifferent between Bundle a and Bundle b, and is indifferent between Bundle b and Bundle c, then the consumer must also be indifferent between Bundle a and Bundle c. Strict preference must also be transitive: If the consumer strictly prefers a to b and b to c, it follows that the consumer must strictly prefer a to c. Also, if the consumer prefers a to b, and is indifferent between b and c, then the consumer must also prefer a to c.

Transitivity is a necessary condition for what most people view as rational behavior. Suppose Amy told you she would prefer a scoop of ice cream to a piece of cake but

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90 CHAPTER 4 Consumer Choice

would prefer a piece of cake to a chocolate bar, and then added that she would prefer a chocolate bar to a scoop of ice cream. You might reasonably accuse her of being irrational or inconsistent. At the very least, it would be difficult to know which dessert to serve her.

More Is Better. The more-is-better property holds that, all else being the same, more of a good is better than less. This property is really just a state- ment of what we mean by a good: a commodity for which more is preferred to less, at least at some levels of consumption. In contrast, a bad is some- thing for which less is preferred to more, as with pollution (which we study in Chapter 16). Because managers primarily care about goods, we will con- centrate on them.

The more-is-better property is not essential for the following analysis of consumer preferences— our most important results would hold even with- out this property. These results would, if properly interpreted, apply to bads and to items we do not care about one way or the other, as well as for goods. However, the more-is-better assumption greatly simplifies the analysis.

Preference Maps Surprisingly, with just the completeness, transitivity, and more-is-better properties, we can tell a lot about a consumer’s preferences. One of the simplest ways to sum- marize information about a consumer’s preferences is to create a graphical interpre- tation—sometimes called a preference map. For graphical simplicity, we concentrate

Mini-Case Not surprisingly, studies based on data from many nations find that wealthier people are happier on average than poorer people (Gere and Schimmack, 2017). But, do people become satiated? Can people be so rich that they can buy every- thing they want such that additional income does not increase their feelings of well-being? Using data from many countries, Stevenson and Wolfers (2013) found no evidence of a satiation point beyond which wealthier countries or wealthier individuals have no further increases in subjective well-being. More- over, they found a clear positive relationship between average levels of self- reported feelings of happiness or satisfaction and income per capita within and across countries, although this effect is small at very high income levels.

Less scientific, but perhaps more compelling, is a survey of wealthy U.S. citizens who were asked, “How much wealth do you need to live comfortably?” On average, those with a net worth of over $1 million said they needed $2.4 million to live comfortably, those with at least $5 million in net worth said they needed $10.4 million, and those with at least $10 million wanted $18.1 million. Apparently, most people never have enough.

You Can’t Have Too Much Money

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914.1 Consumer Preferences

on choices between only two goods, but the model can be generalized algebraically to handle any number of goods.

Each semester, Lisa, who lives for fast food, decides how many pizzas and burri- tos to eat. The various bundles of pizzas and burritos she might consume are shown in panel a of Figure 4.1, with (individual-size) pizzas per semester on the horizontal axis and burritos per semester on the vertical axis.

At Bundle e, for example, Lisa consumes 25 pizzas and 15 burritos per semester. The more-is-better property implies that Lisa prefers all the bundles that lie above and to the right (area A) to Bundle e because they contain at least as much or more

FIGURE 4.1 Bundles of Pizzas and Burritos That Lisa Might Consume

B , B

ur rit

os p

er s

em es

te r

(a)

302515

Z, Pizzas per semester

25

20

15

10

5

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Pizzas per semester are on the horizontal axis, and burritos per semester are on the vertical axis. (a) Lisa prefers more to less, so she prefers Bundle e to any bundle in area B, including d. Similarly, she prefers any bundle in area A, including f, to e.

(b) The indifference curve, I1, shows a set of bundles (including c, e, and a) among which she is indiffer- ent: She likes all three bundles on this curve equally. (c) The three indifference curves, I1, I2, and I3, are part of Lisa’s preference map, which summarizes her preferences.

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92 CHAPTER 4 Consumer Choice

of both pizzas and burritos as Bundle e. Thus, she prefers Bundle f (30 pizzas and 20 burritos) in that region.

By using the more-is-better property, we know that Lisa prefers Bundle e to all the bundles that lie in area B, below and to the left of Bundle e, such as Bundle d (15 pizzas and 10 burritos). All the bundles in area B contain fewer pizzas or fewer bur- ritos or fewer of both than does Bundle e.

From panel a, we do not know whether Lisa prefers Bundle e to bundles such as b (30 pizzas and 10 burritos) in area D, which is the region below and to the right of e, or c (15 pizzas and 25 burritos) in area C, which is the region above and to the left of Bundle e. We can’t use the more-is-better property to determine which bundle she prefers because each of these bundles contains more of one good and less of the other than e does. To be able to state with certainty whether Lisa prefers particular bundles in areas C or D to Bundle e, we have to know more about her tastes for pizza and burritos.

Preferences and Indifference Curves. Suppose we asked Lisa to identify all the bundles that give her the same amount of pleasure she gets from consuming Bundle e. In panel b of Figure 4.1, we use her answers to draw curve I 1 through all bundles she likes as much as she likes e. Curve I 1 is an indifference curve: the set of all bundles of goods that a consumer views as being equally desirable.

Indifference curve I 1 includes Bundles c, e, and a, so Lisa is indifferent about con- suming Bundles c, e, and a. From this indifference curve, we also know that Lisa prefers Bundle e (25 pizzas and 15 burritos) to Bundle b (30 pizzas and 10 burritos). How do we know that? Bundle b lies below and to the left of Bundle a, so Bundle a is preferred to Bundle b due to the more-is-better property. Both Bundle e and Bundle a are on indif- ference curve I 1, so Lisa likes Bundle e as much as Bundle a. Because Lisa is indifferent between e and a and she prefers a to b, she must prefer e to b by transitivity.

If we asked Lisa many, many questions, we could, in principle, draw an entire set of indifference curves through every possible bundle of burritos and pizzas. We summarize Lisa’s preferences in an indifference map or preference map, which is a complete set of indifference curves that summarize a consumer’s tastes. We refer to it as a map because it uses the same principle as a topographical or contour map, in which each line shows all points with the same height or elevation. With an indiffer- ence map, each line shows points (combinations of goods) with the same utility or well-being. Panel c of Figure 4.1 shows three of Lisa’s indifference curves: I 1, I 2, and I 3. In this figure, the indifference curves are parallel, but they need not be.

We can demonstrate that all indifference curve maps must have the following four properties.

1. Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin.

2. An indifference curve goes through every possible bundle. 3. Indifference curves cannot cross. 4. Indifference curves slope downward.

First, we show that bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. By the more-is-better property, Lisa prefers Bundle f to Bundle e in panel c of Figure 4.1. She is indifferent among all the bundles on indifference curve I 3 and Bundle f, just as she is indiffer- ent among all the bundles, such as Bundle c, on indifference curve I 2, and Bundle e. By the more-is-better property, she prefers Bundle f to Bundle e, which she likes as

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934.1 Consumer Preferences

much as Bundle c, so she also prefers Bundle f to Bundle c. By this type of reasoning, she prefers all bundles on I 3 to all bundles on I 2.

Second, we show that an indifference curve goes through every possible bundle. This property is a consequence of the completeness assumption: The consumer can compare any bundle to another. Compared to a given bundle, some bundles are preferred to it, some are enjoyed equally, and some are inferior to it. Connecting the bundles that give the same well-being produces an indifference curve that includes the given bundle.

Third, we show that indifference curves cannot cross. If two indifference curves did cross, the bundle at the point of intersection would be on both indifference curves. But a given bundle cannot be on two indifference curves. Suppose that two indifference curves crossed at Bundle e, as in panel a of Figure 4.2. Because Bundles e and a lie on the same indifference curve I 1, Lisa is indifferent between e and a. Simi- larly, she is indifferent between e and b because both are on I 2. By transitivity, if Lisa is indifferent between e and a, and she is indifferent between e and b, she must be indifferent between a and b. But that’s impossible! Bundle b is above and to the right of Bundle a, which means it contains more of both goods. Thus, Lisa must prefer b to a because of the more-is-better property. Because preferences are transitive and consumers prefer more to less, indifference curves cannot cross.

Finally, we show that indifference curves must be downward sloping. Suppose, to the contrary, that an indifference curve sloped upward, as in panel b of Figure 4.2. The consumer is indifferent between Bundles a and b because both lie on the same indifference curve, I. But the consumer must prefer b to a by the more-is-better prop- erty: Bundle a lies below and to the left of Bundle b. Because of this contradiction— the consumer cannot both be indifferent between a and b and strictly prefer b to a—indifference curves cannot be upward sloping. For example, if Lisa views pizza and burritos as goods, she cannot be indifferent between a bundle of one pizza and one burrito and another bundle with two of each.

Willingness to Substitute Between Goods. Lisa is willing to make some trade-offs between goods. The downward slope of her indifference curves shows that Lisa is willing to give up some burritos for more pizza or vice versa. She is indifferent

FIGURE 4.2 Impossible Indifference Curves

B , B

ur rit

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(a) Crossing

Z, Pizzas per semester

I2

I1 a

b e

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(b) Upward Sloping

Z, Pizzas per semester

I

a

b

(a) Suppose that the indifference curves cross at Bundle e. Lisa is indiffer- ent between e and a on indifference curve I1 and between e and b on I2. If Lisa is indifferent between e and a and she is indifferent between e and b, she must be indifferent between a and b by transitivity. But b has more of both pizzas and burritos than a, so she must prefer a to b. Because of this con- tradiction, indifference curves cannot cross. (b) Suppose that indifference curve I slopes upward. The consumer is indifferent between b and a because they lie on I but prefers b to a by the more-is-better assumption. Because of this contradiction, indifference curves cannot be upward sloping.

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94 CHAPTER 4 Consumer Choice

between Bundles a and b on her indifference curve I in panel a of Figure 4.3. If she initially has Bundle a (eight burritos and three pizzas), she could get to Bundle b (five burritos and four pizzas) by trading three burritos for one more pizza. She is indifferent as to whether or not she makes this trade.

The marginal rate of substitution (MRS) measures Lisa’s willingness to trade one good for another. The MRS shows the rate at which a consumer can substitute one good for another while remaining on the same indifference curve. Graphically, the MRS is the slope of the indifference curve.1 If pizza lies on the horizontal axis, Lisa’s marginal rate of substitution of burritos for pizza is

MRS = ∆B ∆Z

,

where ∆B is the number of burritos Lisa will give up to get ∆Z more pizzas while staying on the same indifference curve. Roughly speaking, we can say that the MRS is the amount of one good a consumer will sacrifice to obtain one more unit of another good while staying on the same indifference curve. If ∆Z is 1, then the associated value of ∆B is the MRS. Thus, if Lisa is willing to give up three burritos (∆B = -3) to get one more pizza (∆Z = 1), then the MRS is -3>1 = -3. We can illustrate why the MRS is negative by moving from Bundle a to Bundle b in panel a of Figure 4.3. The negative sign shows that Lisa is willing to give up some of one good to get more of the other: Her indifference curve slopes downward.

1The slope of a straight line is “the rise over the run”: It describes how much we move along the vertical axis (rise) as we move along the horizontal axis (run). The slope of an indifference curve at a particular point is the slope of a straight line that is tangent to the indifference curve at that point.

FIGURE 4.3 Marginal Rate of Substitution

B , B

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(a) Indifference Curve Convex to the Origin

5

3

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(a) At Bundle a, Lisa is willing to give up three bur- ritos for one more pizza; at b, she is willing to give up only two burritos to obtain another pizza. That is, the relatively more burritos she has, the more she is willing to trade for another pizza. (b) An indifference curve of this shape is unlikely to be observed. Lisa would be willing to give up

more burritos to get one more pizza, the fewer the burritos she has. Moving from Bundle c to b, she will trade one pizza for three burritos, whereas moving from b to a, she will trade one pizza for two burritos, even though she now has relatively more burritos to pizzas.

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954.1 Consumer Preferences

In specifying the MRS, we must be clear about which good is on the horizontal axis. Because pizza is on the horizontal axis in our figure, the MRS of “burritos for pizza” is -3, which is the slope of the indifference curve. If we were to switch axes so that burritos were on the horizontal axis, we could cal- culate the MRS of “pizza for burritos,” which mea- sures how much pizza Lisa would give up to get one more burrito while staying on the same indiffer- ence curve. In this case, the MRS of pizza for burri- tos would be ∆Z>∆B, which is -13. From Lisa’s point of view, one pizza is worth 3 burritos (the MRS of burritos for pizza is -3) or, equivalently, 1 burrito is worth about 13 of a pizza (the MRS of pizza for burritos is -13).

Curvature of Indifference Curves. The indifference curves we have used so far, such as I in panel a of Figure 4.3, are convex to the origin of the graph: that is, the indifference curves are “bowed in” toward the origin.

Because the indifference curve in panel a is convex, when Lisa has a large num- ber of burritos, B, she is willing to give up more of that good to get one more pizza, Z, than she would if she had only a small number of burritos. Starting at Bundle a in panel a of Figure 4.3, Lisa is willing to give up three burritos to obtain one more pizza. If she has Bundle b, she is willing to trade only two burritos for a pizza. If she has Bundle c, she is even less willing to trade; she will give up only one burrito for another pizza. This willingness to trade fewer burritos for one more pizza as we move down and to the right along the indifference curve reflects a diminishing marginal rate of substitution.

An indifference curve doesn’t have to be convex, but casual observation suggests that most people’s indifference curves over most pairs of products are convex. It is unlikely, for example, that Lisa’s indifference curves would be concave, as in panel b of Figure 4.3. If her indifference curve were concave, Lisa would be willing to give up more burritos to get one more pizza when she has fewer burritos. In panel b, she trades one pizza for three burritos moving from Bundle c to b, and she trades one pizza for only two burritos moving from Bundle b to a, even though her ratio of burritos to pizza is greater.

Two extreme types of indifference curves are plausible: straight-line indifference curves and right-angle indifference curves. Straight-line indifference curves reflect perfect substitutes, which are goods that are essentially equivalent from the con- sumer’s point of view. The consumer is completely indifferent between the two goods. For example, if Bill cannot taste any difference between Coca-Cola and Pepsi- Cola, he views them as perfect substitutes: he is indifferent between one additional can of Coke and one additional can of Pepsi. His indifference curves for these two goods are straight, parallel lines with a slope of -1 everywhere along the curve, as in panel a of Figure 4.4. Thus, Bill’s marginal rate of substitution is -1 at every point along these indifference curves.

The slope of indifference curves of perfect substitutes need not always be -1; it can be any constant rate. For example, Helen knows from reading the labels that Clorox bleach is twice as strong as a generic brand, but otherwise no different. As a result,

We are out of tickets for Swan Lake. Do you want tickets for Wrestlemania?

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96 CHAPTER 4 Consumer Choice

she is indifferent between one cup of Clorox and two cups of the generic bleach. If the generic bleach is on the vertical axis, the slope of her indifference curve is -2.2

The other extreme case is perfect complements: goods that an individual wants to consume only in fixed proportions. Cathy doesn’t like pie by itself or vanilla ice cream by itself, but she loves pie à la mode (a slice of pie with a scoop of vanilla ice cream on top). Her indifference curves have right angles in panel b of Figure 4.4. Bundle a consists of one piece of pie and one scoop of ice cream, combining to make one serving of pie à la mode. If she gets an additional scoop of ice cream but no pie to go with it (Bundle d) she remains on the same indifference curve: the extra scoop of ice cream by itself provides no additional benefit to Cathy. Adding a third scoop of ice cream (shown as Bundle e) is also a matter of indifference to Cathy. She gets no extra benefit and remains on the same indifference curve. Similarly, if Cathy has only one scoop of ice cream, additional pieces of pie beyond the first leave her on the same indifference curve.

With preferences like this, Cathy consumes only bundles like a, b, and c, in which pie and ice cream are in equal proportions. She would never want to pay for any additional ice cream that was not matched by a piece of pie, and she would never want to pay for a piece of pie without a scoop of ice cream to go with it. She con- sumes ice cream and pie only in equal proportions.

With a bundle like a, b, or c, she will not substitute a piece of pie for an extra scoop of ice cream. For example, if she were at b, she would be unwilling to give up an extra slice of pie to get, say, two extra scoops of ice cream, as at point e. Indeed, she wouldn’t give up the slice of pie even for a virtually unlimited amount of extra ice cream because the extra ice cream is worthless to her.

2Sometimes it is difficult to guess which goods are close substitutes. According to Harper’s Index 1994, flowers, perfume, and fire extinguishers rank 1, 2, and 3 among “appropriate” Mother’s Day gifts. Few would guess that perfume and fire extinguishers are substitutes.

FIGURE 4.4 Perfect Substitutes, Perfect Complements, Imperfect Substitutes C

ok e,

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(a) Bill views Coke and Pepsi as perfect substitutes. His indifference curves are straight, parallel lines with a marginal rate of substitution (slope) of -1. Bill is willing to exchange one can of Coke for one can of Pepsi. (b) Cathy likes pie à la mode but does not like pie or ice cream by itself: She views ice cream and

pie as perfect complements. She will not substi- tute between the two; she consumes them only in equal quantities. (c) Lisa views burritos and pizza as imperfect sub- stitutes. Her indifference curve lies between the extreme cases of perfect substitutes and perfect complements.

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974.2 Utility

The standard-shaped, convex indifference curve in panel c of Figure 4.4 lies between these two extreme examples. Convex indifference curves show that a con- sumer views two goods as imperfect substitutes.

4.2 Utility Underlying our model of consumer behavior is the belief that consumers can com- pare various bundles of goods and decide which one gives them the greatest pleasure or satisfaction. It is possible to summarize a consumer’s preferences by assigning a numerical value to each possible bundle to reflect the consumer’s relative ranking of these bundles.

Following Jeremy Bentham, John Stuart Mill, and other nineteenth-century British economist-philosophers, economists apply the term utility to this set of numerical values that reflect the relative rankings of various bundles of goods. The statement that “Lorna prefers Bundle x to Bundle y” is equivalent to the statement that “con- suming Bundle x gives Lorna more utility than consuming Bundle y.” For example, Lorna prefers x to y if Bundle x gives Lorna a utility level of 10 and Bundle y gives her a utility level of 8.

Utility Functions If we knew the utility function—the relationship between utility measures and every possible bundle of goods—we could summarize the information in indiffer- ence maps succinctly. Lisa’s utility function, U(B, Z), tells us how much utility she gets from B burritos and Z pizzas. Given that her utility function reflects her prefer- ences, if Lisa prefers Bundle 1, (B1, Z1), to Bundle 2, (B2, Z2), then the utility she gets from the first bundle exceeds that from the second bundle: U(B1, Z1) 7 U(B2, Z2).

For example, suppose that the utility, U, that Lisa gets from burritos and pizzas is

U = 2BZ. From this function, we know that the more she consumes of either good, the greater the utility she receives. Using this function, we can determine whether Lisa would be happier if she had Bundle x with 9 burritos and 16 pizzas or Bundle y with 13 of each. The utility she gets from x is 12 (=29 * 16). The utility she gets from y is 13 (=213 * 13). Therefore, she prefers y to x.

The utility function is a concept that economists use to help them think about consumer behavior; utility functions do not exist in any fundamental sense. If you asked your mother what her utility function is, she would be puzzled—unless, of course, she is an economist. But if you asked her enough questions about choices of bundles of goods, you could construct a function that accurately summarizes her preferences. For example, by questioning people, Rousseas and Hart (1951) con- structed indifference curves between eggs and bacon, and MacCrimmon and Toda (1969) constructed indifference curves between French pastries and money (which can be used to buy all other goods).

Typically, consumers can easily answer questions about whether they prefer one bundle to another, such as, “Do you prefer a bundle with one scoop of ice cream and two pieces of cake to another bundle with two scoops of ice cream and one piece of cake?” But they have difficulty answering questions about how much more they prefer one bundle to another because they don’t have a measure to describe how

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98 CHAPTER 4 Consumer Choice

their pleasure from two goods or bundles differs. Therefore, we may know a con- sumer’s rank-ordering of bundles even if we do not have a good idea of how much that consumer prefers one bundle to another.

Ordinal and Cardinal Utility The term ordinal is used to describe a measure that contains information only about rankings or orderings. For example, a movie critic might give a movie between one and four stars. However, a 4-star movie is not necessarily “twice as good” as a 2-star movie or four times as good as a 1-star movie. All we can say is that the critic likes the 4-star movie better than the 2-star movie, which in turn the critic prefers to the 1-star movie: We know only the critic’s relative rankings. Thus, movie rankings are an ordinal measure, even though numbers (the number of stars) might be used to represent the rankings. With utility, if we know only a consumer’s relative rankings of bundles, our measure of utility is ordinal.

A cardinal measure allows us to make absolute numerical comparisons, as with length or weight. Cardinal measures contain more information than ordinal mea- sures. For example, money is a cardinal measure. If Sofia has $100 and Hu has $50, we know not only that Sofia has more money than Hu (an ordinal comparison), but that she has precisely twice as much as Hu (a cardinal comparison).

Economists sometimes treat utility as a cardinal measure, allowing for statements like “Bundle A is twice as good as Bundle B,” instead of just saying that Bundle A is preferred to Bundle B. However, most of our discussion of consumer choice in this chapter holds if utility has only ordinal properties. If utility is an ordinal measure, we should not put any weight on the absolute difference between the utility associ- ated with one bundle and another. We care only about the relative utility or ranking of the two bundles.

Marginal Utility Using Lisa’s utility function over burritos and pizza, we can show how her utility changes if she gets to consume more of one of the goods. Suppose that Lisa has the utility function in Figure 4.5. The curve in panel a shows how Lisa’s utility rises as she consumes more pizzas while we hold her consumption of burritos fixed at 10. Because pizza is a good, Lisa’s utility rises as she consumes more pizza.

If her consumption of pizzas increases from Z = 4 to 5, ∆Z = 5 - 4 = 1, and her utility increases from U = 230 to 250, ∆U = 250 - 230 = 20. The extra utility (∆U) that she gets from consuming one more unit of a good (∆Z = 1) is the marginal utility from that good. Thus, marginal utility is the slope of the utility function as we hold the quantity of the other good constant.

MUZ = ∆U ∆Z

.

Lisa’s marginal utility from increasing her consumption of pizza from 4 to 5 is

MUZ = ∆U ∆Z

= 20 1

= 20.

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994.2 Utility

Panel b in Figure 4.5 shows that Lisa’s marginal utility from consuming one more pizza varies with the number of pizzas she consumes, holding her consumption of burritos constant. Her marginal utility of pizza curve falls as her consumption of pizza increases, but the marginal utility remains positive: Each extra pizza gives Lisa plea- sure, but it gives her less pleasure relative to other goods than did the previous pizza.

Marginal Utility

Using Calculus The marginal utility from a particular good is the partial derivative of the utility function with respect to that good, which measures how utility changes as we change one good while holding consumption of other goods constant. Thus, if Lisa’s utility function is U(B, Z), her marginal utility from Z is the partial deriva- tive of U with respect to Z: MUZ = 0U(B, Z)>0Z.

FIGURE 4.5 Utility and Marginal Utility

As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases and her marginal utility of pizza, MUZ, decreases (though it remains positive).

(a) If she increases her consumption of pizza from 4 to 5 per semester while holding her consumption of burritos fixed at 10, her utility increases from 230 to 250. Her marginal utility is the extra utility she gets, ∆U = 250 - 230 = 20 from an extra pizza, ∆Z = 1, which is MUZ = ∆U>∆Z = 20>1 = 20. (b) At Z = 5, the height of Lisa’s mar- ginal utility curve is 20.

M U

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100 CHAPTER 4 Consumer Choice

Marginal Rates of Substitution Earlier we learned that the marginal rate of substitution (MRS) is the slope of the indifference curve. The marginal rate of substitution depends on marginal utilities. If Lisa has 10 burritos and 4 pizzas in a semester and gets one more pizza, her utility rises. That extra utility is the marginal utility from the last pizza, MUZ. Similarly, if she receives one extra burrito instead, her marginal utility from the last burrito is MUB.

Suppose that Lisa trades from one bundle on an indifference curve to another by giving up some burritos to gain more pizza. She gains marginal utility from the extra pizza but loses marginal utility from fewer burritos. We can show that the marginal rate of substitution can be written in terms of the marginal utilities:

MRS = ∆B ∆Z

= - MUZ MUB

(4.1)

Equation 4.1 tells us that the MRS, which is the slope of the indifference curve at a par- ticular bundle, depends on the negative of the ratio of the marginal utility of pizza to the marginal utility of burritos. (We derive Equation 4.1 using calculus in Appendix 4A.)

An example illustrates the logic underlying Equation 4.1. Suppose that Lisa gains one unit of utility (one util) if she eats one more burrito, MUB = 1, and two utils if she has one more pizza, MUZ = 2. That is, one more pizza gives her as much extra pleasure as two burritos. Thus, her utility stays the same—she stays on the same indifference curve—if she exchanges two burritos for one pizza, so her MRS = -MUZ>MUB = -2.

4.3 The Budget Constraint Knowing an individual’s preferences is only the first step in analyzing that person’s consumption behavior. Consumers maximize their well-being subject to constraints. The most important constraint most of us face in deciding what to consume is our personal budget constraint.

If we cannot save and borrow, our budget is the income we receive in a given period. If we can save and borrow, we can save money early in life to consume later, such as when we retire, or we can borrow money when we are young and repay those sums later in life. Savings are, in effect, a good that consumers can buy. For simplicity, we assume that each consumer has a fixed amount of money to spend now, so we can use the terms budget and income interchangeably.

For graphical simplicity, we assume that consumers spend their money on only two goods. If Lisa spends all her budget, Y, on pizza and burritos, then her budget constraint is

pBB + pZZ = Y, (4.2)

where pB is the price of burritos, pZ is the price of pizza, pBB is the amount she spends on burritos, and pZZ is the amount she spends on pizzas, Equation 4.2 shows that her expenditures on burritos and pizza use up her entire budget.

How many burritos can Lisa buy? Subtracting pZZ from both sides of Equation 4.2 and dividing both sides by pB, we determine the number of burritos she can purchase to be

B = Y pB

- pZ pB

Z. (4.3)

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1014.3 The Budget Constraint

According to Equation 4.3, Lisa can afford to buy more burritos only if

●● her income (Y) increases, ●● the price of burritos (pB) or pizza (pZ) falls, or ●● she purchases fewer pizzas (Z).

For example, if Lisa has one more dollar of income (Y), she can buy 1>pB more burritos.

If pZ = $1, pB = $2, and Y = $50, Equation 4.3 is

B = $50 $2

- $1 $2

Z = 25 - 12 Z. (4.4)

As Equation 4.4 shows, every two pizzas cost Lisa one burrito. How many burritos can she buy if she spends all her money on burritos? She can buy 25 burritos: By set- ting Z = 0 in Equation 4.3, we find that B = Y>pB = $50>$2 = 25. Similarly, if she spends all her money on pizza, she can buy 50 of them: Setting B = 0, we can solve for Z = Y>pZ = $50>$1 = 50.

Instead of spending all her money on pizza or all on burritos, she can buy some of each. Table 4.1 shows four possible bundles she could buy. For example, she can buy 20 burritos and 10 pizzas with $50.

Equation 4.4 is plotted in Figure 4.6. This line is called a budget line or budget constraint: the bundles of goods that can be bought if the entire budget is spent on those goods at given prices. This budget line shows the combinations of burritos and pizzas that Lisa can buy if she spends all of her $50 on these two goods. The four bundles in Table 4.1 are labeled on this line.

Lisa could, of course, buy any bundle that costs less than $50. The opportunity set is all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint (all those bundles of positive Z and B such that pBB + pZZ … Y). Lisa’s opportunity set is the shaded area in Figure 4.6. She could buy 10 burritos and 15 pieces of pizza for $35, which falls inside the constraint. Unless she wants to spend the other $15 on some other good, though, she might as well spend all of it on the food she loves and pick a bundle on the budget constraint rather than inside it.3

3The budget line in Figure 4.6 is a smooth, continuous line, which implies that Lisa can buy frac- tional numbers of burritos and pizzas. Is that true? Will a restaurant sell you half a burrito? Maybe not. Why, then, don’t we draw the budget line and opportunity set as discrete points (bundles) of whole numbers of burritos and pizzas instead of a continuous line? One reason is that Lisa can buy a burrito at a rate of one-half per time period. If Lisa buys one burrito every other week, she buys an average of one-half burrito every week. Thus, it is plausible that she could purchase fractional amounts over a particular time period.

TABLE 4.1 Allocations of a $50 Budget Between Burritos and Pizza

Bundle Burritos, $2 each Pizza, $1 each

a 25 0

b 20 10

c 10 30

d 0 50

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102 CHAPTER 4 Consumer Choice

Slope of the Budget Line The relative prices of the two goods determine the slope of the budget line. Accord- ing to the budget line, Equation 4.3, B = Y>pB - (pZ>pB)Z, so every extra unit of Z that Lisa purchases reduces B by -pZ>pB. That is, the slope of the budget line is ∆B>∆Z = -pZ>pB. Thus, the slope of the budget line depends on only the relative prices.

Lisa faces prices of pZ = $1 and pB = $2, so the slope of her budget line is -pZ>pB = - $1>$2 = -12. For example, if we reduce the number of pizzas from 10 at point b in Figure 4.6 to 0 at point a, the number of burritos that Lisa can buy rises from 20 at point b to 25 at point a, so ∆B>∆Z = (25 - 20)>(0 - 10) = 5>(-10) = -12.

The slope of the budget line is called the marginal rate of transformation (MRT): the trade-off the market imposes on the consumer in terms of the amount of one good the consumer must give up to purchase more of the other good:

MRT = ∆B ∆Z

= - pZ pB

. (4.5)

Because Lisa’s MRT = -12, she can “trade” an extra pizza for half a burrito or, equiv- alently, she has to give up two pizzas to obtain an extra burrito.

Effects of a Change in Price on the Opportunity Set If the price of pizza doubles but the price of burritos remains unchanged, the budget line swings in toward the origin in panel a of Figure 4.7. If Lisa spends all her money on burritos, she can buy as many burritos as before, so the budget line still hits the burrito axis at 25. If she spends all her money on pizza, however, she can now buy

FIGURE 4.6 The Budget Line

B , B

ur rit

os p

er s

em es

te r

Opportunity set

50 = Y/pZ

Budget line, L1

25 = Y/pB

20

10

100 30

Z, Pizzas per semester

a

b

c

d

If Y = $50, pZ = $1, and pB = $2, Lisa can buy any bundle in the opportunity set, the shaded area, including points on the budget l ine , L1, B = Y>pB - (pZ>pB)Z = $50>$2 - ($1>$2)Z. If Lisa buys one more unit of Z, she must reduce her consumption of B by -(pZ>pB) = -12 to stay within her budget. Thus, the slope, ∆B>∆Z, of her budget line, which is also called the marginal rate of trans- formation (MRT), is -(pZ>pB) = -12.

The Marginal Rate of Transformation

Using Calculus By differentiating the budget constraint, Equation 4.3, B = Y>pB - (pZ>pB)Z, with respect to Z, we confirm that the slope of the budget constraint, or marginal rate of transformation, is MRT = dB>dZ = -pZ>pB, as in Equation 4.5.

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1034.3 The Budget Constraint

only half as many pizzas as before, so the budget line intercepts the pizza axis at 25 instead of at 50.

The new budget line is steeper and lies inside the original one. As the price of pizza increases, the slope of the budget line, MRT, changes. The original line, L1, at the original prices, MRT = -12, shows that Lisa could trade half a burrito for one pizza or two pizzas for one burrito. The new line, L2, MRT = pZ>pB = - $2>$2 = -1, indicates that she can now trade one burrito for one pizza, due to the increase in the price of pizza.

Unless Lisa wants to eat only burritos, she is unambiguously worse off due to this increase in the price of pizza because she can no longer afford the combinations of pizza and burritos in the shaded “Loss” area.

A decrease in the price of pizza would have the opposite effect: The budget line would rotate outward, pivoting around the intercept on the burrito axis. As a result, Lisa’s opportunity set would increase.

Effects of a Change in Income on the Opportunity Set If the consumer’s income increases, the consumer can buy more of all goods. Sup- pose that prices remain at their original levels (pZ = $1 and pB = $2), but Lisa’s income increases by $50 per semester to Y = $100. Her budget line shifts out- ward—away from the origin—and is parallel to the original constraint in panel b of Figure 4.7. Why is the new constraint parallel to the original one? The intercept of the budget line on the burrito axis is Y>pB, and the intercept on the pizza axis is

FIGURE 4.7 Changes in the Budget Line

B , B

ur rit

os p

er s

em es

te r

(a) Price of Pizza Doubles

Loss

50

L1 (pZ = $1)

L2 (pZ = $2)

25

250

Z, Pizzas per semester

B , B

ur rit

os p

er s

em es

te r

(b) Income Doubles

Gain

100

L3 (Y = $100)

L1 (Y = $50)

50

25

500

Z, Pizzas per semester

pZ doubles Income doubles

(a) If the price of pizza increases from $1 to $2 a slice, Lisa’s budget line rotates from L1 to L2 around the intercept on the burrito axis. The slope or MRT of the original budget line, L1, is -12, while the MRT of the new budget line L2 is -1. The shaded area shows the combinations of pizza and burritos that Lisa can no longer afford.

(b) If Lisa’s budget doubles from $50 to $100 and prices don’t change, her new budget line moves from L1 to L3. This shift is parallel: both budget lines have the same slope or MRT of -12. The new opportunity set is larger by the shaded area.

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104 CHAPTER 4 Consumer Choice

Y>pZ. Thus, holding prices constant, the intercepts shift outward in proportion to the change in income. Originally, if she spent all her money on pizza, Lisa could buy 50 = $50>$1 pizzas; now she can buy 100 = $100>$1. Similarly, the burrito axis intercept goes from 25 = $50>$2 to 50 = $100>$2. Initially, if she consumed 25 burritos, Lisa could not consume any pizza; now if she consumes 25 burritos she can also consume 50 pizzas.

A change in income affects only the position and not the slope of the budget line, because the relative prices of pizza and burritos determine the slope. A decrease in the prices of both pizzas and burritos in the same proportion has the same effect as an increase in income, as the next Q&A shows.

Q&A 4.1 Is Lisa better off if her income doubles or if the prices of both the goods she buys fall by half?

Answer Show that Lisa’s budget line and her opportunity set are the same with either change. As panel b of Figure 4.7 shows, if her income doubles, her budget line has a parallel shift outward. The new intercepts at 50 = 2Y>pB = (2 * 50)>2 on the burrito axis and 100 = 2Y>pZ = (2 * 50)>1 on the pizza axis are double the original values. If the prices fall by half, her budget line is the same as if her income doubles. The intercept on the burrito axis is 50 = Y>(pB>2) = 50>(2>2), and the intercept on the pizza axis is 100 = Y>(pZ>2) = 50>(1>2). Therefore, Lisa is equally well off if her income doubles or if prices fall by half.

Mini-Case During emergencies, govern- ments frequently ration food, gas, and other staples rather than let their prices rise, as the United States and the United Kingdom did during World War II. Cuban citizens receive a ration book that limits their purchases of staples such as rice, legumes, potatoes, bread, eggs, and meat.

Water rationing is common during droughts. In recent years, water quotas have been imposed in parts of Austra- lia, Brazil, Egypt, Honduras, India, Kenya, New Zealand, Pakistan, South Africa, United States, Venezuela, and elsewhere. Rationing affects consumers’ opportunity sets because they cannot necessarily buy as much as they want at market prices.

Rationing

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1054.4 Constrained Consumer Choice

4.4 Constrained Consumer Choice Were it not for the budget constraint, consumers who prefer more to less would con- sume unlimited amounts of all goods. Well, they can’t have it all! Instead, consumers maximize their well-being subject to their budget constraints. Now, we have to deter- mine the bundle of goods that maximizes well-being subject to the budget constraint.

The Consumer’s Optimal Bundle My problem lies in reconciling my gross habits with my net income. —Errol Flynn

Given information about Lisa’s preferences (as summarized by her indifference curves) and how much she can spend (as summarized by her budget line), we can determine Lisa’s optimal bundle. Her optimal bundle is the bundle out of all the bundles she can afford that gives her the most pleasure. Here, we use graphical techniques to find her optimal bundle.

We first show that Lisa’s optimal bundle must be on the budget line in Figure 4.8. Bundles that lie on indifference curves above the constraint, such as those on I 3, are not in her opportunity set. Although Lisa prefers Bundle f on indifference curve I 3 to e on I 2, she cannot afford to purchase f. Even though Lisa could buy a bundle inside the budget line, she does not want to do so, because more is better than less: For any bundle inside the constraint (such as d on I 1), another bundle on the constraint has more of at least one of the two goods, and hence she prefers that bundle. Therefore, the optimal bundle must lie on the budget line.

Q&A 4.2 A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?

Answer 1. Draw the original opportunity set using a budget line between water and all other

goods. In the graph, the consumer can afford to buy up to 12 thousand gal- lons of water a month if not constrained. The opportunity set, areas A and B, is bounded by the axes and the budget line. 2. Add a line to the figure showing the quota, and

determine the new opportunity set: A vertical line at 10 thousand on the water axis indi- cates the quota. The new opportunity set, area A, is bounded by the axes, the budget line, and the quota line.

3. Compare the two opportunity sets: Because of the rationing, the consumer loses part of the original opportunity set: the triangle B to the right of the 10 thousand gallons line. The consumer has fewer opportunities because of rationing.

O th

er g

oo ds

p er

m on

th

100

Water, Thousand gallons per month

Budget line

Quota

A B

12

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106 CHAPTER 4 Consumer Choice

We can also show that bundles that lie on indifference curves that cross the budget line (such as I 1, which crosses the constraint at a and c) are less desirable than certain other bundles on the constraint. Only some of the bundles on indifference curve I 1 lie within the opportunity set: Bundles a and c and all the points on I 1 between them, such as d, can be purchased. Because I 1 crosses the budget line, the bundles between a and c on I 1 lie strictly inside the constraint, so bundles in area B of the opportunity set are preferable to these bundles on I 1 and are affordable. By the more-is-better property, Lisa prefers e to d because e has more of both pizza and burritos than d. By transitivity, e is preferred to a, c, and all the other points on I 1—even those, like g, that Lisa can’t afford. Because indifference curve I 1 crosses the budget line, area B contains at least one bundle that is preferred to—lies above and to the right of—at least one bundle on the indifference curve.

Thus, the optimal bundle—the consumer’s optimum—must lie on the budget line and be on an indifference curve that does not cross it. If Lisa is consuming this bundle, she has no incentive to change her behavior by substituting one good for another.

So far, we’ve shown that the optimal bundle must lie on an indifference curve that touches the budget line but does not cross it. This condition can hold in two ways. The first is an interior solution, in which the optimal bundle has positive quantities of both goods and lies between the ends of the budget line. The other possibility, called a corner solution, occurs when the optimal bundle is at one end of the budget line, where the budget line forms a corner with one of the axes.

Interior Solutions. In Figure 4.8, Bundle e on indifference curve I 2 is the optimal bundle. It is in the interior of the budget line away from the corners. Lisa prefers consuming a balanced diet, e, of 10 burritos and 30 pizzas, to eating only one type of food or the other.

For the indifference curve I 2 to touch the budget line but not cross it, it must be tangent to the budget line at point e. At the point of tangency, the budget line and the indifference curve have the same slope at the point e where they touch. The slope of the indifference curve, the marginal rate of substitution, measures the rate at which

FIGURE 4.8 Consumer Maximization, Interior Solution

B , B

ur rit

os p

er s

em es

te r

Budget line

10

20

25

5030100

Z, Pizzas per semester

I1 I2 I3

d

fc

e

a

g

A

B

Lisa’s optimal bundle is e (10 burritos and 30 pizzas) on indifference curve I2. Indifference curve I2 is tangent to her budget line at e. Bundle e is the bundle on the highest indifference curve (highest utility) that she can afford. Any bundle that is preferred to e (such as points on indifference curve I3) lies outside the opportunity set, so she cannot afford them. Bundles inside the opportunity set, such as d, are less desirable than e because they lie on lower indifference curves.

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1074.4 Constrained Consumer Choice

Lisa is willing to trade burritos for pizza: MRS = -MUZ>MUB, Equation 4.1. The slope of the budget line, the marginal rate of transformation, measures the rate at which Lisa can trade burritos for pizza in the market: MRT = -pZ>pB, Equation 4.5. Thus, Lisa’s utility is maximized at the bundle where the rate at which she is willing to trade burritos for pizza equals the rate at which she can trade:

MRS = - MUZ MUB

= - pZ pB

= MRT. (4.6)

(Appendix 4B uses calculus to derive Equation 4.6.) Rearranging terms, this condition is equivalent to

MUZ

pZ =

MUB pB

. (4.7)

Equation 4.7 says that the marginal utility of pizza divided by the price of a pizza (the amount of extra utility from pizza per dollar spent on pizza), MUZ>pZ, equals the marginal utility of burritos divided by the price of a burrito, MUB>pB. Thus, Lisa maximizes her utility if the last dollar she spends on pizza gets her as much extra utility as the last dollar she spends on burritos. If the last dollar spent on pizza gave Lisa more extra utility than the last dollar spent on burritos, Lisa could increase her happiness by spending more on pizza and less on burritos.

Q&A 4.3 Nate’s utility function over raspberry jelly, J, and peanut butter, N, is U = JN. Nate’s marginal utility from jelly is MUJ = N, and his marginal utility from pea- nut butter is MUN = J.4 The raspberry jelly Nate buys is $5 per jar and peanut butter is $10 per jar. Nate has a budget of $100 to allocate to these two items. If Nate maximizes his utility, how much of each good will he consume?

Answer 1. Derive Nate’s budget line by setting his expenditure equal to his available budget.

The expenditure on each item is its price times the amount consumed, so Nate’s budget, 100, equals the sum of the expenditures on these two goods: 100 = 5J + 10N.

2. Use Equation 4.7 to find the relationship between N and J. Equation 4.7 states that Nate maximizes his utility if he equalizes his marginal utility per dollar across jelly and peanut butter: MUJ>5 = MUN>10. That is, N>5 = J>10 or N = J>2.

3. Substitute this utility-maximizing condition into the budget equation to determine J and N. Substituting this optimality condition into the budget constraint, we learn that 100 = 5J + 10N = 5J + 10(J>2) = 10J. Solving this expression for J, we find that J = 10.

4. Substitute the solution for J into the budget line to solve for N. Substituting J = 10 into the budget constraint, we learn that 100 = 5J + 10N = 50 + 10N, or 50 = 10N, or N = 5. Thus, Nate’s utility-maximizing bundle is J = 10 and N = 5.

4The marginal utility with respect to J, MUJ, is 0U>0J = 0(JN )>0J = N. Similarly, MUN = 0( JN )>0N = J.

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108 CHAPTER 4 Consumer Choice

Corner Solutions. Some consumers choose to buy only one of the two goods: a corner solution. They so prefer one good to another that they only purchase the preferred good.

Spenser’s indifference curves in Figure 4.9 are flatter than Lisa’s in Figure 4.8. That is, he is more willing than Lisa to trade pizza for an extra burrito. Spenser’s optimal Bundle e, where he buys 25 burritos and no pizza, lies on an indifference curve that touches the budget line only once, at the upper-left corner. It is on the highest indif- ference curve that touches the budget line.

Mini-Case Are you reading this text electronically? E-books are appearing everywhere in the English-speaking world. Thanks to the popularity of the Kindle, iPad, and other e-book readers, e-books accounted for about 11.5% of the U.K. market and close to 20% of the U.S. market, but only about 4.5% of the German market in 2017.

Why are e-books more successful in the United States than in Germany? Jürgen Harth of the German Publishers and Booksellers Association attributed the difference to tastes or what he called a “cultural issue.” More than others, Germans love printed books. After all, a German invented printing. As Harth said, “On just about every corner there’s a bookshop. That’s the big difference between Germany and the United States.”

An alternative explanation concerns government regulations and taxes that affect prices in Germany. Even if Germans and Americans had the same tastes, Americans would be more likely to buy e-books because they are less expensive than printed books in the United States. However, e-books are more expensive than printed books in Germany. Unlike in the United States, where publishers and booksellers are free to set prices, Germany regulates book prices. To pro- tect small booksellers, Germany’s fixed-price system requires all booksellers to charge the same price for new printed books and for e-books. However, the tax on e-books is higher than on print books, raising the after-tax price of an e-book relative to that of a print book. Is a difference in taste the only reason why U.S. consumers buy relatively more e-books than Germans do, or can different rela- tive prices in the two countries explain this phenomenon?

Why Americans Buy More E-Books Than Do Germans

FIGURE 4.9 Consumer Maximization, Corner Solution

B , B

ur rit

os p

er s

em es

te r

Budget line

25

50

Z, Pizzas per semester

I1

I2

I3

e

Spenser’s indifference curves are flatter than Lisa’s indifference curves in Figure 4.8. That is, he is willing to give up more pizzas for one more burrito than is Lisa. Spenser’s optimal bundle occurs at a corner of the opportunity set at Bundle e: 25 burritos and 0 pizzas.

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1094.4 Constrained Consumer Choice

Promotions Managers often use promotions to induce consumers to purchase more units. Two of the most frequently used promotions are buy one, get one free (BOGO) and buy one, get the second one at half-price. Such deals create kinks in the consumer’s budget line. Consequently, consumers’ responses to such offers depend on their tastes (the shape of their indifference curves).

Buy One, Get One Free. In a BOGO promotion, a customer gets a free unit of the product after buying one unit (or some other number of units) at the regular price. For example, a supermarket might offer a fifth fruit drink for free if the cus- tomer buys four at the regular price. Promotions of this type are often used for items like CDs, restaurant meals, movie tickets, and other relatively inexpensive consumer products. A 2018 search of Google for “buy one get one free” found 285 million Web sites. Remarkably, even a realty company, Michael Crews Development, made a BOGO offer: If you bought a home at $1.6 million or more, you would get a second $400,000 house at no additional charge.

Q&A 4.4 Must we appeal to variations in taste to explain why Germans and Americans read different types of books, or can taxes and price disparities account for this difference? Suppose that Max, a German, and Bob, an American, are avid readers with identical incomes and tastes. Both are indifferent between reading a novel in a traditional printed book or on an e-reader. The after-tax price of e-books in Germany is higher than that of print books, but e-books cost less than print books in the United States. Use an indifference-curve/budget-line analysis to explain why Bob is more likely to buy e-books than is Max.

Answer 1. Describe their indifference curves. Both Max

and Bob view e-books and printed books as perfect substitutes, so their indifference curves have a slope of -1. One such indif- ference curve is I in the figure.

2. Describe the slopes of their budget line. With printed books on the vertical axis, Max faces a budget line, LM, that is relatively steep—steeper than his indifference curve—because the German taxes make e-books relatively expensive. Bob has a budget line that is flatter than his indiffer- ence curve.

3. Use an indifference curve and a budget line to show why Max and Bob make different choices. As the figure shows, Bob maximizes his utility by spending his entire book budget on e-books. He chooses the Bundle eB, where his indifference curve I hits his budget line LB on the e-book axis. In contrast, Max spends his entire book budget on printed books, at point eM. If Bob and Max viewed the two types of books as imperfect substitutes and

had the usual convex indifference curves, they would each buy a mix of e-books and printed books. However, because of the relatively lower price of e-books in the United States, Bob would buy relatively more e-books.

P rin

te d

bo ok

s pe

r ye

ar

E-books per year

l

eM, Max’s optimal bundle

eB, Bob’s optimal bundleL M

LB

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110 CHAPTER 4 Consumer Choice

In 2018, the Four Seasons Resort in the Baha- mas offered one free night at its five-star hotel to customers who paid for three nights at the normal rate. The effect of such promotions on purchas- ing behavior can be illustrated using indifference curves and budget lines. Before the promotion was announced, Angela and Betty were sepa- rately planning to stay at the hotel for two nights each this month. Each has the same income and allocates the same budget to her vacation.

Figure 4.10 shows that Angela takes advantage of the promotion and Betty does not because their tastes differ. Both panels of the figure show the same budget lines. The horizontal axis shows the nights spent at the hotel per month, and the ver-

tical axis measures all other goods per month. Their initial budget line before the promotion, L1, is a standard downward-sloping line, where the slope depends on the ratio of the full price of a hotel room to the price of other goods.

The new BOGO budget line, L2, is the same as the initial budget line for stays of fewer than three nights. However, if Angela or Betty pays for three nights, she gets an extra night for free. That is, she can get a fourth night with no reduction in her consumption of other goods. Therefore, her new budget line has a horizontal segment one night wide starting at three nights. For additional nights (beyond four) she would pay the regular price, so L2 resumes its same downward slope for stays exceeding four nights.

FIGURE 4.10 BOGO Promotion

Angela and Betty are separately deciding how many nights to stay at the resort. Without the pro- motion, both Angela and Betty have an initial bud- get line of L1. With the BOGO promotion where if either stays three nights, she gets the fourth night for free, the new budget line is L2. (a) Without the promotion, Angela’s indifference curve I1 is tangent to L1 at point x, so she chooses to spend two nights at the resort. With the BOGO promotion, Angela prefers to purchase three nights and get an extra night for free with the promotion

than pay for and stay only two nights: because her indifference curve I1 cuts the new budget line L2, she has a higher indifference curve, I2, that touches L2 at point y, so that she chooses to stay four nights. (b) Without the promotion, Betty chooses to stay two nights at x where her indifference curve I3 is tangent to L1. Because I3 does not cut the new budget line L2, no higher indifference curve can touch L2, so Betty stays only two nights, at x, and does not take advantage of the BOGO promotion.

O th

er g

oo ds

p er

m on

th

Rooms, Nights per month

x

L1 L2, BOGOF

I1

2 3 4

I2

y

O th

er g

oo ds

p er

m on

th

Rooms, Nights per month

x

L1

I3

2 3 4 L2, BOGOF

(a) Angela (b) Betty

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1114.5 Deriving Demand Curves

4.5 Deriving Demand Curves We use consumer theory to show how much the quantity demanded of a good falls as its price rises. An individual chooses an optimal bundle of goods by picking the point on the highest indifference curve that touches the budget line. A change in a price causes the budget line to rotate, so that the consumer chooses a new optimal bundle. By varying one price and holding other prices and income constant, we determine how the quantity demanded changes as the price changes, which is the information we need to draw the demand curve.

We derive a demand curve using the information about tastes from indifference curves. To illustrate how to construct a demand curve, we estimated a set of indif- ference curves between recorded music—primarily tracks or songs purchased from iTunes, Amazon, Rhapsody, or other similar sources—and live music (at clubs, con- certs, and so forth) using data for British young people (ages 14–24). Of these young people, university students spend about £18 per quarter on live music and £12 per quarter on music tracks, for a total budget of £30 for music.5

5Data on total expenditures are from The Student Experience Report, 2007, www.unitestudents.com, while budget allocations between live and recorded music are from the 2008 survey into the Music Experience and Behaviour in Young People produced by the British Music Rights and the University of Hertfordshire.

In panel a, Angela’s indifference curve I 1 is tangent to L1 at point x, which is located at two nights on the horizontal axis. Because I 1 is the highest indifference curve that touches her pre-promotion budget line, she chooses to spend two nights at the resort. However, her indifference curve I 1 cuts the new budget line L2, so she can do better. A higher indifference curve, I 2, touches L2 at point y, where she chooses to stay four nights. That is, Angela would prefer to purchase three nights and get an extra night for free with the promotion than pay for and stay only two nights.

Betty’s indifference curves in panel b differ from Angela’s. Again, we assume that initially Betty chooses to stay two nights at Bundle x, where her indifference curve I 3 is tangent to L1. Because I 3 is flatter than Angela’s I 1 in panel a (Betty is willing to give up fewer other goods for another night at the resort than is Angela), I 3 does not cut the new budget line L2. Thus, no higher indifference curve can touch L2, so Betty stays only two nights, at x, and does not take advantage of the promotion.

When deciding whether to use a BOGO promotion, a manager should compare the benefit to the cost. For example, offering such a promotion is more likely to raise the hotel’s profit if it has excess capacity, so that the cost of providing a room for an extra night’s stay is very low. The manager also needs to deter- mine whether it has more customers like Angela or more like Betty. To design an effective promotion, a manager should use experiments to learn about custom- ers’ preferences. For example, a manager could offer each promotion for a short period and keep track of how many customers respond to each promotion, how many nights they choose to stay, and by how much the promotion increases the firm’s profit.

Designing Promotions

Managerial Implication

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112 CHAPTER 4 Consumer Choice

Panel a of Figure 4.11 shows three of the estimated indifference curves for a typical British university student, whom we call Jack.6 These indifference curves are convex to the origin: Jack views live music and tracks as imperfect substitutes. We can con- struct Jack’s demand curve for music tracks by holding his budget, his tastes, and the price of live music constant at their initial levels and varying the price of tracks.

6The estimated utility function is U = M0.6T0.4, where M is the units of live music and T is the number of tracks.

FIGURE 4.11 Deriving an Individual’s Demand Curve

If the price of recorded songs—tracks of music—rises, holding constant the price of live music (at £1 per unit), the music budget (at £30 per quarter), and tastes, the typical British university stu- dent, Jack, buys fewer tracks. This figure is based on our estimate of the typical student’s utility function.

(a) On budget line L3, the price of a track is £0.5. Jack’s indifference curve I3 is tangent to L3 at Bundle e3, where he buys 18 units of live music and 24 tracks per quarter. If the price of a track doubles to £1, the new budget line is L2, and Jack reduces the number of tracks he demands to 12 per quarter. (b) By varying the price of a track, we trace out Jack’s demand curve, D1. The tracks price-quantity combinations E1, E2, and E3 on the demand curve for tracks in panel b correspond to optimal Bundles e1, e2, and e3 in panel a.

6 12 24

18

6

E1

E2

12 24

D1, Demand for tracks

E3

2

1

0.5

L2 (pT = £1) L3 (pT = £0.5)L1 (pT = £2)

e1 e2 e3

T, Tracks per quarter

T, Tracks per quarter

p T , £

p er

tr ac

k M

, L iv

e m

us ic

p er

q ua

rt er

I 3

I 2

I 1

6030

30

(a)

(b)

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1134.6 Behavioral Economics

The vertical axis in panel a measures the amount of live music that Jack consumes each quarter, and the horizontal axis measures the number of tracks he buys per quarter. Jack spends Y = £30 per year on live music and tracks. We set the price of live music, pm, at £1 by choosing the units appropriately (so the units do not cor- respond to a concert or visit to a club). The price of tracks, pt, is £0.5 per track. Jack can buy 30 (= Y>pm = 30>1) units of live music if he spends all his money on that, or up to 60 (= Y>pt = 30>0.5) tracks if he buys only tracks. The slope of his budget line, L3, is -pt>pm = -0.5>1 = -0.5. Given budget line L3, Jack consumes 18 units of live music per quarter and 24 tracks per quarter, Bundle e3, which is determined by the tangency of indifference curve I 3 and budget line L3.

Now suppose that the price of tracks doubles to £1 per track while the price of live music and Jack’s budget remain constant. If he were to spend all his money on live music, he could buy the same 30 units as before, so the intercept on the verti- cal axis of L2 is the same as for L3. However, if he were to spend all his money on tracks, he could buy only half as many as before (30 instead of 60 tracks), so L2 hits the horizontal axis half as far from the origin as L3. As a result, L2 has twice as steep a slope, -pt>pm = -1>1 = -1, as does L3. The slope is steeper because the price of tracks has risen relative to the price of live music.

Because tracks are now relatively more expensive, Jack buys relatively fewer of them. He chooses Bundle e2, where his indifference curve I 2 is tangent to L2. He now buys only 12 tracks per quarter (compared to 24 at e3).7

If the price of a track doubles again to £2, Jack consumes Bundle e1, 6 tracks per quarter. The higher the price of tracks, the less happy Jack is because he consumes less music on the same budget: he is on indifference curve I 1, which is lower than I 2 or I 3.

We can use the information in panel a to draw Jack’s demand curve for tracks, D1, in panel b. Corresponding to each possible price of a track on the vertical axis of panel b, we record on the horizontal axis the number of tracks that Jack chooses in panel a.

Points E1, E2, and E3 on the demand curve in panel b correspond to Bundles e1, e2, and e3 in panel a. Both e1 and E1 show that when the price of a track is £2, Jack demands 6 tracks per quarter. When the price falls to £1, Jack increases his consump- tion to 12 tracks, point E2. The demand curve, D1, is downward sloping, as predicted by the Law of Demand.

4.6 Behavioral Economics So far, we have assumed that consumers are rational, maximizing individuals. A rapidly growing field of study, behavioral economics, adds insights from psychol- ogy and empirical research on human cognitive and emotional biases to the rational economic model to better predict economic decision making.8 We discuss three appli- cations of behavioral economics in this section: tests of transitivity, the endowment effect, and salience. Later in this book, we examine the psychology of decision making in networks (Chapter 9), strategic interactions (Chapter 13), and under uncertainty (Chapter 14).

7The figure shows that he buys the same amount of live music, 18 units, when the price of tracks rises. This property is due to the particular utility function (a Cobb-Douglas) that we use in this example. With most other utility functions, the quantity of live music would change. 8The introductory chapter of Camerer, Lowenstein, and Rabin (2004) and DellaVigna (2009) provide excellent surveys of the major papers in this field and heavily influenced the following discussion.

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Tests of Transitivity In our presentation of the basic consumer choice model at the beginning of this chap- ter, we assumed that consumers make transitive choices. But do consumers actually make transitive choices?

A number of studies of both humans and animals show that preferences usually are transitive and hence consistent with our assumption. However, in some situa- tions, people do not make transitive choices. Weinstein (1968) used an experiment to determine how frequently people fail to respond transitively. In the experiment, the subjects were given choices between 10 goods, offered in pairs, in every possible combination, and were told that each good had a value of $3. (None of the subjects knew the purpose of the experiment.) Weinstein found that 93.5% of the responses of adults—people over 18 years old—were transitive. However, only 79.2% of children aged 9–12 gave transitive responses.

Based on these results, one might conclude that it is appropriate to assume that adults exhibit transitivity for most economic decisions. However, one might modify the theory when applying it to children or when novel goods are introduced.

Economists normally argue that rational people should be allowed to make their own consumption choices so as to maximize their well-being. However, some might conclude that children’s lack of transitivity or rationality provides one justification for political and economic restrictions and protections placed on young people.

Endowment Effects Experiments show that people have a tendency to stick with the bundle of goods they currently possess. One important reason for this tendency is called the endow- ment effect, which occurs when people place a higher value on a good if they own it than if they are considering buying it.

We normally assume that an individual can buy or sell goods at the market price. Rather than rely on income to buy some mix of two goods, an individual who was endowed with several units of one good could sell some and use that money to buy units of another good.

We assume that a consumer’s endowment does not affect the indifference curve map. In a classic buying and selling experiment, Kahneman, Knetsch, and Thaler (1990) challenged this assumption. In an undergraduate law and economics class at Cornell University, 44 students were divided randomly into two groups. Members of one group were given coffee mugs that were available at the student store for $6. Those students endowed with a mug were told they could sell it and were asked the minimum price they would accept for the mug. The subjects in the other group, who did not receive a mug, were asked how much they would pay to buy the mug. Given the standard assumptions of our model and that the subjects were chosen randomly, we would expect no difference between the selling and buying prices. However, the median selling price was $5.75 and the median buying price was $2.25. Sellers wanted more than twice what buyers would pay. This type of experiment has been repeated many times with many variations and consistently demonstrates an endowment effect.

However, some economists believe that this result has to do with the experimental design. Plott and Zeiler (2005) argued that if we take adequate care to train the sub- jects in the procedures and make sure they understand them, we no longer find this result. List (2003) examined the actual behavior of sports memorabilia collectors and found that amateurs who do not trade frequently exhibited an endowment effect, unlike professionals or amateurs who traded a lot. Thus, experience may reduce or

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The following Mini-Case shows that this belief is not always true.

even eliminate the endowment effect, and people who buy goods for resale may be less likely to become attached to these goods.

Others accept the results and have considered how to modify the standard model to reflect the endowment effect (Knetsch, 1992). One implication of these experimen- tal results is that people will trade away from their endowments only if prices change substantially. This resistance to trade could be captured with a kink in the indifference curve at the endowment bundle. (We showed indifference curves with 90° kink in panel b of Figure 4.4.) Such indifference curves could have an angle greater than 90°, and an indifference curve could be curved at points other than at the kink. If the indif- ference curve has a kink, the consumer does not shift to a new bundle in response to a small price change, but may shift if the price change is large.

One practical implication of the endowment effect is that consumers’ response may differ depending on how a choice is posed. However, that’s not the common belief.

Salience We often use economic theories based on the assumption that decision makers are aware of all relevant information. In this chapter, we assume that consumers know their own income, relevant prices, and their own tastes, and hence they make informed decisions.

Behavioral economists and psychologists have demonstrated that people are more likely to consider information if it is presented in a way that grabs their attention or if it takes relatively little thought or calculation to understand. Economists use the term salience, in the sense of striking or obvious, to describe this idea. For example, tax salience is awareness of a tax.

If a store’s posted price includes the sales tax, consumers observe a change in the price as the tax rises. In contrast, if a store posts the pre-tax price and collects the tax at the cash register, consumers are less likely to note that the post-tax price has increased when the tax rate increases. Chetty et al. (2007) compared consumers’ response to a rise in an ad valorem sales tax on beer (called an excise tax) that is

Common Confusion People respond the same way to equivalent questions.

Mini-Case Traditionally, electricity customers in Sacramento, California, paid a single price for each kilowatt of electricity all day. However, the cost of producing electricity is greatest when daily demand peaks during certain hours. Thus, the power company considered charging a higher than traditional price during those hours and a lower rate during the rest of the day. By doing so, they hoped to encourage households to run dishwashers and other appliances during low-production-cost periods.

To find out whether customers would voluntarily agree to switch to time- based pricing, the electric utility ran an experiment. One group of electricity customers was invited to sign up for (opt in) a new time-based pricing structure. Another group was told that they would be put into the new pricing program unless they opt out. Fowlie et al. (2017) reported that only 20% of the first group chose to switch to time-based pricing. However, 90% of the second group stuck with the default choice of time-based pricing. This difference in response dem- onstrates the power of the endowment effect.

How You Ask the Question Matters

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included in the posted price to an increase in a general ad valorem sales tax, which is collected at the cash register but not reflected in the posted price. An increase in either tax has the same effect on the final price, so an increase in either tax should have the same effect on purchases if consumers pay attention to both taxes.9 How- ever, a 10% increase in the posted price, which includes the excise tax, reduces beer consumption by 9%, whereas a 10% increase in the price due to a rise in the sales tax that is not posted reduces consumption by only 2%. Chetty et al. also conducted an experiment in which they posted tax-inclusive prices for 750 products in a grocery store and found that demand for these products fell by about 8% relative to control products in that store and comparable products at nearby stores.

Why might a tax have no effect on consumer behavior? One explanation is consumer ignorance. For example, Furnham (2005) found that even at the age of 14 or 15, young people do not fully understand the nature and purpose of taxes. Similarly, unless the store posts the tax-inclusive price, many consumers ignore or forget about taxes.

An alternative explanation for ignoring taxes is bounded rationality: People have a limited capacity to anticipate, solve complex problems, or enumerate all options. To avoid having to perform hundreds of calculations when making purchasing deci- sions at a grocery store, many people choose not to calculate the tax-inclusive price. However, when post-tax price information is readily available to them without the need to do calculations, consumers make use of it. One way to modify the standard model to incorporate bounded rationality is to assume that people incur a cost in making calculations—such as the time taken or the mental strain—and that deciding whether to incur this cost is part of their rational decision-making process.

People incur this calculation cost only if they think the gain from a better choice of goods exceeds the cost. More people pay attention to a tax when the tax rate is high or when their demand for the good is elastic (they are sensitive to price). Similarly, some people are more likely to pay attention to taxes when making large, one-time pur- chases—such as for a computer or car—rather than small, repeated purchases—such as for a bar of soap. Thus, inattention due to bounded rationality is rational: Consum- ers are doing the best they can given their limited calculation abilities.

9The final price consumers pay is p* = p(1 + β)(1 + α), where p is the pre-tax price, α is the general sales tax, and β is the excise tax on beer.

Today’s consumers often feel overwhelmed by choices. Cable TV subscribers must select from many possible channels, most of which they have never seen. Because consumers have bounded rationality, most dislike considering all the possibilities and making decisions. To avoid making decisions, many consum- ers do not buy these services and goods even though they would greatly benefit from such purchases.

To avoid this problem, good managers make decision making easier for con- sumers. For example, they may offer default bundles so that consumers don’t have to make a large number of difficult decisions. Cable TV companies package groups of channels by content. Instead of choosing between possibly hundreds of individual channels, a consumer can opt for the sports package or the movie package. Rather than thinking through each option, the customer can make a much easier decision, such as “I like sports” or “I like movies,” and is more likely to make a purchase.

Simplifying Consumer Choices

Managerial Implication

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Paying Employees to Relocate

Managerial Solut ion

We conclude our analysis of consumer theory by returning to the managerial problem posed in the introduction of this chapter: How can a firm’s human resources manager use consumer theory to optimally compensate employees who are transferred to other cities?

Relocation managers use government sources to find information about the cost of living in various cities around the world (U.S. Defense Department, U.S. Government Services Administration, U.S. Office of Personnel Management, U.S. State Department), publications (Money Magazine, Monthly Labor Review), web- sites (bestplaces.net, citymayors.com, homefair.com, moving.com), and data and human resources consulting firms (such as EIU Data Services, Mercer Con- sulting, and Runzheimer International).10 From this information, managers know that it is more expensive to buy the same bundle of goods in one city than another and that the relative prices of goods differ across cities.

As we noted in the Managerial Problem, most firms say they pay their employ- ees enough in their new city to buy the same bundle of goods as in their original city. We want to investigate whether such firms are paying employees more than they have to for them to relocate. We illustrate our reasoning with an example using an employee who cares about only two goods.

Alexx’s firm wants to transfer him from its Seattle office to its London office, where he will face a different cost of living with varying prices for goods and services. Alexx, who doesn’t care whether he lives in Seattle or London, spends his money on housing and entertainment. Like most firms, his employer will pay him an after-tax salary in British pounds such that he can buy the same bundle of goods in London that he is currently buying in Seattle. Will Alexx benefit by mov- ing to London? Could his employer have induced him to relocate for less money?

Alexx’s optimal bundle, s, in Seattle is deter- mined by the tangency of his indifference curve I 1 and his Seattle budget line LS in the figure. It cost 53% more to live in London than in Seattle, on aver- age, in 2011. If the prices of all goods are exactly 53% higher in London than in Seattle, the relative costs of housing and entertainment are the same in both cities. In that case, if his firm raises Alexx’s income by 53%, his budget line does not change and he buys the same bundle, s, and his level of utility is unchanged.

However, relative prices are not the same in both cities. Controlling for quality, housing is relatively more expensive, and entertainment—concerts, the- ater, museums, zoos—is relatively less expensive in London than in Seattle. Thus, if Alexx’s firm adjusts his income so that Alexx can buy the same bundle, s, in London as he did in Seattle, his new budget line in London, LL, must go through s but have a

different slope. Because entertainment is relatively less expensive than housing in London compared to Seattle, if Alexx spends all his money on entertainment,

10An international calculator that compares the cost of living in different cities around the world is available at www.numbeo.com/cost-of-living/.

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he can buy more in London than in Seattle. Similarly, if he spends all his money on housing, he can buy less housing in London than in Seattle. As a result, LL hits the vertical axis at a higher point than the LS line and cuts the LS line at Bundle s.

Alexx’s new optimal bundle, l, is determined by the tangency of I 2 and LL. Thus, because relative prices are different in London and Seattle, Alexx is better off with the transfer after receiving the firm’s 53% higher salary. He was on I 1 and is now on I 2. Alexx could buy his original bundle, s, but chooses to substi- tute toward entertainment, which is relatively inexpensive in London, thereby raising his utility.

Consequently, his firm could have induced him to move with less compensa- tion. If the firm lowers his income, the London budget line he faces will be closer to the origin but will have the same slope as LL. The firm can lower his income until his lower-income London budget line, L*, is tangent to his Seattle indif- ference curve, I 1, at Bundle l*. Alexx still substitutes toward the relatively less expensive entertainment in London, but he is only as well off as he was in Seattle (he remains on the same indifference curve as when he lived in Seattle). Thus, his firm can induce Alexx to transfer to London for less than what it would have to pay so that Alexx could buy his original Seattle consumption bundle in London.

SUMMARY

Rational consumers maximize their utility (well-being) subject to constraints based on their income and the prices of goods.

1. Consumer Preferences. To predict consumers’ responses to changes in constraints, economists use a theory about individuals’ preferences. One way of sum- marizing a consumer’s preferences is with a family of indifference curves. An indifference curve consists of all bundles of goods that give the consumer a particu- lar level of utility. On the basis of observations of con- sumers’ behavior, economists assume that consumers’ preferences have three properties: completeness, tran- sitivity, and more is better (nonsatiation). Given these three assumptions, indifference curves have the follow- ing properties:

●● Consumers get more utility or satisfaction from bundles on indifference curves that are farther from the origin.

●● An indifference curve goes through any given bun- dle.

●● Indifference curves cannot cross.

●● Indifference curves slope downward.

2. Utility. Economists use the term utility to describe the set of numerical values that reflect the relative rank- ings of bundles of goods. By comparing the utility a consumer gets from each of two bundles, we know that the consumer prefers the bundle with the higher utility. The marginal utility, MU, from a good is the

extra utility a person gets from consuming one more unit of that good, holding the consumption of all other goods constant. The rate at which a consumer is will- ing to substitute Good 1 for Good 2, the marginal rate of substitution, MRS, depends on the relative amounts of marginal utility the consumer gets from each of the two goods.

3. The Budget Constraint. The amount of goods consumers can buy at given prices is limited by their income. As a result, the greater a consumer’s income or the lower the prices of goods, the more the consumer can buy. The consumer has a larger opportunity set. The marginal rate of transformation (MRT) shows how much of one good the consumer must give up in trade for one more unit of another good. The MRT depends on the relative prices of the two goods.

4. Constrained Consumer Choice. Each person picks an affordable bundle of goods that maximizes his or her utility. If an individual consumes both Good 1 and Good 2 (an interior solution), the individual’s util- ity is maximized when the following four equivalent conditions hold:

●● The indifference curve for Goods 1 and 2 is tangent to the budget line.

●● The consumer buys the bundle of goods that is on the highest obtainable indifference curve.

●● The consumer’s marginal rate of substitution (the slope of the indifference curve) equals the marginal rate of transformation (the slope of the budget line).

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●● The last dollar spent on Good 1 gives the consumer as much extra utility as the last dollar spent on Good 2.

Sometimes, consumers choose to buy only one of the two goods (corner solutions). The last dollar spent on the good that is purchased gives more extra utility than would spending a dollar on the other good, which the consumer chooses not to buy.

5. Deriving Demand Curves. Individual demand curves can be derived by using the information about preferences contained in a consumer’s indifference curve map. By varying the price of one good while holding other prices and income constant, we find out how the quantity demanded varies as its own price changes, which is the information we need to draw the good’s demand curve. Consumers’ preferences, which

are captured by the indifference curves, determine the shape of the demand curve.

6. Behavioral Economics. Using insights from psy- chology and empirical research on human cognition and emotional biases, economists are starting to modify the rational economic model to better predict economic decision making. Some decision makers, particularly children, fail to make transitive choices in certain cir- cumstances. Some consumers exhibit an endowment effect: They place a higher value on a good if they own it than if they are considering buying it. Consequently, they are less sensitive to price changes and hence less likely to trade than would be predicted by the stand- ard economic model. Consumers are more inclined to take into account information that is readily available to them (salient), while ignoring other information.

QUESTIONS

1. Consumer Preferences 1.1 Give as many reasons as you can why we believe that

economists assume that the more-is-better property holds, and explain how these explanations relate to the results in the Mini-Case “You Can’t Have Too Much Money.”

*1.2 Arthur spends his income on bread and chocolate. He views chocolate as a good but is neutral about bread, in that he doesn’t care if he consumes it or not. Draw his indifference curve map.

1.3 Show that an indifference curve

a. Cannot be thick (cannot have positive thick- ness, rather than being just a line).

b. Cannot bend backward (forming a “hook” at the end).

c. Cannot intersect another indifference curve.

1.4 Which of the following pairs of goods are comple- ments and which are substitutes? Are the goods that are substitutes likely to be perfect substitutes for some or all consumers?

a. An e-book version and audiobook version of the same novel.

b. A smartphone and smartphone apps

c. A bag of dog food and a coffee mug

d. Tide laundry detergent and Cheer laundry detergent

1.5 Give as many reasons as you can why we believe that indifference curves are convex to the origin.

2. Utility *2.1 William eats hot dogs only with mustard and con-

sumes mustard only with hot dogs. He puts one unit of mustard on each hot dog he eats. Show his prefer- ence map. What is his utility function?

2.2 If Porsha views 3 glasses of juice as a perfect substi- tute for one cup of soda and vice versa, what is her marginal rate of substitution between juice and soda?

2.3 Javier consumes large pepperoni pizzas (Z) and boxes of graham crackers (G). Each of his indiffer- ence curves reflects strictly diminishing marginal rates of substitution (MRS). If Z = 4 and G = 4, his MRS between pizzas and boxes of graham crackers

equals -1a= - MUP MUG

b . Will he prefer a bundle with 5 pizzas and 3 boxes of graham crackers to the bun- dle with 4 of each? Why?

*2.4 Sanghoon has a utility function over audiobooks, A, and movie downloads, M, given by U = 2AM. Linh has a utility function given by U = AM. Explain why Sanghoon and Linh have the same ordering over any two bundles and therefore have the same ordinal preferences.

*2.5 Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(a, k) = 3a + 5k. That is, his constant marginal utility for apples is 3 and his constant marginal utility for kumquats is 5.

All exercises are available on MyLab Economics; * = answer at the back of this; = this exercise is available in Excel Grader in MyLab Economics.

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What bundle of apples and kumquats should Andy purchase to maximize his utility? Why?

3. The Budget Constraint 3.1 Yuka consumes mangos and oranges. She is given

four mangos and three oranges. She can buy or sell mangos for $2 each. Similarly, she can buy or sell an orange for $1. If Yuka has no other source of income, draw her budget line and write the equation.

3.2 If the budget line is Y = 500 = pBB + pZZ = 5B + 10Z, what is the marginal rate of transforma- tion, MRT, between B (burritos) and Z (pizza)?

3.3 Change Q&A 4.1 so that Lisa’s budget and the price of pizza double, but the price of burritos remains constant. Show how her budget constraint and opportunity set change. Is Lisa necessarily better off than before these changes? (Hint: What happens to the intercepts of the budget line?)

*3.4 Dale goes to the opera and ice hockey games. Draw  a  budget line for Dale. If the government imposes a 25% income tax on her, what happens to her budget line and opportunity set? (Hint: See Q&A 4.2.)

3.5 Sophia spends all her money on gummy worms and apps for her smartphone. A pound of gummy worms and a smartphone app each cost $2. Sophia’s parents give her an allowance of $80 and 2 pounds of gummy worms each month. Draw her opportu- nity set, assuming that she cannot sell the gummy worms to her friends. How does her opportunity set change if she can sell the gummy worms at the market price of $2?

4. Constrained Consumer Choice 4.1 Linda loves buying shoes and going out to dance.

Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U (S, T) = 2ST, so MUS = 2T and MUT = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing. (Hint: See Q&A 4.3.)

a. What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts.

b. What is Linda’s marginal rate of substitution? Explain.

c. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line.

*4.2 Nadia likes spare ribs, R, and fried chicken, C. Her utility function is U = 10R2C. Her marginal utilities are MUR = 20RC and MUC = 10R2. Her weekly

income is $90, which she spends on only ribs and chicken.

a. If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal consumption bun- dle? Show her budget line, indifference curve, and optimal bundle, e1, in a diagram.

b. Suppose the price of chicken doubles to $10. How does her optimal consumption of chicken and ribs change? Show her new budget line and optimal bundle, e2, in your diagram.

4.3 Lucas chooses between water and all other goods. If he spends all his money on water, he can buy 15 thousand gallons per week. At current prices, his optimal bundle is e1, where he buys both types of goods. Show e1 in a diagram. During a drought, the government limits the number of gallons per week that he may purchase to 10 thousand. Using diagrams, discuss under which conditions his new optimal bundle, e2, will be the same as e1. If the two bundles differ, can you state where e2 must be located relative to e1?

*4.4 Gasoline is typically less expensive in the United States than across the border in Canada, but now suppose that the U.S. gasoline price rises above that in Canada due to a change in taxes. How would the gasoline-purchasing behavior of a person who lives equally close to gas stations in both countries change? Answer using an indifference-curve and budget-line diagram.

4.5 Suppose we change Q&A 4.4 so that Max and Bob have indifference curves that are convex to the ori- gin. Use a figure to discuss how the different slopes of their budget lines affect the choices they make. Can you make any unambiguous statements about how many total books each can buy? Can you make an unambiguous statement if you know that Bob’s budget line goes through Max’s optimal bundle?

4.6 Ralph usually buys one pizza and two colas from the local pizzeria. The pizzeria announces a special: All pizzas after the first one are half-price. Show the original and new budget lines. What can you say about the bundle Ralph will choose when faced with the new constraint?

4.7 Until 2012, California, Texas, and Pennsylvania required firms to collect sales taxes for online sales if the chain had a physical presence (a “brick” store as opposed to a “click” store) in those states. Thus, those states collected taxes on Best Buy’s online sales, because it had stores in each of those states, but they did not collect taxes from Amazon.com because it did not have physical locations in those states. Starting in 2012, Amazon had to pay taxes in these states. After the tax was imposed on Amazon,

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Best Buy had a 4% to 6% increase in its online sales in those states relative to the rest of the chain (www .bizjournals.com/twincities/news/2013/01/11/ best-buys-online-sales-up-in-states.html). Use an indifference-curve/budget-line diagram to show why Best Buy’s sales rose after taxes were imposed on Amazon. (Hint: Start by drawing a typical con- sumer’s indifference curve between buying a good from Amazon or from Best Buy.)

4.8 The local swimming pool charges nonmembers $10 per visit. If you join the pool, you can swim for $5 per visit but you have to pay an annual fee of F. Use an indifference-curve diagram to find the value of F such that you are indifferent between joining and not joining. Suppose that the pool charged you exactly that value of F. Would you go to the pool more or fewer times than if you did not join? For simplicity, assume that the price of all other goods is $1.

4.9 Based on panel a in Figure 4.10, show that Angela would accept the BOGO promotion or the half-price promotion. Show that she may choose to stay either three or four nights with the half-price promotion, depending on the exact shape of her indifference curves.

5. Deriving Demand Curves 5.1 Some of the largest import tariffs (taxes on only

imported goods) are on shoes. Strangely, the tariff is higher on cheaper shoes. The highest U.S. tariff, 67%, is on a pair of $3 canvas sneakers, while the tariff on $12 sneakers is 37%, and that on $300 Italian leather imports is 0%. (Adam Davidson, “U.S. Tariffs on Shoes Favor Well-Heeled Buyers,” National Pub- lic Radio, June 12, 2007, www.npr.org/ templates/ story/story.php?storyId=10991519.) Laura buys either inexpensive canvas sneakers ($3 before the tariff) or more expensive gym shoes ($12 before the tariff) for her many children. Use an indifference curve and budget line figure to show how imposing these unequal tariffs affects the bundle of shoes that she buys compared to what she would have bought in the absence of tariffs. Can you confidently predict whether she’ll buy relatively more expensive gym shoes after the tariff? Why or why not?

5.2 Draw diagrams similar to Figure 4.11 but with dif- ferent shape indifference curves to show that as the price of tracks rises, the amount of live music Jack will buy may rise or fall.

5.3 Derive and plot Olivia’s demand curve for pie if she eats pie only à la mode and does not eat either pie or ice cream alone (pie and ice cream are complements).

5.4 At large employers, 48% of employees earning between $10,000 and $24,999 a year participated in

a voluntary retirement savings program, compared to 91% who earned more than $100,000 (www. towerswatson.com/). We can view savings as a good. In a figure, plot savings versus all other goods. Show why people might be more likely to “buy” some savings (put money in a retirement account) as their incomes rise.

5.5 Ajay and Florencia each have a budget of $80 per month to spend on downloaded music tracks and live concerts. At the initial prices, Ajay consumes both goods but Florencia buys only downloaded music and does not go to live concerts. Now the price of live con- certs falls. Use figures to show that Ajay’s utility must increase and that Florencia’s utility may increase or stay the same but cannot fall. (Hint: Look at Figure 4.9.)

6. Behavioral Economics *6.1 Northwestern University neuroscientist Moran Cerf

has a simple approach to ordering food at restaurants. Whenever he goes out, he looks at the restaurant’s list of specials and always picks the second item on the list (www.businessinsider.com/neuroscientist -decision-making-hack-restaurants-2017-7). Show that this approach can lead to choices that are not transitive if a restaurant varies the ordering of menu items from time to time.

6.2 Illustrate the logic of the endowment effect using a kinked indifference curve. Let the angle be greater than 90°. Suppose that the prices change, so the slope of the budget line through the endowment changes. Use the diagram to explain why an individual whose endow- ment point is at the kink will trade from the endow- ment point only if the price change is substantial.

*6.3 Why would a consumer’s demand for a product change when the product price is quoted inclusive of taxes rather than before tax? Do you think fewer people would apply for a job if the salary were quoted after deducting income tax rather than in pre-tax form? Explain briefly.

7. Managerial Problem 7.1 In the Managerial Problem, suppose that entertain-

ment is relatively more expensive in London than in Seattle so that the LL budget line cuts the LS budget line from below rather than from above, as in the fig- ure in the Managerial Solution. Show that the con- clusion that Alexx is better off after his move if his new income allows him to buy bundle s still holds. Explain the logic behind the following statement: “The analysis holds as long as the relative prices dif- fer in the two cities. Whether both prices, one price, or neither price in London is higher than in Seattle is irrelevant to the analysis.”

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122 CHAPTER 4 Consumer Choice

8. MyLab Economics Spreadsheet Exercises11

8.1 Lucy’s company has just promoted her to a manage- rial position and given her a new office. She is very fond of small Persian carpets and Native American paintings and wants to get some carpets and paint- ings for her office. Her utility function for carpets (x) and paintings (y) is given by

U(x, y) = 2xy. Using Excel’s charting tool, draw an indifference curve for U = 4 and another one for U = 6, where both indifference curves contain 1, 2, 4, and 8 carpets on a graph, with carpets on the horizontal axis and paintings on the vertical axis.

8.2 As described in Exercise 8.1, Lucy wants carpets and paintings for her office. Her company has given her a budget of $7,200 for this purpose. Persian carpets of the size that she wants can be purchased for $900 each and paintings from a local Native American artist cost $400 each.

a. Using Excel’s charting tool, draw Lucy’s budget constraint if her budget is $5,000. Use 0, 1, 2, 3, 4, and 5 carpets as possible quantities. Put carpets on the horizontal axis and paintings on the vertical axis.

b. Combining the information in the previous exercise with this exercise, use Excel to illus- trate Lucy’s utility-maximizing solution given

11The spreadsheet exercises in this chapter are based largely on the work of Satyajit Ghosh in cooperation with the authors. The answers are available on MyLab Economics.

that her budget is $5,000, the price of a carpet is $1,000, and the price of a painting is $500.

8.3 Sam’s utility function over iced coffee, C, and tacos, T, is U = min (C, T), where min denotes the minimum value. For example, if C = 2 and T = 3, U = min (2, 3) = 2. Sam spends his entire budget of $12 on coffee and tacos.

a. Which of the panels in Figure 4.4 has indif- ference curves with the same shape as Sam’s indifference curves over iced coffee and tacos? Explain.

b. In Sam’s favorite restaurant, Taco Corner, the price of iced coffee is $2 per cup, and the price of a taco is $1. Using Excel, create a column titled C and enter the values 1, 2, . . . , 6. Those numbers represent different possible numbers of cups of iced coffee Sam might purchase. For each of those values, calculate the number of tacos that Sam can buy if he spends the rest of his $12 budget on tacos. Calculate the resulting utility level for each consumption bundle and determine the combination of iced coffee and tacos that maximizes Sam’s utility. (Hint: Use the min function in Excel.)

c. Taco Corner reduces the price of iced coffee to $1.50 and raises the price of tacos to $1.50. Using Excel, re-do the calculations in part b and determine Sam’s utility-maximizing consump- tion bundle now.

APPENDIX 4A The Marginal Rate of Substitution

We can derive Equation 4.1 using calculus. Lisa’s utility function is U(B, Z). Along an indiffer- ence curve, we hold utility fixed at U = U(B, Z). If we increase Z, we would have to lower B to keep her on the same indifference curve. Let B(Z) be the implicit function that shows how much B it takes to keep Lisa’s utility at U given that she consumes Z. Thus, we can write her indifference curve as U = U(B(Z), Z), which is solely a function of Z.

We want to know how much B must change if we increase Z, dB/dZ, given that we require her utility to remain constant by staying on the original indifference curve. To answer this question, we differentiate U = U(B(Z), Z) with respect to Z and set this derivative to zero because U is constant along an indifference curve:

dU dZ

= 0 = 0U(B(Z), Z)

0B dB dZ

+ 0U(B(Z), Z)

0Z = MUB

dB dZ

+ MUZ.

The partial derivatives show how utility changes as we change either B or Z, holding the other constant. We know that dU>dZ = 0 because U is a constant along the indifference curve. Rearranging terms in this expression, we obtain Equation 4.1 (where dB/dZ replaces ∆B>∆Z): MRS = dB>dZ = -MUZ>MUB.

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123Appendix 4B The Consumer Optimum

APPENDIX 4B The Consumer Optimum

We can derive Equation 4.6 using calculus. Lisa’s objective is to maximize her utility, U(B, Z), subject to (s.t.) a budget constraint:

max B, Z

U(B, Z)

s.t. Y = pBB + pZZ, (4B.1)

where B is the number of burritos she buys at price pB, Z is the number of pizzas she buys at price pZ, Y is her income, and Y = pBB + pZZ is her budget constraint. This mathematical statement of her problem shows that her choice variables are B and Z, which appear under the “max” term in the equation.

Because we cannot directly solve a constrained maximization problem, we want to con- vert Equation 4B.1 into an unconstrained problem by substituting the budget constraint into the utility function. Using algebra, we rearrange her budget constraint so that B is a function of Z: B(Z) = (Y - pZZ)>pB. Substituting this expression for B(Z) into the utility function, we rewrite her problem as

max Z

U(B(Z), Z) = U aY - pzZ pB

, Zb . (4B.2)

Because Equation 4B.2 is unconstrained, we can use standard maximization techniques to solve it. We derive the first-order condition by setting the derivative of Lisa’s utility function with respect to Z equal to zero:

dU dZ

= 0U 0B

dB dZ

+ 0U 0Z

= a- pZ pB

b 0U 0B

+ 0U 0Z

= a- pZ pB

bMUB + MUZ = 0, (4B.3)

where MUB(B, Z) = 0U(B, Z)>0B. Rearranging the terms in Equation 4B.3, we obtain the condi- tion in Equation 4.6 that her utility is maximized if the slope of the indifference curve, MRS, equals the slope of the budget line, MRT:

MRS = - MUZ MUB

= - pZ pB

= MRT. (4B.4)

If the utility function is Cobb-Douglas, the MRS is given by Equation 4A.1, so Equation 4B.4 becomes

MRS = - MUZ MUB

= - (1 - a)

a B Z

= - pZ pB

,

or

(1 - a)pBB = apZZ. (4B.5)

Rearranging the budget constraint, pZZ = Y - pBB. Substituting Y - pBB for pZZ in Equa- tion 4B.5, we obtain (1 - a)pBB = a(Y - pBB). Thus, B = aY>pB. Similarly, by substituting pBB = Y - pZZ in Equation 4B.5, we find that Z = (1 - a)Y>pZ.

For example, the Cobb-Douglas utility function (named after its inventors) is U = BaZ1-a. The marginal utilities are MUB = aBa-1Z1-a = aU>B and MUZ = (1 - a)BaZ-a = (1 - a)U>Z. Thus,

MRS = - MUZ MUB

= - (1 - a)U > Z

aU > B = - (1 - a)

a B Z

. (4A.1)

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124

5 Production Hard work never killed anybody, but why take a chance?

This chapter looks at an important set of decisions that managers have to face. First, the firm must choose its production process, selecting how much labor and capital to use. Second, if a firm wants to expand its output, it must decide how to do that in both the short run and the long run. In the short run, a firm can usually expand output by hiring extra workers or extending the workweek (more shifts per day or more workdays per week) and using extra materials. To expand output even further, the firm may need to install more equipment or build a new plant, which takes more time. Third, given its ability to change its output level, a firm must determine how large to grow based on its expectations about future demand and costs.

Firms and the managers who run them perform the fundamental economic func- tion of producing output—the goods and services that consumers want. The main lesson of this chapter is that firms are not black boxes that mysteriously transform inputs (such as labor, capital, and materials) into outputs. Economic theory explains how firms make decisions about production processes, the types of inputs to use, and the volume of output to produce.

In this chapter, we examine five main topics:

Why has a measure of labor productivity—the output produced per worker—risen for many firms during recent recessions (Lazear, Shaw, and Stanton, 2016)? During the Great Recession (fourth quarter of 2007 through the third quarter of 2009), labor productivity rose by 3.2% in nonfarm businesses. In contrast, in the two years before the Great Recession, labor productivity rose by only 2.2%.

Firms produce less output during recessions as demand for their products falls. Managers must consider whether to reduce production by laying workers off and, if so, how many workers to lay off. To make this decision, they face a managerial problem: How much will the output produced per worker rise or fall with each additional layoff?

In the Managerial Solution to this problem, we will exam- ine whether the productivity of a beer bottling plant rises or falls. If we know the firm’s production process, can we predict whether output produced per worker will rise or fall with each additional layoff?

Labor Productivity During Recessions

Managerial Problem

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1255.1 Production Functions

5.1 Production Functions A firm uses a production process to transform inputs or factors of production into out- puts. Firms use many types of inputs. Most of these inputs can be grouped into three broad categories:

●● Capital (K). Services provided by long-lived inputs such as land, buildings (such as factories and stores), and equipment (such as machines and trucks)

●● Labor (L). Human services such as those provided by managers, skilled workers (such as architects, economists, engineers, and plumbers), and less-skilled work- ers (such as custodians, construction laborers, and assembly-line workers)

●● Materials (M). Natural resources and raw goods (e.g., oil, water, and wheat) and processed products (e.g., aluminum, plastic, paper, and steel)

The output can be a service, such as an automobile tune-up by a mechanic, or a physi- cal product, such as a computer chip or a potato chip.

Firms can transform inputs into outputs in many different ways. Companies that manufacture candy differ in the skills of their workforce and the amount of equip- ment they use. While all employ a chef, a manager, and some relatively unskilled workers, many candy firms also use skilled technicians and modern equipment. In small candy companies, the relatively unskilled workers shape the candy, decorate it, package it, and box it by hand. In slightly larger firms, relatively unskilled workers may use conveyor belts and other equipment that was invented decades ago. In mod- ern, large-scale plants, the relatively unskilled laborers work with robots and other state-of-the-art machines, which are maintained by skilled technicians. Before decid- ing which production process to use, a firm needs to consider its various options.

The different ways in which inputs can be transformed into output are summarized in the production function: the relationship between the quantities of inputs used and the maximum quantity of output that can be pro- duced, given current knowledge about technology and organization.

The production function for a firm that uses only labor and capital is

q = f(L, K), (5.1) where q units of output (such as wrapped candy bars) are produced using L units of labor services (such as hours of work by assembly-line workers) and K units of capital (such as the number of conveyor belts).

The production function shows only the maximum amount of output that can be produced from given levels of labor and capital, because the production function

Production FunctionInputs

Output

Learning Objectives

1. Use a production function to describe the relationship between inputs and output.

2. Predict the effects of short-run changes in labor on output.

3. Explain the long-run trade-off between labor and capital in production.

4. Determine whether a production function has decreasing, constant, or increasing returns to scale.

5. Describe the effects of innovation on production.

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126 CHAPTER 5 Production

includes only efficient production processes. A firm engages in efficient produc- tion (achieves technical efficiency) if it cannot produce its current level of output with fewer inputs, given existing knowledge about technology and the organization of production. A profit-maximizing firm is not interested in production processes that are inefficient and waste inputs: Such firms do not want to use two workers to do a job that can be done just as well by one worker.

A firm can more easily adjust its inputs in the long run than in the short run. Typi- cally, a firm can vary the amounts of materials and relatively unskilled labor it uses comparatively quickly. However, it needs more time to find and hire skilled workers, order new equipment, or build a new manufacturing plant.

The more time a firm has to adjust its inputs, the more factors of production it can alter. The short run is a period so brief that at least one factor of production can- not be varied practically. A factor that cannot be varied practically in the short run is called a fixed input. In contrast, a variable input is a factor of production whose quantity can be changed readily by the firm during the relevant period. The long run is a lengthy enough period that all relevant inputs can be varied. Thus, in the long run, no inputs are fixed.

Suppose that a painting company’s customers all want their homes painted by the end of the day. With its current inputs, the firm cannot complete all the jobs today. To do so, it needs to use more inputs. However, the firm does not have time to buy or rent an extra truck and purchase another compressor to run a power sprayer; these inputs are fixed in the short run. To get the work done that afternoon, the firm uses the company’s one truck to pick up and drop off temporary workers, each equipped with only a brush and paint, at the last job. In the long run, however, the firm can adjust all its inputs. If the firm wants to paint more houses every day, it can hire more full-time workers, get a second truck, purchase more compressors to run the power sprayers, and buy a computer to track its projects.

How long it takes for all inputs to be variable depends on the factors a firm uses. For a janitorial service whose only major input is workers, the short run is brief. In contrast, an automobile manufacturer may need several years to build a new manufacturing plant or to design and construct a new type of assembly machine. A pistachio farmer needs the better part of a decade before newly planted trees yield a substantial crop of nuts.

For many firms, materials and often labor are variable inputs over a month. How- ever, labor is not always a variable input. Finding additional highly skilled workers may take substantial time. Similarly, capital may be a variable or a fixed input. A firm can rent small capital assets (such as trucks or office furniture) quickly, but it may take the firm years to obtain larger capital assets (buildings and large, specialized pieces of equipment).

To illustrate the greater flexibility that a firm has in the long run than in the short run, we examine the production function in Equation 5.1, in which output is a func- tion of only labor and capital. We look first at the short-run and then at the long-run production processes.

5.2 Short-Run Production The short run is a period in which at least one input is fixed. Focusing on a produc- tion process in which capital and labor are the only inputs, we assume that capital is the fixed input and labor is variable. The firm can therefore increase output only by

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1275.2 Short-Run Production

increasing the amount of labor it uses. In the short run, the firm’s production func- tion, Equation 5.1, becomes

q = f(L, K), (5.2)

where q is output, L is the amount of labor, and K is the firm’s fixed amount of capital. To illustrate the short-run production process, we consider a firm that assembles

computers for a manufacturing firm that supplies it with the necessary parts, such as computer chips and disk drives. If the assembly firm wants to increase its output in the short run, it cannot do so by increasing its capital (eight workbenches fully equipped with tools, electronic probes, and other equipment for testing computers). However, it can increase output in the short run by hiring extra workers or paying current workers extra to work overtime.

The Total Product Function The exact relationship between output or total product and labor can be illustrated by using a particular function, Equation 5.2, a table, or a figure. Table 5.1 shows the relation- ship between output and labor when a firm’s capital is fixed. The first column lists the fixed amount of capital: eight fully equipped workbenches. The second column shows how much of the variable input, labor, the firm uses. In this example, the labor input is measured by the number of workers, as all work the same number of hours. Total output—the number of computers assembled in a day—is listed in the third column. As the number of workers increases, total output first increases and then decreases.

With zero workers, no computers are assembled. One worker with access to the firm’s equipment assembles 5 computers in a day. As the number of workers

Capital, K Labor, L Output, Total

Product of Labor q Marginal Product of

Labor,  MPL = ∆q ,∆L Average Product of Labor, APL = q ,L

8 0 0

8 1 5 5 5

8 2 18 13 9

8 3 36 18 12

8 4 56 20 14

8 5 75 19 15

8 6 90 15 15

8 7 98 8 14

8 8 104 6 13

8 9 108 4 12

8 10 110 2 11

8 11 110 0 10

8 12 108 -2 9 8 13 104 -4 8

TABLE 5.1 Total Product, Marginal Product, and Average Product of Labor with Fixed Capital

Labor is measured in workers per day. Capital is fixed at eight fully equipped workbenches.

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128 CHAPTER 5 Production

increases, so does output: 1 worker assembles 5 computers in a day, 2 workers assem- ble 18, 3 workers assemble 36, and so forth. The maximum number of computers that can be assembled with the capital on hand, however, is limited to 110 per day. That maximum can be produced with 10 or 11 workers. If the firm were to use 12 or more workers, the workers would get in each other’s way and production would be lower than with 11 workers. The dashed line in the table indicates that a firm would not use more than 11 workers, because it would be inefficient to do so. We can show how extra workers affect the total product by using two additional concepts: the marginal product of labor and the average product of labor.

The Marginal Product of Labor Before deciding whether to employ more labor, a manager wants to determine how much an extra unit of labor, ∆L = 1, will increase output, ∆q. That is, the manager wants to know the marginal product of labor (MPL): the change in total output resulting from using an extra unit of labor, holding other factors (capital) constant. If output changes by ∆q when the amount of labor increases by ∆L, the change in output per unit of labor is

MPL = ∆q ∆L

.

As Table 5.1 shows, if the number of workers increases from 1 to 2, ∆L = 1, output rises by ∆q = 13 = 18 - 5, so the marginal product of labor is 13.

Calculating the Marginal Product of Labor

Using Calculus The short-run production function, q = f(L, K), can be written as solely a func- tion of L because capital is fixed: q = g(L). The calculus definition of the mar- ginal product of labor is the derivative of this production function with respect to labor: MPL = dg(L) >dL.

In the long run, when both labor and capital are free to vary, the marginal product of labor is the partial derivative of the production function, Equation 5.1, q = f(L, K), with respect to labor:

MPL = 0q 0L

= 0f(L, K)

0L .

We use the symbol 0q>0L instead of dq>dL because we are taking a partial deriva- tive.1 We use partial derivatives when we want to change only one explanatory variable in a function that has more than one such variable. Here, q is a function of both labor, L, and capital, K. To obtain a partial derivative with respect to one variable, say L, we differentiate as usual where we treat the other variables (here just K) as constants.

1Above, we defined the marginal product as the extra output due to a discrete change in labor, such as an additional worker or an extra hour of work. In contrast, the calculus definition of the marginal product—the partial derivative—is the rate of change of output with respect to the labor for a very small (infinitesimal) change in labor. As a result, the numerical calculation of marginal products can differ slightly if derivatives rather than discrete changes are used.

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1295.2 Short-Run Production

The Average Product of Labor Before hiring extra workers, a manager may also want to know whether output will rise in proportion to this extra labor. To answer this question, the firm determines how extra labor affects the average product of labor (APL): the ratio of output to the amount of labor used to produce that output,

APL = q L

.

Table 5.1 shows that 9 workers can assemble 108 computers a day, so the average product of labor for 9 workers is 12 ( = 108>9) computers a day. Ten workers can assemble 110 computers in a day, so the average product of labor for 10 workers is 11 ( = 110>10) computers. Thus, increasing the labor force from 9 to 10 workers low- ers the average product per worker.

Graphing the Product Curves Figure 5.1 and Table 5.1 show how output (total product), the average product of labor, and the marginal product of labor vary with the number of workers. (The figure’s curves are smooth because the firm can hire a “fraction of a worker” by employing a worker for a fraction of a day.) The curve in panel a of Figure 5.1 shows the relationship between the amount of labor and total product, which is the amount of output that can be produced by a given amount of labor. Output rises with labor until it reaches its maximum of 110 computers at 11 workers at point B. Using addi- tional workers beyond this maximum reduces the number of computers assembled.

Panel b of the figure shows how the average product of labor and marginal prod- uct of labor vary with the number of workers. We can line up the figures in panels a and b vertically because the units along the horizontal axes of both figures, the number of workers per day, are the same. The vertical axes differ, however. The vertical axis is total product in panel a and the average or marginal product of labor in panel b.

The Effect of Extra Labor. In most production processes, the average product of labor first rises and then falls as labor increases. One reason the APL curve initially rises in Figure 5.1 is that it helps to have more than two hands when assembling a

Q&A 5.1 For a linear production function q = f(L, K) = 2L + K and a multiplicative pro- duction function q = LK, what are the short-run production functions given that capital is fixed at K = 100? What are the marginal products of labor for these short-run production functions?

Answer 1. Obtain the short-run production functions by setting K = 100. The short-run linear

production function is q = 2L + 100 and the short-run multiplicative function is q = L * 100 = 100L.

2. Determine the marginal products of labor by differentiating the short-run pro- duction functions with respect to labor. The marginal product of labor is MPL = d(2L + 100) >dL = 2 for the short-run linear production function and MPL = d(100L) >dL = 100 for the short-run multiplicative production function.

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130 CHAPTER 5 Production

computer. One worker holds a part in place while another one bolts it down. As a result, output increases more than in proportion to labor, so the average product of labor rises. Doubling the number of workers from one to two more than doubles the output from 5 to 18 and causes the average product of labor to rise from 5 to 9, as Table 5.1 shows.

Similarly, output may initially rise more than in proportion to labor because of greater specialization of activities. With greater specialization, workers are assigned to tasks at which they are particularly adept, and time is saved by not having work- ers move from task to task.

FIGURE 5.1 Production Relationships with Variable Labor

(a) The total product of labor curve shows how many computers, q, can be assembled with eight fully equipped workbenches and a varying number of workers, L, who work eight-hour days (see columns 2 and 3 in Table 5.1). Where extra workers reduce the number of computers assembled (beyond point B), the total product curve is a dashed line, which indi- cates that such production is inefficient and is thus not part of the production function. The slope of the

line from the origin to point A is the average prod- uct of labor for six workers. (b) Where the marginal product of labor (MPL = ∆q>∆L, column 4 of Table 5.1) curve is above the average product of labor (APL = q>L, column 5 of Table 5.1) curve, the APL must rise. Similarly, if the MPL curve is below the APL curve, the APL must fall. Thus, the MPL curve inter- sects the APL curve at the peak of the APL curve, point b, where the firm uses six workers.

O ut

pu t,

q, U

ni ts

p er

d ay

A

B

1160 L, Workers per day

Marginal product, MPL

Average product, APL

A P

L, M

P L

110

90

(a)

a

b

1160

L, Workers per day

20

15

(b)

Total product

Slope of this line = 90/6 = 15

4

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1315.2 Short-Run Production

As the number of workers rises further, however, output may not increase by as much per worker because workers might have to wait to use a particular piece of equipment or they might get in each other’s way. In Figure 5.1, when the number of workers exceeds 6, total output increases less than in proportion to labor, so the average product falls.

If more than 11 workers are used, the total product curve falls with each extra worker as the crowding of workers gets worse. Because that much labor is not effi- cient, that section of the curve is drawn with a dashed line to indicate it is not part of the production function, which includes only efficient combinations of labor and capital. Similarly, the dashed portions of the average and marginal product curves are irrelevant because no firm would hire additional workers if doing so meant that output would fall.

Relationships Among Product Curves. The three curves are geometrically related. First we use panel b to illustrate the relationship between the average and marginal product of labor curves. Then we use panels a and b to show the relation- ship between the total product of labor curve and the other two curves.

An extra hour of work increases the average product of labor if the marginal product of labor exceeds the average product. Similarly, if an extra hour of work generates less extra output than the average, the average product falls. Therefore, the average product rises with extra labor if the marginal product curve is above the average product curve, and the average product falls if the marginal product curve is below the average product curve. Consequently, the average product curve reaches its peak, point a in panel b of Figure 5.1, where the marginal product and average product are equal: where the curves cross.

The geometric relationship between the total product curve and the average and marginal product curves is illustrated in panels a and b of Figure 5.1. We can deter- mine the average product of labor using the total product of labor curve. The average product of labor for L workers equals the slope of a straight line from the origin to a point on the total product of labor curve for L workers in panel a. The slope of this line equals output divided by the number of workers, which is the definition of the average product of labor. For example, the slope of the straight line drawn from the origin to point A (L = 6, q = 90) is 15, which equals the “rise” of q = 90 divided by the “run” of L = 6. As panel b shows, the average product of labor for 6 workers at point a is 15.

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132 CHAPTER 5 Production

The marginal product of labor also has a geometric relationship to the total prod- uct curve. The slope of the total product curve at a given point equals the marginal product of labor. That is, the marginal product of labor equals the slope of a straight line that is tangent to the total output curve at a given point. For example, at point B in panel a, where the firm uses 11 workers, the line tangent to the total product curve is flat so the marginal product of labor is zero (point b in panel b): A little extra labor has no effect on output. The total product curve is upward sloping when the firm uses fewer than 11 workers, so the marginal product of labor is positive. If the firm is foolish enough to hire more than 11 workers, the total product curve slopes downward (dashed line), so the MPL is negative: Extra workers lower output.

When the firm uses 6 workers, the average product of labor equals the marginal product of labor. The line from the origin to point A in panel a is tangent to the total product curve, so the slope of that line, 15, is the marginal product of labor and the average product of labor at point a in panel b, which is the peak of the APL curve.

The Law of Diminishing Marginal Returns Next to supply equals demand, the most commonly used economic phrase is that there are diminishing marginal returns: If a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will eventually become smaller (diminish). As most observed production functions have this property, this pattern is often called the law of diminishing marginal returns. This law determines the shape of the marginal product of labor curves: If only one input is increased, the marginal product of that input will diminish eventually.

In Table 5.1, if the firm goes from 1 to 2 workers, the marginal product of labor of the second worker is 13. If 1 or 2 more workers are used, the marginal product rises: The marginal product for the third worker is 18, and the marginal product for the fourth worker is 20. However, if the firm increases the number of workers beyond 4, the marginal product falls: The marginal product of a fifth worker is 19, and that of the sixth worker is 15. Beyond 4 workers, each extra worker adds less and less extra output, so the total product of labor curve rises by smaller increments. At 11 workers, the marginal product is zero. This diminishing return to extra labor might be due to crowding, as workers get in each other’s way.

Instead of referring to the law of diminishing marginal returns, some people talk about the law of diminishing returns—leaving out the word marginal. Making this change invites a misunderstanding, as it is not clear if the phrase refers to marginal returns or total returns. If the marginal return falls but remains positive as labor increases, the total return rises. In panel b of Figure 5.1, marginal returns start to diminish when the labor input exceeds 4, but total returns rise, as panel a shows, until the labor input exceeds 11, where the marginal returns become negative.

In addition, many people misstate the law of diminishing returns.

This claim is true only if as we add more of an input, we hold technology and other inputs constant. If we increase labor while simultaneously increasing other factors or adopting superior technologies, the marginal product of labor may rise indefinitely.

Common Confusion An input’s marginal product must eventually fall as a firm uses more of the input.

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1335.2 Short-Run Production

Mini-Case [W]hoever makes two ears of corn, or two blades of grass, to grow upon a spot of ground where only one grew before, would deserve better of mankind, and do more essential service to his country, than the whole race of politicians put together. —Jonathan Swift, Gulliver’s Travels

In 1798, Thomas Malthus—a clergyman and professor of political economy— predicted that (unchecked) population would grow more rapidly than food production because the quantity of land was fixed. The problem, he believed,

was that the fixed amount of land would lead to a diminishing marginal product of labor, so output would rise less than in pro- portion to the increase in farm workers, possibly leading to wide- spread starvation and other “natural” checks on population, such as disease and violent conflict. Brander and Taylor (1998) argue that such a disaster might have occurred on Easter Island about 500 years ago.

Today the earth supports a population about eight times as large as when Malthus made his predictions. Why haven’t most of us starved to death? The answer is that a typical agricultural worker produces vastly more food today than was possible when Malthus was alive. The output of a U.S. farm worker today is more than double that of an average worker just 50 years ago. We have not seen diminishing marginal returns to labor because the production function has changed due to dramatic improvements in agricultural production methods and because farmers make greater use of other inputs such as fertilizers and capital.

Two hundred years ago, most of the world’s population had to work in agriculture to feed themselves. Today, less than 1% of the U.S. population works in agriculture. Over the past century, food production grew substantially faster than the population in most developed countries.

Of course, the risk of malnutrition and even starvation remains significant in many low-income countries. Fortunately, agricul- tural production in these nations increased dramatically during the second half of the twentieth century, saving an estimated one billion lives. This increased production resulted from a set of innovations called the Green Revolution. These innovations, including drought- and insect-resistant crop varieties, improved irrigation, better use of fertilizer and pesticides, scientific crop rotation, and improved equipment, were introduced primarily in the third quarter of the twentieth century, although progress has continued.

Norman Borlaug, the most important contributor to the Green Revolution, won the Nobel Peace Prize in 1970. However, as he noted in his Nobel Prize speech, superior science is not the complete answer to preventing starvation. A sound economic system and a stable political environment are also needed.

Economic and political failures such as the breakdown of economic produc- tion and distribution systems due to wars have caused widespread starvation and malnutrition, particularly in parts of sub-Saharan Africa. Environmental problems such as shifting rainfall patterns caused by global warming and soil

Malthus and the Green Revolution

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134 CHAPTER 5 Production

5.3 Long-Run Production We started our analysis of production functions by looking at a short-run production function in which one input, capital, was fixed, and the other, labor, was variable. In the long run, however, both of these inputs are variable. With both factors variable, a firm can usually produce a given level of output by using a great deal of labor and very little capital, a great deal of capital and very little labor, or moderate amounts of both. That is, the firm can substitute one input for another while continuing to pro- duce the same level of output, in much the same way that a consumer can maintain a given level of utility by substituting one good for another.

Typically, a firm can produce in a number of different ways, some of which require more labor than others. For example, a lumberyard can produce 200 planks an hour with 10 workers using hand saws, with 4 workers using handheld power saws, or with 2 workers using bench power saws.

We illustrate a firm’s ability to substitute between inputs in Table 5.2, which shows the amount of output per day the firm produces with various combinations of labor per day and capital per day. The labor inputs are along the top of the table, and the capital inputs are in the first column. The table shows four combinations of labor and capital that the firm can use to produce 24 units of output (numbers in bold): The firm may employ (a) 1 worker and 6 units of capital, (b) 2 workers and 3 units of capital, (c) 3 workers and 2 units of capital, or (d) 6 workers and 1 unit of capital.

Isoquants These four combinations of labor and capital are labeled a, b, c, and d on the “q = 24” curve in Figure 5.2. We call such a curve an isoquant, which is a curve that shows the efficient combinations of labor and capital that can produce the same (iso) level of output (quantity). The isoquant shows the smallest amounts of inputs that will

degradation have also become a major concern. According to the 2017 annual report on food insecurity of the United Nations Food and Agriculture Organiza- tion, about 11% of the world’s population suffers from significant undernourish- ment, with a particularly high concentration in sub-Saharan Africa.

Labor, L

Capital, K 1 2 3 4 5 6

1 10 14 17 20 22 24

2 14 20 24 28 32 35

3 17 24 30 35 39 42

4 20 28 35 40 45 49

5 22 32 39 45 50 55

6 24 35 42 49 55 60

TABLE 5.2 Output Produced with Two Variable Inputs

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1355.3 Long-Run Production

produce a given amount of output. That is, if a firm reduced either input, it could not produce as much output. If the production function is q = f(L, K), then the equation for an isoquant where output is held constant at q is

q = f(L, K).

An isoquant shows the flexibility that a firm has in producing a given level of out- put. Figure 5.2 shows three isoquants corresponding to three levels of output. These isoquants are smooth curves because the firm can use fractional units of each input.

We can use these isoquants to illustrate what happens in the short run when capi- tal is fixed and only labor varies. As Table 5.2 shows, if capital is constant at 2 units, 1 worker produces 14 units of output (point e in Figure 5.2), 3 workers produce 24 units (point c), and 6 workers produce 35 units (point f ). Thus, if the firm holds one factor constant and varies another factor, it moves from one isoquant to another. In contrast, if the firm increases one input while lowering the other appropriately, the firm stays on a single isoquant.

Properties of Isoquants. Isoquants have most of the same properties as indif- ference curves. The biggest distinction between indifference curves and isoquants is that an isoquant holds quantity constant, whereas an indifference curve holds utility constant. We now discuss three major properties of isoquants. These properties result from firms producing efficiently.

First, the farther an isoquant is from the origin, the greater is the level of output. That is, the more inputs a firm uses, the more output it gets if it produces efficiently. At point e in Figure 5.2, the firm is producing 14 units of output with 1 worker and 2 units of capital. If the firm holds capital constant and adds 2 more workers, it pro- duces at point c. Point c must be on an isoquant with a higher level of output—here, 24 units—if the firm is producing efficiently and not wasting the extra labor.

FIGURE 5.2 A Family of Isoquants

These isoquants show the combinations of labor and capital that produce 14, 24, or 35 units of output, q. Isoquants farther from the origin correspond to higher levels of output. Points a, b, c, and d are various combi- nations of labor and capital the firm can use to produce q = 24 units of output. If the firm holds capital con- stant at 2 and increases labor from 1 (point e on the q = 14 isoquant) to 3 (c), its output increases to q = 24 isoquant. If the firm then increases labor to 6 (f), its output rises to q = 35.

K , U

ni ts

o f c

ap ita

l p er

d ay

e

b

a

d

fc

63210 L, Workers per day

6

3

2

1

q = 14

q = 24

q = 35

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136 CHAPTER 5 Production

Second, isoquants do not cross. Such intersections are inconsistent with the require- ment that the firm always produces efficiently. For example, if the q = 15 and q = 20 isoquants crossed, the firm could produce at either output level with the same com- bination of labor and capital. The firm must be producing inefficiently if it produces q = 15 when it could produce q = 20. So that labor-capital combination should not lie on the q = 15 isoquant, which should include only efficient combinations of inputs. Thus, efficiency requires that isoquants do not cross.

Third, isoquants slope downward. If an isoquant sloped upward, the firm could pro- duce the same level of output with relatively few inputs or relatively many inputs. If an isoquant sloped upward, the firm could produce the same level of output with a set of relatively few inputs or with more of the same inputs. Producing with more inputs would be inefficient. Virtually the same argument can be used to show that isoquants must be thin.

Shapes of Isoquants. The curvature of an isoquant shows how readily a firm can substitute one input for another. The two extreme cases are production processes in which inputs are perfect substitutes or in which they cannot be substituted for each other.

If the inputs are perfect substitutes, each isoquant is a straight line. Suppose either potatoes from Maine, x, or potatoes from Idaho, y, both of which are measured in pounds per day, can be used to produce potato salad, q, measured in pounds. The production function is

q = x + y.

We can produce 1 pound of potato salad by using 1 pound of Idaho potatoes and no Maine potatoes, 1 pound of Maine potatoes and no Idaho potatoes, or any combina- tion that adds up to 1 pound in total. Panel a of Figure 5.3 shows the q = 1, 2, and 3 isoquants. These isoquants are straight lines with a slope of -1 because we need to

FIGURE 5.3 Substitutability of Inputs

(a) If inputs are perfect substitutes, each isoquant is a straight line. (b) If the inputs cannot be substituted at all, the iso- quants are right angles (the dashed lines show that the isoquants would be right angles if we included inefficient production).

(c) Typical isoquants lie between the extreme cases of straight lines and right angles. Along a curved iso- quant, the ability to substitute one input for another varies.

y, Id

ah o

po ta

to es

p er

d ay

(a)

x, Maine potatoes per day

q = 3

q = 2

q = 1

B ox

es p

er d

ay

(b)

Cereal per day

q = 3

q = 2

q = 1

45° line q = 1

K , C

ap ita

l p er

u ni

t o f t

im e

(c)

L, Labor per unit of time

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1375.3 Long-Run Production

Mini-Case We can show why isoquants curve away from the origin by deriving an isoquant for trucking.

Self-driving trucks are poised to have a major impact on long-haul trucking. Otto (owned by Uber), Tesla, Embark, Peloton, and over 50 other companies are investing more than $1 billion on developing self-driving trucks and other high-tech trucking technologies.

Autonomous trucks are starting to hit the road. In 2016, an Otto self- driving truck carried 2,000 cases of Budweiser beer from Fort Collins, Colorado, to Colo- rado Springs along Interstate 25. In 2017, Embark autonomous trucks started hauling Frigidaire refrigerators 650 miles along the I-10 freeway from El Paso, Texas, to Palm Springs, California. Uber predicts that between 500,000 and 1.5 million self-driving trucks will be on the road by 2028.

Soon, a company that wants to transport a given amount of goods from one city to another will choose between two technologies:

●● Traditional: A trucker drives the entire route. ●● Self-driving: A trucker drives the first and last few miles through complex ur-

ban roads, but an autonomous truck drives the highway portion unattended.

A driver is legally restricted to 11 hours of driving a day and 60 hours a week. Given that big rigs cost $150,000 or more, leaving them idle for part of the day is wasteful. A self-driving truck can operate around the clock, with various human drivers handling the short distances at either end of a route. The alternative is to have the traditional big rig driven by several drivers.

The diagram shows the isoquant for 10 trips between Los Angeles and Phoe- nix. The vertical axis measures the amount of capital, and the horizontal records the amount of labor. Both technologies use labor and capital in fixed propor- tions. The diagram shows the two right-angle isoquants corresponding to each of these technologies.

The traditional truck contains less capital, K1, than does the self-driving truck, K2, which also includes artificial intelligence (AI). However, the traditional tech- nology uses more labor, L1, than does the self-driving technology.

A truck company could use a combination of tra- ditional and self-driving trucks. By doing so, the firm can produce using intermediate combina- tions of labor and capital, as the solid-line, kinked isoquant illustrates.

With the introduction of new processes in the future, the isoquant will have more and more kinks (one for each new, efficient process) and will begin to resemble the smooth, con- vex isoquants we’ve been drawing.

Self-Driving Trucks

K , U

ni ts

o f c

ap ita

l p er

d ay

Traditional truck

Self-driving truck

10 trips between Los Angeles and Phoenix

L1 L, Workers per dayL2

K2

K1

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138 CHAPTER 5 Production

use an extra pound of Maine potatoes for every pound fewer of Idaho potatoes used.2

Sometimes it is impossible to substitute one input for the other: Inputs must be used in fixed proportions. Such a production function is called a fixed-proportions production function. For example, the inputs needed to produce 12-ounce boxes of cereal are cereal (in 12-ounce units per day) and cardboard boxes (boxes per day). If the firm has one unit of cereal and one box, it can produce one box of cereal. If it has one unit of cereal and two boxes, it can still make only one box of cereal. Thus, in panel b, the only efficient points of production are the large dots along the 45° line.3 Dashed lines show that the isoquants would be right angles if isoquants could include inefficient production processes.

Other production processes allow imperfect substitution between inputs. These processes have isoquants that are convex to the origin (so the middle of the isoquant is closer to the origin than it would be if the isoquant were a straight line). They do not have the same slope at every point, unlike the straight-line isoquants. Most iso- quants are smooth, slope downward, curve away from the origin, and lie between the extreme cases of straight lines (perfect substitutes) and right angles (fixed pro- portions), as panel c illustrates.

Substituting Inputs The slope of an isoquant shows the ability of a firm to replace one input with another while holding output constant. Figure 5.4 illustrates this substitution using an esti- mated isoquant for a “personal and other service” firm (such as gardening, hairdress- ers, and laundries), which uses labor, L, and capital, K, to produce q units of service.4 The isoquant shows various combinations of L and K by which the firm can produce 10 units of output.

The firm can produce 10 units of output using the combination of inputs at a or b. At point a, the firm uses 2 workers and 16 units of capital. The firm could produce the same amount of output with ∆K = -6 fewer units of capital if it used one more worker, ∆L = 1, point b. If we drew a straight line from a to b, its slope would be ∆K>∆L = -6. Thus, this slope tells us how many fewer units of capital (6) the firm can use if it hires one more worker.5

The slope of an isoquant is called the marginal rate of technical substitution (MRTS):

MRTS = change in capital

change in labor =

∆K ∆L

.

2The isoquant for q = 1 pound of potato salad is 1 = x + y, or y = 1 - x. This equation shows that the isoquant is a straight line with a slope of -1. 3This fixed-proportions production function is the minimum of g and b, q = min(g, b), where g is the number of 12-ounce measures of cereal, b is the number of boxes used in a day, and the min function means “the minimum number of g or b.” For example, if g is 4 and b is 3, q is 3. 4The isoquant for q = 10 is based on the estimated “personal and other service” production function q = 2.35L0.5K0.4 (Devine, Doan, and Stevens, 2012), where a unit of labor, L, is a worker-day. Because capital, K, includes various types of machines, and output, q, reflects different types of service, their units cannot be described by any common terms. 5The slope of the isoquant at a point equals the slope of a straight line that is tangent to the isoquant at that point. Thus, the straight line between two nearby points on an isoquant has nearly the same slope as that of the isoquant.

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1395.3 Long-Run Production

The marginal rate of technical substitution tells us how many units of capital the firm can replace with an extra unit of labor while holding output constant. Because isoquants slope downward, the MRTS is negative. That is, the firm can produce a given level of output by substituting more capital for less labor (or vice versa).

Substitutability of Inputs Varies Along an Isoquant. The MRTS varies along a curved isoquant, as in Figure 5.4. If the firm is initially at point a and it hires one more worker (∆L = 1), the firm can give up six units of capital (∆K = -6) and yet remain on the same isoquant (at point b), so the MRTS is ∆K>∆L = -6. If the firm hires another worker, the firm can reduce its capital by three units and stay on the same isoquant, moving from point b to c, so the MRTS is -3. This decline in the MRTS (in absolute value) along an isoquant as the firm increases labor illustrates a diminishing MRTS. The more labor and less capital the firm has, the harder it is to replace remaining capital with labor and the flatter the isoquant becomes.

In the special case in which isoquants are straight lines, isoquants do not exhibit diminishing marginal rates of technical substitution because neither input becomes more valuable in the production process: The inputs remain perfect substitutes. Q&A 5.2 illustrates this result.

Substitutability of Inputs and Marginal Products. The marginal rate of technical substitution is equal to the ratio of marginal products. The marginal product of labor, MPL = ∆q>∆L, is the increase in output from an extra unit of labor, holding capital fixed. If the firm hires ∆L more workers, its output increases by MPL * ∆L. For example, if the MPL is 2 and the firm hires one extra worker, its out- put rises by 2 units.

Similarly, the marginal product of capital, MPK = ∆q>∆K, is the increase in output from an extra unit of capital, holding other inputs fixed. Thus, a decrease in capital, holding labor fixed, causes output to fall by MPK * ∆K. If the firm increases labor and decreases capital to keep output constant (∆q = 0), the fall in output caused by reducing capital must exactly equal the increase in output from increasing labor:

(MPL * ∆L) + (MPK * ∆K) = 0.

Q&A 5.2 A manufacturer produces a container of potato salad using 1 pound of Idaho potatoes, 1 pound of Maine potatoes, or 1 pound of a mixture of the two types of potatoes. Does the marginal rate of technical substitution vary along the iso- quant? What is the MRTS at each point along the isoquant?

Answer 1. Determine the shape of the isoquant. As panel a of Figure 5.3 illustrates, the potato

salad isoquants are straight lines because the two types of potatoes are perfect substitutes.

2. On the basis of the shape, conclude whether the MRTS is constant along the isoquant. Because the isoquant is a straight line, the slope is the same at every point, so the MRTS is constant.

3. Determine the MRTS at each point. Earlier, we showed that the slope of this isoquant was -1, so the MRTS is -1 at each point along the isoquant. That is, because the two inputs are perfect substitutes, 1 pound of Idaho potatoes can be replaced by 1 pound of Maine potatoes.

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140 CHAPTER 5 Production

Rearranging these terms, we find that

- MPL MPK

= ∆K ∆L

= MRTS. (5.3)

Thus, the ratio of marginal products equals the MRTS (in absolute value). We can use Equation 5.3 to explain why marginal rates of technical substitution

diminish as we move to the right along the isoquant in Figure 5.4. As we replace capital with labor (moving down and to the right along the isoquant), the mar- ginal product of capital increases—if each firm has few pieces of equipment, each remaining piece is more useful—and the marginal product of labor falls, so the MRTS = - MPL>MPK falls in absolute value. Cobb-Douglas Production Functions. We can illustrate how to determine the MRTS for a particular production function, the Cobb-Douglas production func- tion. It is named after its inventors, Charles W. Cobb, a mathematician, and Paul H. Douglas, an economist and U.S. Senator. Through empirical studies, economists have found that the production processes in a large number of industries can be accurately summarized by the Cobb-Douglas production function, which is

q = ALaKb, (5.4)

where A, a, and b are all positive constants. For example, we used the estimated “personal and other service” Cobb-Douglas production function, q = 2.35L0.5K0.4, to draw Figure 5.4, where A = 2.35, a = 0.5, and b = 0.4.

The constants a and b determine the relationships between the marginal and average products of labor and capital. The marginal product of labor is a times the average product of labor, APL = q>L. That is, MPL = aq>L = aAPL (as we show in the following Using Calculus section). By dividing both sides of the expres- sion by APL , we find that a equals the ratio of the marginal product of labor to the

FIGURE 5.4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant

Moving from point a to b, a U.S. printing firm (Hsieh, 1995) can produce the same amount of output, q = 10, using six fewer units of capital, ∆K = -6, if it uses one more worker, ∆L = 1. Thus, its MRTS = ∆K>∆L = -6. Moving from point b to c, its MRTS is -3. If it adds yet another worker, moving from c to d, its MRTS is -2. Finally, if it moves from d to e, its MRTS is -1. Thus, because the isoquant is convex to the origin, it exhibits a diminishing marginal rate of technical substitution. That is, each extra worker allows the firm to reduce capital by a smaller amount as the ratio of capital to labor falls.

K , U

ni ts

o f c

ap ita

l p er

d ay

L, Workers per day

4 5

7

10

16 a

b

c d

e

q = 10

DK = –6

DL = 1

0 1

1

1

1

2 3

–3

–2

–1

4 5 6 7 8 9 10

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1415.4 Returns to Scale

average product of labor: a = MPL>APL. Similarly, the marginal product of capital is MPK = bq>K = bAPK, and b = MPK>APK.

The marginal rate of technical substitution along an isoquant that holds output fixed at q is

MRTS = - MPL MPK

= - aq>L bq>K = -

a b

K L

. (5.5)

For example, given the personal and other service production function, q = 2.35L0.5K0.4, its MPL = aAPL = 0.5APL, and its MRTS = - (0.5>0.4)K>L = -1.25K>L. The MRTS tells the firm’s managers the rate at which they can substitute capital for labor without reducing output.

5.4 Returns to Scale So far, we have examined the effects of increasing one input while holding the other input constant (shifting from one isoquant to another) or decreasing the other input by an offsetting amount (moving along an isoquant). We now turn to the question of how much output changes if a firm increases all its inputs proportionately. The answer helps a firm determine its scale or size in the long run.

In the long run, a firm can increase its output by building a second plant and staff- ing it with the same number of workers as in the first one. Whether the firm chooses to do so depends in part on whether its output increases less than in proportion, in proportion, or more than in proportion to its inputs.

Constant, Increasing, and Decreasing Returns to Scale If, when all inputs are increased by a certain proportion, output increases by that same proportion, the production function is said to exhibit constant returns to scale (CRS). A firm’s production process, q = f(L, K), has constant returns to scale if, when the firm doubles its inputs—by, for example, building an identical second

Cobb-Douglas Marginal Products

Using Calculus To obtain the marginal product of labor for the Cobb-Douglas production func-tion, Equation 5.4, q = ALaKb, we partially differentiate the production function with respect to labor, holding capital fixed:

MPL = 0q 0L

= aALa - 1Kb = a ALaKb

L = a

q L

.

We obtain the last equality by substituting q = ALaKb. Similarly, we can derive the marginal product of capital by partially differentiating the production func- tion with respect to K:

MPK = 0q 0K

= bALaKb - 1 = b ALaKb

K = b

q K

.

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142 CHAPTER 5 Production

plant and using the same amount of labor and equipment as in the first plant—it doubles its output:

f(2L, 2K) = 2f(L, K) = 2q.

We can check whether the potato salad production function has constant returns to scale. If a firm uses x1 pounds of Idaho potatoes and y1 pounds of Maine potatoes, it produces q1 = x1 + y1 pounds of potato salad. If it doubles both inputs, using x2 = 2x1 Idaho and y2 = 2y1 Maine potatoes, it doubles its output:

q2 = x2 + y2 = 2x1 + 2y1 = 2(x1 + y1) = 2q1.

Thus, the potato salad production function exhibits constant returns to scale. If output rises more than in proportion to an equal proportional increase in all

inputs, the production function is said to exhibit increasing returns to scale (IRS). A technology exhibits increasing returns to scale if doubling inputs more than doubles the output:

f(2L, 2K) 7 2f(L, K) = 2q.

Why might a production function have increasing returns to scale? One reason is that although it could build a copy of its original small factory and double its output, the firm might be able to more than double its output by building a sin- gle large plant, thereby allowing for greater specialization of labor or capital. In the two smaller plants, workers have to perform many unrelated tasks, such as operating, maintaining, and fixing the machines they use. In the large plant, some workers may specialize in maintaining and fixing machines, thereby increasing effi- ciency. Similarly, a firm may use specialized equipment in a large plant but not in a small one.

If output rises less than in proportion to an equal proportional increase in all inputs, the production function exhibits decreasing returns to scale (DRS). A technology exhibits decreasing returns to scale if doubling inputs causes output to rise less than in proportion:

f(2L, 2K) 6 2f(L, K) = 2q.

One reason for decreasing returns to scale is that the difficulty of organizing, coordinating, and inte- grating activities increases with firm size. An owner may be able to manage one plant well but may have trouble running two plants. In some sense, the decreasing returns to scale stemming from the own- er’s difficulties in running a larger firm may reflect our failure to take into account some factor such as management skills in our production function. If a firm increases various inputs but does not increase the management input in proportion, the “decreas- ing returns to scale” may occur because one of the inputs to production, management skills, is fixed.

Another reason is that large teams of workers may not function as well as small teams, in which each individual takes greater personal responsibility.

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1435.4 Returns to Scale

Q&A 5.3 Under what conditions does a Cobb-Douglas production function, Equation 5.4, q = ALaKb, exhibit decreasing, constant, or increasing returns to scale?

Answer 1. Show how output changes if both inputs are doubled. If the firm initially uses L

and K amounts of inputs, it produces q1 = ALaKb. After the firm doubles the amount of both labor and capital it uses, it produces

q2 = A (2L)a (2K)b = 2a+bALaKb = 2a + bq1. (5.6)

That is, q2 is 2a + b times q1. If we define g = a + b, then Equation 5.6 tells us that

q2 = 2gq1. (5.7)

Thus, if the inputs double, output increases by 2g. 2. Give a rule for determining the returns to scale. If g = 1, we know from Equation 5.7

that q2 = 21q1 = 2q1. That is, output doubles when the inputs double, so the Cobb-Douglas production function has constant returns to scale. If g 6 1, then q2 = 2gq1 6 2q1 because 2g 6 2 if g 6 1. That is, when input doubles, output increases less than in proportion, so this Cobb-Douglas production function exhibits decreasing returns to scale. Finally, the Cobb-Douglas production function has increasing returns to scale if g 7 1 so that q2 7 2q1. Thus, the rule for determining returns to scale for a Cobb-Douglas production func- tion is that the returns to scale are decreasing if g 6 1, constant if g = 1, and increasing if g 7 1.

Comment: One interpretation of g is that, as all inputs increase by 1%, output increases by g%. Thus, for example, if g = 1, a 1% increase in all inputs increases output by 1%.

Mini-Case Crocs, a foam-resin shoe manufactured by Crocs, Inc., took the shoe market by storm over the past dozen years. Popular with both children and their parents, these light, colorful, and inexpensive shoes are sold in 90 countries around the world.

We used regression analysis to estimate a  Cobb-Douglas production function for Crocs.6 The estimated production function is q =ALaKb = 22.7L0.88K0.48. That is, A = 22.7, a = 0.88, and b = 0.48. Because a + b = 0.88 + 0.48 = 1.36 7 1, Croc production exhib- its incre asing returns to scale. Labor is measured in thousands of employees; capital is an index of plant, property, and equipment (PPE); and one unit of output is a million dollars’ worth of shoes, which is about 40,000 pairs of shoes.

The graph uses isoquants to illustrate Crocs’ increasing returns to scale. A combination of

6The data are from the Crocs, Inc., annual reports from 2004 through 2017, as reported in Compustat.

Returns to Scale for Crocs

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Varying Returns to Scale For a Cobb-Douglas production function, the returns to scale are the same at all lev- els of output. However, for other production functions, the returns to scale may vary as the output level changes. Many production functions have increasing returns to scale for small amounts of output, constant returns for moderate amounts of output, and decreasing returns for large amounts of output. When a firm is small, increasing labor and capital allows for gains from cooperation between workers and greater specialization of workers and equipment—returns to specialization—so the produc- tion function exhibits increasing returns to scale. As the firm grows, returns to scale are eventually exhausted, so the production process has constant returns to scale. If the firm continues to grow, the owner starts having difficulty managing everyone, so the firm suffers from decreasing returns to scale.

We show such a pattern in Figure 5.5. The spacing of the isoquants reflects the returns to scale. Initially, the firm has one worker and one piece of equipment, point a, and produces 1 unit of output on the q = 1 isoquant. If the firm doubles its inputs, it produces at b, where L = 2 and K = 2, which lies on the dashed line through the origin and point a. Output more than doubles to q = 3, so the production function exhibits increasing returns to scale in this range. Another doubling of inputs to c causes output to double to 6 units, so the production function has constant returns to scale in this range. Another doubling of inputs to d causes output to increase by only a third, to q = 8, so the production function has decreasing returns to scale in this range.

2 units of labor and 7 units of capital produces 107 units of output and is one point on the q = 107 isoquant: q = 22.7(20.88) (70.48) ≈ 107. That is, 2 (thou- sand) workers and 7 units of capital produce about 107 million dollars’ worth of shoes. If the firm doubles both of its inputs to 4 units of labor and 14 units of capital, it is operating on the 276-unit isoquant, which is more than double the initial output.

K , U

ni ts

o f c

ap ita

l p er

y ea

r

L, Units of labor per year

7

14

q = 107

q = 214

q = 276

0 2 4

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1455.4 Returns to Scale

FIGURE 5.5 Varying Scale Economies

The production function that corresponds to these isoquants exhibits varying returns to scale. Initially, the firm uses one worker and one unit of capital, point a. Point b has double the amount of labor and capi- tal that a has. Similarly, c has double the inputs of b, and d has double the inputs of c. All these points lie along the dashed 45° line. The first time the inputs are doubled, a to b, output more than doubles from q = 1 to q = 3, so the production function has increasing returns to scale. The next doubling, b to c, causes a proportionate increase in output, constant returns to scale. At the last doubling, from c to d, the production function exhibits decreasing returns to scale.

U ni

ts o

f c ap

ita l p

er d

ay

41 2

a

b

d

c

c d : Decreasing returns to scale

b c: Constant returns to scale

a b: Increasing returns to scale

8 Workers per day

4

2

1

0

8

q = 8

q = 6

q = 3 q = 1

Over the years, the typical factory has grown in size to take advantage of increas- ing returns to scale. However, three-dimensional (3D) printing may reverse this trend by making input requirements per unit to manufacture one item as low as when making thousands.

With 3D printing, an employee gives instructions—essentially a blueprint— to the machine, presses print, and the machine builds the object from the ground up, either by depositing material from a nozzle or by selectively solidify- ing a thin layer of plastic or metal dust using drops of glue or a tightly focused beam.

Until recently, firms primarily used 3D printers to create prototypes in the aerospace, medical, and automotive industries. Then, they manufactured the final products using conventional techniques. However, 3D printing has improved so much so that it can now be used for manufacturing final products, particularly in industries that need small numbers of customized parts. Nike is using 3D printers to produce the Zoom Superfly Skyknit running shoe. These printers are useful in creating customized prostheses for people with amputations.

Biomedical and aerospace companies make use of 3D printing for just-in-time manufacturing. With this technique, companies can fabricate small, highly cus- tomized batches of products as end-users need them. By 2018, Boeing and Airbus were each using thousands of different printed parts in their aircraft. The printers produce lighter parts, which lower the weight of planes (saving fuel) and can be quickly redesigned. Perhaps more striking, Airbus introduced the world’s first entirely 3D-printed aircraft, a drone, in 2016.

Small Is Beautiful

Managerial Implication

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5.5 Innovation Innovation—a new idea, device, or method—affects markets in many ways. Over the past century, new product innovations such as antibiotics, television, jet aircraft, personal computers, and the internet have transformed the way we live and do business. Innovations that have dramatic effects on the products we consume or on the nature of production are often called disruptive innovations. Possibly 3D printing, described in the Managerial Implication “Small Is Beautiful,” will turn out to be a disruptive innovation. Most innovations, however, are incremental.

Process innovations, which improve the method of production for existing prod- ucts to increase output, occur much more frequently than new product innovations. For example, the life-saving innovations in the Mini-Case “Malthus and the Green Revolution” include process innovations such as irrigation and optimal crop rotation that greatly increased food production.

Organizational innovations—new ways of organizing firms—also increase output. For example, the Zappos online shoe retailer is experimenting with a new organiza- tional structure, holacracy, in which workers are arranged in groups (circles) without top-down supervisors.

A successful process innovation or organizational innovation is an advance in knowledge that allows more output to be produced with the same level of inputs and is often called technical progress. Technical progress may be a matter of engi- neering, such as improving the design of robotic arms used in assembling cars. But such innovations may also be organizational or managerial, such as improving the way managers interact with workers.

Process Innovation A process innovation changes the production function. Last year a firm produced

q1 = f(L, K)

units of output using L units of labor services and K units of capital service. Due to technical progress from a process innovation, this year’s production function differs from last year’s. For example, if this technical progress allows a firm to produce 10% more output with the same inputs, the production function becomes

q2 = 1.1f(L, K).

Flath, (2011) estimated the annual rate of technical progress in Japanese manufactur- ing firms to be 0.91% for electric copper, 0.87% for medicine, 0.33% for steel pipes and tubes, 0.19% for cement, and 0.08% for beer.

This type of technical progress reflects neutral technical progress, in which more output is produced using the same ratio of inputs. However, technical progress may

Managers should use this technology to experiment. They can produce small initial runs to determine the size of the market and consumers’ acceptance of the product. Based on information from early adopters, managers can determine if the market warrants further production and can quickly modify designs to meet end-users’ desires.

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be nonneutral. Rather than increasing output for a given mix of inputs, technical prog- ress could be capital saving, whereby the firm can produce the same level of output as before, using less capital and the same amount of other inputs.

Alternatively, technical progress may be labor saving. The development of self- driving trucks is an example of labor-saving technical progress. Basker (2012) found that the introduction of barcode scanners in grocery stores increased the average product of labor by 4.5%, on average, across stores. Amazon makes extensive use of robots to move items in its warehouses, partially replacing workers. Other robots help doctors perform surgery more quickly and reduce patients’ recovery times.

Organizational Innovation Organizational innovation may also alter the production function and increase the amount of output produced by a given amount of inputs. In the early 1900s, Henry Ford revolutionized the mass production of automobiles through two organizational innovations. First, he introduced interchangeable parts, which cut the time required to install parts because workers no longer had to file or machine individually made parts to get them to fit.

Second, Ford introduced a conveyor belt and an assembly line to his produc- tion process. Before this change, workers walked around the car, and each worker performed many assembly activities. In Ford’s plant, each worker specialized in a single activity, such as attaching the right rear fender to the chassis. A conveyor belt moved the car at a constant speed from worker to worker along the assembly line. Because his workers gained proficiency from specializing in only a few activities and because the conveyor belts reduced the number of movements workers had to make, Ford could produce more automobiles with the same number of workers. These

Mini-Case

Robots and the Food You Eat

Robots have been used in manufacturing for many years. They are now gaining a foothold in agriculture. Well over half the wine grapes in California are picked by robots, and robots are also used to harvest strawberries, tomatoes, lettuce, and other crops. The Hackney Nursery in Florida uses robots to assess whether

flowers have adequate room for optimal growth and to move the flowers around accordingly. And fully autonomous cow-milking robots are widely used.

Not just the farming end of the food busi- ness is using robots. The Dalu Robot Restau- rant in Jinan, China, uses robots to wait on tables, greet customers, and provide entertain- ment. Each robot serving food has a motion sensor that tells it to stop when someone is in its path so customers can reach for dishes they want. But perhaps the most popular employee is a female robot, complete with batting eye- lashes, who greets people with an electronic

“welcome.” First-time customer Li Xiaomei praised the robots, claiming that “they have a better service attitude than humans.”

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innovations reduced the ratio of labor to capital used. In 1908, the Ford Model T sold for $850, while rival vehicles sold for $2,000. By the early 1920s, Ford had increased production from fewer than a thousand cars per year to two million per year.

Mini-Case Does a good supervisor make workers more productive? To answer this ques- tion, Lazear, Shaw, and Stanton (2015) looked at a large service-oriented com- pany. Supervisor quality varied substantially as measured by the boss’s effect on worker productivity. Replacing one of the 10% worst bosses with one of the 10% best ones raised a team’s output by about the same amount as adding one worker to a nine-member team. Thus, differences in managers can cause one firm to be more productive than another.

A Good Boss Raises Productivity

In some industries, an important part of being a good manager involves adopting new technologies and looking for better ways to organize the firm. A firm that achieves a successful process or organizational innovation can produce more output with the same input levels than its rivals, which gives it a competitive advantage.

Technical Progress and Competitive Advantage

Managerial Implication

Labor Productivity During Recessions

Managerial Solut ion

During a recession, a manager of a Japanese beer bottling plant has to reduce output and decides to lay off workers. Will the firm’s labor productivity—average product of labor—go up and improve the firm’s situation or go down and harm it?

Layoffs have the positive effect of freeing up machines to be used by remain- ing workers. However, if layoffs force the remaining workers to perform a wide variety of tasks, the firm will lose the benefits from specialization. When the firm has many workers, the advantage of freeing up machines is important and increased multitasking is unlikely to be a problem. When the firm has only a few workers, freeing up more machines does not help much (some machines might stand idle some of the time), while multitasking becomes a more serious problem.

Holding capital constant, a change in the number of workers affects a firm’s average product of labor. Labor productivity could rise or fall. For example, in panel b of Figure 5.1, the average product of labor rises as L increases up to 6 workers per day and then falls as the number of workers increases further. The average product of labor falls if the firm has six or fewer workers and lays one off, but rises if the firm initially has seven or more workers and lays off a worker.

Consider a Cobb-Douglas production function, q = ALaKb, where APL= q>L = q = ALa-1Kb. The rate of change of the APL with respect to labor (its deriva- tive) is (a - 1)ALa - 2Kb. Thus, if a is less than one, so that a - 1 is negative, the APL falls with extra labor.

For example, for the beer firm’s estimated Cobb-Douglas production func- tion (Flath, 2011), q = AL0.6K0.4, a = 0.6 is less than 1, so the APL curve slopes downward at every quantity. We can illustrate how much the APL rises with a layoff for this particular production function. If A = 1 and L = K = 10 initially, then the firm’s output is q = 100.6 * 100.4 = 10, and its average product of labor is APL = q>L = 10>10 = 1. If the number of workers is reduced by one, then

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output falls to q = 90.6 * 100.4 ≈ 9.39, and the average product of labor rises to APL ≈ 9.39>9 ≈ 1. 04. That is, a 10% reduction in labor causes output to fall by 6.1%, but causes the average product of labor to rise by 4%. The firm’s output falls less than 10% because each remaining worker is more productive.

Until recently, most large Japanese firms did not lay off workers during down- turns. Thus, in contrast to U.S. firms, their average product of labor fell during recessions because their output fell while labor remained constant. Similarly, European firms have 30% less employment volatility over time than do U.S. firms, at least in part because many European firms that fire workers are subject to a tax. Consequently, with other factors held constant in the short run, reces- sions might be more damaging to the profit of a Japanese or European firm than to the profit of a comparable U.S. firm. However, retaining good workers over short-run downturns might be a good long-run policy.

SUMMARY

1. Production Functions. A production function summa- rizes how a firm combines inputs such as labor, capital, and materials to produce output using the current state of knowledge about technology and management. A produc- tion function shows how much output can be produced efficiently from various levels of inputs. A firm produces efficiently if it cannot produce its current level of output with less of any one input, holding other inputs constant.

2. Short-Run Production. In the short run, a firm can- not adjust the quantity of some inputs, such as capital. The firm varies its output in the short run by adjusting its variable inputs, such as labor. If all factors are fixed except labor, and a firm that was using very little labor increases its use of labor, its output may rise more than in proportion to the increase in labor because of greater specialization of workers. Eventually, however, as more workers are hired, the workers get in each other’s way or must wait to share equipment, so output increases by smaller and smaller amounts. This latter phenomenon is described by the law of diminishing marginal returns: The marginal product of an input—the extra output from the last unit of input—eventually decreases as more of that input is used, holding other inputs fixed.

3. Long-Run Production. In the long run, when all inputs are variable, firms can substitute between inputs.

An isoquant shows the combinations of inputs that can produce a given level of output. The marginal rate of technical substitution is the absolute value of the slope of the isoquant and indicates how easily the firm can substitute one factor of production for another. Usually, the more of one input the firm uses, the more difficult it is to substitute that input for another input. That is, the marginal rate of technical substitution diminishes as the firm uses more of an input.

4. Returns to Scale. When a firm increases all inputs in proportion and its output increases by the same propor- tion, the production process is said to exhibit constant returns to scale. If output increases less than in propor- tion to the increase in inputs, the production process has decreasing returns to scale; if it increases more than in proportion, it has increasing returns to scale. All three types of returns to scale are common. Many production processes exhibit first increasing, then con- stant, and finally decreasing returns to scale as the size of the firm increases.

5. Innovation. Using process innovation or organiza- tional innovations, firms achieve technical progress: They can produce more output than before with the same inputs. This technical progress changes the pro- duction function.

QUESTIONS

1. Production Functions

1.1 What are the main types of capital and labor that can be used to produce candy?

*1.2 Suppose that for the function q = f(L, K), if L = 3 and K = 5 then q = 10. Is it possible that L = 3 and

K = 6 also yields q = 10 for this production func- tion? Why or why not?

1.3 As in Question 1.2, suppose that the production function shows that if L = 3 and K = 5 then q = 10. Is it possible that L = 3 and K = 6 yields q = 11 for this production function? Explain briefly.

All exercises are available on MyLab Economics; * = answer at the back of this book; = this exercise is available in Excel Grader in MyLab Economics.

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1.4 Consider Boeing (a producer of jet aircraft), General Mills (a producer of breakfast cereals), and Wacky Jack’s (which claims to be the largest U.S. provider of singing telegrams). For which of these firms is the short run the longest period? For which is the long run the shortest? Explain.

2. Short-Run Production *2.1 If each extra worker produces an additional unit of

output, how do the total product of labor, average product of labor, and marginal product of labor vary with labor? Plot these curves in a graph similar to Figure 5.1.

2.2 Each extra worker produces an additional unit of out- put up to six workers. As more workers are added, no additional output is produced. Draw the total product of labor, average product of labor, and marginal prod- uct of labor curves in a graph similar to Figure 5.1.

*2.3 Suppose that the production function is q = L0.75K0.25. (Hint: See Q&A 5.1.)

a. What is the average product of labor, holding capital fixed at K?

b. What is the marginal product of labor?

c. How is the marginal product of labor related to the average product of labor?

2.4 In the short run, a firm cannot vary its capital and operates with K = 9. It can, however, vary the amount of labor (L) that it uses. For each production function below, explain why the firm will or will not experience diminishing marginal returns to labor in the short run.

a. q = 35L + 40K b. q = L0.5K0.5

c. q = min{3L, 2K} 2.5 Based on the information in the Mini-Case “Malthus

and the Green Revolution,” how did the average product of labor in food production change over time?

*2.6 The 2017 report of the United Nations Food and Agriculture Organization (FAO) notes that the share of world population that is undernourished rose between 2014 and 2016, following a long period of decline. This increase occurred even though agricultural output per acre rose between 2014 and 2016. What factors might cause undernourishment to rise even though agricultural land productivity rose?

3. Long-Run Production 3.1 Why must isoquants be thin?

3.2 Set up by a former University of North Carolina (UNC) student, Morris Gelblum, the firm Sweeps uses UNC, Duke, North Carolina State, and other college students to perform a variety of short-term

jobs, such as cleaning, yard work, painting, tech help, tutoring, and moving. A customer describes the work desired on the firm’s website, and the firm provides workers. For one job, they provide “21 guys dressed up like Frankenstein.” The firm’s motto is “College Students, On-Demand.” What input(s) does the firm use in the long run?

3.3 The isoquant in the Mini-Case “Self-Driving Trucks” is based on two technologies. Suppose that a company develops a third technology that assists but does not replace a human driver. It uses more labor and less capital than the fully self-driving technology, but less labor and more capital than the traditional technology. In the isoquant diagram, the input combination needed to produce 10 trips lies below the straight line joining the input combinations for the traditional and self- driving technologies. Illustrate the resulting isoquant.

3.4 Using the information given in Table 5.2, draw the isoquant corresponding to an output level of 20. Starting from L = 4 and K = 1, how much extra capital is needed to keep output constant if the labor is reduced by one unit to L = 3? How much extra capital is needed to keep output constant if labor is reduced by one more unit to L = 2?

*3.5 To produce a recorded DVD, q = 1, a firm uses one blank disk, D = 1, and the services of a recording machine, M = 1, for one hour. (Hint: See Q&A 5.2.)

a. Draw the isoquants for this production function and explain its shape.

b. What is the MRTS at each point along the iso- quant corresponding to q = 100?

c. Draw the total product, average product, and marginal product of labor curves for this produc- tion function. Use two diagrams, as in Figure 5.1.

3.6 The production function at Ginko’s Copy Shop is q = 1,000 * min(L, 3K), where q is the number of copies per hour, L is the number of workers, and K is the number of copy machines. As an example, if L = 4 and K = 1, then the minimum of L and 3K, min(L, 3K) = 3, and q = 3,000.

a. Draw the isoquants for this production function.

b. Draw the total product, average product, and marginal product of labor curves for this production function for some fixed level of capital.

3.7 Using the figure in the Mini-Case “Self-Driving Trucks,” show that as the firm employs additional fixed-proportion technologies, the firm’s overall iso- quant approaches a smooth curve similar to that in panel c of Figure 5.3.

*3.8 A laundry cleans white clothes using the produc- tion function q = B + 2G, where B is the number of cups of Clorox bleach, G is the number of cups of a

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generic bleach that is half as potent, and q is the bas- ketfuls of clothes that are cleaned. Draw an isoquant for one basketful of clothes. What is the marginal product of B? What is the marginal rate of technical substitution at each point on an isoquant?

*3.9 At L = 4, K = 4, the marginal product of labor is 2 and the marginal product of capital is 3. What is the marginal rate of technical substitution (MRTS)?

*3.10 Consider a Cobb-Douglas production function q = 10L0.5K0.5. If L = 16 and K = 25, calculate out- put, q, the marginal product of labor, and the mar- ginal product of capital? (Hint: Use the marginal product formulas in Using Calculus “Cobb-Douglas Marginal Products.”)

4. Returns to Scale 4.1 To speed relief to isolated South Asian communities

that were devastated by the December 2004 tsunami, the U.S. government doubled the number of Navy heli- copters from 45 to 90 in early 2005. The Navy admiral in charge indicated that doubling the number of heli- copters would provide “close to twice as much” relief. Identify the outputs and inputs, and describe the pro- duction process. Is the admiral discussing a production process with nearly constant returns to scale, or is he referring to another property of the production process?

*4.2 The production function for the automotive and parts industry is q = L0.27K0.16M0.61, where M is energy and materials (based on Klein, 2003). What  kind of returns to scale does this production function exhibit? What is the marginal product of materials?

4.3 Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? (Hint: See Q&A 5.3.)

a. q = L + K. b. q = L + LaKb + K.

4.4 A production function has the property that f(xL, xK) = x2f(L, K) for any positive value of x. What kind of returns to scale does this production function exhibit? If the firm doubles L and K, show that the marginal product of labor and the marginal product of capital also double.

*4.5 Show in a diagram that a production function can have diminishing marginal returns to a factor and constant returns to scale.

4.6 Is it possible that a firm’s production function exhib- its increasing returns to scale while exhibiting dimin- ishing marginal productivity of each of its inputs? To answer this question, calculate the marginal produc- tivities of capital and labor for the production of Crocs using the production q = ALaKb = 22.7L0.88K0.48 given in the Mini-Case “Returns to Scale for Crocs.”

*4.7 The Crocs production function is q = 22.7L0.88K0.48, where L is labor and K is capital. Epple, Gordon, and

Sieg (2010) estimated that the production function for U.S. housing is q = 1.38L0.144M0.856, where L is land and M is an aggregate of all other mobile, non- land factors, which we call materials. Haskel and Sadun (2012) estimated the production function for U.K. supermarkets is q = L0.23K0.10M0.66, where L is labor, K is capital, and M is materials. Are the returns to scale decreasing, constant, or increasing for each of these production functions?

4.8 Michelle’s business produces ceramic cups using labor, clay, and a kiln. She uses labor and clay in a fixed pro- portion, but has only one kiln. She can manufacture 25 cups a day with one worker and 35 with two workers.

a. Does this information illustrate decreasing returns to scale or a diminishing marginal prod- uct of labor? What is the likely explanation for why output doesn’t increase proportionately with the number of workers?

b. Michelle believes that if she could use two kilns and two workers, she could produce 55 cups a day. If so, what can you say about returns to scale?

4.9 Does it follow that because we observe that the aver- age product of labor is higher for Firm 1 than for Firm 2, Firm 1 is more productive in the sense that it can produce more output from a given amount of inputs? Why?

5. Innovation 5.1 Over the past 10 years, cloud storage services such

as Dropbox, Google Drive, Apple’s iCloud, and Microsoft’s OneDrive have taken over computer storage. In addition, many major corporations have adopted “flatter” organizational structures, with fewer layers of middle management. At the same time, major corporations have greatly increased their use of online meeting technologies such as Cisco’s WebEx, GoToMeeting, Google+ Hangouts,  and others. Which of these innovations is a new product innovation, which is a process innovation, and which is an organizational innovation. Explain.

*5.2 Firm 1 and Firm 2 use the same type of production function, but Firm 1 is only 90% as productive as Firm 2. That is, the production function of Firm 2 is q2 = f(L, K), and the production function of Firm 1 is q1 = 0.9f(L, K). At a particular level of inputs, how does the marginal product of labor differ between the firms?

5.3 In a manufacturing plant, workers use a special- ized machine to produce belts. A new labor-saving machine is introduced. With the new machine, the firm uses fewer workers to produce the same num- ber of belts as it did using the old machine. In the long run, both labor and capital (the machine) are variable. From what you know, what is the effect of this invention on the APL, MPL, and returns to scale?

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If you require more information to answer this ques- tion, specify what you need to know.

5.4 Until the mid-eighteenth century, when spinning became mechanized, cotton was an expensive and relatively unimportant textile (Virginia Postrel, “What Separates Rich Nations from Poor Nations?” New York Times, January 1, 2004). Where it used to take a hand-spinner 50,000 hours to hand-spin 100 pounds of cotton, an operator of a 1760s-era hand- operated cotton mule-spinning machine could pro- duce 100 pounds of stronger thread in 300 hours. When the self-acting mule spinner automated the process after 1825, the time dropped to 135 hours, and cotton became an inexpensive, common cloth. In a figure, show how these process innovations affected isoquants. Explain briefly.

5.5 A firm initially has a linear production function q = 10L + 12K. The firm undertakes an organiza- tional innovation that doubles the marginal product of labor but does not affect the marginal product of capital. What is the new production function?

6. Managerial Problem 6.1 If a firm lays off workers during a recession, how

will the firm’s marginal product of labor change? (Hint: See Figure 5.1.)

*6.2 During recessions, U.S. firms lay off a larger propor- tion of their workers than Japanese firms do. (It has been claimed that Japanese firms continue to produce at high levels and store the output or sell it at relatively low prices during the recession.) Assuming that the production function remains unchanged over a period that is long enough to include many recessions and expansions, would you expect the average product of labor to be higher in Japan or the United States? Why?

7. MyLab Economics Spreadsheet Exercises7

7.1 Labor, L, and capital, K, are the only inputs in each of the following production functions:

a. q1 = (L + K)2. b. q2 = ( 2L + 2K)2 c. q3 = (20 + 2L + 2K)2

For each production function, use a spreadsheet to find the output associated with the following output

7The spreadsheet exercises in this chapter are based largely on the work of Satyajit Ghosh, in cooperation with the authors. The answers are available on MyLab Economics.

combinations: L = 2, K = 2; L = 4, K = 4; and L = 8, K = 8. Determine whether each production function exhibits increasing returns to scale, decreas- ing returns to scale, constant returns to scale, or vari- able returns to scale over this range.

7.2 The Green Revolution (see the Mini-Case “Malthus and the Green Revolution”) was based in part on extensive experimentation. The following data illus- trate the relationship between nitrogen fertilizer (in pounds of nitrogen) and the output of a particular type of wheat (in bushels). Each observation is based on one acre of land, and all other relevant inputs to production (such as water, labor, and capital) are held constant. The fertilizer levels are 20, 40, 60, 80, 100, 120, 140, and 160, and the associated output lev- els are 47, 86, 107, 131, 136, 148, 149, and 142.

a. Use Excel to estimate the short-run production function showing the relationship between fer- tilizer input and output. (Hint: As described in Chapter 3, use the Trendline option to regress output on fertilizer input. Try a linear function and try a quadratic function and determine which function fits the data better.)

b. Does fertilizer exhibit the law of diminishing mar- ginal returns? What is the largest amount of fer- tilizer that should ever be used, even if it is free?

7.3 Summit Farms hires unskilled daily workers to pick strawberries in their fields. Output depends on the number of workers and on random factors such as weather. Summit Farms wishes to estimate its short- run production function and has collected the follow- ing data over 15 days on the number of workers, L, and output, q, measured in pounds of strawberries.

a. Use Excel’s Regression tool to estimate a pro- duction function of the form q = aL2 + bL3 for Summit Farms. (Hint: This production function implies that output is zero when L = 0. There- fore, you should set the constant term in the regression to zero, which is an option in the Regression tool.)

b. Use the estimated function and Excel’s charting tool to plot the estimated total product, average product of labor, and marginal product of labor curves. (Hint: See Figure 5.1.)

Question 7.3

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 L 5 7 8 6 6 8 10 11 12 9 10 10 8 7 8 q 250 385 442 331 324 442 500 478 432 490 480 494 317 399 448

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153

6 Costs Too caustic? To hell with the costs, we’ll make the picture anyway.—Samuel Goldwyn

Afirm uses a two-step procedure to determine the most efficient way to pro-duce a certain amount of output. First, the firm ascertains which production processes are technically efficient so that it can produce the desired level of output without any wasted or unnecessary inputs. As we saw in Chapter 5, the firm uses engineering and other information to determine its production function, which summarizes the many technically efficient production processes available. A firm’s production function shows the maximum output that can be produced with any specified combination of inputs or factors of production, such as labor, capital, energy, and materials.

The manager of a semiconductor manufacturing firm, who can choose from many different production technologies, must determine whether to use the same tech- nology in its foreign plant that it uses in its domestic plant. U.S. semiconductor manu- facturing firms have been moving much of their production abroad since 1961, when Fairchild Semiconductor built a plant in Hong Kong. According to the Semi- conductor Industry Association, worldwide semiconductor sales from the Americas dropped from 66% in 1976 to 34% in 1998, and to 17% in 2011, and then rose slightly to 22% in 2018.

Semiconductor firms moved their production abroad because of lower taxes, lower labor costs, and capital grant benefits. Capital grants are funds provided by a foreign government to firms to induce them to produce in that country. Such grants can reduce the cost of owning and operating an overseas semiconductor

fabrication facility by as much as 25%, compared to the costs of running a U.S.-based plant. However, starting in 2012, China, Thailand, and other Asian countries substantially raised their mini- mum wages, which reduced the incentive of U.S. firms to move production to those locations.

The semiconductor manufacturer can produce a chip using either sophisticated equipment and relatively few workers or many workers and less complex equipment. In the United States, firms use a relatively capital-intensive technology, because doing so minimizes their cost of producing a given level of out- put. Will that same technology be cost minimizing if they move their production abroad?

Technology Choice at Home Versus Abroad

Managerial Problem

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154 CHAPTER 6 Costs

The firm’s second step is to pick from these technically efficient production pro- cesses the one that is also economically efficient, minimizing the cost of producing a specified output level.1 To find out which process minimizes its cost of production, the firm uses information about the production function and the cost of inputs.

Managers and economists need to understand the relationship between costs of inputs and production to determine the least costly way to produce. By minimizing the cost of producing a given level of output, a firm can increase its profit.

1Similarly, economically efficient production implies that the quantity of output is maximized for any given level of cost.

6.1 The Nature of Costs Making sound managerial decisions about investment and production requires information about the associated costs. Legally required financial accounting state- ments provide some cost information. However, such statements do not provide suf- ficient cost information for good decision making. Financial accounting statements correctly measure costs for tax purposes and to meet other legal requirements, but good managerial decisions require a different perspective on costs.

To produce a particular amount of output, a firm incurs costs for the required inputs, such as labor, capital, energy, and materials. A firm’s manager (or accountant) determines the cost of labor, energy, and materials by multiplying the price of the factor times the number of units used. If workers earn $20 per hour and the firm hires 100 hours of labor per day, then the firm’s cost of labor is $20 * 100 = $2,000 per day. The manager can easily calculate these explicit costs, which are its direct, out-of-pocket payments for inputs to its production process during a given period. While calculating explicit costs is straightforward, some costs are implicit in that they reflect only a foregone opportunity rather than explicit, current expenditure. Prop- erly taking account of foregone opportunities requires especially careful attention when dealing with durable capital goods, as past expenditures for an input may be irrelevant to current cost calculations if that input has no current, alternative use.

Opportunity Costs An economist is a person who, when invited to give a talk at a banquet, tells the audience “There’s no such thing as a free lunch.”

A fundamental principle of managerial decision making is that managers should focus on opportunity costs. The opportunity cost of a resource is the value of the best alternative use of that resource. Explicit costs are opportunity costs. If a firm

Learning Objectives

1. Explain why managers should use opportunity costs in decision making.

2. Draw marginal cost, average cost, and other cost curves.

3. Explain how to choose inputs to minimize cost.

4. Predict how experience-based learning reduces costs.

5. Describe when it pays to produce two or more goods simultaneously.

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1556.1 The Nature of Costs

purchases an input in a market and uses that input immediately, the input’s oppor- tunity cost is the amount the firm pays for it, the market price. After all, if the firm did not use the input in its production process, its best alternative would be to sell the input to someone else at the market price. The opportunity cost concept is par- ticularly useful when the firm uses an input that it cannot purchase in a market or that was purchased in a market in the past.

An important example of such an opportunity cost is the value of a manager’s time. For example, Maoyong owns and manages a firm. He pays himself only a small monthly salary of $1,000 because he also receives the firm’s profit. However, Mao- yong could work for another firm and earn $11,000 a month. Thus, the opportunity cost of his time is $11,000—from his best alternative use of his time—not the $1,000 he actually pays himself.

A financial statement may not include such an opportunity cost, but Maoyong needs to take account of this opportunity cost to make decisions that maximize his profit. Suppose that the explicit cost of operating his firm is $40,000, including the rent for work space, the cost of materials, the wage payments to an employee, and the $1,000 a month he pays himself. The full, opportunity cost of the firm is $50,000, which includes the extra $10,000 in opportunity cost for Maoyong’s time beyond the $1,000 that he already pays himself. If his firm’s revenue is $49,000 per month and he considers only his explicit costs of $40,000, it appears that his firm makes a profit of $9,000. In contrast, if he takes account of the full opportunity cost of $50,000, his firm incurs a loss of $1,000.

Another example of an opportunity cost is captured in the well-known phrase “There’s no such thing as a free lunch.” Suppose your parents come to town and offer to take you to lunch. Although they pay the explicit cost—the restaurant’s tab—for the lunch, you still incur the opportunity cost of your time. No doubt the best alter- native use of your time is studying this text book, but you could also consider work- ing at a job for a wage or surfing the internet as possible alternatives. In considering whether to accept the “free” lunch, you need to compare this true opportunity cost against the benefit of dining with your parents.

At one point or another, most of us have held the following false belief:

The fallacy in this belief is that we have ignored the opportunity cost of our time. Have you ever tried to fix a plumbing problem and ended up taking hours to make a repair that a professional plumber could have done in a few minutes? Fixing the problem yourself only makes sense if the opportunity cost of your time is very low or the plumber’s fee is very high. Similarly, growing our own food would cost most of us much more than buying it from a store once we take into account the value of our time.

Common Confusion I can save money by doing things myself rather than buying goods and services from firms.

Mini-Case During major economic downturns, do applications to MBA programs fall, hold steady, or rise? Knowledge of opportunity costs helps us answer this question.

The biggest cost of attending an MBA program is often the opportunity cost of giving up a well-paying job. Someone who leaves a job paying $6,000 per month to attend an MBA program is, in effect, incurring a $6,000 per month opportunity cost, in addition to the tuition and cost of textbooks (though this one is well worth the money).

The Opportunity Cost of an MBA

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156 CHAPTER 6 Costs

Costs of Durable Inputs Determining the opportunity cost of capital such as land, buildings, or equipment is more complex than calculating the cost of inputs that are bought and used in the same period, such as labor services, energy, or materials. Capital is a durable good: a product that is usable for a long period, perhaps for many years. Two problems may arise in measuring the cost of a firm’s capital. The first is how to allocate the initial purchase cost over time. The second is what to do if the value of the capital changes over time.

We can avoid these two measurement problems if capital is rented instead of pur- chased. For example, suppose a firm can rent a pick-up truck for $500 a month or buy it outright for $25,000. If the firm rents the truck, the rental payment is the relevant opportunity cost per month. The truck is rented month by month, so the firm does

Q&A 6.1 Meredith’s firm has sent her to a conference for managers and paid her registra- tion fee. Included in the registration fee is free admission to a class on how to price derivative securities, such as options. She is considering attending, but her most attractive alternative opportunity is to attend a talk given at the same time by Warren Buffett on his investment strategies. She would be willing to pay $100 to hear his talk, and the cost of a ticket is $40. Given that attending either talk involves no other costs, what is Meredith’s opportunity cost of attending the derivatives talk?

Answer To determine her opportunity cost, determine the benefit that Meredith would forego by attending the derivatives class. Because she incurs no additional fee to attend the derivatives talk, Meredith’s opportunity cost is the foregone benefit of hearing the Buffett speech. Because she values hearing the Buffett speech at $100, but only has to pay $40, her net benefit from hearing that talk is $60 (= $100 - $40). Thus, her opportunity cost of attending the derivatives talk is $60.

Thus, it is not surprising that MBA applications rise in bad economic times when outside opportunities decline. People thinking of going back to school face a reduced opportunity cost of entering an MBA program if they think they might be laid off or might not be promoted during an economic downturn. As Stacey Kole, deputy dean for the MBA program at the University of Chicago’s Graduate School of Business, observed, “When there’s a go-go economy, fewer people decide to go back to school. When things go south, the opportunity cost of leaving work is lower.”

During the Great Recession in 2008, when U.S. unemployment rose sharply and the economy was in poor shape, the number of people seeking admission to MBA programs also rose sharply. Applications continued to rise as unem- ployment remained high for several years. The U.S. unemployment rate peaked at 10% in late 2009 and did not fall below 8% until 2012. However the U.S. unemployment rate dropped below 5% by late 2015, and continued to fall. Cor- respondingly, U.S. MBA applications fell in the 2015, 2016, and 2017 admission years.

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1576.1 The Nature of Costs

not have to worry about how to allocate the purchase cost of a truck over time. Moreover, the rental rate would adjust if the cost of trucks changes over time. Thus, if the firm can rent capital for short periods, it calculates the cost of this capital in the same way that it calculates the cost of nondurable inputs such as labor services or materials.

The firm faces a more complicated problem in determining the opportunity cost of the truck if it purchases the truck. The firm’s accountant may expense the truck’s purchase price by treating the full $25,000 as a cost when the truck is purchased, or the accountant may amortize the cost by spreading the $25,000 over the life of the truck, following rules set by an accounting organization or by a relevant government authority such as the Internal Revenue Service (IRS).

A manager who wants to make sound decisions about operating the truck should not focus on these cost accounting conventions but should use opportunity cost instead. The firm’s opportunity cost of using the truck is the amount that the firm would earn if it rented the truck to others. Thus, even though the firm owns the truck, the manager should view the opportunity cost of this capital good as a rent per time period. If the value of an older truck is less than that of a newer one, the rental rate for the truck falls over time.

If no rental market for trucks exists, we must determine the opportunity cost in another way. Suppose that the firm has two choices: It can choose not to buy the truck and keep the truck’s purchase price of $25,000, or it can use the truck for a year and sell it for $22,000 at the end of the year. If the firm did not purchase the truck, it would deposit the $25,000 in a bank account that pays, for example, 2% per year, earning $500 in interest and therefore having $25,500 at the end of the year. Thus, the oppor- tunity cost of capital of using the truck for a year is $25,500 - $22,000 = $3,500.2 This $3,500 opportunity cost equals the depreciation of the truck of $3,000 (= $25,000 - $22,000) plus the $500 in foregone interest that the firm could have earned over the year if the firm had invested the $25,000.

The value of trucks, machines, and other equipment declines over time, leading to declining rental values and therefore to declining opportunity costs. In contrast, the value of some land, buildings, and other forms of capital may rise over time. To maximize its economic profit, a firm must properly measure the opportunity cost of a piece of capital even if its value rises over time. If a beauty parlor buys a building when similar buildings in that area rent for $1,000 per month, then the opportunity cost of using the building is $1,000 a month. If land values rise, causing rents in the area to rise to $2,000 per month, the beauty parlor’s opportunity cost of its building increases to $2,000 per month.

Sunk Costs An opportunity cost is not always easy to observe but should always be taken into account in deciding how much to produce. In contrast, even though a sunk cost—a past expenditure that cannot be recovered—is easily observed, it is not relevant to a manager when deciding how much to produce now. If an expenditure is sunk, it is not an opportunity cost. Nonetheless, a cost paid for a specialized input should still be deducted from income before paying taxes even if that cost is sunk, and must therefore appear in financial accounts.

2The firm would also pay for gasoline, insurance, and other operating costs, but these items would all be expensed as operating costs and would not appear in the firm’s accounts as capital costs.

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158 CHAPTER 6 Costs

If a firm buys a forklift for $30,000 and can resell it for the same price, then the expenditure is not sunk, and the opportunity cost of using the forklift is $30,000. If instead the firm buys a specialized piece of equipment for $30,000 and can- not resell it, then the original expenditure is a sunk cost—it cannot be recovered. Because this equipment has no alternative use—it cannot be resold—its opportu- nity cost is zero, and hence should not be included in the firm’s current cost calcu- lations. If the  specialized equipment that originally cost $30,000 can be resold for $20,000, then only $10,000 of the original expenditure is sunk, and the opportunity cost is $20,000.

6.2 Short-Run Costs When making short-run and long-run production and investment decisions, manag- ers must take the relevant costs into account. As noted in Chapter 5, the short run is the period over which some inputs, such as labor, can be varied while other inputs, such as capital, are fixed. In contrast, in the long run, the firm can vary all its inputs. For simplicity in our graphs, we concentrate on firms that use only two inputs, labor and capital. We focus on the case in which labor is the only variable input in the short run, and both labor and capital are variable in the long run. However, we can generalize our analysis to examine a firm that uses any number of inputs.

We start by examining various measures of cost and cost curves that can be used to analyze costs in both the short run and the long run. Then we show how the shapes of the short-run cost curves are related to the firm’s production function.

A manager should ignore sunk costs when making current decisions. To see why, consider a firm that paid $300,000 for a parcel of land for which the market value has fallen to $200,000, which is the land’s current opportunity cost. The $100,000 difference between the $300,000 purchase price and the current market value of $200,000 is a sunk cost that has already been incurred and cannot be recov- ered. The land is worth $240,000 to the firm if it builds a plant on this parcel. Is it worth carrying out production on this land or should the land be sold for its market value of $200,000? A manager who uses the original purchase price in the decision-making process would incorrectly conclude that using the land for pro- duction will result in a $60,000 loss: the value of using the land of $240,000 minus the purchase price of $300,000. Instead, the firm should use the land because it is worth $40,000 more as a production facility than the firm’s next best alternative of selling the land for $200,000. Thus, in making its decisions, the firm should use the land’s opportunity cost and ignore the land’s sunk cost—in short, “no use crying over spilt milk,” “what’s done is done,” and “don’t throw good money after bad.”

Ignoring Sunk Costs

Managerial Implication

Mini-Case What are the short-run costs of building an electric guitar? Online guitar seller Reverb described the cost of building a base-level, generic slab-body, two- pickup, T-style guitar with a bolt-on neck.

For an inexpensive guitar, a computer numeric control (CNC) router is used to cut, carve, machine, and mill the wood. A CNC router can make a guitar

Costs of Building a Guitar

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1596.2 Short-Run Costs

Common Measures of Cost All firms use the same basic cost measures for making both short-run and long-run decisions. The measures should be based on the opportunity costs of inputs.

Fixed Cost, Variable Cost, and Total Cost. A fixed cost (F ) does not vary with the level of output. Fixed costs, which include expenditures on land, office space, production facilities, and other overhead expenses, cannot be avoided by reduc- ing output and must be incurred as long as the firm stays in business.

Fixed costs are often sunk costs, but not always. For example, a restaurant rents space for $2,000 per month on a month-to-month lease. This rent does not vary with the number of meals served (its output level), so it is a fixed cost. Because the restaurant has already paid this month’s rent, this fixed cost is a sunk cost: The res- taurant cannot get the $2,000 back even if it goes out of business. Next month, if the

restaurant stays open, it will have to pay the fixed, $2,000 rent. If the restaurant has a month-to-month rental agreement, next month’s fixed cost of $2,000 is an avoidable cost, not a sunk cost. The restaurant can shut down, cancel its rental agreement, and avoid paying this fixed cost. Therefore, in planning for next month, the restaurant should treat the $2,000 rent as a fixed cost but not as a sunk cost. The $2,000 per month rent is a fixed cost in both the short run (this month) and the long run. However, it is a sunk cost only in the short run.

A variable cost (VC) changes as the quantity of output changes. Variable costs are the costs of variable  inputs, which are inputs that the firm can adjust to alter its output level, such as labor and materials.

body in minutes that would take a craftsman hours to produce. A desktop CNC machine for a small shop costs about $10,000. These machines and the shop are the capital used to make a basic guitar.

A guitar also requires materials, particularly wood, and components such as tuners, pickups, wiring, and switches. These items are readily available. Labor is by far the most costly factor of production in making guitars. Enormous amounts of handwork go “into sanding, fitting, and finishing every nook and

cranny on a body and a neck” of a guitar. Quality work on the fit and finish, including paint and fret work, requires yet more labor.

Labor’s share of producing the hardshell case for a guitar is particu- larly large. The cost is $45 to $50. However, the cost of a mandolin case, which is one-quarter the size of a guitar case, is only $2 less. Labor is 95% of the cost, and the labor is the same for both cases.

In the short run, labor and materials are variable inputs and capital is fixed. The firm can increase production only by using more labor. In the long run, the firm can also increase its capital by buying more CNC machines and expanding its shop size.

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160 CHAPTER 6 Costs

A firm’s cost or total cost (C) is the sum of a firm’s variable cost and fixed cost:

C = VC + F.

Because variable costs change as the output level changes, so does total cost. For example, in Table 6.1, if the fixed cost is F = $48 and the firm produces 5 units of output, its variable cost is VC = $100, so its total cost is C = $48 + $100 = $148.

Average Cost. Managers use three average cost measures corresponding to fixed, variable, and total costs. The average fixed cost (AFC) is the fixed cost divided by the units of output produced: AFC = F>q. The average fixed cost falls as output rises because the fixed cost is spread over more units. The average fixed cost falls from $48 for 1 unit of output to $4 for 12 units of output in Table 6.1.

The average variable cost (AVC), or variable cost per unit of output, is the variable cost divided by the units of output produced: AVC = VC>q. Because the variable cost increases with output, the average variable cost may either increase or decrease as output rises. In Table 6.1, the average variable cost is $25 at 1 unit, falls until it reaches a minimum of $20 at 6 units, and then rises.

The average cost (AC)—or average total cost—is the total cost divided by the units of output produced: AC = C>q. Because total cost is C = VC + F, if we divide both sides of the equation by q, we find that average cost is the sum of the average fixed cost and the average variable cost:

AC = C q

= F q

+ VC q

= AFC + AVC.

In Table 6.1, AFC falls with output and AVC eventually rises with output. Average cost, the sum of AFC and AVC, falls until output is 8 units and then rises.

Output, q Fixed

Cost, F Variable Cost, VC

Total Cost, C

Marginal Cost, MC

Average Fixed Cost, AFC ∙ F ,q

Average Variable Cost, AVC ∙ VC ,q

Average Cost, AC ∙ C ,q

0 48 0 48

1 48 25 73 25 48 25 73

2 48 46 94 21 24 23 47

3 48 66 114 20 16 22 38

4 48 82 130 16 12 20.5 32.5

5 48 100 148 18 9.6 20 29.6

6 48 120 168 20 8 20 28

7 48 141 189 21 6.9 20.1 27

8 48 168 216 27 6 21 27

9 48 198 246 30 5.3 22 27.3

10 48 230 278 32 4.8 23 27.8

11 48 272 320 42 4.4 24.7 29.1

12 48 321 369 49 4.0 26.8 30.8

TABLE 6.1 How Cost Varies with Output

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1616.2 Short-Run Costs

Marginal Cost. A firm’s marginal cost (MC) is the amount by which a firm’s cost changes if the firm produces one more unit of output. The marginal cost is

MC = ∆C ∆q

,

where ∆C is the change in cost when the change in output, ∆q, is 1 unit in Table 6.1. If the firm increases its output from 2 to 3 units (∆q = 1), its total cost rises from $94 to $114, so ∆C = $20. Thus its marginal cost is ∆C>∆q = $20>1 = $20.

Because only variable cost changes with output, marginal cost also equals the change in variable cost from a one-unit increase in output:

MC = ∆VC ∆q

.

As the firm increases output from 2 to 3 units, its variable cost increases by ∆VC = $20 = $66 - $46, so its marginal cost is MC = ∆VC>∆q = $20>1 = $20. A firm takes account of its marginal cost curve to decide whether it pays to change its output level.

Cost Curves We illustrate the relationship between output and the various cost measures in Figure 6.1. Panel a shows the variable cost, fixed cost, and total cost curves that cor- respond to Table 6.1. The fixed cost, which does not vary with output, is a horizontal line at $48. The variable cost curve is zero at zero units of output and rises with output. The total cost curve, which is the vertical sum of the variable cost curve and the fixed cost line, is $48 higher than the variable cost curve at every output level, so the variable cost and total cost curves are parallel.

Panel b shows the average fixed cost, average variable cost, average cost, and mar- ginal cost curves. The average fixed cost curve falls as output increases. It approaches zero as output gets large because the fixed cost is spread over many units of output. The average cost curve is the vertical sum of the average fixed cost and average variable cost curves. For example, at 6 units of output, the average variable cost is 20 and the average fixed cost is 8, so the average (total) cost is 28.

The relationships between the average and marginal cost curves and the total cost curve are similar to those between the average and marginal product curves and the total product curve (as discussed in Chapter 5). The average cost at a particular output level is the slope of a line from the origin to the corresponding point on the

Calculating Marginal Cost

Using Calculus Using calculus, marginal cost is MC = dC>dq, which is the rate of change of cost as we make an infinitesimally small change in output. Given that C = VC + F, it follows that MC = dVC>dq + dF>dq = dVC>dq, because fixed costs do not change as output changes: dF>dq = 0.

For example, suppose that the variable cost is VC = 4q + 6q2 and the fixed cost is F = 10, so the total cost is C = VC + F = 4q + 6q2 + 10. Using the variable cost, the marginal cost is dVC>dq = d(4q + 6q2)>dq = 4 + 12q. We get the same expression for marginal cost if we use the total cost: dC>dq = d(4q + 6q2 + 10)>dq = 4 + 12q.

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162 CHAPTER 6 Costs

total cost curve. The slope of that line is the rise (the cost at that output level) divided by the run (the output level), which is the definition of the average cost. In panel a, the slope of the line from the origin to point A is the average cost for 8 units of out- put. The height of the cost curve at A is 216, so the slope is 216>8 = 27, which is the height of the average cost curve at the corresponding point a in panel b.

Similarly, the average variable cost is the slope of a line from the origin to a point on the variable cost curve. The slope of the thin black line from the origin to B in panel a is 20 (the height of the variable cost curve, 120, divided by the number of units of output, 6), which is also the height of the average variable cost curve at 6 units of output, point b in panel b.

The marginal cost is the slope of either the cost curve or the variable cost curve at a given output level. Because the total cost and variable cost curves are parallel,

FIGURE 6.1 Cost Curves

(a) Because the total cost differs from the variable cost by the fixed cost, F, of $48, the total cost curve, C, is parallel to the variable cost curve, VC. (b) The marginal cost curve, MC, cuts the average variable cost, AVC, and average cost, AC, curves at their minimums. The height of the AC curve at point a equals the slope of the line from the origin to the cost curve at A. The height of the AVC at b equals the slope of the line from the origin to the variable cost curve at B. The height of the marginal cost is the slope of either the C or VC curve at that quantity.

120

216

400

48

0 6 10

10

42 8

Quantity, q, Units per day 6

b

a

B

A

42 8

C

F

1

1

27

20

VC

MC

AC

AVC

AFC

C os

t, $

C os

t p er

u ni

t, $

(a)

(b)

60

28 27

20

8

0

Quantity, q, Units per day

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1636.2 Short-Run Costs

they have the same slope at any given output. The difference between total cost and variable cost is fixed cost, which does not affect marginal cost.

The thin black line from the origin is tangent to the cost curve at A in panel a. Thus, the slope of the thin black line equals both the average cost and the marginal cost at point a (8 units of output). This equality occurs at the corresponding point a in panel b, where the marginal cost curve intersects the average cost.

Where the marginal cost curve is below the average cost, the average cost curve declines with output. Table 6.1 shows that the average cost of producing the first two units is 47. Because this average cost for 2 units is greater than the marginal cost of the third unit, 20, the average cost for 3 units falls to 38.3 Where the marginal cost is above the average cost, the average cost curve rises with output. At 8 units, the mar- ginal cost equals the average cost (at point a in panel b, the minimum point of the average cost curve), so the average is unchanging.

Because the thin black line from the origin through point B in panel a is tangent to the variable cost curve at B, the marginal cost equals the average variable cost at the corresponding point b in panel b. Again, where marginal cost is above average variable cost, the average variable cost curve rises with output; where marginal cost is below average variable cost, the average variable cost curve falls with output. Because the average cost curve is above the average variable cost curve everywhere and the marginal cost curve is rising where it crosses both average curves, the mini- mum of the average variable cost curve, b, is at a lower output level than the mini- mum of the average cost curve, a.

3The average cost of the first two units is 47. If we add a third unit with a marginal cost of 20, the new average can be calculated by adding the average values of the first two units plus the marginal cost of the third unit and dividing by 3: (47 + 47 + 20)>3 = 38. Thus, if we add a marginal cost that is less than the old average cost, the new average cost must fall.

Q&A 6.2 Suppose that a small guitar firm has experimented with the cost of producing different quantities of output per hour by varying the number of workers, holding the size of the plant fixed and using just one CNC machine. It has estimated its cost function as C = 125 + 10q - 5q2 + q3 where q is quantity produced per hour and C is measured in dollars. The corresponding marginal cost function is MC = 10 - 10q + 3q2.4 Use an Excel spreadsheet to show the fixed cost, and to calculate variable cost, total cost, average cost, and marginal cost for output levels from 1 to 10 in one-unit increments. Use the spreadsheet to find the output level at which average cost is minimized and verify that AC = MC at this output level.

Answer 1. Open an Excel spreadsheet and put titles Quantity, Fixed Cost, Variable Cost, Total

Cost, Average Cost, and Marginal Cost in cells A1 through F1. Fill in the numbers 1 through 10 in one-unit increments in cells A2–A11 and enter the number 125 (fixed cost) in each cell from B2 through B11.

2. Fill in the other columns using appropriate formulas. Enter “=10*A2- 5*A2^2+A2^3” in cell C2 and copy this formula into the remaining cells in column C. Enter “=B2+C2” in cell D2, then copy that formula into the rest of column D up to cell D11. Enter “=D2>A2” into cell E2 and copy that formula

4You could approximate the marginal cost by determining the change in total cost as output increases by one unit. However, this formula is exact and should be used here.

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164 CHAPTER 6 Costs

Production Functions and the Shapes of Cost Curves The production function determines the shape of a firm’s cost curves. This function shows the amount of inputs needed to produce a given level of output (Chapter 5). The firm calculates its variable cost by multiplying the quantity of each input by its price and summing the costs of the variable inputs.

In this section, we focus on cost curves in the short run. If a firm produces output using capital and labor, and its capital is fixed in the short run, the firm’s variable cost is its cost of labor. Its labor cost is the wage per hour, w, times the number of hours of labor, L, employed by the firm: VC = wL.

into the rest of column E. Enter “=10-10*A2+3*A2^2” into cell F2 and also copy that formula into the rest of column F. The formulas are shown in the screenshot.

3. Look in the Average Cost column to identify the output at which average cost is minimized. Average cost reaches its lowest level in cell E6, where the quantity produced is 5 and average cost is 35. At this output level, marginal cost is also equal to 35, as the screenshot shows. (The average cost column has been for- matted to show two digits after the decimal point.)

Note: It is possible to use Excel to draw any of the cost curves by inserting a scatterplot. The screenshot shows the average and marginal cost curves.

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1656.2 Short-Run Costs

In the short run, when the firm’s capital is fixed, the only way the firm can increase its output is to use more labor. If the firm increases its labor enough, it reaches the point of diminishing marginal returns to labor, at which each extra worker increases output by a smaller amount. We can use this information about the relationship between labor and output—the production function—to determine the shape of the variable cost curve and its related curves.

The Variable Cost Curve. If input prices are constant, the firm’s production function determines the shape of the variable cost curve. We illustrate this relation- ship in Figure 6.2. The firm faces a constant input price for labor, the wage, of $20 per hour.

The total product of labor curve in Figure 6.2 shows the firm’s short-run produc- tion function relationship between output and labor when capital is held fixed. At point a, the firm uses 5 hours of labor to produce 1 unit of output. At point b, it takes 20 hours of labor to produce 5 units of output. Here, output increases more than in proportion to labor: Output rises 5 times when labor increases 4 times. In contrast, as the firm moves from b to c, output increases less than in proportion to labor. Output doubles to 10 as a result of increasing labor from 20 to 46—an increase of 2.3 times. The movement from c to d results in an even smaller increase in output relative to labor. This flattening of the total product curve at higher levels of labor reflects diminishing marginal returns to labor.

This curve shows both the production relation of output to labor and the variable cost relation of output to cost. Because each hour of work costs the firm $20, we can relabel the horizontal axis in Figure 6.2 to show the firm’s variable cost, its cost of

Q ua

nt ity

, q , U

ni ts

p er

d ay

46 920

20 400

5 100

77 1,540

Total product, Variable cost

5

1

10

13

L, Hours of labor per day VC = wL, Variable cost, $

c

d

b

a

e

6

24 480

FIGURE 6.2 Variable Cost and Total Product

The firm’s short-run variable cost curve and its total product curve have the same shape. The total product curve uses the horizontal axis, measuring

hours of work. The variable cost curve uses the hori- zontal axis, measuring labor cost, which is the only variable cost.

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166 CHAPTER 6 Costs

labor. To produce 5 units of output takes 20 hours of labor, so the firm’s variable cost is $400. By using the variable cost labels on the horizontal axis, the total product of labor curve becomes the variable cost curve.

As output increases, the variable cost increases more than proportionally due to the diminishing marginal returns. Because the production function determines the shape of the variable cost curve, it also determines the shape of the marginal, aver- age variable, and average cost curves. We now examine the shape of each of these cost curves in detail, because when making decisions, managers rely more on these per-unit cost measures than on total variable cost.

The Marginal Cost Curve. The marginal cost is the change in variable cost as output increases by one unit: MC = ∆VC>∆q. In the short run, capital is fixed, so the only way the firm can produce more output is to use extra labor. The extra labor required to produce one more unit of output is ∆L>∆q. The extra labor costs the firm w per unit, so the firm’s cost rises by w(∆L>∆q). As a result, the firm’s marginal cost is

MC = ∆VC ∆q

= w ∆L ∆q

.

The marginal cost equals the wage times the extra labor necessary to produce one more unit of output. To increase output by one unit from 5 to 6 units takes 4 extra hours of work in Figure 6.2. If the wage is $20 per hour, the marginal cost is $80.

How do we know how much extra labor we need to produce one more unit of output? That information comes from the production function. The marginal product of labor—the amount of extra output produced by another unit of labor, holding other inputs fixed—is MPL = ∆q>∆L. Thus, the extra labor we need to produce one more unit of output, ∆L>∆q, is 1>MPL, so the firm’s marginal cost is

MC = w

MPL . (6.1)

Equation 6.1 says that the marginal cost equals the wage divided by the marginal product of labor. If the firm is producing 5 units of output, it takes 4 extra hours of labor to produce 1 more unit of output in Figure 6.2, so the marginal product of an hour of labor is 14 unit of output. Given a wage of $20 an hour, the marginal cost of the sixth unit is $20 divided by 14, or $80.

Equation 6.1 shows that the marginal product of labor and marginal cost move in opposite directions as output changes. At low levels of labor, the marginal product of labor commonly rises with additional labor because extra workers help the original workers and they can collectively make better use of the firm’s equipment. As the marginal product of labor rises, the marginal cost falls.

Eventually, however, as the number of workers increases, workers must share the fixed amount of equipment and may get in each other’s way. As more workers are added, the marginal product of each additional worker begins to fall and the marginal cost of each additional unit of product rises. As a result, the marginal cost curve slopes upward because of diminishing marginal returns to labor. Thus, the marginal cost first falls and then rises.

The Average Cost Curves. Because they determine the shape of the variable cost curve, diminishing marginal returns to labor also determine the shape of the average variable cost curve. The average variable cost is the variable cost divided

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1676.2 Short-Run Costs

by output: AVC = VC>q. For the firm we’ve been examining, whose only variable input is labor, variable cost is wL, so average variable cost is

AVC = VC q

= wL q

.

Because the average product of labor, APL, is q>L, average variable cost is the wage divided by the average product of labor:

AVC = w

APL . (6.2)

In Figure 6.2, at 6 units of output, the average product of labor is 14 (=q>L = 6>24), so the average variable cost is $80, which is the wage, $20, divided by the average product of labor, 14.

With a constant wage, the average variable cost moves in the opposite direction of the average product of labor in Equation 6.2. As we discussed in Chapter 5, the average product of labor tends to rise and then fall, so the average cost tends to fall and then rise, as in panel b of Figure 6.1.

The average cost curve is the vertical sum of the average variable cost curve and the average fixed cost curve, as in panel b of Figure 6.1. If the average variable cost curve is U-shaped, adding the strictly falling average fixed cost makes the average cost fall more steeply than the average variable cost curve at low output levels. At high output levels, the average cost and average variable cost curves differ by ever smaller amounts, as the average fixed cost, F>q, approaches zero. Thus, the average cost curve is also U-shaped.

In Appendix 6A we derive the average, marginal, and variable cost functions aris- ing from a Cobb-Douglas production function (Chapter 5).

Short-Run Cost Summary We use cost curves to illustrate three cost level concepts—total cost, fixed cost, and variable cost—and four cost-per-unit cost concepts—average cost, average fixed cost, average variable cost, and marginal cost. Understanding the shapes of these curves and the relationships among them is crucial to the analysis of firm behav- ior in the rest of this book. Fortunately, we can derive most of what we need to know about the shapes and the relationships between the short-run curves using four basic concepts:

1. In the short run, the cost associated with inputs that cannot be adjusted is fixed, while the cost from inputs that can be adjusted is variable.

2. Given that input prices are constant, the shapes of the variable cost and the cost- per-unit curves are determined by the production function.

3. Where a variable input exhibits diminishing marginal returns, the variable cost and cost curves become relatively steep as output increases, so the average cost, average variable cost, and marginal cost curves rise with output.

4. Because of the relationship between marginal values and average values, both the average cost and average variable cost curves fall when marginal cost is below them and rise when marginal cost is above them. Thus, the marginal cost cuts both these average cost curves at their minimum points.

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168 CHAPTER 6 Costs

6.3 Long-Run Costs In the long run, the firm adjusts all its inputs so that its cost of production is as low as possible. The firm can change its plant size, design and build new machines, and otherwise adjust inputs that were fixed in the short run.

Although firms may incur fixed costs in the long run, these fixed costs are avoid- able (rather than sunk, as they are in the short run). The rent of F per month that a restaurant pays is a fixed cost because it does not vary with the number of meals (output) served. In the short run, this fixed cost is sunk: The firm must pay F even if the restaurant does not operate. In the long run, this fixed cost is avoidable because the restaurant need not renew its rental agreement. The firm does not have to pay this rent if it shuts down. This cost is still a fixed cost, even in the long run, but it is not sunk in the long run.

To simplify our long-run analysis, we use examples with no long-run fixed costs (F = 0). Consequently, average cost and average variable cost are identical.

To produce a given quantity of output at minimum cost, our firm uses informa- tion about its production function and the price of labor and capital. In the long run when capital is variable, the firm chooses how much labor and capital to use; in the short run when capital is fixed, the firm chooses only how much labor to use. As a consequence, the firm’s long-run cost of production is lower than its short-run cost if it has to use the “wrong” level of capital in the short run. In this section, we show how a firm picks the cost-minimizing combination of inputs in the long run.

Mini-Case Construction companies traditionally view workers’ earnings as a variable cost and the capital that the firm owns—particularly heavy equipment such as bull- dozers—as a fixed cost. The sharing economy is changing that.

When Platinum Pipeline Inc., a firm that installs water and sewer lines, won a new job, it needed a third bulldozer. Rather than buy one, the firm’s president, Manuel de Freitas, merely called up an app on his phone and found a Caterpillar D6T dozer that he could rent for two months at $7,500 a month. The rental firm, Yard Club Inc., finds idle heavy equipment and rents it—much as Airbnb Inc.

does with spare bedrooms. Often, rental companies own this equipment.

Renting construction equipment is catching on. In 2014, rental companies owned 54% of U.S. con- struction equipment, up from 40% a decade earlier. According to one forecast, the share could top 60% within the next 5 to 10 years. In 2018, Global Market Insights predicted that the construction equipment rental market will grow at over 4% a year from 2018 to 2024.

If construction firms can rent heavy equipment, their long run may be much shorter than if they have to buy the equipment.

Short Run Versus Long Run in the Sharing Economy

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1696.3 Long-Run Costs

Input Choice A firm can produce a given level of output using many different technically efficient combinations of inputs, as summarized by an isoquant (see Chapter 5). From among these technically efficient combinations of inputs, a firm wants to choose that bundle of inputs with the lowest cost of production, which is the economically efficient com- bination of inputs. To do so, the firm combines information about technology from the isoquant with information about the cost of production.

The Isocost Line. The cost of producing a given level of output depends on the price of labor and capital. The firm hires L hours of labor services at a constant wage of w per hour, so its labor cost is wL. The firm rents K hours of machine services at a constant rental rate of r per hour, so its capital cost is rK. (If the firm owns the capital, r is the implicit rental rate.) The firm’s total cost is the sum of its labor and capital costs:

C = wL + rK. (6.3)

A firm can hire as much labor and capital as it wants at these constant input prices from competitive labor and capital markets.

The firm can use many combinations of labor and capital that cost the same amount. Suppose that the wage rate, w, is $20 an hour and the rental rate of capital, r, is $40. Five of the many combinations of labor and capital that the firm can use that cost $200 are listed in Table 6.2. These combinations of labor and capital are plotted on an isocost line, which represents all the combinations of inputs that have the same (iso-) total cost. Figure 6.3 shows three isocost lines. The $400 isocost line represents all the combinations of labor and capital that the firm can buy for $400, including the combinations a through e in Table 6.2.

Along an isocost line, cost is fixed at a particular level, C, so by setting cost at C in Equation 6.3, we can write the equation for the C isocost line as

C = wL + rK.

Using algebra, we can rewrite this equation to show how much capital the firm can buy if it spends a total of C and purchases L units of labor:

K = C r

- w r

L. (6.4)

By substituting C = $400, w = $20, and r = $40 in Equation 6.4, we find that the $400 isocost line is K = 10 - 12 L. We can use Equation 6.4 to derive three properties of isocost lines.

TABLE 6.2 Bundles of Labor and Capital That Cost the Firm $400

Bundle Labor, L Capital, K Labor Cost, wL ∙ $20L

Capital Cost, rK ∙ $40K

Total Cost, wL ∙ rK

a 20 0 $400 $0 $400

b 14 3 $280 $120 $400

c 10 5 $200 $200 $400

d 6 7 $120 $280 $400

e 0 10 $0 $400 $400

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170 CHAPTER 6 Costs

First, the points at which the isocost lines hit the capital and labor axes depend on the firm’s cost, C, and on the input prices. The C isocost line intersects the capital axis where the firm is using only capital. Setting L = 0 in Equation 6.7, we find that the firm buys K = C>r units of capital. In Figure 6.3, the $400 isocost line intersects the capital axis at $400>$40 = 10 units of capital. Similarly, the intersection of the isocost line with the labor axis is at C>w, which is the amount of labor the firm hires if it uses only labor. In the figure, the intersection of the $400 isocost line with the labor axis occurs at L = 20, where K = 10 - 12 * 20 = 0.

Second, isocost lines that are farther from the origin have higher costs than those closer to the origin. Because the isocost lines intersect the capital axis at C>r and the labor axis at C>w, an increase in the cost shifts these intersections with the axes proportionately outward. The $200 isocost line hits the capital axis at 5 and the labor axis at 10, whereas the $400 isocost line intersects at 10 and 20.

Third, the slope of each isocost line is the same. From Equation 6.4, if the firm increases labor by ∆L, it must decrease capital by

∆K = - w r

∆L.

Dividing both sides of this expression by ∆L, we find that the slope of an isocost line, ∆K>∆L, is -w>r. Thus, the slope of the isocost line depends on the relative prices of the inputs. The slope of the isocost lines in the figure is -w>r = - $20>$40 = -12. If the firm uses two more units of labor, ∆L = 2, it must reduce capital by one unit,

FIGURE 6.3 A Family of Isocost Lines

An isocost line shows all the combinations of labor and capital that cost the firm the same amount. The greater the total cost, the farther from the origin the isocost lies. All the isocosts have the same slope, -w>r = -12. The slope shows the rate

at which the firm can substitute capital for labor holding total cost constant: For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant.

K , U

ni ts

o f c

ap ita

l p er

y ea

r

a

b

d

e

c

$600 isocost$400 isocost$200 isocost

$400 $20

= 20 $600 $20

= 30 $200 $20

= 10

$400 $40

10 =

$200 $40

5 =

$600 $40

15 =

L, Units of labor per year

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1716.3 Long-Run Costs

∆K = -12 ∆L = -1, to keep its total cost constant. Because all isocost lines are based on the same relative prices, they all have the same slope, so they are parallel.

The isocost line plays a similar role in the firm’s decision making as the budget line does in consumer decision making. Both an isocost line and a budget line are straight lines with a slope that depends on relative prices. However, they differ in an important way. The consumer has a single budget line that depends on the con- sumer’s income. The firm faces many isocost lines, each of which corresponds to a different level of expenditure the firm might make. A firm may incur a relatively low cost by producing relatively little output with few inputs, or it may incur a relatively high cost by producing a relatively large quantity.

Combining Cost and Production Information. By combining the information about costs contained in the isocost lines with information about efficient production summarized by an isoquant, a firm chooses the lowest-cost way to produce a given level of output. We illustrate how a Japanese beer manu- facturer picks the combination of labor and capital that minimizes its cost of pro- ducing 100 units of output. Figure 6.4 shows the isoquant for 100 units of output (based on the estimates of Flath, 2011, q = 100 = 1.52L0.6K0.4) and the isocost lines for which the rental rate of a unit of capital is $8 per hour and the wage rate is $24 per hour.

The firm minimizes its cost by using the combination of inputs on the isoquant that is on the lowest isocost line that touches the isoquant. The lowest possible iso- cost line that will allow the beer manufacturer to produce 100 units of output is the $2,000 isocost line. This isocost line touches the isoquant at the bundle of inputs x,

K , U

ni ts

o f c

ap ita

l p er

h ou

r

x

y

z

11650240 L, Units of labor per hour

27

100

303

q = 100 isoquant

$3,000 isocost

$2,000 isocost

$1,000 isocost

FIGURE 6.4 Cost Minimization

The beer manufacturer minimizes its cost of pro- ducing 100 units of output by producing at x (L = 50 and K = 100). This cost- minimizing combination of inputs is determined by the tangency between the q = 100 isoquant and the lowest isocost line, $2,000, that touches that isoquant. At x, the isocost is tangent to the isoquant, so the slope of the isocost, -w>r = -3, equals the slope of the iso- quant, which is the nega- tive of the marginal rate of technical substitution. That is, the rate at which the firm can trade capital for labor in the input markets equals the rate at which it can sub- stitute capital for labor in the production process.

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172 CHAPTER 6 Costs

-w>r = -24>8 = -3. In contrast, at y, the isocost cuts the isoquant so the slopes are not equal. At y, the MRTS is -18.9375, which is greater in magnitude than the negative of the ratio of the input prices, -3. Because the slopes are not equal at y, the firm can produce the same output at lower cost. As the figure shows, the cost of producing at y is $3,000, whereas the cost of producing at x is only $2,000.

We can interpret the condition in Equation 6.5 in another way. We showed in Chapter 5 that the marginal rate of technical substitution equals the negative of the ratio of the marginal product of labor to that of capital: MRTS = -MPL>MPK. Thus, the cost-minimizing condition in Equation 6.5 (multiplying both sides by -1) is6

MPL MPK

= w r

. (6.6)

Equation 6.6 may be rewritten as

MPL

w =

MPK r

. (6.7)

Equation 6.7 states the last-dollar rule: Cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital.

The beer firm’s marginal product of labor is MPL = 0.6q>L, and its marginal prod- uct of capital is MPK = 0.4q>K.7 At Bundle x in Figure 6.4, the beer firm’s marginal product of labor is 1.2 (= 0.6 * 100>50) and its marginal product of capital is 0.4. The last dollar spent on labor gets the firm

MPL w

= 1.2 24

= 0.05

more units of output. The last dollar spent on capital also gets the firm

MPK r

= 0.4 8

= 0.05

more units of output. Thus, spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. Equation 6.7 holds, so the firm is minimizing its cost of producing 100 units of output.

If instead the firm uses more capital and less labor, producing at y, its MPL is 2.5 (= 0.6q>L = 0.6 * 100>24) and the MPK is approximately 0.13 (≈ 0.4q>K = 0.4 * 100>303). As a result, the last dollar spent on labor yields MPL>w ≈ 0.1 more output, whereas the last dollar spent on capital yields only a fourth as much extra output, MPK>r ≈ 0.017. At y, if the firm shifts one dollar from capital to labor, the reduction in capital causes output to fall by 0.017 units. Off- setting that reduction, the increase in labor causes output to increase by 0.1 units. Thus, the net gain is 0.083 units of output at the same cost. The firm should shift even more resources from capital to labor—which increases the marginal product

5The production function is q = 1.52L0.6K0.4, so the marginal product of labor is MPL = 0q>0L = (0.6)1.52L-0.4K0.4, and MPK = 0q>0K = (0.4)1.52L0.6K-0.6. Thus, MRTS = -MPL>MPK = -1.5K>L.

6See Appendix 6B at the end of this chapter for a calculus derivation of this cost-minimizing condition. 7Because the beer manufacturer’s production function is q = 1.52L0.6K0.4, the marginal product of labor is MPL = (0.6)1.52L(0.6 - 1)K0.4 = 0.6q>L. Similarly, MPK = (0.4)1.52L0.6K(0.4 - 1) = 0.4q>K.

where the firm uses L = 50 workers and K = 100 units of capital.

How do we know that x is the least costly way to produce 100 units of output? We need to dem- onstrate that other practical combinations of input produce less than 100 units or produce 100 units at greater cost.

If the firm spent less than $2,000, it could not pro- duce 100 units of output. For example, each combi- nation of inputs on the $1,000 isocost line lies below the isoquant, so the firm cannot produce 100 units of output for $1,000.

The firm can produce 100 units of output using other combinations of inputs besides x; however,

using these other bundles of inputs is more expensive. For example, the firm can produce 100 units of output using the combinations y (L = 24, K = 303) or z (L = 116, K = 27), but both of these combinations cost the firm $3,000.

At the minimum-cost bundle, x, the isoquant is tangent to the isocost line: The slopes of the isocost line and the isoquant are equal and the isocost line touches the isoquant at only one point. Suppose that an isocost line hits the isoquant but is not tangent to it. Then the isocost line must cross the isoquant twice, as the $3,000 isocost line does at points y and z. However, if the isocost line crosses the isoquant twice, then part of the isoquant must lie below the isocost line. Consequently, another lower isocost line also touches the isoquant. Only if the isocost line is tangent to the isoquant—so that it touches the isoquant only once—can we conclude that we are on the lowest possible isocost line.

At the point of tangency, the slope of the isoquant equals the slope of the isocost line. As we discussed in Chapter 5, the slope of the isoquant is the firm’s marginal rate of technical substitution, which tells us how many units of capital the firm can replace with an extra unit of labor while holding output constant given its produc- tion function. The slope of the isocost line is the negative of the ratio of the wage to the cost of capital, -w>r, the rate at which the firm can trade capital for labor in input markets. Thus, at the input bundle where the firm minimizes its cost of producing a given level of output, the isoquant is tangent to the isocost line. Therefore, the firm chooses its inputs so that the marginal rate of technical substitution equals the nega- tive of the relative input prices:

MRTS = - w r

. (6.5)

To minimize the cost of producing a given level of output, the firm picks the bundle of inputs where the rate at which it can substitute capital for labor in the production process, the MRTS, exactly equals the rate at which it can trade capital for labor in input markets, -w>r.

The beer manufacturer’s marginal rate of technical substitution is MRTS = -1.5K>L.5 At the minimum-cost input bundle x, K = 100 and L = 50, so its MRTS is -3, which equals the negative of the ratio of the input prices it faces,

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1736.3 Long-Run Costs

-w>r = -24>8 = -3. In contrast, at y, the isocost cuts the isoquant so the slopes are not equal. At y, the MRTS is -18.9375, which is greater in magnitude than the negative of the ratio of the input prices, -3. Because the slopes are not equal at y, the firm can produce the same output at lower cost. As the figure shows, the cost of producing at y is $3,000, whereas the cost of producing at x is only $2,000.

We can interpret the condition in Equation 6.5 in another way. We showed in Chapter 5 that the marginal rate of technical substitution equals the negative of the ratio of the marginal product of labor to that of capital: MRTS = -MPL>MPK. Thus, the cost-minimizing condition in Equation 6.5 (multiplying both sides by -1) is6

MPL MPK

= w r

. (6.6)

Equation 6.6 may be rewritten as

MPL

w =

MPK r

. (6.7)

Equation 6.7 states the last-dollar rule: Cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital.

The beer firm’s marginal product of labor is MPL = 0.6q>L, and its marginal prod- uct of capital is MPK = 0.4q>K.7 At Bundle x in Figure 6.4, the beer firm’s marginal product of labor is 1.2 (= 0.6 * 100>50) and its marginal product of capital is 0.4. The last dollar spent on labor gets the firm

MPL w

= 1.2 24

= 0.05

more units of output. The last dollar spent on capital also gets the firm

MPK r

= 0.4 8

= 0.05

more units of output. Thus, spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. Equation 6.7 holds, so the firm is minimizing its cost of producing 100 units of output.

If instead the firm uses more capital and less labor, producing at y, its MPL is 2.5 (= 0.6q>L = 0.6 * 100>24) and the MPK is approximately 0.13 (≈ 0.4q>K = 0.4 * 100>303). As a result, the last dollar spent on labor yields MPL>w ≈ 0.1 more output, whereas the last dollar spent on capital yields only a fourth as much extra output, MPK>r ≈ 0.017. At y, if the firm shifts one dollar from capital to labor, the reduction in capital causes output to fall by 0.017 units. Off- setting that reduction, the increase in labor causes output to increase by 0.1 units. Thus, the net gain is 0.083 units of output at the same cost. The firm should shift even more resources from capital to labor—which increases the marginal product

5The production function is q = 1.52L0.6K0.4, so the marginal product of labor is MPL = 0q>0L = (0.6)1.52L-0.4K0.4, and MPK = 0q>0K = (0.4)1.52L0.6K-0.6. Thus, MRTS = -MPL>MPK = -1.5K>L.

6See Appendix 6B at the end of this chapter for a calculus derivation of this cost-minimizing condition. 7Because the beer manufacturer’s production function is q = 1.52L0.6K0.4, the marginal product of labor is MPL = (0.6)1.52L(0.6 - 1)K0.4 = 0.6q>L. Similarly, MPK = (0.4)1.52L0.6K(0.4 - 1) = 0.4q>K.

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174 CHAPTER 6 Costs

of capital and decreases the marginal product of labor—until the firm is operating with the capital-labor bundle x, where Equation 6.7 holds and the last dollar spent on labor increases output just as much as the last dollar spent on capital.

To summarize, a manager can use three equivalent rules to pick the lowest-cost combination of inputs to produce a given level of output when isoquants are smooth: the lowest-isocost rule, the tangency rule (Equation 6.6), and the last-dollar rule (Equation 6.7).

Factor Price Changes. Once the beer manufacturer determines the lowest- cost combination of inputs to produce a given level of output, it uses that method as long as the input prices remain constant. How should the firm change its behavior if the cost of one of the factors changes? Suppose that the wage falls from $24 to $8 but the rental rate of capital stays constant at $8.

The firm minimizes its new cost by substituting away from the now relatively more expensive input, capital, toward the input whose price has fallen, labor. The change in the wage does not affect technological efficiency, so it does not affect the isoquant in Figure 6.5. However, because of the wage decrease, the new isocost lines

How can a manager minimize cost if the manager does not know the firm’s production function? The manager can use the last-dollar rule to determine the cost-minimizing combination of inputs through trial and error. The manager can experiment by adjusting each input slightly, holding other inputs constant, to learn how production and cost change, and then use that information to choose a cost-minimizing bundle of inputs.

That is, managers don’t draw isoquants and isocost lines to make decisions. Instead, they use an insight from such an analysis to employ the last-dollar rule.

Cost Minimization by Trial and Error

Managerial Implication

FIGURE 6.5 Effect of a Change in a Factor Price

Originally, the wage was $24 and the rental rate of capital was $8, so the lowest isocost line ($2,000) was tangent to the q = 100 isoquant at x (L = 50, K = 100). When the wage fell to $8, the isocost lines became flatter: Labor became relatively less expensive than capital. The slope of the isocost lines falls from -w>r = -24>8 = -3 to -8>8 = -1. The new lowest isocost line ($1,032) is tangent at v (L = 77, K = 52). Thus, when the wage falls, the firm uses more labor and less capital to produce a given level of output, and the cost of production falls from $2,000 to $1,032.

K , U

ni ts

o f c

ap ita

l p er

h ou

r

v

x

77500 L, Workers per hour

100

52

q = 100 isoquant

Original isocost, $2,000

New isocost, $1,032

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1756.3 Long-Run Costs

have a flatter slope, -w>r = -8>8 = -1, than the original isocost lines, -w>r = -24>8 = -3.

The relatively steep original isocost line is tangent to the 100-unit isoquant at Bundle x (L = 50, K = 100). The new, flatter isocost line is tangent to the isoquant at Bundle v (L = 77, K = 52). Thus, the firm uses more labor and less capital as labor becomes relatively less expensive. Moreover, the firm’s cost of producing 100 units falls from $2,000 to $1,032 because of the fall in the wage. This example illustrates that a change in the relative prices of inputs affects the mix of inputs that a firm uses.

Mini-Case To start a children’s pajama business, Philip Chigos and Mary Domenico designed their products, chose fabrics, and searched for low-cost workers in China or Mexico from an office in the basement below their San Francisco apart- ment. Increasingly, such mom-and-pop operations are sending their clothing, jewelry, and programming work to Sri Lanka, China, India, Mexico, and Eastern Europe.

A firm outsources if it retains others to provide services that the firm had previously performed itself. Firms have always used outsourcing. For example, restaurants buy goods such as butter and flour or finished products such as bread and pies from other firms. Outsourcing increases profits if others can produce a good or service for less than the firm’s own cost.

Many news outlets and politicians in high-wage countries have been wring- ing their hands about outsourcing to other countries. The different factor prices that firms face in low-wage countries may allow them to produce at lower cost.

In the past, most small firms could not practically outsource to other coun- tries because of the high transaction costs of finding partners abroad and communicating with them. Now they can use the internet and e-mail to inex- pensively communicate with foreign factories.

Mr. Chigos used the internet to find potential Chinese and Mexican manu- facturers for the pajamas that Ms. Domenico designed. Hiring foreign workers is crucial. Mr. Chigos claims, “We’d love it to say ‘Made in the U.S.A.’ and use American textiles and production.” However, if they did so, their cost would rise four to ten times, and “We didn’t want to sell our pajamas for $120.” One result of easy access to cheap manufacturing, he said, is that more American entrepreneurs may be able to turn an idea into a product.

The would-be pajama tycoons plan to outsource to U.S. firms as well. They will use a Richmond, California, freight management company to receive the shipments, check the quality of the merchandise, and ship it to customers. They will market their clothes on the internet and through boutique retailers. They have no manufacturing plant, storefront, or warehouse. As Mr. Chigos notes, “With the technology available today, we’ll never touch the product.” Lower communication costs have made it feasible to take advantage of low foreign costs for outsourced activities.

If relative factor prices (and hence slopes of isocost lines) are different abroad than at home, the manager of a firm with smooth isoquants should use a dif- ferent factor mix when producing abroad, as Figure 6.5 illustrates. However, Q&A 6.3 shows that if all foreign prices for capital and labor are proportionally lower than domestic prices so that relative factor prices are the same, the firm should use the same technology as at home.

The Internet and Outsourcing

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176 CHAPTER 6 Costs

The Shapes of Long-Run Cost Curves The shapes of the long-run average cost and marginal cost curves depend on the shape of the long-run total cost curve. The long-run cost curve in panel a of Figure 6.6 corresponds to the long-run average and marginal cost curves in panel b. The long- run cost curve of this firm rises less than in proportion to increases in output at outputs below q* and then rises more rapidly. The corresponding long-run average cost curve first falls and then rises.

The explanation for why the long-run average cost curve is U-shaped differs from the explanation for why the short-run average cost curves are U-shaped. A key rea- son why the short-run average cost is initially downward sloping is that the average fixed cost curve is downward sloping: Spreading the fixed cost over more units of output lowers the average fixed cost per unit. In the long run, fixed costs are less important than in the short run, and may be absent altogether, as we have assumed in this section. Therefore, we cannot rely on fixed costs to explain the initial down- ward slope of the long-run average cost curve.

A major reason why the short-run average cost curve slopes upward at higher levels of output is diminishing marginal returns. In the long run, however, all factors can be increased, so diminishing marginal returns do not explain the upward slope of a long-run average cost curve.

As with the short-run curves, the shape of the long-run curves is determined by the production function relationship between output and inputs. In the long run, returns to scale play a major role in determining the shape of the average cost curve and other cost curves.

Q&A 6.3 If a firm manufactures at home, it faces input prices for labor and capital of w and r and produces q units of output using L units of labor and K units of capital. Abroad, the wage and cost of capital are both half as much as at home. If the firm manufactures abroad, will it change the amount of labor and capital it uses to produce q? What happens to its cost of producing quantity q?

Answer 1. Determine whether the change in factor prices affects the slopes of the isoquant or the

isocost lines. The change in input prices does not affect the isoquant, which depends only on technology (the production function). Moreover, cutting both the input prices in half does not affect the slope of the isocost lines. The original slope was -w>r, and the new slope is -(w>2)>(r>2) = -w>r.

2. Using a rule for cost minimization, determine whether the firm changes its input mix. A firm minimizes its cost by producing where its isoquant is tangent to the lowest possible isocost line. That is, the firm produces where the slope of its isoquant, MRTS, equals the slope of its isocost line, -w>r. Because the slopes of the isoquant and the isocost lines are unchanged after input prices are cut in half, the firm continues to produce using the same amount of labor, L, and capital, K, as originally.

3. Calculate the original cost and the new cost and compare them. The firm’s original cost of producing q units of output was wL + rK = C. Its new cost of produc- ing the same amount of output is (w>2)L + (r>2)K = C>2. Thus, its cost of pro- ducing q falls by half when the input prices are halved. The isocost lines have the same slope as before, but the cost associated with each isocost line is halved.

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1776.3 Long-Run Costs

A cost function exhibits economies of scale if the average cost of production falls as output expands. If input prices are constant, increasing returns to scale is a sufficient condition for economies of scale. If a production function has increasing returns to scale, then the corresponding cost function has economies of scale: Dou- bling inputs more than doubles output, so average cost falls with higher output. However, even with constant input prices, it might be cost effective to use differ- ent factor proportions (such as using more robots and fewer workers) as the firm increases output. If so, the cost function might exhibit economies of scale even if the production function does not have increasing returns to scale.

If an increase in output has no effect on average cost, the production process has no economies of scale. We sometimes refer to such a cost function as exhibiting constant costs, because average cost does not change with output. Finally, a firm suffers from diseconomies of scale if average cost rises when output increases. To illustrate the relationship between returns to scale and long-run average cost, we use the returns-to-scale data in Table 6.3, which shows the cost-minimizing method of producing various quantities. The firm produces one unit of output using a unit each of labor and capital. Given a wage and rental cost of capital of $12 per unit, the total cost and average cost of producing this unit are both $24. Doubling both inputs causes output to increase more than in proportion to

FIGURE 6.6 Long-Run Cost Curves

(a) The long-run cost curve rises less rapidly than output at output levels below q* and more rapidly at higher output levels. (b) As a consequence, the marginal cost and average cost curves are U-shaped. The marginal cost crosses the average cost at its mini- mum at q*.

C os

t, $

q* q, Quantity per day

(a) Cost Curve

C

C os

t p er

u ni

t, $

q* q, Quantity per day

MC

AC

(b) Marginal and Average Cost Curves

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178 CHAPTER 6 Costs

TABLE 6.3 Returns to Scale and Long-Run Costs

Output, Q Labour, L Capital, K Cost,

C ∙ wL ∙ rK Average Cost,

AC ∙ C ,q Returns to Scale

1 1 1 24 24

3 2 2 48 16 Increasing

6 4 4 96 16 Constant

8 8 8 192 24 Decreasing

3 units, reflecting increasing returns to scale. Because cost only doubles while output triples, the average cost falls and the cost function has economies of scale over this range of output.

Doubling the inputs again causes output to double as well—constant returns to scale—and average cost remains constant. Doubling the inputs once more causes only a small increase in output—decreasing returns to scale—so average cost increases.

Average long-run cost curves can have many different shapes. Perfectly competi- tive firms typically have U-shaped average cost curves. Average cost curves in non- competitive markets may be U-shaped, L-shaped (average cost at first falls rapidly and then levels off as output increases), everywhere downward sloping, or every- where upward sloping, or they may have other shapes.

w = r = $12 per unit.

Mini-Case Google has become a leader in data storage, offering access to what it calls Google Cloud Storage. People access their data from Google’s massive data stor- age devices using the internet, as though from a cloud in the sky. By operating at a gigantic size and using a new approach, Google is able to lower its average cost and achieve economies of scale.

In the past, a firm would buy as many large hard disk units as it needed. Once the firm was buying the largest possible unit, to get more storage it would just buy more such hard disk units and its costs would rise in proportion to the number of units it needed.

Rather than buying off-the-shelf completed hard-disk units, Google buys raw computer parts in massive quantities, and assembles custom units on open racks without unnecessary components such as individual cases and fans. Google automatically backs up data on multiple hard disks. Thus, when a disk fails, a worker quickly yanks it out and replaces it with a new unit without spending time on a tedious manual backup. By sharing cooling and labor costs over many units, it lowers its average cost of storing data.

These lower costs that derive from greater economies of scale have allowed Google, Amazon, and a few other firms to create a new, disruptive industry. These firms provide disk storage with excellent backup in the cloud to indi- viduals and firms who no longer have to buy relatively expensive, smaller hard drives and rely on themselves to back up their data.

Economies of Scale at Google

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179 6.4 The Learning Curve

6.4 The Learning Curve Average cost may fall over time for three reasons. First, operating at a larger scale in the long run may lower average cost due to increasing returns to scale (IRS). Second, technological progress (Chapter 5) may increase productivity and thereby lower average cost. Third, a firm may benefit from learning by doing: the productive skills and knowledge that workers and managers gain from experience. Workers who are given a new task may perform it slowly the first few times they try, but their speed increases with practice. Managers may learn how to organize production more efficiently, discover which workers to assign to particular tasks, and determine where more inventories are needed and where they can be reduced. Engineers may optimize product designs by experimenting with various production methods. For these and other reasons, the average cost of production tends to fall over time, and the effect is particularly strong with new products.

In some firms, learning by doing is a function of the time elapsed since a particular product or production process was introduced. However, more commonly, learning is a function of cumulative output: the total number of units of output produced since the product was introduced. The learning curve is the relationship between average costs and cumulative output. The learning curve for Intel central processing units (CPUs) in panel a of Figure 6.7 shows that Intel’s average cost fell very rapidly with the first few million units of cumulative output, but then dropped relatively slowly with additional units (Salgado, 2008).

If a firm is operating in the economies of scale section of its average cost curve, expanding output lowers its cost for two reasons. Its average cost falls today because of economies of scale, and for any given level of output, its average cost is lower in the next period due to learning by doing.

In panel b of Figure 6.7, the firm is producing q1 units of output at point A on average cost curve AC1 in the first period. We assume that each period is long enough that the firm can vary all factors of production. If the firm expands its

Q&A 6.4 What is the shape of the long-run cost function for a fixed-proportion production function (see Chapter 5) in which it takes one unit of labor and one unit of capital to produce one unit of output? What is the shape of the average cost curve? Does it have economies or diseconomies of scale?

Answer 1. Because no substitution is possible with a fixed-proportion production function,

multiply the inputs (= the number of units of output) by their prices, and sum to determine total cost. The long-run cost of producing q units of output is C(q) = wL = rK = wq + rq = (w + r)q. Cost rises in proportion to output. The long-run cost curve is a straight line with a slope of w + r.

2. Divide the total cost function by q to get the average cost function. The average cost function is AC(q) = C(q)>q = [(w + r)q]>q = w + r. Because the average cost for any quantity is w + r, the average cost curve is a horizontal straight line at w + r. Moreover, because the average cost does not change when the quantity of output changes, the cost function has constant costs: it does not have either economies or diseconomies of scale.

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180 CHAPTER 6 Costs

output to q2 in Period 1, its average cost falls to B because of economies of scale. The learning by doing in Period 1 results in a lower average cost curve, AC2 in Period 2. If the firm continues to produce q2 units of output in Period 2, its average cost falls to b on AC2.

If instead of expanding output to q2 in Period 1, the firm expands to q3, its aver- age cost is even lower in Period 1 (C on AC1) due to even greater economies of scale. Moreover, its average cost curve, AC3, in Period 2 is even lower due to the extra experience gained from producing more output in Period 1. If the firm continues to produce q3 in Period 2, its average cost is c on AC3. Thus, all else being the same, if learning by doing depends on cumulative output, firms have an incentive to produce more in any one period than they otherwise would to lower their costs in the future.

(a) As Intel produced more cumulative CPUs, the average cost of production fell (Salgado, 2008). (b) In any one period, extra production reduces a firm’s average cost due to economies of scale: because q1 6 q2 6 q3, A is higher than B, which is higher than C. Extra production in one period reduces average cost in the future because of learning by doing. To produce q2 this period costs B on AC

1, but to produce that same output in the next period

would cost only b on AC2. If the firm produces q3 instead of q2 in this period, its average cost in the next period is AC3 instead of AC2 because of addi- tional learning by doing. Thus, extra output in this period lowers the firm’s cost in two ways: It lowers average cost in this period due to economies of scale and lowers average cost for any given output level in the next period due to learning by doing.

A ve

ra ge

c os

t, $

AA BB

CC bb

cc

q, Output per period

(b) Economies of Scale and Learning by Doing

Learning by doing

Economies of scale

q2 q3

AC3 AC2 AC1

q1

20

40

60

80

$100

0 50 100 150 200

A ve

ra ge

c os

t p er

C P

U , $

(a) Learning Curve for Intel Central Processing Units

Cumulative production of Pentium CPU, Millions of units

FIGURE 6.7 Learning by Doing

Mini-Case

Solar Power Learning Curves

Learning by doing substantially reduces the cost of installing solar photovoltaic systems, which makes installation much less expensive in some countries than in others. If you want solar power for your home, you need to buy the module, which converts sunlight to electricity, and install the system by paying for labor and components, such as cables, inverters, and mounts. Modules are sold glob- ally. However, the installation costs vary by country due to labor and other dif- ferences, as well as how many systems have been installed in the country.

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1816.5 The Costs of Producing Multiple Goods

Elshurafa et al. (2018) estimated learning curves for residential solar system installations, showing how the marginal cost varies with cumu- lative residential and commercial installations. On average, the global learning curve is 89%, which means that every time cumulative quan- tity doubles, the cost of installation falls to 89% of the previous level. The table shows these learning curve numbers for various countries or regions.

Country or Region Learning Curve (%)

Sweden 74

United Kingdom 84

Japan 87

Europe 91

Australia 93

Canada 93

Mexico 93

United States 93

China 96

6.5 The Costs of Producing Multiple Goods If a firm produces two or more goods, the cost of one good may depend on the output level of another. Outputs are linked if a single input is used to produce both of them. For example, cattle provide beef and hides (for leather), and petro- leum supplies both heating fuel and gasoline. It is less expensive to produce beef and hides together than separately. If the goods are produced together, a single animal yields one unit of beef and one hide. If beef and hides are produced sepa- rately (throwing away the unused good), the same amount of output requires two animals and more labor.

A cost function exhibits economies of scope if it is less expensive to produce goods jointly than separately (Panzar and Willig, 1977, 1981). All else the same, if a firm has such a cost function, it can lower its total cost by producing its products together (say, at one plant) rather than separately (at two plants).

A measure of the degree of economies of scope (SC) is

SC = C(q1, 0) + C(0, q2) - C(q1, q2)

C(q1, q2) ,

where C(q1, 0) is the cost of producing q1 units of the first good by itself, C(0, q2) is the cost of producing q2 units of the second good, and C(q1, q2) is the cost of pro- ducing both goods together. If the cost of producing the two goods separately, C(q1, 0) + C(0, q2), is the same as producing them together, C(q1, q2), then SC is zero. If it is cheaper to produce the goods jointly, SC is positive. A production process has diseconomies of scope if it is less expensive to produce the two goods separately, so SC is negative.

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182 CHAPTER 6 Costs

Mini-Case Empirical studies show that some medical production processes have economies of scope, others have none, and some have diseconomies of scope. Is it cost effective to separate outpatient and inpatient surgical procedures in a general hospital, or should outpatient surgeries be provided separately? Carey, Burgess, and Young (2015) estimate small scope economies (SC = 0.12) at the median for-profit hospital.

Gonçalves and Barros (2013) examined whether providing auxiliary clinical services in Portuguese hospitals is cost effective. They did not find economies of scope between the clinical chemistry service and other medical services, so outsourcing that service would not raise costs. However, in medical imaging, computed tomography exhibits scope economies with most other services, which suggests that outsourcing computed tomography would raise the costs of producing those other outputs.

Freeman, Savva, and Scholtes (2018) found significant diseconomies of scope between emergency admissions and non-emergency admissions in English hos- pitals. However, within the emergency category, there are positive economies of scope between the different major specialties. Non-emergency admissions do not exhibit economies of scope across specialties. The authors conclude that significant gains would arise from concentrating emergency care in hospitals focusing on emergency services.

Medical Economies of Scope

Technology Choice at Home Versus Abroad

Managerial Solut ion

If a U.S. semiconductor manufacturing firm shifts production from the firm’s home plant to one abroad, should it use the same mix of inputs as at home? The firm may choose to use a different technology because the firm’s cost of labor relative to capital is lower abroad than in the United States.

If the firm’s isoquant is smooth, the firm uses a different bundle of inputs abroad than at home given that the relative factor prices differ (as Figure 6.5 shows). However, semiconductor manufacturers have kinked isoquants. Firms can use three different technologies to produce semiconductors. One technology is based on machines called aligners. This technology requires a relatively large amount of labor to reach any particular output level. The stepper technology uses more sophisticated machines and less labor, and advanced steppers called wafer-handling steppers represent an even larger capital input and correspondingly require less labor to reach any target output. Figure 6.8 shows a firm’s q = 200 semiconductor chips isoquant. In its U.S. plant, the semiconductor manufactur- ing firm uses a wafer-handling stepper technology because the C1 isocost line, which is the lowest isocost line that touches the isoquant, hits the isoquant at that technology.

The firm’s cost of both inputs is less abroad than in the United States, and its cost of labor is relatively less than the cost of capital at its foreign plant than at its U.S. plant. The slope of its isocost line is -w>r, where w is the wage and r is the rental cost of the manufacturing equipment. The smaller w is relative to r, the less steeply sloped is its isocost curve. Thus, the firm’s foreign isocost line is flatter than its domestic C1 isocost line.

If the firm’s isoquant were smooth, the firm would certainly use a different technology at its foreign plant than in its home plant. However, its isoquant

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1836.5 The Costs of Producing Multiple Goods

has kinks, so a small change in the relative input prices does not necessarily lead to a change in production technology. The firm could face either the C2 or C3 isocost curves, both of which are flatter than the C1 isocost. If the firm faces the C2 isocost line, which is only slightly flatter than the C1 isocost, the firm still uses the capital-intensive wafer-handling stepper technology in its foreign plant. However, if the firm faces the much flatter C3 isocost line, which hits the isoquant at the stepper technology, it switches technologies. (If the isocost line were even flatter, it could hit the isoquant at the aligner technology.)

Even if the wage change is small so that the firm’s isocost line is C2 and the firm does not switch technologies abroad, the firm’s cost will be lower abroad with the same technology because C2 is less than C1. However, if the wage is low enough that it can shift to a more labor-intensive technology, its costs will be even lower: C3 is less than C2.

Thus, whether the firm uses a different technology in its foreign plant than in its domestic plant turns on the relative factor prices in the two locations and whether the firm’s isoquant is smooth. If the isoquant is smooth, even a slight difference in relative factor prices will induce the firm to shift along the isoquant and use a different technology with a different capital-labor ratio. However, if the isoquant has kinks, the firm will use a different technology only if the relative factor prices differ substantially.

In the United States, the semiconduc- tor manufacturer produces using a wafer-handling stepper on isocost C1. At its plant abroad, the wage is lower, so it faces a flatter isocost curve. If the

wage is only slightly lower, so that its iso- cost is C2, it produces the same way as at home. However, if the wage is much lower so that the isocost is C3, it switches to a stepper technology.

1 3 8

K , U

ni ts

o f c

ap ita

l p er

d ay

L, Workers per day

Wafer-handling stepper

q = 200 isoquant

Stepper

Aligner

C1 isocost C2 isocost C3 isocost

FIGURE 6.8 Technology Choice

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184 CHAPTER 6 Costs

QUESTIONS

All exercises are available on MyLab Economics; * = answer at the back of this book; C = use of calculus may be necessary; = this exercise is available in Excel Grader in MyLab Economics.

for the Taking,” San Francisco Chronicle, August 28, 2005). Because of the large U.S. trade imbalance with major Asian nations, cargo ships arrive at West Coast seaports fully loaded but return to Asia half to completely empty. Use the concept of opportunity cost to help explain the differential shipping rates.

1. The Nature of Costs 1.1 Executives at Leonesse Cellars, a premium winery

in Southern California, were surprised to learn that shipping wine by sea to some cities in Asia was less expensive than sending it to the East Coast of the United States, so they started shipping to Asia (David Armstrong, “Discount Cargo Rates Ripe

SUMMARY

From all technically efficient production processes, a cost- minimizing firm chooses the one that is economically effi- cient. The economically efficient production process is the technically efficient process for which the cost of produc- ing a given quantity of output is lowest.

1. The Nature of Costs. In making decisions about pro- duction, managers need to take into account the oppor- tunity cost of an input, which is the value of the input’s best alternative use. For example, if the manager is the owner of the company and does not receive a salary, the amount that the owner could have earned elsewhere— the foregone earnings—is the opportunity cost of the manager’s time and is relevant in deciding whether the firm should produce or not. A durable good’s opportu- nity cost depends on its current alternative use. If the past expenditure for a durable good is sunk—that is, it cannot be recovered—then that input has no opportu- nity cost and the sunk cost should not influence current production decisions.

2. Short-Run Costs. In the short run, the firm can adjust some factors, such as labor, while other factors, such as capital, are fixed. Consequently, total cost is the sum of variable costs and fixed costs. Average cost is total cost divided by the number of units of output produced. Similarly, average variable cost is variable cost divided by output. Marginal cost is the amount by which a firm’s cost changes if the firm produces one more unit of output. At quantities where the marginal cost curve is below the average cost curve, the average cost curve is downward sloping. Where the mar- ginal cost curve is above the average cost curve, the average cost curve is upward sloping. Thus, the mar- ginal cost curve cuts the average cost curve at its mini- mum point. Given that input prices are constant, the shapes of the variable cost and the cost-per-unit curves are determined by the production function. If labor is

the only variable factor in the short run, the shape of short-run cost curves reflects the marginal product of labor.

3. Long-Run Costs. Over a long-run planning horizon, the firm can adjust all inputs. Therefore all costs are avoidable in the long run. The firm uses the combina- tion of inputs that minimizes its cost. To produce a given output level, the firm chooses the lowest isocost line that touches the relevant isoquant, which is tangent to the isoquant. Equivalently, to minimize cost, the firm adjusts inputs until the last dollar spent on any input increases output by as much as the last dollar spent on any other input. If the firm calculates the cost of producing every possible output level given current input prices, it knows its cost function: Cost is a function of the input prices and the output level. If the firm’s average cost falls as output expands, its production process has economies of scale. If its average cost rises as output expands, its production process has diseconomies of scale.

4. The Learning Curve. A firm that introduces a new product or service often benefits from increased pro- ductivity as it gains experience and learns how to pro- duce at lower cost, a process called learning by doing. Workers who are given a new task will typically speed up and make fewer mistakes with practice. The learn- ing curve describes the relationship between average cost and cumulative output over time. This curve typi- cally slopes downward, reflecting the decline in cost that arises from learning by doing.

5. The Costs of Producing Multiple Goods. If it is less expensive for a firm to produce two goods jointly rather than separately, its production process exhibits economies of scope. If diseconomies of scope exist, it is less expensive to produce the goods separately. The presence of economies of scope is important in deter- mining the goods that the firm produces.

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1.2 Ming lives in Seattle and recently bought a $375 ticket to attend a Seattle Seahawks game. He is a huge fan, so even though the ticket is pricey it is well below his willingness to pay of $600. However, as game day approaches, Ming receives an invitation from his friend, Cassandra, to spend the day at the Museum of Pop Culture touring a big exhibit on Marvel super- heroes. The museum visit would only cost $75, but Ming (being a big Marvel fan too) would be willing to pay $250. What is his opportunity cost of going to the museum? (Hint: See Q&A 6.1.)

1.3 Many corporations allow CEOs to use the firm’s cor- porate jet for personal travel. The Internal Revenue Service (IRS) requires that the firm report personal use of its corporate jet as taxable executive income, and the Securities and Exchange Commission (SEC) requires that publicly traded corporations report the value of this benefit to shareholders. An important issue is determining the value of this benefit. The IRS values a CEO’s personal flight at or below the price of a first-class ticket. The SEC values the flight at the “incremental” cost of the flight: the additional costs to the corporation of the flight. The third alternative is the market value of chartering an aircraft. Of the three methods, the first-class ticket is least expensive and the chartered flight is most expensive.

a. What factors (such as fuel) determine the mar- ginal explicit cost to a corporation of an execu- tive’s personal flight? Does any one of the three valuation methods correctly determine the mar- ginal explicit cost?

b. What is the marginal opportunity cost to the corporation of an executive’s personal flight?

*1.4 A firm purchased copper pipes a few years ago at $10 per pipe and stored them, using them only as the need arises. The firm could sell its remaining pipes in the market at the current price of $9. What is the oppor- tunity cost of each pipe and what is the sunk cost?

1.5 You won a ticket to a hockey playoff game by hav- ing your name drawn from a hat at a charity event. You were excited about going, but on the day of the game, a major snowstorm has hit and conditions are miserable. Would you be more likely to go if you had bought the ticket yourself instead of winning it? Relate your answer to opportunity costs and sunk costs.

2. Short-Run Costs *2.1 Nicolas has purchased a streaming audio service for

$8.00 per month. As he listens to more songs in a month, he spreads this fixed cost over a larger quan- tity, q. Derive an algebraic formula for his average fixed cost per song and draw it in a diagram. One of his friends says to Nicolas, “The more music you

listen to, the less you pay per song so you should spend all your time listening to music.” What is wrong with this reasoning?

2.2 Platinum Pipeline Inc. needs a Caterpillar D6T dozer to install water and sewer lines. How does its fixed cost change if it can rent a dozer rather than buy one? (Hint: See Mini-Case “Short-Run Versus Long- Run in the Sharing Economy.”)

2.3 In the twentieth century, department stores and supermarkets largely replaced smaller specialty stores, as consumers found it more efficient to go to one store rather than many. In the early part of this century, many shoppers changed their behavior again and began to favor online shopping over visiting a brick-and-mortar store. Consumers incur a transac- tion or search cost to shop, primarily the opportunity cost of their time. This transaction cost consists of a fixed cost of traveling to and from the store and a var- iable cost that rises with the number of different types of items the consumer tries to find on the shelves. By shopping online a consumer can avoid some of the fixed transaction costs of traveling to a physical store. Use math to explain why a shopper’s average costs may be lower when buying online rather than from a physical store and then explain why online shopping hasn’t eliminated brick-and-mortar stores altogether.

2.4 Give the formulas for and plot AFC, MC, AVC, and AC if the cost function is

a. C = 10 + 10q, b. C = 10 + q2, or c. C = 10 + 10q - 4q2 + q3. C

2.5 In 1796, Gottfried Christoph Härtel, a German music publisher, calculated the cost of printing music using an engraved plate technology and applied these esti- mated cost functions in making production deci- sions. Härtel figured that the fixed cost of printing a musical page—the cost of engraving the plates—was 900 pfennigs. The marginal cost of each additional copy of the page is 5 pfennigs (Scherer, 2001).

a. Graph the total cost, average cost, average vari- able cost, and marginal cost functions.

b. Is cost lower if only one music publisher prints a given composition? Why?

c. Härtel used his data to do the following type of analysis. Suppose he expects to sell exactly 300 copies of a composition at 15 pfennigs per page of the composition. What is the greatest amount the publisher is willing to pay the composer per page of the composition?

2.6 Gail works in a flower shop, where she produces 10 floral arrangements per hour. She is paid $15 an hour for the first eight hours she works and

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$20 an hour for each additional hour she works. What is the firm’s cost function? What are its AC, AVC, and MC functions? Draw the AC, AVC, and MC curves.

*2.7 A firm builds shipping crates out of wood. How does the cost of producing a 1-cubic-foot crate (each side is 1-foot square) compare to the cost of build- ing an 8-cubic-foot crate if wood costs $1 a square foot and the firm has no labor or other costs? More generally, how does cost vary with volume?

2.8 The only variable input a janitorial service firm uses to clean offices is workers who are paid a wage, w, of $16 an hour. Each worker can clean four offices in an hour. Use math to determine the variable cost, the average variable cost, and the marginal cost of cleaning one more office. Draw a diagram like Fig- ure 6.1 to show the variable cost, average variable cost, and marginal cost curves.

2.9 A firm has a Cobb-Douglas production function, q = 2L0.5K0.5. If it faces factor prices of w = 20 and r = 40 and its capital is fixed at K = 100, what are its short-run average fixed cost, average variable cost, and marginal cost functions? Plot these curves. (Hint: See Appendix 6A.)

2.10 A firm has two plants that produce identical out- put. The cost functions are C1 = 10q - 4q2 + q3 and C2 = 10q - 2q2 + q3.

a. At what output levels does the average cost curve of each plant reach its minimum?

b. If the firm wants to produce four units of output, how much should it produce in each plant? C

3. Long-Run Costs 3.1 A newly invented machine serves as a mobile sta-

tion for receiving and accumulating packed flats of strawberries close to where they are picked, which reduces workers’ time and burden of carrying full flats of strawberries. According to Rosenberg (2004), a machine-assisted crew of 15 pickers produces as much output, q*, as that of an unaided crew of 25 workers. In a 6-day, 50-hour workweek, the machine replaces 500 worker-hours. At an hourly wage cost of $10, a machine saves $5,000 per week in labor costs, or $130,000 over a 26-week harvesting season. The cost of machine operation and maintenance expressed as a daily rental is $200, or $1,200 for a six-day week. Thus, the net savings equal $3,800 per week, or $98,800 for 26 weeks.

a. Draw the q* isoquant, assuming that only two production methods are available (pure labor and labor-machine). Label the isoquant and axes as thoroughly as possible.

b. Add an isocost line to show which technology the firm chooses (be sure to measure wage and rental costs on a comparable time basis).

c. Draw the corresponding cost curves (with and without the machine), assuming constant returns to scale, and label the curves and the axes as thoroughly as possible.

*3.2 A bottling company uses two inputs to produce bot- tles of the soft drink Sludge: bottling machines (K) and workers (L). The isoquants have the usual smooth shape. The machine costs $1,000 per day to run and the workers earn $200 per day. At the current level of production, the marginal product of the machine is an additional 200 bottles per day, and the marginal product of labor is 50 more bottles per day. Is this firm producing at minimum cost? If it is minimizing cost, explain why. If it is not minimizing cost, explain how the firm should change the ratio of inputs it uses to lower its cost. (Hint: Examine the conditions for mini- mizing cost in Equations 6.5, 6.6, and 6.7.)

3.3 Suppose that the government subsidizes the cost of workers by paying for 25% of the wage (the rate offered by the U.S. government in the late 1970s under the New Jobs Tax Credit program). What effect will this subsidy have on the firm’s choice of labor and capital to produce a given level of output? What happens if both capital and labor are subsi- dized at 25%? (Hint: See Q&A 6.3.)

*3.4 The all-American baseball is made using cork from Portugal, rubber from Malaysia, yarn from Aus- tralia, and leather from France, and it is stitched (108 stitches exactly) by workers in Costa Rica. To assem- ble a baseball takes one unit each of these inputs. Ultimately, the finished product must be shipped to its final destination—say, Cooperstown, New York. The materials used cost the same anywhere. Labor costs are lower in Costa Rica than in a possible alter- native manufacturing site in Georgia, but shipping costs from Costa Rica are higher. What production function is used? What is the cost function? What can you conclude about shipping costs if it is less expensive to produce baseballs in Costa Rica than in Georgia?

3.5 California’s State Board of Equalization imposed a higher tax on “alcopops,” flavored beers contain- ing more than 0.5% alcohol-based flavorings, such as vanilla extract (Guy L. Smith, “On Regulation of ‘Alcopops,’” San Francisco Chronicle, April 10, 2009). Such beers are taxed as distilled spirits at $3.30 a gal- lon rather than as beer at 20¢ a gallon. In response, manufacturers reformulated their beverages to avoid the tax. By early 2009, instead of collecting a predicted $38 million a year in new taxes, the state collected only about $9,000. Use an isocost-isoquant

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187Questions

diagram to explain the firms’ response. (Hint: Alcohol-based flavors and other flavors may be close to perfect substitutes.)

3.6 A U.S. electronics firm is considering moving its pro- duction to a plant in Mexico. Its estimated produc- tion function is q = L0.5K0.5 (based on Hsieh, 1995). The U.S. factor prices are w = r = 10. In Mexico, the wage is half that in the United States, but the firm faces the same cost of capital: w* = 5 and r* = r = 10. What are L and K, and what is the cost of producing q = 100 units in both countries?

3.7 The Mini-Case “Economies of Scale at Google” describes economies of scale for Google Cloud Storage. The cost function for this service is well approximated by C = F + cq, where C is total cost, F is fixed cost, c is a constant, and q is output. What is marginal cost for this cost function? What are the average fixed cost, average variable cost, and average cost? Over what range of output does Google have economies of scale?

*3.8 What is the long-run cost function for a fixed- proportions production function for which it takes two units of labor and one unit of capital to produce one unit of output as a function of the wage, w, and the price of capital, r? What is the cost function if the pro- duction function is q = L + K? (Hint: See Q&A 6.4.)

3.9 Trader Joe’s sells very cheap and popular wine pro- duced by Bronco Wine (Hayley Peterson, “The Real Reasons Trader Joe’s Wine Is So Cheap,” Business Insider, May 6, 2017). When asked why the wine is so cheap, Bronco winemaker Ed Moody emphasizes the volume of output, stating that it is easier to make wine “in a 700,000-gallon tank than . . . in a 700-gallon one because there is less exposure to air and oxygen is the enemy in winemaking.” Wine educator Keith Wallace emphasizes the role of machines: “The com- pany uses machines to harvest the grapes, which helps keep labor costs low, but also increases the chances that bad grapes end up in the wine.” One of these reasons is based on choosing input propor- tions to minimize cost and one is based on econo- mies of scale. State which is which and explain.

4. The Learning Curve 4.1 In what types of industry would you expect to see

substantial learning by doing? Why?

*4.2 A firm’s learning curve, which shows the relation- ship between average cost and cumulative output (the sum of its output since the firm started produc- ing), is AC = a + bN-r, where AC is its average cost; N is its cumulative output; a, b, and r are constants; and 0 … r 6 1.

a. What is the firm’s AC if r = 0? What can you say about the firm’s ability to learn by doing?

b. If r exceeds zero, what can you say about the firm’s ability to learn by doing? What hap- pens to its AC as its cumulative output, N, gets extremely large? Given this result, what is your interpretation of a?

4.3 Panel a of Figure 6.7 shows that Intel’s average cost in a given year falls with the quantity it produces. In addition, extra production this year lowers the average cost curve next year. For example, in year 1, AC = 50 if quantity is 20 and AC = 40 if quantity is 60. If Intel produces 20 in year 1 and 40 in year 2, the average cost in year 2 will be 40. However, for every extra 10 units it produces in year 1, its AC for any given quantity in year 2 falls by 10%.

a. What is the total cost and the average cost over the two years combined if the firm produces 20 in year 1 and 40 in year 2?

b. What is the total cost and average cost over the two years combined if the firm produces 60 in year 1 and 40 in year 2?

c. Over the two years combined, what is the true additional cost of producing 60 instead of 20 in year 1?

4.4 In the Mini-Case “Solar Power Learning Curves,” the cost of solar power installations fell as the installed base (cumulative experience) in a given country rose. If N represents cumulative national experience, would an average cost curve AC = a + bN-r exhibit such learning by doing? Explain. (Note: a, b, and r are all positive constants.)

5. The Costs of Producing Multiple Goods 5.1 The United Kingdom started regulating the size of

grocery stores in the early 1990s, and today the aver- age size of a typical U.K. grocery store is roughly half the size of a typical U.S. store and two-thirds the size of a typical French store (Haskel and Sadun, 2012). What implications would such a restriction on size have for a store’s average costs? Discuss in terms of economies of scale and scope.

5.2 Conner runs a rafting company on a local river. He runs two kinds of trips – a wild whitewater experi- ence and a more mellow wildlife tour. If he spends the day only doing whitewater trips, he can do 3 trips per day; if he spends the day only doing wild- life trips, he can do 4 trips. If he does some of each, however, he can do more total trips: 2 whitewater trips and 3 wildlife trips. Suppose that Conner’s time is valued at $20 an hour. What can you say about his economies of scope? That is, what is the sign of his measure of economies of scope, SC?

*5.3 A refiner produces heating fuel and gasoline from crude oil in virtually fixed proportions. What can you

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say about economies of scope for such a firm? What is the sign of its measure of economies of scope, SC?

5.4 Many hospitals have regularly scheduled surgery and active emergency departments. Based on the information in the Mini-Case “Medical Economies of Scope,” could it be more cost effective to have separate emergency centers? What do you think are the reasons for these economies or diseconomies of scope?

6. Managerial Problem *6.1 In Figure 6.8, show that for some wages and capital

rental costs the firm is indifferent between using the wafer-handling stepper technology and the stepper technology. How does this wage-cost of capital ratio compare to those in the C2 and C3 isocost lines?

7. MyLab Economics Spreadsheet Exercises8

7.1 The production function for a firm is

q = -0.6L3 + 18L2K + 10L,

where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is $100 and the rental rate is $800 per time period.

a. Using Excel, calculate the total short-run out- put, q(L), for L = 0, 1, 2, c , 20, given that capital is fixed in the short run at K = 1. Also, calculate the average product of labor, APL, and the marginal product of labor, MPL. (You can estimate the MPL for L = 2 as q(2) - q(1), and so on for other levels of L.)

b. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using Excel, draw the AVC, AC, and MC curves in a diagram. (Hint: See Q&A 3.2.)

c. For each quantity of labor in (a), calculate w>APL and w>MPL and show that they equal AVC and MC, respectively. Explain why these relationships hold.

7.2 A furniture company has opened a small plant that builds tables. Jill, the production manager, knows the fixed cost of the plant, F = $78 per day, and includes the cost of the building, tools, and equip- ment. Variable costs include labor, energy costs, and wood. Jill wants to know the cost function. She con- ducts an experiment in which she varies the daily

8The spreadsheet exercises in this chapter are based on the work of Satyajit Ghosh in cooperation with the authors. The answers are available on MyLab Economics.

production level over a 10-day period and observes the associated daily cost. The daily output levels assigned are 1, 2, 4, 5, 7, 8, 10, 12, 15, and 16. The associated total costs for these output levels are 125, 161, 181, 202, 207, 222, 230, 275, 390, and 535, respectively.

a. Use the Trendline tool in Excel to estimate a cost function by regressing cost on output (Chapter 3). Try a linear specification (C = a + bq), a quad- ratic specification (C = a + bq + dq2), and a cubic specification (C = a + bq + dq2 + eq3). Based on the plotted regressions, which speci- fication would you recommend that Jill use? Would it make sense to use the Set Intercept option? If so, what value would you choose? (Hint: Put output in column A and cost in column B. To obtain quadratic and cubic cost specifications, select the Polynomial option from the Trendline menu and set Order at 2 for the quadratic specification and at 3 for the cubic function.)

b. Generate the corresponding average cost data by dividing the known cost by output for each experimental output level. Estimate an average cost curve using the Trendline tool.

7.3 A Korean electronic chip manufacturer has a pro- duction function given by q = L0.5K0.5.

a. Use Excel to determine the amount of capital, K, needed to produce 10 units of output for each value of labor, L, starting from L = 2 and going to L = 20 in increments of 1. Plot this iso- quant. (Hint: The formula for that isoquant is 10 = L0.5K0.5. Squaring both sides of this equa- tion, we obtain 100 = LK. Dividing both sides of the equation by L, we learn that K = 100>L.)

b. Use Excel to determine the cost of each of these combinations of labor and capital if the wage rate, w, and the cost of capital, r, are each $30 per unit. Which combination of inputs mini- mizes the cost of producing 10 units of output?

c. The slope of the isoquant is -100>L2. Calculate the slope of the isoquant for each combina- tion of inputs. The slope of the isocost line is -w>r = -30>30 = -1. Verify that the cost- minimizing input combination occurs where the slope of the isoquant equals the slope of the isocost line. Draw the isoquant and the isocost line and show that they are tangent at the cost- minimizing combination of inputs.

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189Appendix 6A Calculating Cost Curves

C os

ts p

er u

ni t,

$

100 200 300

q, Units per year

AFC

AVC AC

MC

0

20

30

40

50

10

APPENDIX 6A Calculating Cost Curves

If we know the production function for a product (Chapter 5) and the factor prices, we can use math to derive the various cost functions. Based on the estimates of Flath (2011), the Cobb- Douglas production function of a typical Japanese beer manufacturer (Chapter 5) is

q = 1.52L0.6K0.4,

where labor, L, is measured in hours, K is the number of units of capital, and q is the amount of output.

We assume that the firm’s capital is fixed at K = 100 units in the short run. If the rental rate of a unit of capital is $8, the fixed cost, F, is $800, and the average fixed cost is

AFC = F>q = 800>q, which falls as output increases.

We can use the production function to derive the variable cost. Given that capital is fixed in the short run, the short-run production function is solely a function of labor:

q = 1.52L0.61000.4 ≈ 9.59L0.6.

Rearranging this expression, we can write the number of workers, L, needed to produce q units of output as a function solely of output:

L(q) = ¢ q 9.59

≤ 10.6 = ¢ 1 9.59

≤1.67q1.67 ≈ 0.023q1.67. (6A.1) Now that we know how labor and output are related, we can calculate variable cost directly.

The only variable input is labor, so if the wage is $24, the firm’s variable cost is

VC(q) = wL(q) = 24L(q). (6A.2)

Substituting for L(q) using Equation 6A.1 into the variable cost Equation 6A.2, we see how vari- able cost varies with output:

VC(q) = 24L(q) = 24(0.023q1.67) ≈ 0.55q1.67. (6A.3)

Using this expression for variable cost, we can construct the other cost measures.

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190 CHAPTER 6 Costs

APPENDIX 6B Long-Run Cost Minimization

We can use calculus to derive the tangency rule, cost- minimization condition, Equation 6.6. The problem the firm faces in the long run is to choose labor, L, and capital, K, to minimize the cost of producing a particular level of output, q, given a wage of w and a rental rate of capital of r.

The firm’s production function is q = f(L, K), so the marginal products of labor and capital are MPL(L, K) = 0f(L, K)>0L 7 0 and MPK = 0f(L, K)>0K 7 0. The firm’s problem is to mini- mize its cost of production, C, through its choice of labor and capital,

min L,K

C = wL + rK,

subject to the constraint that a given amount of output, q, is to be produced:

f(L, K) = q. (6B.1)

Equation 6B.1 is the formula for the q isoquant. We can change this constrained minimization problem into an unconstrained problem by

using the Lagrangian technique. The corresponding Lagrangian, ℒ, is

ℒ = wL + rK - λ[ f(L, K) - q ],

where λ is the Lagrange multiplier. The first-order conditions are obtained by differentiating ℒ with respect to L, K, and λ and

setting the derivatives equal to zero:

0ℒ>0L = w - λMPL(L, K) = 0, (6B.2) 0ℒ>0K = r - λMPK(L, K) = 0, (6B.3) 0ℒ>0λ = f(L, K) - q = 0. (6B.4)

Using algebra, we can rewrite Equations 6B.2 and 6B.3 as w = λMPL(L, K) and r = λMPK(L, K). Taking the ratio of these two expressions, we obtain

MPL(L, K) MPK(L, K)

= w r

, (6B.5)

which is the same as Equation 6.6. This condition states that cost is minimized when the ratio of marginal products is the same as the factor price ratio, w>r.

To obtain the equation for marginal cost as a function of output, we differentiate the vari- able cost, VC(q), in Equation 6A.3 with respect to output:

MC(q) = dVC(q)

dq ≈

d(0.55q1.67)

dq

= 1.67 * 0.55q0.67 ≈ 0.92q0.67.

We can also calculate total cost, C = F + VC, average cost, AC = C>q, and average variable cost, AVC = VC>q, using algebra. The figure plots the beer firm’s AFC, AVC, AC, and MC curves.

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7Firm Organization and Market Structure I won’t belong to any organization that would have me as a member. —Groucho Marx

H aving examined firms’ production and cost decisions in earlier chapters, we now turn to some of the firm’s other crucial decisions. We start by describing the organization and governance of firms. Next, we consider the firm’s objectives, starting with profit maximization. We show

how managers can choose output to maximize profit, and we describe the firm’s

Amazon has a problem: It’s too successful. It controls 44% of the U.S. e-commerce market, has well over $200 billion in annual sales; ships more than 1.2 billion packages a year; and has more than 100 warehouses, 7,500 truck trailers, and 40 airplanes. However, its rapid growth has made quick and inexpensive delivery of packages crucial to its operations. In 2017, it spent nearly $22 billion on shipping globally, or about 12% of its overall revenue.

Amazon has relied on shipping using United Parcel Service (UPS), FedEx, and the U.S. Postal Service (USPS). Amazon worries that these delivery services are relatively expensive and have trouble delivering on time, especially during heavy shipping periods, such as near the holidays in December. Consequently, Amazon says that it needs to develop its own delivery services.

It is using or considering three approaches. First, its Flex service contracts with individuals who drive their own cars to deliver packages for “the last mile.” Second, it is developing a new service in which it would also contract with individuals to deliver packages for the last mile; however, these persons would use Amazon’s new gray-and-blue delivery vans and wear black hats and blue-collared shirts with an Amazon logo.

A third option is for Amazon to create a shipping service to compete with UPS, FedEx, and USPS. Starting initially in Los Angeles, Shipping With Amazon (SWA) will pick up packages from businesses and deliver them to customers. However, to develop such a service able to compete with the large shipping companies would

require an investment of many billions of dollars. FedEx has 650 aircraft, 150,000 trucks, 400,000 employees, and 4,800 operating facilities globally. UPS planned to spend $7 billion to upgrade its delivery network in 2018 alone.

What issues should Amazon consider in deciding whether to rely primarily on other delivery services or develop its own capabilities? Given that the up-front investment in SWA will cause Amazon to lose money for the first few years before turning a profit, how should Amazon decide whether this investment is worthwhile?

Amazon’s Delivery Services

Managerial Problem

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decision of when to shut down. We then examine firms that pursue social objectives. However, we point out two market forces that lead most firms to maximize profits.

We next use the concept of present value to address how managers make decisions when profits vary over time, such as when firms make investments that have short- term costs but lead to longer-term gains.

In pursuing a firm’s objectives, such as profit maximization, managers must decide on the vertical structure of the firm—whether the firm produces needed inputs internally or buys them. Whether the firm makes or buys an input depends on the relative costs of these two approaches. The size of the market affects these costs, and thereby affects the make or buy decision. We show that as a market grows, firms typi- cally change from producing their own inputs to buying them from others, but as the market grows even larger, firms may revert to producing the inputs themselves.

The size of the market affects not only individual firms’ organizational structure but also the overall structure of the market. A market’s structure depends on the number of firms, how easily they can enter or exit the market, their ability to set prices, whether they differentiate their products, and how the firms interact. And sometimes managers must cope with disruptive innovations that may dramatically change market structure or other factors that affect managerial decision making.

7.1 Ownership and Governance of Firms A firm may be owned by a government, by other firms, by private individuals, or by some combination. A country’s legal and governmental system affects whether firms are privately owned, how owners run firms, and whether or not they pursue profits.

Private, Public, and Nonprofit Firms Atheism is a non-prophet organization. —George Carlin

Firms operate in the private sector, the public sector, or the nonprofit sector. The private sector—sometimes referred to as the for-profit private sector or for-profit sector— consists of firms that are owned by individuals or other nongovernmental entities and whose owners may earn a profit. Most of the firms that we discuss throughout this book—such as Apple, Nike, and Toyota—belong to the private sector. In almost every country, this sector provides most of that country’s gross domestic product (GDP), which is a measure of the value of a country’s total output.

The public sector consists of firms and other organizations that are owned by governments or government agencies, called state-owned enterprises. An example of a public-sector firm is the National Railroad Passenger Corporation (Amtrak),

Learning Objectives

1. Explain how firms differ by type of ownership and organization.

2. Determine a firm’s profit-maximizing output.

3. Use present values to compare costs and revenues that occur at different times.

4. Discuss profit-maximizing vertical organization.

5. Describe the four main types of market structure.

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which is owned primarily by the U.S. government. The armed forces and the court system are also part of the public sector, as are most schools, colleges, and universities.

In most countries, the government produces between 10% and 20% of the coun- try’s GDP. Examples include the United States (11%), India (11%), Australia (16%), Germany (18%), Canada (17%), South Africa (19%), and the United Kingdom (19%).1 The government’s share is higher in a few countries that provide a high level of government services—such as Sweden (23%)—or maintain a relatively large army, such as Israel (23%).

The nonprofit sector consists of organizations that are neither government-owned nor intended to earn a profit, but typically pursue social or public interest objectives. Literally, this sector should be called the nongovernment, not-for-profit sector, but this term is normally shortened to just the nonprofit sector. Well-known examples include Greenpeace and Alcoholics Anonymous, along with many other charitable, educa- tional, health, and religious organizations.

In 2018, the private sector created 76% of the U.S. gross domestic product, while nonprofits and households produced about 13%, and the government sector accounted for the remaining 11%.2

Sometimes all three sectors play an important role in the same industry. For exam- ple, in the United States, Canada, the United Kingdom, and many other countries, for-profit, nonprofit, and government-owned hospitals coexist. Similarly, while most schools and other educational institutions are government-owned, many are not, including some of the most prominent U.S. universities, such as Harvard, Stanford, and the Massachusetts Institute of Technology (MIT). These universities are often referred to as private universities. Most private universities are nonprofit organiza- tions. However, some educational institutions, such as the University of Phoenix, are intended to earn profits and are part of the for-profit private sector.

A single enterprise may be partially owned by a government and partially owned by private interests. For example, during the 2007–2009 Great Recession, the U.S. government took a partial ownership position in many firms in the financial and automobile industries. If the government is the dominant owner, it is normal to view the enterprise as part of the public sector. Conversely, if the government has only a small ownership interest in a for-profit enterprise, that enterprise would be viewed as part of the private sector. Organizations or projects with significant government ownership and significant private ownership are sometimes referred to as mixed enterprises or public-private partnerships.

1The data in this paragraph are from Version 9.0 of the Penn World Table as of October 2017, available for download at www.rug.nl/ggdc/productivity/pwt/. For a description of this data, see Feenstra, Inklaar, and Timmer (2015). 2https://fred.stlouisfed.org/release/tables?rid=53&eid=13416&snid=13423.

Mini-Case Before 1978, virtually all Chinese industrial firms were state-owned enterprises (SOEs). Since then, China has been transitioning to a market-based economy, gradually increasing the role of private-sector firms. It has dramatically reduced the number of SOEs, keeping mainly the largest ones.

By 1999, SOEs comprised only about 36% of Chinese industrial firms but still controlled nearly 68% of industrial assets (capital). Since 2000, the Chinese

Chinese State-Owned Enterprises

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194 CHAPTER 7 Firm Organization and Market Structure

Ownership of For-Profit Firms In this textbook, we focus on the private sector. The private sector has three main types of organizations: the sole proprietorship, the partnership, and the corporation.

Sole proprietorships are firms owned and controlled by a single individual. Partnerships are businesses jointly owned and controlled by two or more people

operating under a partnership agreement. Corporations are owned by shareholders, who own the firm’s shares (also called

stock). Each share (or unit of stock) is a unit of ownership in the firm. Therefore, shareholders own the firm in proportion to the number of shares they hold. The shareholders elect a board of directors to represent them. In turn, the board of direc- tors usually hires managers who manage the firm’s operations. Some corporations are very small and have a single shareholder, often an owner-manager who owns and runs the business. Others are very large and have thousands of shareholders. The legal name of a corporation often includes the term Incorporated (Inc.) or Lim- ited (Ltd.) to indicate its corporate status.

Publicly Traded and Closely Held Corporations. Corporations may be either publicly traded or closely held. The term public in this context has a differ- ent meaning than its use in the term public sector. A publicly traded corporation is a corporation whose shares can be readily bought and sold by the general public. The shares of most of these corporations trade on major organized stock exchanges, such as the New York Stock Exchange, the NASDAQ (National Association of Securi- ties Dealers Automated Quotations), the Tokyo Stock Exchange, the Shanghai Stock Exchange, the Toronto Stock Exchange, or the London Stock Exchange. For example, IBM shares can be readily bought and sold on the New York Stock Exchange.

The stock of a closely held corporation, sometimes referred to as private equity, is not available for purchase or sale on an organized exchange. Typically, a small group of individuals own this stock. The transition from closely held to publicly traded status is often an important step in the evolution of a corporation.

In making the transition from privately held to publicly traded status, the closely held firm will make an initial public offering (or IPO) of its shares on an organized stock exchange. This IPO is a way to raise money for the firm. For example, the 2018 IPO of Dropbox, a file-sharing and storage platform, raised over $750 million.3 This ability to raise money by issuing stock is one major advantage of going public. How- ever, a major disadvantage from the point of view of the original owners is that ownership of the firm becomes broadly distributed, possibly causing the original owners to lose control of the firm.

3Alex Barinka, “Dropbox Raises $756 Million After Pricing IPO Above Range,” Bloomberg, March 22, 2018.

government has allowed many small SOEs to be privatized or go bankrupt, while it continues to subsidize many large SOEs. In 2017, SOEs accounted for 29% of industrial assets, and still accounted for 30% to 40% of China’s GDP. China is also creating mixed enterprises by selling shares in state-owned enter- prises to private investors. For example, in 2017, the giant state-owned mobile carrier China Unicom announced a plan to sell $11.7 billion in shares, corre- sponding to about one-third of the company, to private sector investors.

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It is also possible for a publicly traded firm to go private and become closely held. Such a change occurs when a group of investors buys all or most of the shares held by the general public and takes the corporation out of any organized exchanges where its stock previously traded. Sometimes senior managers of the corporation are among the buyers. Commonly, the buyers include private equity firms that special- ize in taking firms private, often in combination with other outside investors. One of the best-known private equity firms is KKR, which has taken many publicly traded firms private. For example, in 2018 KKR announced its purchase of Envision Healthcare Corporation in a deal valued at over $5.5 billion.4

Traditionally, the owners of sole proprietorships and partnerships were fully liable, individually and collectively, for any debts of the firm. In contrast, the own- ers of a corporation are not personally liable for the firm’s debts; they have limited liability: The personal assets of the corporate owners cannot be taken to pay a cor- poration’s debts even if it goes into bankruptcy. Because of the limited liability of corporations, the most that shareholders can lose is the amount they paid for their stock, which typically becomes worthless if the corporation goes bankrupt.

Changes in the laws in many countries have allowed a sole proprietorship or a partnership to obtain the advantages of limited liability by becoming a limited liability company (LLC).5 These LLC firms can otherwise do business as usual and need not adopt other aspects of the corporate form such as filing corporate tax returns. The precise regulations that apply to LLCs vary from country to country, and from state to state within the United States. Adopting the LLC form has some costs that many firms are not willing to incur, including registration fees, and firms in some indus- tries are not eligible. Therefore, traditional sole proprietorships and partnerships with unlimited personal liability for the owners remain very common. However, the LLC form has significantly extended the availability of limited liability.6

Firm Size. The purpose of limiting the liability of owners of corporations was to allow firms to raise funds and grow larger than was possible when owners risked everything they owned on any firm in which they invested. Consequently, most large firms were (and still are) corporations. According to the latest available Internal Revenue Service (IRS) statistics, U.S. corporations are responsible for 81% of busi- ness receipts and 58% of net business income even though they are only 18% of all nonfarm firms. Nonfarm sole proprietorships are 72% of firms but make only 4% of the sales revenue and earn 15% of net income. Partnerships are 10% of firms, account for 15% of revenue, and make 27% of net income.

As these statistics illustrate, larger firms tend to be corporations and smaller firms are often sole proprietorships. This pattern reflects a natural evolution in the life cycle of the firm, as an entrepreneur may start a small business as a sole proprietorship and then incorporate as the firm’s operations expand.

4Aparajita Saxena, “KKR to Take Envision Private for $5.57 Billion in Healthcare Push,” Reuters, June 11, 2018. 5In the United States, a few states had longstanding provisions for LLCs. National acceptance and standardization of this form dates from the Uniform Limited Liability Company Act of 1996. 6Forming a limited partnership has become an alternative method for a partnership to gain the advantages of limited liability. Such firms are owned in whole or in part by limited partners, whose financial liability is limited in the sense that they cannot lose more than the amount of their invest- ment. Limited partnerships may also have one or more general partners who, like sole proprietors, are personally responsible for the firm’s debts.

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Indeed, successful corporations typically expand, and a relatively small number of corporations account for most of the revenue and income in the U.S. economy. According to the IRS, 81% of all corporations earn less than $1 million a year, and they account for only 3% of corporate revenue. In contrast, less than 1% of all corpo- rations earn over $50 million, but they make 77% of total corporate revenue. In 2017, the U.S. corporation with the largest worldwide revenue was Walmart. Its revenue of $500 billion exceeded the annual GDP of fairly large countries, such as Austria ($478 billion) and Thailand ($483 billion).7

Firm Governance In a small private-sector firm with a single owner-manager, the governance of the firm is straightforward: The owner-manager makes the important decisions for the firm. In contrast, governance in a large modern publicly traded corporation is more complex.

The shareholders own the corporation. However, most shareholders do not play an important role in day-to-day decision making or even in long-range planning in the firm and therefore do not control the firm in any meaningful sense. They are passive shareholders. Many people own shares in corporations like Microsoft and Sony, but virtually none of these individuals influence or even have knowledge about these firms’ day-to-day managerial decisions.

Many of the ownership rights of shareholders are delegated to a board of directors that is elected by the shareholders, often referred to simply as the board. The board of a large publicly traded corporation normally includes outside directors, who are not employed as managers by the corporation, and inside directors, such as the chief executive officer (CEO) of the corporation and other senior executives. Some corpora- tions have former politicians and other prominent people as outside directors, such as former U.S. Vice President Al Gore (Apple), but most directors are people with relevant business experience, particularly former CEOs. For example, former Hewlett Packard CEO Meg Whitman serves as a director for Procter & Gamble and for Dropbox.

7.2 Profit Maximization The managers of all types of firms pursue goals. Managers of government agencies, charitable organizations, and other nonprofit organizations are supposed to take actions that benefit specific groups of people. Economists assume that most owners of private-sector firms want to maximize their profits. One reason for this belief is that owners and managers often state that profit maximization is their objective. Indeed, that’s why private-sector firms are called for-profit businesses.

Profit A firm’s profit, π, is the difference between a firm’s revenues, R, and its cost, C:

π = R - C.

If profit is negative, π 6 0, the firm makes a loss.

7Fortune magazine annually provides a list of the largest corporations: http://fortune.com/ fortune500. GDP data are from the International Monetary Fund for 2017.

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1977.2 Profit Maximization

Measuring a firm’s revenue is straightforward: It is the proceeds from selling the firm’s products. Measuring cost is more challenging. For an economist, the correct measure of cost is the economic cost or opportunity cost: the value of the best alterna- tive use of any input the firm employs. As discussed in Chapter 6, the opportunity cost of inputs often exceeds the explicit or out-of-pocket costs recorded in financial accounting statements. This distinction is important because a firm may make a seri- ous mistake if it ignores some relevant opportunity costs.

Economic profit is revenue minus opportunity cost. When we refer to just profit, we mean economic profit. Economic profit is often different from the profit reported in a firm’s financial accounting statements. For tax requirements and for other rea- sons, these accounting profits are often calculated using only explicit costs, leaving out important implicit opportunity costs. If implicit costs are left out, then a firm’s accounting profit may be larger than its economic profit. An example illustrates the difference in the two profit measures and the importance of this distinction in dispelling a misconception:

That conclusion may not follow if accounting profit ignores implicit opportunity costs. For small firms owned and managed by one person, the main difference between

explicit costs and the opportunity cost is often the implicit cost of the owner- manager’s time. Kahlil owns and manages a small restaurant with monthly revenues of $50,000 and has explicit monthly costs (rent, materials, and labor) of $45,000 a month. Thus, his accounting profit is $50,000 - $45,000 = $5,000 per month.

However, the best alternative use of his time is to work at another job where he could earn $6,000 a month. Thus, the opportunity cost of Kahlil’s time spent running his restaurant is $6,000 per month. As a result, his opportunity cost of operating the restaurant is $45,000 + $6,000 = $51,000, so his firm’s economic profit is $50,000 - $51,000 = - $1,000, which is negative—he is making a loss. Kahil can earn more money by shutting down his restaurant and working for someone else.

The owners of a firm may put other resources into a firm in addition to their own labor. The opportunity cost of these resources should also be included when calcu- lating economic profit. In large corporations, the owners of the firm are sharehold- ers who may provide no labor to the firm but still incur an opportunity cost: They cannot use the money they invested in the firm elsewhere. To be willing to invest in the firm, the owners must receive payments at least equal to the opportunity cost of their investment. This necessary payment to the owners is an implicit cost of doing business. If a firm earns an accounting profit of $100,000 but must pay $40,000 to the firm’s owners to cover their opportunity cost, the firm has an economic profit of only $60,000. Businesses often refer to the amount that must be earned to cover the implicit costs of the owners as normal profit and call economic profit above-normal profit.

Two Steps to Maximizing Profit Because both the firm’s revenue and cost vary with its output, q, the firm’s profit also varies with output:

π(q) = R(q) - C(q), (7.1)

Common Confusion You should operate your firm if you are making an accounting profit.

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198 CHAPTER 7 Firm Organization and Market Structure

where R(q) is its revenue function and C(q) is its cost function. A firm decides how much output to sell to maximize its profit, Equation 7.1. To maximize its profit, any firm must answer two questions:

●● Output decision: If the firm produces, what output level, q, maximizes its profit or minimizes its loss?

●● Shutdown decision: Is it more profitable to produce q or to shut down and produce no output?

The profit curve in Figure 7.1 illustrates these two basic decisions. This firm makes losses at very low and very high output levels and positive profits at moderate output levels. The profit curve first rises and then falls, reaching a maximum profit of π* when its output is q*. As this profit level is positive, the firm chooses to produce output q* rather than shut down and earn no profit.

Output Rules. A firm can use one of three equivalent rules to choose how much output to produce. These rules are just three different ways of stating essentially the same thing. The most straightforward rule is:

Output Rule 1: The firm sets its output where its profit is maximized.

If the firm knows its entire profit curve in Figure 7.1, it sets its output at q* to maxi- mize its profit at π*.

Even if the firm does not know the exact shape of its profit curve, it may be able to find the maximum by experimenting. The firm slightly increases its output. If profit increases, the firm increases the output more. The firm keeps increasing out- put until profit does not change. At that output, the firm is at the peak of the profit curve. If profit falls when the firm first increases its output, the firm tries decreasing its output. It keeps decreasing its output until it reaches the peak of the profit curve.

What the firm is doing is experimentally determining the slope of the profit curve. The slope of the profit curve is the firm’s marginal profit: the change in the profit the firm gets from selling one more unit of output, ∆π>∆q, where ∆q = 1. In Figure 7.1, the marginal profit or slope of the profit curve is positive when output is less than q*, zero when output is q*, and negative when output is greater than q*. Thus,

Output Rule 2: A firm sets its output where its marginal profit is zero.

FIGURE 7.1 Maximizing Profit

By setting its output at q*, the firm maximizes its profit at π*, where the profit curve reaches its peak.

p , P

ro fit

Dp > 0 Dp < 0

q* q, Units per day

Profit

11

p*

0

Dp = 0

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1997.2 Profit Maximization

A third way to express this profit-maximizing output rule is in terms of cost and revenue. The marginal profit depends on a firm’s marginal cost and marginal revenue. A firm’s marginal cost (MC) is the amount by which a firm’s cost changes if it pro- duces one more unit of output: MC = ∆C>∆q, where ∆C is the change in cost when ∆q = 1. Similarly, a firm’s marginal revenue (MR) is the change in revenue it gets from selling one more unit of output: ∆R>∆q, where ∆R is the change in revenue when ∆q = 1. Provided MR is positive at output q, the firm earns more revenue by selling more units of output, but the firm also incurs an additional cost, MC(q), which must be deducted from MR(q) to determine the net effect on marginal profit. The change in the firm’s profit is

Marginal profit(q) = MR(q) - MC(q).

Does it pay for a firm to produce one more unit of output? If the marginal rev- enue from this last unit of output exceeds its marginal cost, MR(q) 7 MC(q), the firm’s marginal profit is positive, MR(q) - MC(q) 7 0, so it pays to increase output. The firm keeps increasing its output until it is producing the q, where its marginal profit (q) = MR(q) - MC(q) = 0. That is, the firm picks the q where its marginal revenue equals its marginal cost: MR(q) = MC(q). Were the firm to produce more output so that its marginal cost exceeded its marginal revenue, MR(q) 6 MC(q), the extra output would reduce the firm’s profit. Thus, a third, equivalent rule is:

Output Rule 3: A firm sets its output where its marginal revenue equals its marginal cost:

MR(q) = MC(q). (7.2)

Maximizing Profit

Using Calculus We can use calculus to derive the condition that marginal revenue must equal marginal cost at the output level that maximizes profit. Using calculus, we define marginal revenue as the derivative of revenue with respect to output:

MR(q) = dR(q)

dq .

The derivative dR(q)>dq is the limit of ∆R(q) >∆q as ∆q gets very small. Our earlier definition of marginal revenue, ∆R(q) >∆q for ∆q = 1, is nearly equiva- lent to the calculus definition if ∆q = 1 is a “very small” change. Similarly, marginal cost is the derivative of cost with respect to output, MC(q) = dC(q) >dq (Chapter 6).

To maximize profit in Equation 7.1, π(q) = R(q) - C(q), the firm operates at the quantity q where the derivative of profit with respect to quantity is zero:

dπ(q)

dq =

dR(q)

dq -

dC(q)

dq = MR(q) - MC(q) = 0. (7.3)

The left side of Equation 7.3, dπ>dq, is the firm’s marginal profit. This result shows that marginal profit equals the difference in marginal revenue and

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200 CHAPTER 7 Firm Organization and Market Structure

Shutdown Rules. Producing the output level q such that MR(q) = MC(q) is a necessary condition to maximize profit if the firm produces a positive output level. However, the firm might make losses even at the best possible positive output (although a smaller loss than at other positive outputs).

Q&A 7.1 If a firm’s revenue function is R(q) = 120q - 2q 2 and its cost function is

C(q) = 100 + q2, what output level maximizes its profit? Answer 1. Determine the marginal revenue and marginal cost by differentiating the revenue

and cost functions. The firm’s marginal revenue is dR(q) >dq = 120 - 4q. Its marginal cost is dC(q) >dq = 2q.

2. Equate the marginal revenue and marginal cost expressions to determine the output that maximizes profit. Setting the marginal revenue equal to the marginal cost, we find that 120 - 4q = 2q. Solving for q, we learn that the profit-maximizing output is q = 20.

3. Alternatively, determine the profit function and then differentiate the profit function to find the maximum. The profit function is π(q) = R(q) - C(q) = [120q - 2q2] - [100 + q2] = 120q - 3q2 - 100. Taking the derivative of the profit function with respect to quantity (the marginal profit) and setting it equal to zero, we learn that dπ(q) >dq = 120 - 6q = 0. Consequently, the profit-maximizing output is q = 20.

One of the most important implications of economics is that marginal analysis is very valuable to managers. If a manager knows the entire profit function (as in Figure 7.1), then it’s easy to choose the profit-maximizing output. However, many managers are uncertain about what profit would be at output levels that differ significantly from the current level.

Such a manager can use marginal reasoning to maximize profit. By experi- menting, the manager can determine if increasing output slightly raises profit— that is, the firm’s marginal profit is positive (or, equivalently, its marginal revenue is greater than its marginal cost). If so, the manager should continue to increase output until the marginal profit is zero (marginal revenue equals marginal cost). Similarly, if marginal profit is negative, the manager should decrease output until marginal profit is zero.

Marginal Decision Making

Managerial Implication

marginal cost. Because this profit-maximizing condition requires that MR(q) - MC(q) = 0, it follows that the firm maximizes its profit when it chooses output such that MR(q) = MC(q), which is the same condition as in Equation 7.2.8

8For the quantity determined by the marginal condition, MR = MC or dπ>dq = 0, to maximize profit, a second-order condition must also hold: d2π>dq2 6 0. It is possible to have more than one local profit maximum, each of which satisfies the marginal condition. If the marginal condition holds at more than one quantity, the one with the highest profit is the global profit maximum.

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2017.2 Profit Maximization

Should the firm shut down if its profit is negative? Surprisingly, the answer is “It depends.” The general rule, which holds for all types of firms in both the short run and the long run, is:

Shutdown Rule 1: The firm shuts down only if it can reduce its loss by doing so.

In the short run, the firm has variable costs, such as for labor and materials, and fixed costs, such as from plant and equipment (Chapter 6). If the fixed cost is sunk, this expense cannot be avoided by stopping operations—the firm pays this cost whether it shuts down or not. Thus, the sunk fixed cost is irrelevant to the shutdown decision. By shutting down, the firm stops receiving revenue and stops paying the avoidable costs (Chapter 6), but it is still stuck with its fixed cost. Thus, it pays for the firm to shut down only if its revenue is less than its avoidable cost.

Suppose that a firm’s weekly revenue is R = $2,000, its variable cost is VC = $1,000, and its fixed cost is F = $3,000, which is the price it paid for a machine that it cannot resell or use for any other purpose. This firm is making a short-run nega- tive profit π (a loss):

π = R - VC - F = $2,000 - $1,000 - $3,000 = - $2,000.

If the firm shuts down, it still has to pay its fixed cost of $3,000, and hence it loses $3,000, which is a greater loss than the $2,000 it loses if it operates. Because its fixed cost is sunk, the firm should ignore it when making its shutdown decision. Ignoring the fixed cost, the firm sees that its $2,000 revenue exceeds its $1,000 avoidable, vari- able cost by $1,000, so it does not shut down. The extra $1,000 can be used to offset some of the fixed cost, reducing the firm’s loss from $3,000 to $2,000.

However, if its revenue is only $500, it cannot cover its $1,000 avoidable, variable cost and loses an additional $500. When it adds this $500 loss to the $3,000 it must pay in fixed cost, the firm’s total loss is $3,500. Because the firm can reduce its loss from $3,500 to $3,000 by ceasing operations, it shuts down. (Remember the shutdown rule: The firm shuts down only if it can reduce its loss by doing so.)

The firm’s variable costs are always avoidable: The firm pays the variable costs only if it operates. In contrast, the firm’s short-run fixed cost is usually unavoid- able: The firm incurs the fixed cost whether or not it shuts down. Therefore, if the firm shuts down in the short run it incurs a loss equal to its fixed cost because it has no revenue (R = 0) or variable cost (VC = 0), so its profit is negative: π = R - VC - F = 0 - 0 - F = -F. If the firm operates and its revenue more than covers its variable cost, R 7 VC, then the firm does better by operating because π = R - VC - F 7 -F. Thus, the firm shuts down only if its revenue is less than its avoidable, variable cost: R 6 VC.

In conclusion, the firm compares its revenue to only its avoidable, variable costs when deciding whether to stop operating. If the fixed cost is sunk, the firm pays this cost whether it shuts down or not. The sunk fixed cost is irrelevant to the shutdown decision.

We usually assume that a fixed cost is sunk. However, if a firm can sell its capital for as much as it paid, its fixed cost is avoidable and should be taken into account when the firm is considering whether to shut down. A firm with a fully avoidable fixed cost always shuts down if it makes a short-run loss. If a firm buys a specialized piece of machinery for $1,000 that can be used only in its business but can be sold for scrap metal for $100, then $100 of the fixed cost is avoidable and $900 is sunk. Only the avoidable portion of fixed cost is relevant for the shutdown decision.

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All capital and other inputs are adjustable in the long run, so all costs are avoid- able. Thus, the firm can eliminate all costs by shutting down—it has no sunk fixed costs. In the long run, it pays to shut down if the firm faces any loss at all. As a result, we can restate the shutdown rule, which holds for all types of firms in both the short run and the long run, as:

Shutdown Rule 2: The firm shuts down only if its revenue is less than its avoidable cost.

Social Responsibility Some managers pursue social objectives rather than maximize profit. Most enter- prises in the nonprofit sector such as charities and religious organizations have social rather than financial objectives. Public-sector enterprises are often required by law to provide public services at prices below the profit-maximizing level. In the United States, public-sector corporations such as the Export-Import Bank and the Federal Deposit Insurance Corporation exist to support private-sector activity, not to maxi- mize profit. Government-owned garbage companies may provide services at prices below what a profit-maximizing firm would charge.

Even some private-sector firms give up profit to achieve certain social goals. How- ever, Milton Friedman, a Nobel Prize–winning economist, objected to such behavior. He argued that the sole responsibility of managers is to the owners of the firm, so managers should maximize profit.9

The philosopher and business professor R. Edward Freeman (1984) disagreed. According to his stakeholder theory, managers have obligations to several groups in addition to shareholders, including workers, customers, and the communities in which firms reside and operate. He contended that corporations should not use child labor in poor countries; they should provide safe working conditions and safe products; and they should not contaminate communities where they operate with toxic waste, even if such corporate policies reduce profit.

The pursuit of social objectives by corporations is called corporate social responsibil- ity (CSR). However, as social responsibility is also relevant for unincorporated firms and for other types of organizations, many people refer to the environmental, social, and governance (ESG) objective.10

ESG has become increasingly important in managerial decision making, espe- cially in large corporations. Most large corporations such as Exxon and Sony provide annual ESG reports.

Charitable Activities. ESG decisions are made by a firm’s CEO and other senior managers, who often commit the firm to providing large contributions to hospitals, universities, environmental projects, disadvantaged groups, and other

9Milton Friedman, “The Social Responsibility of Business Is to Increase Its Profits,” New York Times Magazine, September 13, 1970: 32–33. 10The world’s largest developer of voluntary international standards, the International Organization for Standardization (ISO), has attempted to provide standards for social responsibility (www.iso .org/iso/home/standards/management-standards/iso26000.htm). The ISO defines social respon- sibility as “acting in an ethical and transparent way that contributes to the health and welfare of society.” It identifies several major areas of social responsibility for business organizations, includ- ing the environment (or sustainability), governance, and other social issues such as treatment of employees, consumer safety, and charitable giving.

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2037.2 Profit Maximization

causes. A well-known example of corporate philanthropy is Ronald McDonald House Charities. It provides temporary housing and other support in over 50 countries for families of children who are hospitalized for extended periods.

However, such contributions may reduce returns to shareholders. These causes might seem worthy but, after all, as Friedman argued, if shareholders want to donate money for a new hospital or a new building on a university campus, they can do so directly. Shareholders might not want managers of the firms they invest in making such decisions for them.

Nonetheless, corporate shareholders sometimes propose ESG initiatives at shareholder meetings. Such ESG-related shareholder activism has been growing in frequency and raises the issue that different groups of shareholders might have dif- ferent objectives.

In such circumstances, just what are the legal and ethical obligations of managers to shareholders? This topic has been the subject of much litigation. Courts have increasingly decided that businesses have implicit obligations to various stakeholders that often go beyond what is explicitly covered in formal contracts.

Strategic ESG. Purely altruistic ESG activities are costly to shareholders. However, some costly ESG activities may provide shareholders with significant benefits that more than offset the costs. For example, if consumers are willing to pay more for environmentally friendly products, then producing such products may raise a firm’s profits. Similarly, a firm that acquires a reputation for treating its workers fairly may increase its sales or may be able to charge a higher price for its products.11

ESG activities that are intended to increase profits are called strategic ESG and are often described as “doing well by doing good.” For example, McDonald’s receives extensive, favorable media exposure and other reputational benefits from its Ronald McDonald Houses. ESG expenditures can often be more effective than conventional advertising in building consumer goodwill. In addition, some corporations believe that ESG activities prevent potentially costly government interventions.

11Several fair trade labeling organizations, including Fairtrade International, designate certain products as fair trade products. The designation implies that certain standards of sustainability and treatment of workers have been met. Some consumers are willing to pay more for fair trade products (De Pelsmacker, Driesen, and Rayp, 2005).

Mini-Case In the past few years, several trends in social responsibility have emerged. Not all of these activities reduce profits, but all are potentially important for the suc- cess of firms and society.

1. End of Workplace Harassment: Susan Fowler published a whistle-blower essay in 2017 about sexism during her time at Uber. By 2018, the #MeToo movement was running strong, telling companies that women should not have to deal with sexual harassment any longer. As a result, founders, senior management, and others resigned or were fired at Uber, Fox, and other corporations.

2. Increase Diversity: Companies are under increasing pressure to hire and pro- mote women, minorities, and other workers whom they have largely ignored or discriminated against in the past.

Trends in Social Responsibility

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204 CHAPTER 7 Firm Organization and Market Structure

Forcing Firms to Maximize Profit: The Survivor Principle and Competition for Corporate Control Not all private-sector managers try to maximize profits. As we’ve seen, some have social objectives. Others fail to maximize profits through incompetence. Finally, some managers have selfish objectives that are inconsistent with owners’ desire to maximize profits. They may want to gain personal prestige, to avoid working hard, or to maximize their own income.12

Why, then, do economists assume that most private-sector firms maximize profit? The two key reasons are the survivor principle and competition for corporate control.

Survivor Principle. According to the survivor principle, in perfectly competitive markets, the only firms that survive are those that maximize profit. Firms that fail to maximize profit lose money and are driven out of business.

The Struggle for Corporate Control. Managers who fail to maximize profit can be disciplined through competition for corporate control, where outside investors use the stock market to buy enough shares to take over control of an underperform- ing publicly traded corporation. An outsider may profit by seizing control of a com- pany in which the current managers fail to maximize profits. After acquiring a controlling interest in an underperforming firm’s stock, the acquirer can replace the current board and the current management, improve the profitability of the firm, and realize an attractive return on investment. Even if outside investors do not acquire full control of the firm, they can demand that the board replace current senior managers or that current managers pursue different policies. Such activist investors made demands on 805 companies in 2017, up from 570 in 2013.13

Of course, managers who fear losing their jobs resist such a takeover. For example, Sophia, the manager of an underperforming company, is worried because a

12For example, if a manager’s compensation is based on sales, which are easy for owners to observe, rather than profit, which owners may not be able to observe, a manger may maximize revenue rather than profit. In Chapter 15, we analyze such conflicts between owners and managers and describe how to reduce their negative impact. 13Schulte, Roth, and Zabel, The Activist Investing Annual Review, 2018.

3. Involvement in Politics: Corporations have always lobbied for special treat- ment, but, increasingly, heads of firms such as Facebook and Microsoft are speaking out on issues of social justice, such as border enforcement of immi- gration laws and anti-discrimination laws.

4. Protect the Environment: Many corporations, such as Google and Nike, are trying to slow global warming by reducing their carbon footprints and are lobbying for pro-environment policies.

5. Brand Strategies Based on Philanthropy: Some firms commit to making chari- table contributions for each item consumers buy. For example, TOMS Shoes “Buy One, Give One” marketing strategy involves giving a poor child a pair of shoes for each pair purchased. Firms hope that some socially concerned consumers will buy from these companies rather than from their competitors for this reason.

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2057.2 Profit Maximization

well-known corporate raider (such as Carl Icahn, Kirk Kerkorian, or T. Boone Pickens) is buying many shares of her firm.14 She fears that the raider is planning a hostile takeover and will replace the current managers with new managers to turn around the underperforming firm. How does Sophia keep her job? If she can’t instantly improve the firm’s performance, she may hire the cleverest corporate law- yer she can find to construct takeover defenses.

Common defenses in the United States include a shareholder rights plan, which is better known as a poison pill. (See Table 7.1 for a list of takeover defense terminology.) A poison pill is a provision that a corporate board adds to its bylaws or charter that makes the firm a less attractive takeover target.

The law on the use of poison pills is evolving, with many countries limiting their use, including the United Kingdom and many other European countries. In Canada, regulatory authorities can remove provisions deemed to be poison pills from take- over bids, and they frequently do.

Poison pills do not always work in preventing a takeover, but they frequently cause some of the profits arising from the takeover to go to the original managers or

14Corporate raiders are large investors who make hostile takeovers bids—seeking to buy a control- ling interest in a firm despite the opposition of senior management. Sometimes, however, a raider will engage in greenmail, buying enough shares to credibly threaten a takeover, but agreeing to sell those shares back to the firm at a premium to end the takeover attempt.

TABLE 7.1 Some Takeover Defense Terms

back-end plan: Provision that gives shareholders the right to cash or debt securities at an above-market price previously defined by the company’s board in the event of a hostile takeover.

dead-hand: Provision that allows only the directors who introduce the poison pill to remove it for a fixed period after they have been replaced, thereby delaying a new board’s ability to sell the firm.

flip-in: Provision that gives current shareholders of the firm other than the hostile acquirer the right to purchase additional shares of stocks at a discount price after the acquirer obtains a certain percentage of the firm’s shares (usually between 20% and 50%).

flip-over: Provision that allows shareholders to buy the acquiring firm’s shares at a discount price after a merger or takeover.

golden handcuffs: Employment clauses that require top employees to give back lucrative bonuses or incentives if they leave the firm within a specified period. As a poison pill, these clauses cease to hold after a hostile takeover so that the employees may quit immediately after cashing their stock options.

macaroni defense (similar to a flip-over): The issuance of many bonds with the condition they must be redeemed at an above-market price if the company is taken over.

poison pill, porcupine provision, shareholder rights plan, or shark repellent: Defensive provisions that corporate boards include in the firm’s corporate charter or bylaws that make a takeover less profitable.

poison puts: The issuance of bonds that investors may cash before they mature in the event of a hostile takeover attempt.

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206 CHAPTER 7 Firm Organization and Market Structure

boards of directors, so that they do not fight the takeover. The use of poison pills in the United States has declined significantly over the past two decades. Part of this decline resulted from requirements that shareholders vote on poison pills.

7.3 Profits Over Time The rules for profit maximization described in the previous section apply when a firm’s owners want the firm to maximize profit in the current period. This approach makes sense if actions today do not affect future profits, so the firm can ignore the future for now.

However, for many firms, their actions today affect future profits. A firm might make a costly investment today that will yield large profits in the future. For exam- ple, internet retailing giant Amazon lost money for years, investing much of the revenue it earned in improving its technology to increase its profits in future years. Such a firm should not necessarily shut down when incurring losses in early periods.

Managers must have some way of comparing early losses with later gains. They use interest rates to make these comparisons.

Interest Rates Virtually everyone believes that a dollar today is more valuable than a dollar in the future. Consequently, a bank will only agree to loan you $1,000 for a year if you agree to return the $1,000 at the end of the year plus some additional amount. This addi- tional amount, called interest, is determined by an interest rate: the percentage more that must be repaid to borrow money for a fixed period.15

Suppose a firm borrows $10,000 from a bank for one year at an annual interest rate of 5% (= 0.05). That is, the firm promises to repay the bank $1.05 one year from now for every dollar that it borrowed. At the end of the year, the firm must pay the bank $10,500 (= $10,000 * 1.05), which is the amount it borrowed, $10,000, plus the interest it owes, $10,000 * 0.05 = $500.

More generally, the amount of money the firm borrows today is the present value (PV) and the amount it must repay is the future value (FV). At an interest rate of i, at the end of the first year, the firm must repay

FV = PV (1 + i). (7.4)

Compounding. Now suppose that the firm borrows the $10,000 for two years. Because it didn’t pay the $500 interest it owed at the end of the first year, it is essen- tially borrowing $10,500 for the second year. Thus, for the second year, it owes inter- est on the $10,000 initial amount and on the $500 deferred interest payment. That is, it owes “interest on the interest.” This accumulation of interest is called compounding. At the end of the second year, the firm owes

$1,102.50 = ( $10,000 * 1.05) * 1.05 = $10,000 * 1.052.

15For simplicity, we refer to the interest rate throughout this chapter, but there are many interest rates. For example, a firm will usually have to pay a higher interest rate if it wants to borrow money for a longer period.

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2077.3 Profits Over Time

Generalizing, if the firm were to borrow for t years, it would owe $10,000 * 1.05t at the end of the last year.

Using Interest Rates to Connect Present and Future Values. Interest rates connect the value of money that a firm borrows today, the present value (PV), with the future value (FV) that it must repay later. The FV is the present value plus interest. As we’ve just seen, if the firm borrows PV today and allows the interest to compound for t years at an interest rate of i, then the future value, FV, it must repay is

FV = PV (1 + i)t. (7.5)

Similarly, if a firm is to receive a payment, FV, t years from now, the present value is

PV = FV

(1 + i)t . (7.6)

We obtain this last equation by dividing both sides of Equation 7.5 by (1 + i)t. For example, if the interest rate is 5% and the firm will receive a payment of $10,500 with certainty one year from now, the present value of this future payment is PV = $10,500>(1.05) = $10,000.

At high interest rates, money significantly in the future is worth very little today. Using Equation 7.6, we can calculate that a $1,000 payment 25 years from now is worth only slightly more than $10 today at a 20% interest rate: PV = 1,000> (1.2)25 ≈ 10,000>95.4 ≈ $10.50.

Sometimes we want to calculate the present value of a stream of payments, such as the firm’s annual profits over the next 15 years. We can generalize the relationships we have already developed to determine the present value of the stream of payments by calculating the present value of each future payment and then summing them.

Suppose an investor has a share of stock that pays $10 in dividends at the end of each year for three years and nothing thereafter. If the interest rate is 10%, the present value of this series of payments is

PV = $10 1.1

+ $10 1.12

+ $10 1.13

≈ $24.87.

More generally, a stream of payments of Y per year for t years given interest rate i has a present value of

PV = Y c 1 (1 + i)

+ 1

(1 + i)2 + c + 1

(1 + i)t d . (7.7)

If these payments are made at the end of each year forever, Equation 7.7 can be simplified. If the firm invests PV at i per year forever, it receives a payment of Y = PV * i each year forever. Dividing both sides of this equation by i, we find that

PV = Y i

. (7.8)

Therefore, for a perpetual income flow of Y per period, the present value is simply the amount of the flow divided by the interest rate.

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208 CHAPTER 7 Firm Organization and Market Structure

Investing and Profit Maximizing Over Time How does a firm profit maximize over time? It maximizes the present value of the flow of its profits over time. Using interest rates, a firm can determine the present value of its profits over time. For example, if the interest rate is i, and the firm expects its profit to be π1 in the first year, π2 in the second year, π3 in the third year, and zero thereafter, then the present value of this stream of profits is

PV = π1

1 + i +

π2 (1 + i)2

+ π3

(1 + i)3 .

We can use this approach to consider whether firms should make investments. Suppose that a firm makes a large investment this year, which lowers its profit this year, so that it will make a larger profit next year. The firm makes the investment if doing so raises the present value of its profits over the two years. For example, if the firm does not make the investment, it expects to make a $100,000 profit at the end of this year and at the end of next year. At an interest rate of 5%, its present value is

$185,941.04 = $100,000

1.05 +

$100,000 1.052

.

However, if it makes a $50,000 investment this year, its profit this year falls to $50,000, but its profit next year is $175,000. The present value of this stream of profits is

$206,349.19 = $50,000

1.05 +

$175,000 1.052

.

Q&A 7.2 You are the owner of a small building. You are considering two possibilities. First, you can sell the building for $550,000. Second, a major retail chain agrees to rent the property for the next five years, paying you an annual rent of $25,000, at the end of each of the five years. Then, at the end of the fifth year, it will buy the store from you for $600,000, so the final payment at the end of the fifth year is $625,000, including the last year’s rent.

Use a spreadsheet to determine the present value of the second, rental option for interest rates of 3%, 5%, and 7%. What decision would you make for each interest rate?

Answer 1. Open an Excel spreadsheet and put titles in the first row. Put Year in cell A1, Payment

in cell B1, 3% rate in cell C1, 5% rate in cell D1, and 7% rate in cell E1. 2. Fill in columns A and B using the numbers given in the question. Enter numbers 1

through 5 in cells A2 through A6, enter 25,000 in cells B2 through B5, and enter 625,000 in cell B6. Note that cell B6 incorporates the final rental payment of 25,000 and the sale price of 600,000.

3. Enter the appropriate formulas to determine the present value of each payment in col- umns C through E. Enter “=B2> (1.03)^A2” in cell C2, then copy this cell into cells C3 through C6. Enter “=B2> (1.05)^A2” in cell D2, then copy this cell into cells D3 through D6. And enter “=B2> (1.07)^A2” in cell C2, then copy this cell into cells E3 through E6.

4. Calculate present values. Put the title Present Value in cell A7. Then enter “=sum(C2:C6)” in cell C7 and copy this cell into cells D7 and E7.

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2097.3 Profits Over Time

After formatting, your spreadsheet should look as shown in the screenshot.

5. Determine which of your two options has a higher present value for each interest rate. Compare the present value under each interest rate with the present value of the first option to sell now, which is $550,000. If the interest rate is 3%, yielding a present value of $632,058, or 5%, yielding a present value of $578,353, you should opt for the rental option. If the interest rate is 7%, where the present value is $530,297, you should sell now.

Comment: The higher the rate, the lower the present value of a large payment that occurs five years from now.

Many newspaper articles and business shows focus almost exclusively on the price of a share of the firm’s stock rather than on its annual profit. Should a man- ager be more concerned about a firm’s stock price than its profit?

It makes no difference whether the manager maximizes the stock price or profit if the stock price reflects the firm’s profit, in which case the cumulative value of the firm’s stock is the present value of owning the firm. The owner of stock in a corpo- ration receives a share in the current and future profits of the firm. Therefore, the stock price should reflect current and future profits. The sum of the value of all the shares is the present value investors place on the flow of current and future profits.

If the firm earns an annual profit of π per year forever, the present value of that profit stream is π>i, where i is the interest rate (Equation 7.8). For example, if the firm earns $10 million a year forever and the interest rate is 5%, then the present value is $10>0.05 = $200 million. If shareholders expect this level of profit and the same interest rate to continue in the future and the firm issued one million shares of stock, then each share would sell for $200.

If the firm’s profit were higher, then its present value would also be higher. For example, if the annual profit were expected to be $11 million per year forever (instead of $10 million), then the firm’s present value would be $220 million and the value of each share would be $220. Thus, maximizing a constant profit flow maxi- mizes the value of the firm and is therefore equivalent to maximizing the stock price.

However, if a firm’s profit flow varies over time, then the link between a firm’s profit and its stock price is more complex, and the stock price might be more relevant to managers than the current profit. Consider a firm that makes a major investment that causes it to suffer a loss this year but that results in higher profits in the future. If investors understand that the investment will pay off in the long run, the stock price rises after the investment is made. Thus, a manager who is concerned about a firm’s long-run profit stream may try to maximize the present

Stock Prices Versus Profit

Managerial Implication

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210 CHAPTER 7 Firm Organization and Market Structure

7.4 The Make or Buy Decision Managers make many decisions that affect the horizontal and vertical dimensions of a firm’s organization. The horizontal dimension refers to the size of the firm in its primary market, while the vertical dimension refers to the various stages of the production process in which the firm participates.

To produce a good and sell it to consumers involves many sequential stages of production, marketing, and distribution activities. A manager must decide how many stages the firm itself will undertake. At each stage, a manager chooses whether to carry out the activity within the firm or to pay for it to be done by others. Deciding which stages of the production process to handle inter- nally and which to buy from others is part of what is referred to as supply chain management.

Stages of Production The turkey sandwich you purchase at your local food stand is produced and deliv- ered through the actions of many firms and individuals. Farmers grow wheat and raise turkeys using inputs they purchase from other firms; processors convert these raw inputs into bread and turkey slices; wholesalers transfer these products from the food processors to the food stand; and, finally, employees at the food stand combine various ingredients to make a sandwich, wrap it, and sell it to you.

Figure 7.2 illustrates the sequential or vertical stages of a relatively simple pro- duction process. At the top of the figure, firms use raw inputs (such as wheat) to produce semi-processed materials (such as flour). Then the same or other firms use the semi-processed materials and labor to produce the final good (such as bread). In the last stage, the final consumers buy the product.

In the nineteenth century, production often took place along a river. Early stages of production occurred upstream, and then the partially finished goods were shipped by barge downstream—going with the flow of the river—to other firms that finished the product. These anachronistic river terms are still used to indicate the order of production: Upstream refers to earlier stages of production and downstream refers to later stages.

Vertical Integration The number of separate firms involved in producing your turkey sandwich depends on how many steps of the process each firm handles. One possibility is that the food stand carries out many steps itself: making the sandwich, wrapping it, and selling it to you. An alternative is that one firm makes and wraps the sandwich and delivers it to another firm that sells it to you.

value of profit or, equivalently, maximize the firm’s stock value, rather than con- centrate on the profit this period. However, if investors are not well informed about the firm’s current and expected future profits, so that the stock price does not closely track the present value of profits, then maximizing the stock price is not equivalent to maximizing the present value of profits.

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2117.4 The Make or Buy Decision

A firm that participates in more than one successive stage of the production or distribution of goods or services is vertically integrated. A firm may vertically inte- grate backward or upstream and produce its own inputs. For example, after years of buying its unique auto bodies from Fisher Body, General Motors purchased Fisher in a vertical merger. Or a firm may vertically integrate forward or downstream and buy its former customer. At different times, the car manufacturers General Motors and Ford have owned Hertz, the first car-rental company.16

The alternative to a firm producing an input or activity itself is to buy it. Firms may buy inputs from a market (such as buying corn on the Chicago Board of Trade or copper in the London Metal Exchange). Increasingly, many firms reach agree- ments with other firms to buy services from them on a continuing basis, a practice called outsourcing. For example, many U.S. computer manufacturing firms retain firms located in the United States, India, and elsewhere to provide services such as giving technical advice to their customers.

A firm can be partially vertically integrated. It may produce a good but rely on others to market it. Or it may produce some inputs itself and buy others from the market.

Quasi-Vertical Integration. Some firms buy from a small number of sup- pliers or sell through a small number of distributors. These firms often control the actions of the firms with whom they deal by writing contracts that restrict the actions of those other firms. These contractual vertical restraints approximate the outcome from vertically merging. Such tight relationships between firms are referred to as quasi-vertical integration.

For example, a franchisor and a franchisee have a close relationship that is gov- erned by a contract. Some franchisors such as Kentucky Fried Chicken (KFC) sell a proven method of doing business to individual franchisees, who are owners of

16Hertz, founded in 1918, was purchased by General Motors in 1926, which subsequently sold it. In 1954, Hertz went public. It was sold to a Ford Motor subsidiary in 1987 and became a fully owned Ford subsidiary in 1994. Hertz went public again in 2006.

Final good q = f (M, L)

Labor L

Materials M

Inputs

Downstream

Upstream

Consumers q

FIGURE 7.2 Vertical Organization

Raw inputs produced upstream are combined using a production process, q = f(M, L), downstream to produce a final good.

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212 CHAPTER 7 Firm Organization and Market Structure

KFC outlets. Such a fast-food franchisor may dictate the types of raw products its franchisees buy, the franchisees’ cooking methods, the restaurants’ appearance, and the franchisees’ advertising.

Similarly, a manufacturer that contracts with a distributor to sell its product may place vertical restrictions on the distributor’s actions beyond requiring it to pay the wholesale price for the product. These vertical restrictions are determined through contractual negotiations between the manufacturer and the distributor. The manu- facturer imposes these restrictions to approximate the outcome that would occur if the firms vertically integrated. Examples of restrictions include requirements that the distributor sell a minimum number of units, that distributors not locate near each other, that distributors not sell competing products, and that distributors charge no lower than a particular price.

Contracts Versus Spot Markets. Even if a company does not use the detailed contracts needed for quasi-vertical integration, it may sign long-term contracts that provide some features of vertical integration. For example, a furniture maker might enter into a multi-year contract to buy some specific annual quantity of wood from a lumber company at a fixed price. The furniture maker can then rely on a steady supply of wood at an affordable price, just as it would if it produced its own lumber in a vertically integrated structure.

If the furniture firm does not sign a long-term contract and does not vertically integrate, it buys lumber as it needs it at the current price from a variety of lumber- yards or in a spot market or cash market: an organized market that sells commodities for immediate delivery (such as the Chicago Mercantile Exchange).

Degrees of Vertical Integration. We see a spectrum of vertical integration ranging from full integration through quasi-integration and long-term contracts, to relying on spot markets. All firms are vertically integrated to some degree, but they differ substantially as to how many successive stages of production they perform internally. At one extreme, we have firms that perform only one major task and rely on markets and outsourcing for all others. For example, some retailers, such as computer retailers, buy products from a variety of manufacturers or markets, sell them to final consumers, and have any related service such as technical support for customers provided by other firms through outsourcing arrangements.

At the other extreme, we have firms that perform most stages of the production pro- cess. The leading broiler chicken producers, such as Tyson, Purdue, and Foster Farms, have integrated or quasi-vertically integrated (through the use of contracts) into virtu- ally every production stage except the final stage of distribution to consumers.

The vertically integrated firms provide supplies to breeder farms that produce eggs. The breeder farms send eggs to a hatchery and the hatched chicks are sent to grow-out farms, where the birds grow to market weight. From there, the chickens go to the processing plant to be slaughtered and packed (either frozen or chilled). Packed chicken is then shipped to another company-owned plant for further pro- cessing into products such as frozen nuggets and chicken dinners. Finally, the prod- ucts are sold to other firms such as fast-food restaurants and grocery stores for sale to final consumers (Martinez, 1999). By vertically integrating, these firms are able to take advantage of very large economies of scale at virtually every stage of the production process.

However, no firm is completely integrated: It would have to run the entire econ- omy. Even Foster Farms buys some inputs, such as its equipment, from outside markets. As Carl Sagan observed, “If you want to make an apple pie from scratch, you must first create the universe.”

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2137.4 The Make or Buy Decision

Profitability and the Supply Chain Decision Firms decide whether to vertically integrate, quasi-vertically integrate, or buy goods and services from markets or other firms, depending on which approach is the most profitable.17 Although at first glance this profitability rule seems very simple, it has a number of tricky aspects. First, the firm has to take into account all relevant costs, including some that are not easy to quantify, such as transaction costs. Second, the firm must ensure a steady and timely supply of needed inputs to its production process. Third, the firm may vertically integrate, even if doing so raises its cost of doing business, so as to avoid government regulations.18

However, by vertically integrating and becoming larger and more complex, the firm may increase its managerial costs. Thus, firms do not always vertically integrate to avoid transaction costs and opportunistic behavior.

As a consequence of these complexities, firms in the same industry may reach different decisions about the optimal level of integration. We observe that such firms handle the supply chain in different ways. In the auto industry, Toyota is known as a leader in successful outsourcing and is less vertically integrated than its rivals such as General Motors and Ford.

Firms in some markets differ in how much they integrate because their managers have different strengths or the firms face different costs (such as costs that vary across countries). However, some of these firms could be making a mistake by being more or less integrated than other firms, if it lowers their profits and may drive them out of business.

Transaction Costs and Opportunistic Behavior. Among the most impor- tant reasons to integrate is to reduce transaction costs and to avoid opportunistic behavior: taking advantage of someone when circumstances permit.

By integrating, a firm can avoid the transaction costs of negotiating contracts. Instead of regularly negotiating deals with independent supply companies, a man- ager of a vertically integrated firm simply directs the input-producing section of the company to send the supplies. It can also minimize communication problems and better handle the timing of deliveries by vertically integrating.

Firms also vertically integrate to avoid opportunistic behavior. A firm may try to interpret the terms of a contract to its advantage, especially when terms are vague or missing. Such behavior is particularly likely when a firm deals with only one other firm: a classic principal-agent problem. If an electronic game manufacturer can buy computer chips from only one firm, it is at the mercy of that chip supplier. The supplier could take advantage of the situation by increasing its price substan- tially just before the holiday buying season. The game manufacturer may vertically integrate—manufacturing the chip itself—to avoid such opportunistic behavior.

Security and Flexibility of Supply. A common reason for vertical integration is to ensure supply of important inputs. Having inputs available on a timely basis is critical in many, if not most, industries. Costs would skyrocket if a car manufacturer

17For a more detailed analysis of the pros and cons of vertical integration, see Perry (1989) and Carlton and Perloff (2005). Two classic articles on vertical integration are Coase (1937) and Williamson (1975). 18Firms may also vertically integrate for reasons related to market power, allowing the firm to charge higher prices than it otherwise would or to reduce prices it would otherwise pay for its inputs. We discuss market power issues in later chapters.

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214 CHAPTER 7 Firm Organization and Market Structure

had to stop assembling cars while waiting for a part. Backward (upstream) integra- tion to produce the part itself may help to ensure timely arrival of parts. Alterna- tively, this problem may be eliminated through quasi-vertical integration, in which the buyer and seller agree to a contract whereby the supplier is rewarded for prompt delivery and penalized for delays. Toyota and other Japanese manufacturers pio- neered the just-in-time system of having suppliers deliver inputs at the time needed to process them, thus minimizing inventory costs and avoiding bottlenecks.

Similarly, it is often important that a firm be able to vary its production quickly. If the demand curve shifts to the left during a recession, a firm may want to cut output, and hence temporarily reduce its use of essential inputs. By vertically inte- grating, firms may gain greater flexibility. PepsiCo Inc. offered to buy its two largest bottlers, Pepsi Bottling Group and PepsiAmericas, because, as PepsiCo Chairwoman and Chief Executive Officer Indra Nooyi said, “We could unlock significant cost synergies, improve the speed of decision making and increase our strategic flexibility.”19

19“PepsiCo Bids to Buy Its Bottlers,” MarketWatch, April 20, 2009, www.marketwatch.com/story/ pepsico-bids-buy-bottlers-reports.

Mini-Case Netflix, a movie and television show distributor, disrupted the television industry. It currently has about 118 million streaming subscribers in 190 countries.

Netflix’s chief executive, Reed Hastings, was asked whether Netflix was interested in vertically integrating forward into internet service provision or backward into producing its own shows. He replied,

Vertical integration to the data transmission layer, no. In terms of content, we’re now producing a lot of content ourselves. So that is a form of vertical integration that’s been very successful for us.

He noted that Netflix works with about 600 internet service providers around the world, and that “Netflix is an application on top of the internet.” Netflix benefits from letting subscribers connect to Netflix using whichever provider they prefer.

In contrast, vertically integrating into con- tent provision works for them for three reasons: obtaining unique content, flexibility, and avoid- ing opportunistic behavior by film studios.

Although Netflix has 55 million U.S. sub- scribers, the average length of a subscription is only 43 months. In developing greater loy- alty among its customers by providing high- quality, unique shows, such as Stranger Things, Netflix can keep subscribers longer.

With a steady stream of content, Netflix has flexibility in releasing films and a reliable pipeline.

By producing its own content, Netflix can avoid being the victim of opportunism. Netflix benefits from producing its own programming globally. For example, its globally popular show

Netflix

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2157.4 The Make or Buy Decision

Government Regulations. Firms may also vertically integrate to avoid gov- ernment price controls, taxes, and regulations. A vertically integrated firm avoids price controls by selling to itself. For example, the U.S. government has set a maxi- mum price for steel products on several occasions since World War II. Under such price controls, steel producers did not want to sell as much steel as before the con- trols took effect. Consequently, they rationed steel, selling their long-time customers only a fraction of what they had sold before the controls went into effect.

Because transactions within a company were unaffected by price controls, a buyer who really desired more steel could purchase a steel company and obtain all the steel it wanted (and at least one firm did so). Thus, purchasing a steel company allowed firms to avoid price controls. Were it not for the high transaction costs, firms could completely avoid price controls by vertically integrating.

More commonly, firms integrate to lower their taxes. Tax rates vary by country, state, and type of product. A vertically integrated firm can shift profit from one of its operations to another simply by changing the transfer price at which it sells its internally produced materials from one division to another. By shifting profits from a high-tax state or country to a low-tax state or country, a firm can increase its after- tax profits. The Internal Revenue Service tries to restrict such behavior by requiring that firms use market prices for internal transfers where possible.

Government regulations create additional incentives for a firm to integrate verti- cally (or horizontally) when the profits of only one division of a firm are regulated. When the government restricts the profit that a local telephone company earns on local services but not its profit on other services, such as selling telephones in com- petition with other suppliers, the telephone company tries to shift profits from its regulated division to its unregulated division.

Narcos was produced for Netflix by a French company in Bogotá, Colombia, with a Brazilian star. Thus, Netflix is no longer dependent on a relatively small number of Hollywood production companies. These firms previously could subject Netflix to opportunistic behavior, threatening to cut off the supply of movies and shows with little notice unless Netflix paid them large sums.

Mini-Case Traditionally, most firms vertically integrated by hiring workers instead of con- tracting with others to provide labor. The gig economy is disrupting this labor- employer relationship. In a gig economy, temporary jobs are common and firms contract with independent workers for short-term activities. For example, delivery services such as FedEx and UPS contract with extra temporary workers during the December holiday rush. Other gig jobs include driving for Lyft or Uber, freelance writing, and employment through temporary work agencies. The Federal Reserve reported in 2018 that nearly one-third of adults participate in gig work, either as their primary employment or to supplement other sources of income.

Part of the reason for the recent growth of the gig economy is that computers and smartphone apps have greatly reduced the transaction costs of short-term contracting, as when someone orders a Lyft ride. By contracting with temporary workers as needed, firms achieve greater flexibility and are able to avoid over- head costs such as providing work space and human resources services.

The Gig Economy

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216 CHAPTER 7 Firm Organization and Market Structure

Market Size and the Life Cycle of a Firm Why do workers commonly engage in highly specialized activities? They do so because it is generally more efficient to divide production processes into several small steps in which workers specialize, with each worker becoming skilled in a certain activity.

Adam Smith, writing in Scotland at the time of the American Revolution, gave an example of a pin factory in The Wealth of Nations to illustrate that the division of labor can have important advantages in the “very trifling manufacture” of pins:

[A] workman not educated to this business . . . nor acquainted with the use of machinery employed in it . . . could scarce, perhaps, with his utmost industry, make one pin a day, and certainly could not make twenty. But in the way in which this business is now carried on, not only the whole work is a peculiar trade, but it is divided into a number of branches, of which the greater part are likewise peculiar trades. One man draws out the wire, another straightens it, a third cuts it, a fourth points it, a fifth grinds it to the top for receiving the head; to make the head requires two or three distinct operations; to put it on, is a peculiar business, to whiten the pins is another; it is even a trade by itself to put them into the paper; and the important business of making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are all performed by distinct hands, though in others the same man will sometimes perform two or three of them. I have seen a small manufac- tory of this kind where ten men only were employed, and where some of them consequently performed two or three distinct operations. . . . [T]hey could, when they exerted themselves, make among them about twelve pounds of pins in a day [or] upward of forty-eight thousand pins in a day.

Using this insight about specialization, Henry Ford became the largest and prob- ably the most profitable automobile manufacturer in the early 1900s by developing mass production techniques. He adapted the conveyor belt and assembly line so that he could produce a standardized, inexpensive car in a series of tasks in which individual workers specialized. By doing so, he achieved cost savings despite paying wages that were considerably above average.

Specialization is just as important in the modern economy as it was in Adam Smith’s eighteenth-century pin factory or on Henry Ford’s early twentieth-century assembly line. Recent research shows that surgeons who specialize in just a few procedures—performing each of those procedures many times—have much better results than surgeons who are less specialized. The value of specialization varies depending on the procedure and, not surprisingly, is greater for more complex procedures.20

20Melanie Evans, “A New Factor in Choosing a Surgeon,” Wall Street Journal, September 19, 2016.

In addition, a major reason firms like using independent contractors is that the firms avoid having to pay half of the Social Security and Medicare taxes, which are 15% of income, as they must for full-time employees. They also avoid paying for unemployment insurance and workers’ compensation in case of injury. Thus, government insurance requirements that apply only to full-time workers are a major cause of the trend toward gig employment.

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2177.5 Market Structure

Despite the advantages of specialization, many workers and many firms do not specialize. Why? According to Adam Smith, the answer is that “the division of labor is limited by the extent of the market.” That is, a firm can take advantage of spe- cialization and economies of scale only if it produces a sufficiently large amount of output, which it produces only if enough consumers are willing to buy it.

Stigler (1951) and Williamson (1975) showed that Adam Smith’s insight provides a theory of the life cycle of firms. They explain why firms rely on markets during certain periods, while during other periods, they vertically integrate. The key insight is that the degree of integration depends on the size of the market. If demand for a product at the current price is low so that the collective output of all the firms in the industry is small, each firm must undertake all the activities associated with produc- ing the final output itself.

Why don’t some firms specialize in making one of several inputs that they then sell to another firm to use in assembling the final product? The answer is that when the industry is small, it does not pay for a firm to specialize in one activity even given increasing returns to scale. A specialized firm may have a large setup or fixed cost. If the specialized firm produces large quantities of output, the average fixed cost per unit is small. In contrast, the average fixed cost is large in a small industry. Therefore, if specialized firms are to earn a profit, the sum of the specialized firms’ prices must be higher than the cost of a firm that produces everything for itself.

As the industry expands, it may become profitable for a firm to specialize, because the per-unit transaction costs fall. That is, as the industry grows, firms vertically disintegrate. When the industry was small, each firm produced all successive steps of the production process, so that all firms were vertically integrated. In the larger industry, each firm does not handle every stage of production itself but rather buys services or products from specialized firms.

As an industry matures further, new products often develop and reduce much of the demand for the original product, so that the industry shrinks. As a result, firms again vertically integrate.

7.5 Market Structure When making their horizontal and vertical decisions, managers need to take account of the behavior of actual and potential rival firms, which affect the profit function the manager’s firm faces. So far, we have implicitly ignored the role of other firms. However, a firm’s manager must take into account how its profit is affected by rival firms’ output levels, the prices rivals set, or whether additional firms are likely to enter the market if the firm makes a large profit.

How rivals behave depends on the organization of the industry in which the firms operate. A firm will behave differently if it is one of a very large number of firms rather than the only one in the market. The behavior of firms depends on the market structure: the number of firms in the market, the ease with which firms can enter and leave the market, and the ability of firms to differentiate their products from those of their rivals.

The Four Main Market Structures Most industries fit into one of four common market structures: perfect competition, monopoly, oligopoly, and monopolistic competition.

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218 CHAPTER 7 Firm Organization and Market Structure

Perfect Competition. When most people talk about competitive firms, they mean firms that are rivals for the same customers. By this interpretation, any mar- ket that has more than one firm is competitive. However, economists often use the term competitive to refer to markets that satisfy the conditions for perfect competi- tion (Chapter 2) or that closely approximate perfect competition.

Economists say that a market is perfectly competitive if each firm in the market is a price taker: a firm that cannot significantly affect the market price for its output or the prices at which it buys its inputs. Firms are likely to be price takers in markets where all firms in the market sell identical products, firms can freely enter and exit the market in the long run, all buyers and sellers know the prices charged by firms, and transac- tion costs are low. If any one of the 26,000 tomato producers in the United States were to stop producing or to double its production, the market price of tomatoes would not change appreciably. Similarly, by stopping production or doubling its production, a producer would have little or no effect on the price for fertilizer, labor, or other inputs.

Because firms can enter freely, firms enter whenever they see an opportunity to make a profit. This entry continues until the profit of the last firm to enter—the marginal firm—is zero.

Monopoly. A monopoly is the only supplier of a good that has no close substi- tute. De Beers, until recently, controlled the global diamond market. Monsanto has a monopoly in many genetically modified (GM) seeds. Many local public utilities such as cable television companies are local monopolies. Patents give monopoly rights to sell inventions, such as particular pharmaceuticals or GM seeds. A firm may be a monopoly if its costs are substantially below those of other potential firms.

A monopoly can set its price—it is not a price taker like a competitive firm. A monopoly’s output is the market output, and the demand curve a monopoly faces is the market demand curve. Because the market demand curve is downward slop- ing, the monopoly—unlike a competitive firm—doesn’t lose all its sales if it raises its price. As a consequence, the monopoly typically charges relatively high prices— much higher than the price set in a perfectly competitive market.

Oligopoly. An oligopoly is a market with only a few firms and with substantial barriers to entry, which prevent other firms from entering. A barrier to entry could be a government licensing law that limits the number of firms or patents that prevent other firms from using low-cost technologies. Nintendo, Microsoft, and Sony are oligopolistic firms that dominate the video game market. Only a handful of firms control the automobile, television, and aircraft manufacturing markets.

Because relatively few firms compete in an oligopolistic market, each can influ- ence the price. One reason why oligopolies are price setters is because many oli- gopolies differentiate their products from those of their rivals. Because consumers perceive differences between a Honda Accord and a Toyota Camry, Toyota can raise the price of its Camry above the price of an Accord without losing all its sales. Some customers who prefer the Camry to the Accord will buy a Camry even if it costs more than an Accord.

Moreover, because an oligopoly has few firms, the actions of each firm affect its rivals. An oligopoly firm that ignores or inaccurately predicts its rivals’ behavior is likely to lose profit. For example, as Toyota produces more cars, the price Honda can get for its cars falls. If Honda underestimates how many cars Toyota will produce, Honda may produce too many automobiles and lose money.

The need to consider the strategies of rival firms makes analyzing an oligopoly firm’s profit-maximization decision more difficult than that of a monopoly or a

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2197.5 Market Structure

competitive firm. A monopoly has no rivals, and a perfectly competitive firm ignores the behavior of individual rivals—it considers only the market price and its own costs in choosing its profit-maximizing output.

Oligopolistic firms may act independently or may coordinate their actions. A group of firms that explicitly agree (collude) to coordinate their activities is called a cartel. These firms may agree on how much each firm will sell or on a common price. By cooperating and behaving like a monopoly, the members of a cartel seek to earn the monopoly profit collectively—the maximum possible profit. In most developed countries, cartels are illegal. If oligopolistic firms do not collude, they earn lower profits than a monopoly, but usually earn higher profits than do firms in a competitive industry.

Monopolistic Competition. Monopolistic competition is a market structure in which firms are price setters but entry is easy. As in a monopoly or oligopoly, the market has few enough firms that each can affect the price. Indeed, monopolistically competitive firms often differentiate their products, which facilitates their ability to be price setters. However, as in competition, firms can freely enter, so the marginal firm earns zero profit.

Comparison of Market Structures Table 7.2 summarizes the major features of these four market structures. The first row notes that perfectly competitive firms are price takers, whereas monopolies, oligopo- lies, and monopolistically competitive firms are price setters. Typically, monopolies charge higher prices than oligopolies and monopolistically competitive firms, while competitive firms charge lower prices.

In the long run in both competitive and monopolistically competitive markets, entry occurs until no new firm can profitably enter, so the marginal firm earns zero

TABLE 7.2 Properties of Monopoly, Oligopoly, Monopolistic Competition, and Perfect Competition

Monopoly Oligopoly Monopolistic Competition

Perfect Competition

1. Ability to set price

Price setter Price setter Price setter Price taker

2. Price level Very high High High Low

3. Entry conditions No entry Limited entry Free entry Free entry

4. Number of firms 1 Few Few or many Many

5. Long-run profit Ú0 Ú0 0 0

6. Strategy dependent on individual rival firms’ behavior

No (has no rivals)

Yes Yes No (cares only about market price)

7. Products Single product May be differentiated

May be differentiated

Undifferentiated

8. Example Producer of patented drug

Automobile manufacturers

Plumbers in a small town

Apple farmers

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220 CHAPTER 7 Firm Organization and Market Structure

economic profit. Monopolistically competitive markets typically have fewer firms than perfectly competitive markets do. Barriers to entry in a market result in a monopoly with one firm or an oligopoly with few firms. Monopolies and oligopo- lies may earn positive economic profits.

Oligopolistic and monopolistically competitive firms must pay attention to rival firms’ behavior, in contrast to monopolistic or competitive firms. A monopoly has no rivals. A competitive firm ignores the behavior of individual rivals in choos- ing its output because the market price tells the firm everything it needs to know about its competitors. Oligopolistic and monopolistically competitive firms may produce differentiated products in contrast to monopolies and competitive firms.

Disruptive Innovations and the Evolution of Market Structure Market structure is not static and can be affected by technological or organizational innovation. Most innovations are incremental, but some are sufficiently disruptive to dramatically change the way an industry is structured—or even to create new industries and destroy old ones. Trying to anticipate, join, or react to such disruptive innovations is an important challenge for modern managers.

Joseph Schumpeter (1942) referred to this process as creative destruction, while Clay- ton Christensen (1997) called it disruptive innovation. Christensen described the disrup- tive role of initially small innovators who displace large incumbents, often opening up a product class to a large group of new consumers. He noted that disruptive innova- tions need not be based on sophisticated advances in technology. Rather, a market dis- ruption often arises from using “off-the-shelf” technologies in new and creative ways.

Small start-up companies often have a stronger incentive to innovate than incumbents precisely because they do not have an established position. An established firm that develops a new product that is better or cheaper than its existing product line runs the risk of cannibalizing its traditional business. A new start-up is free from such concerns.

Apple founders Steve Jobs and Steve Wozniak provide a classic example of such a disruption. They created the first commercially successful personal computer while working in the garage of Steve Jobs’s parents with parts scavenged from nearby elec- tronics stores. Ultimately, personal computers forced most of the traditional computer producers out of business, although IBM survived by quickly embracing the new tech- nology. This innovation also brought the power of computing to the mass market, trans- forming many other industries along the way. This disruptive innovation of personal computers initially changed an oligopoly into a more competitive market (although later Apple and a few other personal computer companies formed a new oligopoly).

In contrast, a disruptive innovation might transform a competitive industry into a concentrated market. For example, the taxi industry has traditionally been competi- tive, but the disruptive innovation created by Uber in providing rides to passengers has given Uber an unprecedented level of market power in the industry. Amazon’s innovations in e-commerce have already driven many “bricks and mortar” stores out of business and have allowed Amazon to develop an increasingly dominant position.

Road Map to the Rest of the Book In Chapters 8 through 13, we examine the market outcomes under perfect competition, monopoly, oligopoly, and monopolistic competition. We start by exam- ining competitive and monopoly firms, which can ignore the behavior of other firms.

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221Summary

Then we turn to oligopolies and other markets where firms need to develop strategies to compete with rival firms. In these chapters, we maintain the assumption that firms seek to maximize profits. In contrast, in Chapters 14 through 16 we return to the realis- tic issues introduced in this chapter concerning uncertainty, unequal information, and government regulation, which lead to agency problems. In Chapter 17, many of the issues raised in this chapter, such as outsourcing, are considered in a global context.

Amazon’s Delivery Services

Managerial Solut ion

What issues should Amazon consider in deciding whether to rely primarily on other delivery services or develop its own capabilities? Given that the up- front investment in Shipping with Amazon (SWA) would cause Amazon to lose money for the first few years before turning a profit, how should Amazon decide whether this investment is worthwhile?

The answer to the first question turns on whether it is cost effective to rely on markets or to vertically integrate or quasi-vertically integrate. Initially, Ama- zon used markets, contracting with UPS, FedEx, USPS, and others to deliver its package. Now, Amazon believes that relying solely on those services results in high shipping costs, reduces its flexibility, results in unreliable services during periods of peak demand, and leaves it open to opportunistic behavior by these companies.

Amazon’s first response, Flex, was to contract with individuals, which lowers its costs; increases its flexibility; and decreases its reliance on the major delivery services, reducing the possibility of opportunistic behavior. Its second option of contracting with individuals to use its trucks for delivery is a form of quasi- vertical integration. It is similar to the Flex program.

The third option, SWA, is a form of vertical integration. It requires a major investment initially, with a payoff in the future. This investment cannot pay unless its present value is positive. To simplify the story, we consider a two-year planning horizon. Suppose that the large investment causes Amazon’s profit to be negative in year 1, π1 6 0, so it is making a loss. However, its profit in year 2 is a large positive number, π2 7 0. Thus, at an interest rate of i, the present value of this investment is PV = π1 + π2>(1 + i). If this amount is greater than the present value of Amazon’s profits over the two years if it does not make this investment, then the investment pays.

SUMMARY

1. Ownership and Governance of Firms. For-profit firms are normally organized as sole proprietorships, partnerships, or corporations. Owners may manage small companies (particularly sole proprietorships and partnerships) themselves, but owners of larger firms (particularly corporations) typically hire managers to run such firms. Most firms and most economic activ- ity are in the for-profit sector, but government-owned firms and nonprofit firms are also important.

2. Profit Maximization. Most firms maximize economic profit, which is revenue minus opportunity cost. A firm

earning zero economic profit is making as much as it could if its resources were devoted to their best alterna- tive uses. To maximize profit, a firm must make two decisions. First, the firm determines the quantity at which its profit is highest. Profit is maximized when marginal profit is zero or, equivalently, when marginal revenue equals marginal cost. Second, the firm decides whether to produce at all. It shuts down if doing so reduces a loss (negative profit) it would otherwise suf- fer. Nonprofit firms do not maximize profit, such as non- profit hospitals. In addition, some for-profit firms may

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222 CHAPTER 7 Firm Organization and Market Structure

forego some profits to pursue social objectives. How- ever, market pressures make it difficult for most firms to deviate substantially from profit-maximizing behavior.

3. Profits Over Time. Interest rates reflect how much more people value a dollar today than a dollar in the future. To compare a future payment to one made today, we calculate the present value of the future pay- ments using the relevant interest rate. A firm chooses between two options with different cash flows over time by picking the one with the higher present value.

4. The Make or Buy Decision. A firm may engage in many sequential stages of production itself; per- form only a few stages itself and rely on markets for others; or use contracts or other means to coordinate its activities with those of other firms, depending on which approach is most profitable. A firm may verti- cally integrate (participate in more than one succes- sive stage of the production or distribution of goods or services); quasi-vertically integrate (use contracts or

other means to control firms with which it has vertical relations); or buy from others, depending on which is more profitable. Key incentives to vertically integrate include lowering transaction costs, ensuring a steady supply, and avoiding government restrictions.

5. Market Structure. A firm’s profit depends in large part on the market structure, which reflects the number of firms in the market, the ease with which firms can enter and leave the market, and the ability of firms to differentiate their products from those of their rivals. The major market structures are perfect competition, monopoly, oligopoly, and monopolistic competition. Competitive firms are price takers, whereas others are price setters. Oligopolies and monopolistically compet- itive firms, unlike competitive firms and monopolies, must take account of rivals’ strategies and may differen- tiate their products. Competitive and monopolistically competitive firms are in markets where entry by poten- tial rivals is easy, so economic profit is driven to zero.

QUESTIONS

All exercises are available on MyLab Economics; * = answer at the back of this book; C = use of calculus may be necessary; = this exercise is available in Excel Grader in MyLab Economics.

1. Ownership and Governance of Firms 1.1 What types of firms would not normally maximize

profit?

*1.2 Describe three important consequences of “going public” by selling shares in an initial public offering.

1.3 What types of firm organization allow owners of a firm to obtain the advantages of limited liability?

1.4 Has Chinese government control of industrial pro- duction declined significantly over the past several decades? Quantify your answer. (Hint: See the Mini- Case “Chinese State-Owned Enterprises.”)

2. Profit Maximization 2.1 A firm has three different production facilities, all

of which produce the same product. While review- ing the firm’s cost data, Jasmin, a manager, discov- ers that one of the plants has a higher average cost than the other plants and suggests closing this plant. Another manager, Joshua, notes that the high-cost plant has high fixed costs but that the marginal cost in this plant is lower than in the other plants. He says that the high-cost plant should not be shut down but should expand its operations. Who is right?

*2.2 A firm has revenue given by R (q) = 100q - 3q2 and its cost function is C (q) = 100 + 10q. What is the profit-maximizing level of output? What profit does the firm earn at this output level? (Hint: See Q&A 7.1.) C

2.3 Should a firm ever produce if it is losing money? Why or why not?

*2.4 Should a firm shut down if its weekly revenue is $1,000, its variable cost is $500, and its fixed cost is $800, of which $600 is avoidable if it shuts down? Why?

2.5 A firm has to pay a tax equal to 25% of its revenue. Give a condition that determines the output level at which it maximizes its after-tax profit. (Hint: See “Using Calculus: Maximizing Profit” and Q&A 7.1.) C

2.6 Milton Friedman argued that managers should try to maximize profit. Does his view conflict with the actions taken by senior executives of McDonald’s to use corporate resources to support Ronald McDon- ald House projects? Explain.

2.7 According to stakeholder theory, what are the social responsibilities of managers?

2.8 The Mini-Case “Trends in Social Responsibility” lists several themes related to social responsibil- ity in business that have generated recent atten- tion. Is it possible that efforts made by managers to address some of these themes would increase prof- its? Explain briefly.

2.9 Why does competition for corporate control encour- age firms to maximize profits?

2.10 Give examples of steps taken by corporate manage- ment to avoid takeovers that are not in shareholders’ best interests.

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223Questions

2.11 An acquiring firm, A, seeks to buy a target firm, T. The acquiring firm has better managers. The value of the target firm, if acquired by A, is $100 million. The value of the target firm under its current man- agement is only $80 million. However, the managers of T can impose a poison pill that would reduce the value of firm T to the acquirer by amount P without providing any benefit to shareholders of T. What is the minimum value of P that would prevent A from acquiring T? What is the cost of this poison pill to shareholders of the two firms?

3. Profits Over Time 3.1 Many retirement funds charge an administrative

fee equal to 0.25% on managed assets. Suppose that Alexx and Spenser each invest $5,000 in the same stock this year. Alexx invests directly and earns 5% a year. Spenser uses a retirement fund and earns 4.75%. At the end of one year, how much will Alexx and Spenser have?

3.2 Using the information from the previous question, if Alexx and Spenser leave their investments in place for 30 years, with annual compounding of the inter- est, how much more will Alexx have than Spenser at the end of the 30-year period? (Hint: You can answer this question using a spreadsheet as in Q&A 7.2.)

3.3 A local pizzeria buys a used car to make pizza deliv- eries. It pays $2,000 down and $2,000 a year for two more years. What is the present value of these pay- ments at a 5% interest rate?

3.4 A firm that owns and manages rental properties is considering buying a building that would cost $800,000 this year, but would yield an annual rev- enue stream of $50,000 per year for the foreseeable future. For interest rates smaller than what value would this purchase increase the present value of the firm?

3.5 At the time of its initial public offering (initial sale of stock), Groupon, an internet company that pro- vides discount coupons, used unusual measures of its business performance (Michael J. de la Merced, “Abracadabra! Magic Trumps Math at Web Start- Ups,” dealbook.nytimes.com, June 17, 2011). One such measure used by Groupon was acsoi (pro- nounced “ack-soy” or, alternatively, “ack-swa”) for “adjusted consolidated segment operating income.” Acsoi is operating profit before subtracting the year's online marketing and acquisition expenses. The firm’s profit was negative, but its acsoi was positive. Groupon argued that acsoi marketing and acquisi- tion expenses were an investment that would build future business and whose costs should therefore be amortized (spread out over time). If sharehold- ers care about the stock price or the present value of the company, is acsoi an appropriate measure?

3.6 You work for a large mineral exploration company and propose buying new state-of-the-art equip- ment. The equipment is expensive and so is training employees to use it, but it will increase the yield of exploration activities in the future. The CEO of the company says that because your plan has high cur- rent costs it will depress the stock market value of the company. Does an investment that lowers current profit but increases future profit necessarily lower current stock prices? Explain briefly. (Hint: See the Managerial Implication “Stock Prices Versus Profit”).

4. The Make or Buy Decision *4.1 In 2012, the Campbell Soup Company acquired

Bolthouse Farms for $1.55 billion. This acquisition increased the level of vertical integration in Campbell, as Bolthouse Farms owned and operated extensive farming operations where it produced many food items used in Campbell’s products. Suppose that the value of produce provided by these farms after the acquisition would be $75 million per year for Camp- bell and that, in addition, Campbell could save $10 million per year in costs it would otherwise spend in searching for and negotiating over equivalent pro- duce. However, the transaction cost of the acquisition (lawyers’ fees, relocating some production facilities, paying severance to unnecessary employees, etc.) required a one-time payment of $50 million. If the interest rate used to discount future earnings is 5%, what is the gain to Campbell’s from the acquisition?

4.2 Katie’s Quilts is a small retailer of quilts and other bed linen products. Katie currently purchases quilts from a large producer for $100 each and sells them in her store at a price that does not change with the number of quilts she sells. Katie is considering ver- tically integrating by making her own quilts. If the fixed cost of vertically integrating is $10,000 and she can produce quilts at $50 per quilt, her total cost of producing quilts, q, herself is C = 10,000 + 50q. How many quilts does Katie need to sell for vertical integration to be a profitable decision?

4.3 A producer of ballpoint pens has been purchasing ink from an ink supplier and is considering acquir- ing the ink supplier. Would the pen company be more or less likely to vertically integrate by buying the ink manufacturer if the government taxes ink?

4.4 Based on the Mini-Case “NetFlix,” did NetFlix undertake backward or forward integration? What were the primary benefits from the integration strat- egy that it chose?

4.5 As described in the Mini-Case “The Gig Economy,” has the gig economy increased or decreased the extent of vertical integration? Explain briefly. What is the role of technological progress and what is the role of government policy in the growth of the gig economy?

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224 CHAPTER 7 Firm Organization and Market Structure

4.6 When the western part of the United States was sparsely populated, many small towns had a single schoolhouse in which one teacher taught all subjects to students of all ages. Now, in large cities, teachers are often highly specialized, teaching a single subject, such as mathematics, to just one grade level. Explain why this change occurred by making reference to Adam Smith’s famous description of a pin factory.

4.7 What are some of the major reasons that firms ver- tically integrate? Why don’t these factors cause all firms to vertically integrate?

5. Market Structure 5.1 Which market structure best describes (a) airplane

manufacturing, (b) electricians in a small town, (c) farms that grow tomatoes, and (d) cable television in a city? Explain your reasoning.

5.2 Describe the effects of the internet on the empirical relevance of perfect competition. Focus specifically on how the internet has affected the availability of price and product information, whether it has increased or decreased search costs and other trans- action costs, and whether it has increased the ability of large numbers of buyers and sellers to interact.

5.3 The development of mini-mills was a disruptive innovation in the steel industry. Before mini-mills, steel production had substantial economies of scale and steel companies had to be very large to take full advantage of those economies. Mini-mills elimi- nated the advantage of large size in steel production. What effect do you think mini-mills had on market structure in the steel industry?

6. Managerial Problem 6.1 Would an increase in interest rates make the Ship-

ping With Amazon (SWA) option more attractive or less attractive to Amazon? Show formally using an equation involving interest rates to explain your answer

7. MyLab Economics Spreadsheet Exercises21

*7.1 A firm’s revenue function is R (q) = 90q - 2q2. Its cost function is C (q) = 104 + 6q + 1.5q2.

a. Using Excel, calculate the levels of revenue, total cost, and profit for the firm for q = 0, 1, 2, . . . , 24. Determine the profit- maximizing output and the maximum profit for the firm.

b. Using Excel, draw the graph of the profit curve and determine the profit-maximizing level of output.

c. The firm’s marginal revenue function is MR = 90 - 4q and the marginal cost function is MC = 6 + 3q. Using Excel, calculate MR and MC for q = 0, 1, 2, . . . , 24. Verify that the “MR = MC” rule determines the same profit- maximizing output as you found in part a.

7.2 A firm has the same revenue and cost function as in Spreadsheet Exercise 7.1.

a. The shareholders of the firm hire a manager on a profit-sharing basis whose payment, M, is 25% of the firm’s profit: M = 0.25(R - C). The shareholders receive the remaining 75%, so their income is S = 0.75(R - C). Add col- umns for M and S to the spreadsheet in part a of Spreadsheet Exercise 7.1 and calculate the man- ager’s payment and the shareholders’ income for q = 0, 1, 2, . . . , 20. Determine the amount of output that the manager will produce if the manager’s objective is to maximize his or her own compensation.

b. Now suppose that the manager receives com- pensation equal to 10% of revenue, so that the return to the owners is S = 0.9R - C. Use Excel to determine the return to the manager and the return to the owners for q = 0, 1, 2, . . . , 20.

*7.3 Second Look Enterprises (SLE) buys old comput- ers, fixes them up, and resells them. Its weekly revenue function is R = 40q - 2q2, so its marginal revenue is MR = 40 - 4q. Its weekly cost func- tion is C = 10q + 0.5q2, so its marginal cost is MC = 10 + q.

a. Use Excel to calculate SLE’s revenue, cost, and profit for q = 1 to q = 20 in increments of 1. SLE’s manager wants to maximize profit. Based on these calculations, what output does the manager choose? Create columns in your spreadsheet for MR and MC and verify that MR = MC at the profit-maximizing output level.

b. Now assume that SLE is run by a manager who is paid 10% of the revenue and therefore wants to maximize revenue. How much output does the firm produce now? What is marginal rev- enue at this output level?

c. Now suppose that SLE is acquired and man- aged by a philanthropist who wants to promote recycling of used computers and therefore pro- duces as much output as possible as long as the firm does not make losses. What output does SLE produce now?

21The spreadsheet exercises in this chapter are based largely on the work of Satyajit Ghosh, in cooperation with the authors. The answers are available on MyLab Economics.

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225

To answer questions about industry price and quantity, we need to combine our understanding of demand curves with knowledge about firm and market supply curves. We start our analysis of firm behavior by addressing the fundamental question: “How much should a firm produce?” To pick a level of output that maximizes its profit, a firm must consider its cost function and how much it can

8Competitive Firms and Markets The love of money is the root of all virtue.

—George Bernard Shaw

To plan properly, managers need to be able to predict the impact of new govern- ment regulations on their firms’ costs, their sales, and their probability of surviving. Managers complain constantly about the costs and red tape that government regulations impose on them. The highly competitive U.S. trucking industry has a particular beef. In recent years, federal and state fees have increased substantially and truckers have had to adhere to many new regulations.

The Federal Motor Carrier Safety Administration (FMCSA), along with state trans- portation agencies in 41 states, administers interstate trucking licenses through the Unified Carrier Registration Agreement. According to FMCSA’s website in 2018, it has 40 different areas of regulation, each of which contains multiple specific items, including regulations on noise, drivers, hazardous materials, preserving records, and transporting migrant workers. A trucker must also maintain minimum insurance cov- erage, pay registration fees, and follow policies that differ across states before the FMCSA will grant permission to operate. The registration process is so complex and time consuming that firms pay substantial amounts to brokers who expedite the application process and take care of state licensing requirements.

For a large truck, the annual federal interstate registration fee can exceed $8,000. To operate, truckers and firms must pay for many additional fees and costly

regulations. These largely lump-sum costs—which are not related to the number of miles driven—have increased substantially in recent years. In 2017, regu- lations took effect requiring each truck to have an electronic onboard recorder, which documents travel time and distance, with an annualized cost of several hundred dollars per truck.

What effect do these new fixed costs have on the trucking industry’s market price and quantity? Are individual firms providing more or fewer trucking ser- vices? Does the number of firms in the market rise or fall? (As we’ll discuss at the end of the chapter, the answer to one of these questions is surprising.)

The Rising Cost of Keeping On Truckin’

Managerial Problem

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226 CHAPTER 8 Competitive Firms and Markets

sell at a given price. The amount the firm thinks it can sell depends on the market demand of consumers and on its beliefs about how other firms in the market will behave. As described in Chapter 7, how a firm should approach such issues depends on the market’s structure. We identified four primary market structures—monopoly, oligopoly, monopolistic competition, and perfect competition—that differ based on such attributes as the number of firms in the market, the control firms have over market prices, the ease with which firms can enter and leave the market, and the ability of firms to differentiate their products from those of their rivals.

This chapter focuses on perfect competition, a market structure in which there are so many buyers and sellers that each market participant is a price taker, who cannot affect the market’s equilibrium price. Perfect competition is an important market structure for two main reasons. First, a significant part of the economy—including much of agriculture, finance, construction, real estate, wholesale and retail trade, and many service industries—is highly competitive and is well described by the model of perfect competition. Second, a competitive market is the only market structure that maximizes a commonly used measure of economic well-being (total surplus) and thus serves as a baseline against which to compare the economic outcomes of other market structures.

8.1 Perfect Competition Perfect competition is a market structure in which buyers and sellers are price takers. A price-taking firm cannot affect the market price for the product it sells. A firm is a price taker if it faces a demand curve for its product that is horizontal at the market price. That is, it can sell as much as it wants at the market price, so it has no incentive to lower its price to gain more sales. If it raises its price even slightly, it sells nothing, as consumers can buy the product for less elsewhere. Thus, the firm sells its product at the market price. In this section, we discuss how the characteristics of a perfectly competitive market lead to price taking and how much a market can deviate from these characteristics and still be regarded as a competitive market.

Characteristics of a Perfectly Competitive Market Perfectly competitive markets have five characteristics that force firms to be price takers:

1. The market consists of many small buyers and sellers. 2. All firms produce identical products. 3. All market participants have full information about price and product

characteristics. 4. Transaction costs are negligible. 5. Firms can freely enter and exit the market in the long run.

Learning Objectives

1. Describe the characteristics of perfect competition.

2. Graphically identify the competitive equilibrium and derive the short-run supply curve.

3. Contrast the short-run and long-run competitive equilibria and supply curves.

4. Use the concept of surplus to show the main advantage of perfect competition.

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2278.1 Perfect Competition

Large Numbers of Buyers and Sellers. If the sellers in a market are small and numerous, no single firm can raise or lower the market price. The more firms in a market, the less any one firm’s output affects the market output and hence the market price.

For example, the 316,000 U.S. corn farmers are price takers. If a typical grower were to drop out of the market, market supply would fall by only 1>316,000 = 0.00032%, so the market price would not be noticeably affected. Each corn farm can sell as much output as it can produce at the prevailing market equilibrium price, so each farm faces a demand curve that is a horizontal line at the market price.

Similarly, perfect competition requires that buyers be price takers as well. In con- trast, if firms sell to only a single buyer—such as producers of weapons that are allowed to sell to only the government—then the buyer can set the price and the market is not perfectly competitive.

Identical Products. Firms in a perfectly competitive market sell identical or homogeneous products. Consumers do not ask which farm grew a particular Granny Smith apple because they view all Granny Smith apples as essentially identical prod- ucts. If the products of all firms are identical, it is difficult for any single firm to raise its price above the going price charged by other firms.

In contrast, in the automobile market, which is not perfectly competitive, the characteristics of a Ferrari and a Honda Civic differ substantially. These products are differentiated or heterogeneous. Competition from Civics is not in itself a very strong force preventing Ferrari from raising its price.

Full Information. If buyers know that different firms are producing identical products and they know the prices charged by all firms, no single firm can unilater- ally raise its price above the market equilibrium price. If it tried to do so, consum- ers would buy the identical product from another firm. However, if consumers are unaware that products are identical or they don’t know the prices charged by other firms, a single firm may be able to raise its price and still make sales.

Negligible Transaction Costs. Perfectly competitive markets have very low transaction costs. Buyers and sellers can easily find each other and can trade without hiring lawyers to write contracts. If transaction costs are low, it is easy for a customer to buy from a rival firm if the customer’s usual supplier raises its price.

In contrast, if transaction costs are high, customers may absorb a price increase from their traditional supplier to avoid incurring a substantial transaction cost in finding and contracting with a new supplier. Because some consumers prefer to buy a carton of milk at a local convenience store rather than travel several extra miles to a supermarket, the convenience store can charge slightly more than the supermarket without losing all its customers.

In some perfectly competitive markets, many buyers and sellers are brought together in a single room or online so that transaction costs are virtually zero. Trans- action costs are very low at Flora Holland’s daily plant and cut flower auctions in the Netherlands, which attract 7,000 suppliers and 4,500 buyers from around the world. The auction has about 125,000 transactions every day, with 12 billion cut flowers and 1.3 billion plants trading in a year.

Free Entry and Exit. The ability of firms to enter and exit a market freely in the long run leads to a large number of firms in a market and promotes price taking. Suppose a firm could raise its price and make a higher profit. If other firms can quickly and easily enter the market, the higher profit encourages entry by new firms

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228 CHAPTER 8 Competitive Firms and Markets

until the price is driven back to the original level. Free exit is also important: If firms can freely enter a market but cannot quickly exit if prices decline, they are reluctant to enter the market in response to a possibly temporary profit opportunity.1

Perfect Competition in the Chicago Mercantile Exchange. The Chicago Mercantile Exchange, where buyers and sellers can trade wheat and other commodities, exhibits the characteristics of perfect competition, including a very large number of buyers and sellers who are price takers. Anyone can be a buyer or a seller. Indeed, a trader might buy wheat in the morning and sell it in the after- noon. They trade virtually identical products. Buyers and sellers have full information about products and prices, which is posted for everyone to see. Market participants waste no time finding someone who wants to trade and they can easily place buy or sell orders in person, over the telephone, or electronically without paperwork, so transaction costs are negligible. Finally, buyers and sellers can easily enter this market and trade wheat. These characteristics lead to an abundance of buyers and sellers and to price-taking behavior by these market participants.

Deviations from Perfect Competition Many markets possess some, but not all, the characteristics of perfect competition. Such markets are still highly competitive, so that buyers and sellers are, for all practi- cal purposes, price takers. For example, a government may limit entry into a market, but if the market has many buyers and sellers, they may still be price takers. Many cities use zoning laws to limit the number of certain types of stores or motels, yet such cities still have a large number of these firms. Other cities impose moderately large transaction costs on entrants by requiring them to buy licenses, post bonds, and deal with a slow-moving city bureaucracy, yet a significant number of firms still enter the market. Similarly, even if only some customers have full information, that may be sufficient to prevent firms from deviating significantly from price taking. For example, tourists do not know the prices at various stores, but, because locals know, no store can stay in business if it charges unusually high prices.

Economists use the terms competition and competitive more restrictively than do others. To an economist, a competitive firm is a price taker. In contrast, when most people talk about competitive firms, they mean that firms are rivals for the same customers. Even in an oligopolistic market (Chapter 7) with only a few firms, the firms compete for the same customers so they are competitive in this broader sense. From now on, we will use the terms competition and competitive to refer to all markets in which no buyer or seller can significantly affect the market price—they are price takers—even if the market is not perfectly competitive.

8.2 Competition in the Short Run In this section, we examine the profit-maximizing behavior of competitive firms, derive their supply curves, and determine the competitive equilibrium in the short run. In the next section, we examine the same issues in the long run.

1For example, some governments, particularly in Europe, require firms to give workers six months’ warning before they can exit the market.

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2298.2 Competition in the Short Run

The short run is a period short enough that at least one input cannot be var- ied (Chapter 5). Because a firm cannot quickly build a new plant or make other large capital expenditures, a new firm cannot enter a market in the short run. Simi- larly, a firm cannot fully exit in the short run. It can choose not to produce—to shut down—but it is stuck with some fixed inputs such as a plant or other capital that it cannot quickly sell or assign to other uses. In the long run, all inputs can be varied so firms can enter and fully exit the industry.

We treat the short run and the long run separately for two reasons. First, profit- maximizing firms may choose to operate at a loss in the short run, whereas they do not do so in the long run. Second, a firm’s long-run supply curve typically differs from its short-run supply curve.

Economists usually assume that all firms—not just competitive firms—want to maximize their profits. This assumption is reasonable for at least two reasons (Chap- ter 7). First, many owners and managers of firms say that their objective is to maxi- mize profits. Second, firms—especially competitive firms—that do not maximize profit are likely to lose money and be driven out of business. As we showed in Chapter 7, all firms—not just competitive firms—use a two-step decision-making process to determine how to maximize profit:

1. How much to produce. A firm first determines the output that maximizes its profit or minimizes its loss.

2. Whether to produce. Given that it has determined its profit-maximizing output, the firm decides whether to produce this quantity or shut down, producing no output.

How Much to Produce As Chapter 7 shows, any operating firm—not just a competitive firm—maximizes its profit or minimizes its loss by setting its output where its marginal profit is zero or, equivalently, where its marginal revenue equals its marginal cost: MR(q) = MC(q).2 A competitive firm can easily determine its marginal revenue. Because it faces a horizontal demand curve, a competitive firm can sell as many units of output as it wants at the market price, p. Thus, a competitive firm’s revenue, R = pq, increases by p if it sells one more unit of output, so its marginal revenue is p. For example, if the firm faces a market price of $1 per unit, its revenue is $5 if it sells 5 units and $6 if it sells 6 units, so its marginal revenue for the sixth unit is $1 = $6 - $5, which is the market price.3 Thus, because a competitive firm’s marginal revenue equals the market price, a profit-maximizing competitive firm produces the amount of output, q, at which the market price, p, equals its marginal cost, MC:

p = MC(q). (8.1)

2As explained in Chapter 7, if MR 7 MC, then a small increase in quantity causes revenue to rise by more than cost, so maximizing profit requires an increase in output. If MR 6 MC, then maximizing profit requires a decrease in quantity as the reduction in cost exceeds the reduction in revenue. Only if MR = MC is the firm maximizing profit. 3We can use calculus to show that marginal revenue equals price for a competitive firm. Because p is constant and R(q) = pq, MR(q) = dR(q)>dq = d(pq)>dq = p. Therefore, to maximize profit, a competitive firm must produce the quantity such that p = MC. In calculus, this is the called the first order condition. To make sure that we have found a maximum, a second order condition must also be satisfied. For a competitive firm, the second order condition implies that the marginal cost curve must be upward-sloping at the profit maximizing quantity.

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230 CHAPTER 8 Competitive Firms and Markets

To illustrate how a competitive firm maximizes its profit, we examine a represen- tative firm in the highly competitive Canadian lime manufacturing industry. Lime is a nonmetallic mineral used in mortars, plasters, cements, bleaching powders, steel, paper, glass, and other products. The lime plant’s estimated average cost curve, AC, first falls and then rises in panel a of Figure 8.1.4 As always, the marginal cost curve, MC, intersects the average cost curve at its minimum point.

4The figure is based on Robidoux and Lester’s (1988) estimated variable cost function. In the fig- ure, we assume that the minimum of the average variable cost curve is $5 at 50,000 metric tons of output. Based on information from Statistics Canada, we set the fixed cost so that the average cost is $6 at 140,000 tons.

FIGURE 8.1 How a Competitive Firm Maximizes Profit

P ro

fit , $

th ou

sa nd

p er

y ea

r

0

426

–100

(b)

p (q)

p, $

p er

to n

e

2841400 q, Thousand metric tons of lime per year

8

6.50

6

10

(a)

p = MR

p = $426,000

AC

MC

140 284 q, Thousand metric tons of lime per year

(a) A competitive lime manufacturing firm maxi- mizes its profit at π* = $426,000 where its marginal revenue, MR, which is the market price, p = $8, equals its marginal cost, MC.

(b) The corresponding profit curve reaches its peak at 284 units of lime. Estimated cost curves are based on Robidoux and Lester (1988).

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2318.2 Competition in the Short Run

If the market price of lime is p = $8 per metric ton, the competitive firm faces a horizontal demand curve (marginal revenue curve) at $8. The MC curve crosses the firm’s demand curve (or price or marginal revenue curve) at point e, where the firm’s output is 284 units (where a unit is a thousand metric tons).

Thus, at a market price of $8, the competitive firm maximizes its profit by produc- ing 284 units. If the firm produced fewer than 284 units, the market price would be above its marginal cost. As a result, the firm could increase its profit by expanding output because the firm earns more on the next ton, p = $8, than it costs to produce it, MC 6 $8. If the firm were to produce more than 284 units, the market price would be below its marginal cost, MC 7 $8, and the firm could increase its profit by reducing its output. Thus, the competitive firm maximizes its profit by produc- ing that output at which its marginal cost equals its marginal revenue, which is the market price.5

At that 284 units, the firm’s profit is π = $426,000, which is the shaded rectangle in panel a. The length of the rectangle is the number of units sold, q = 284,000 (or 284 units). The height of the rectangle is the firm’s average profit per unit. Because the firm’s profit is its revenue, R(q) = pq, minus its cost, π(q) = R(q) - C(q), its aver- age profit per unit is the difference between the market price (or average revenue), p = R(q)>q = pq>q, and its average cost, AC = C(q)>q:

π(q)

q =

R(q) - C(q) q

= R(q)

q -

C(q) q

= p - AC. (8.2)

At 284 units, the lime firm’s average profit per unit is $1.50 = p - AC(284) = $8 - $6.50, and the firm’s profit is π = $1.50 * 284,000 = $426,000. Panel b shows that this profit is the maximum possible profit because it is the peak of the profit curve.

5The firm chooses its output level to maximize its total profit rather than its average profit per ton. If the firm were to produce 140 units, where its average cost is minimized at $6, the firm would maximize its average profit at $2, but its total profit would be only $280,000. Although the firm gives up 50¢ in profit per ton when it produces 284 units instead of 140 units, it more than makes up for that lost profit per ton by selling an extra 144 units. At $1.50 profit per ton, the firm’s total profit is $426,000, which is $146,000 higher than it is at 140 units.

Q&A 8.1 If a competitive firm’s cost increases due to an increase in the price of a factor of production or a tax, the firm’s manager can quickly determine by how much to adjust output by calculating how the firm’s marginal cost has changed and applying the profit-maximization rule. Suppose that the Canadian province of Manitoba imposes a specific (per-unit) tax of t per ton of lime produced in the province. No other provincial government imposes such a tax. Manitoba has only one lime-producing firm, so the tax affects only that firm and hence has virtually no effect on the market price. Given the tax, how should the Manitoba firm change its output level to maximize its profit, and how does its maximum profit change?

Answer 1. Show how the tax shifts the marginal cost and average cost curves. The firm’s before-

tax marginal cost curve is MC1 and its before-tax average cost curve is AC1. Because the specific tax adds t to the per-unit cost, it shifts the after-tax mar- ginal cost curve up to MC2 = MC1 + t and the after-tax average cost curve to AC2 = AC1 + t.

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232 CHAPTER 8 Competitive Firms and Markets

Profit Maximization with a Specific Tax

Using Calculus We can use calculus to solve the problem in Q&A 8.1. After the government imposes the specific tax t, the competitive firm’s profit is π = pq-[C(q) + tq],

where C(q) is the firm’s before-tax cost and C(q) + tq is its after-tax cost. We obtain a necessary condition for the firm to maximize its after-tax profit by taking the first derivative of profit with respect to quantity and setting it equal to zero:

dπ dq

= d(pq)

dq -

d[C(q) + tq] dq

= p - c dC(q) dq

+ t d = p-[MC + t] = 0.

Thus, the competitive firm maximizes its profit by choosing q such that its after- tax marginal cost, MC + t, equals the market price.

2. Determine the before-tax and after-tax equilibria and the amount by which the firm adjusts its output. Where the before-tax marginal cost curve, MC1, hits the hori- zontal demand curve, p, at e1, the profit-maximizing quantity is q1. The after- tax marginal cost curve, MC2, intersects the demand curve, p, at e2, where the profit-maximizing quantity is q2. Thus, in response to the tax, the firm produces q1 - q2 fewer units of output.

3. Show how the profit changes after the tax. Because the market price is constant but the firm’s average cost curve shifts upward, the firm’s profit at every output level falls. The firm sells fewer units (because of the increase in MC) and makes less profit per unit (because of the increase in AC). The after-tax profit is area A = π2 = [p - AC2(q2)]q2, and the before-tax profit is area A + B = π1 = [p - AC1(q1)]q1, so profit falls by area B due to the tax.

t

p, $

p er

u ni

t

q1q2

e1

t

e2

q, Units per year

p p = MR

AC1

MC1

MC2 = MC1 + t

AC2 = AC1 + t

AC 2(q2)

AC 1(q1)

A

B

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2338.2 Competition in the Short Run

Whether to Produce Once a firm determines the output level that maximizes its profit or minimizes its loss, it must decide whether to produce that output level or to shut down and pro- duce nothing. This decision is easy for the lime firm in Figure 8.1 because, at the output that maximizes its profit, it makes a positive profit. However, the question remains whether a firm should shut down if it is making a loss in the short run.

Most people’s intuition is wrong about this decision:

This intuition holds if the firm is making a loss in the long run, but it may be wrong in the short run. In the short run, a firm should operate if it can more than cover its variable cost, even if it cannot fully cover its unavoidable fixed cost.

In Chapter 7, we showed that all firms—not just competitive firms—use the same shutdown rule: The firm shuts down only if it can reduce its loss by doing so. Equiva- lently, the firm shuts down only if its revenue is less than its avoidable variable cost (VC): R 6 VC. If the firm shuts down, it does not incur the variable cost, so its only loss is its fixed cost (F), which we assume is unavoidable.

For a competitive firm, this rule is R = pq 6 VC. Dividing both sides of this inequality by output, we find that a competitive firm shuts down only if the market price is less than its average variable cost: p 6 AVC = VC>q.

We illustrate the logic behind this rule using our lime firm example. We look at three cases where the market price is (1) above the minimum average cost (AC), (2) less than the minimum average cost but at least equal to or above the minimum average variable cost, or (3) below the minimum average variable cost.

The Market Price Is Above Minimum AC. If the market price is above the firm’s average cost at the quantity that it’s producing, the firm makes a profit and so it operates. In panel a of Figure 8.1, the competitive lime firm’s average cost curve reaches its minimum of $6 per ton at 140 units. Thus, if the market price is above $6, the firm makes a profit of p - AC on each unit it sells and operates. In the figure, the market price is $8, and the firm makes a profit of $426,000.

The Market Price Is Between the Minimum AC and the Minimum AVC. The tricky case is when the market price is less than the minimum average cost but is at least as great as the minimum average variable cost. If the price is in this range, the firm makes a loss, but it reduces its loss by operating rather than shutting down.

Figure 8.2 (which reproduces the marginal and average cost curves from panel a of Figure 8.1 and adds the average variable cost curve) illustrates this case for the lime firm. The lime firm’s average cost curve reaches a minimum of $6 at 140 units, while its average variable cost curve hits its minimum of $5 at 50 units. If the market price is between $5 and $6, the lime firm loses money (its profit is negative) because the price is less than its AC, but the firm does not shut down.

For example, if the market price is $5.50, the firm minimizes its loss by produc- ing 100 units where the marginal cost curve crosses the price line. At 100 units, the average cost is $6.12, so the firm’s loss is -62¢ = p - AC(100) = $5.50 - $6.12 on each unit that it sells.

Why does the firm produce given that it is making a loss? The reason is that the firm reduces its loss by operating rather than shutting down because its revenue exceeds its variable cost—or equivalently, the market price exceeds its average variable cost.

Common Confusion A firm should shut down if it is making a loss.

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234 CHAPTER 8 Competitive Firms and Markets

If the firm shuts down in the short run, it incurs a loss equal to its fixed cost of $98,000, which is the sum of rectangles A and B.6 If the firm operates and produces q = 100 units, its average variable cost is AVC = $5.14, which is less than the market price of p = $5.50 per ton. It makes 36¢ = p - AVC = $5.50 - $5.14 more on each ton than its average variable cost. The difference between the firm’s revenue and its variable cost, R - VC, is the rectangle B = $36,000, which has a length of 100 thou- sand tons and a height of 36¢. Thus, if the firm operates, it loses only $62,000 (rect- angle A), which is less than its loss if it shuts down, $98,000. The firm makes a smaller loss by operating than by shutting down because its revenue more than covers its variable cost and hence helps to reduce the loss from the fixed cost.

The Market Price Is Less Than the Minimum AVC. If the market price dips below the minimum of the average variable cost, $5 in Figure 8.2, then the firm should shut down in the short run. Thus, the minimum of the average variable cost curve is the firm’s shutdown point. At any price less than the minimum average vari- able cost, the firm’s revenue is less than its variable cost, so it makes a greater loss by operating than by shutting down because it loses money on each unit sold in addition to the fixed cost that it loses if it shuts down.

In summary, a competitive firm uses a two-step decision-making process to maxi- mize its profit. First, the competitive firm determines the output that maximizes its profit or minimizes its loss when its marginal cost equals the market price (which is its marginal revenue): p = MC. Second, the firm chooses to produce that quantity

6From Chapter 6, we know that the average cost is the sum of the average variable cost and the average fixed cost, AC = AVC + F>q. Thus, the gap between the average cost and the average vari- able cost curves at any given output is AC - AVC = F>q. Consequently, the height of the rectangle A + B is AC(100) - AVC(100) = F>100, and the length of the rectangle is 100 units, so the area of the rectangle is F, or $98,000 = $62,000 + $36,000.

FIGURE 8.2 The Short-Run Shutdown Decision

p, $

p er

to n

10050 140 q, Thousand metric tons of lime per year

AVC

AC

MC

p

a

e

b

0

5.14

5.50

6.00 6.12

5.00

A = $62,000

B = $36,000

The competitive lime man- ufacturing plant operates if the market price is above the minimum of the average variable cost curve, point a, at $5. With a market price of $5.50, the firm produces 100 units because that price is above AVC(100) = $5.14, so the firm more than cov- ers its out-of-pocket, vari- able costs. At that price, the firm makes a loss of area A = $62,000 because the price is less than the aver- age cost of $6.12. If it shuts down, its loss is its fixed cost, area A + B = $98,000. Thus, the firm does not shut down.

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2358.2 Competition in the Short Run

unless it would lose more by operating than by shutting down. The competitive firm shuts down in the short run only if the market price is less than the minimum of its average variable cost, p 6 AVC.

Mini-Case Oil production starts and stops in the short run as the market price fluctuates. In 1998–1999 when oil prices were historically low, U.S. oil-producing firms shut down or abandoned 74,000 of 136,000 oil wells. History repeats itself. From 2011 through the first half of 2014, oil prices were above $100 per barrel—nearly hit- ting $130 at one point—which was above the shutdown point for virtually all U.S. wells. However, when oil prices fell below $50 a barrel in 2015 and below $30 a barrel in 2016, many U.S. wells shut down. From 2014–2016, 1,764 wells under development were left incomplete.

Conventional oil wells—which essentially stick a pipe in the ground and pump oil—have low enough shutdown points that they operated in 2014 and 2015. Some Middle Eastern oil wells break even at a price as low as $10 a barrel. Older Texas wells often have a break-even point at $20 to $30 per barrel.

Most new U.S. oil wells use hydraulic fracturing (fracking). Fracking pumps pressurized liquid consisting of water, sand, and chemicals to fracture oil shale (rock containing oil), which releases natural gas and oil.7 Current fracking opera- tions have a shutdown point at between $50 and $77 per barrel, with an average

of about $65. Thus, fracking opera- tions were more likely to shut down than were conven- tional wells during the recent period of low prices.

By mid-2018, the price of oil exceed- ed $65, and many fracking wells were operating again. In addition, oil com- panies had almost 7,000 wells that had been drilled but not fracked that were starting to come online.

7The first fracking experiment took place in 1947. At first, fracking wells had a minimum average variable cost that was too high to operate profitably. However, in recent years, technological innova- tion substantially lowered this cost, and the global price of oil was often high enough for fracking to be widely used. Due to fracking, U.S. oil production rose from 5.6 million barrels a day in 2010 to 9.3 million in 2015. Fracking is controversial because opponents fear it will create environmental problems and trigger earthquakes.

Fracking and Shutdowns

Water, sand, and chemical agents injected at high pressure into the well Gas flows out

SHALE

WATER TABLE

WELL

FISSURES Water, sand, and chemical agents

Gas flows out

Gas flows out

Fissure

Shale

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236 CHAPTER 8 Competitive Firms and Markets

Q&A 8.2 A competitive firm has a cost function C = 80 + 70q - 12q 2 + q3. Its fixed cost

of 80 is sunk (unavoidable) in the short run. The corresponding marginal cost is MC = 70 - 24q + 3q2. For prices p = 34, p = 49 and p = 70, use a spread- sheet to calculate the profit for each quantity between 4 and 10 and identify the profit-maximizing quantity. Show that price equals marginal cost at the profit- maximizing quantity. Would the firm choose to shut down in the short run at any of these prices?

Answer 1. Open an Excel spreadsheet and put titles Quantity, Cost, MC, Profit (p = 34),

Profit (p = 49), and Profit (p = 70) in cells A1 through F1. 2. Enter the quantities in column A and the cost formulas in columns B and C. In

cells A2 though A8 enter the numbers 4 through 10. In cell B2 enter the cost formula “= 80+70*A2-12*A2^2+A2^3”, then copy and paste this formula into cells B3 through B8. In cell C2, enter the marginal cost (MC) formula “= 70-24*A2+3*A2^2”. Copy and paste this MC formula into cells C3 through C8.

3. Enter the profit formulas into columns D through F. For column D, price is 34. Revenue is 34q, so profit, which is revenue minus cost, should be entered in cell D2 as “= 34*A2-B2”. Copy and paste this formula into cells D3 through D8. Follow the same procedure for columns E and F using prices 49 and 70 respectively instead of 34. The screenshot shows what your spreadsheet should look like.

4. For each price (columns D through F), determine the maximum profit (or minimum loss). For the prices 34, 49, and 70, we have highlighted the maximum profit in the screenshot. Cell D4 shows a minimum loss and the other two highlighted cells show positive profits. The corresponding quantities are 6, 7, and 8.

5. For each price, confirm that the maximum profit or minimum loss occurs where MC equals that price. By inspection, we see that the maximum profit occurs where MC equals the price. For example, at a price of 49, the maximum profit of 18 occurs where MC = 49 (and quantity is 7).

6. Decide whether the firm should shut down at any of these prices. At the prices 49 and 70, the firm makes a profit, so it does not shut down. However, at a price of 34, it makes a loss, so it should check the shutdown condition. At this price, the firm just covers its variable cost and makes no contribution toward its fixed cost. It is indifferent between shutting down and operating in the short run.

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2378.2 Competition in the Short Run

The Short-Run Firm Supply Curve We just demonstrated how a competitive firm chooses its output for a given market price in a way that maximizes its profit or minimizes its losses. By repeating this analysis at different possible market prices, we can show how the amount the com- petitive firm supplies varies with the market price.

As the market price increases from p1 = $5 to p2 = $6 to p3 = $7 to p4 = $8, the lime firm increases its output from 50 to 140 to 215 to 285 units per year, as Figure 8.3 shows. The profit-maximizing output at each market price is determined by the intersection of the relevant demand curve—market price line—and the firm’s marginal cost curve, as equilibria e1 through e4 illustrate. That is, as the market price increases, the equilibria trace out the marginal cost curve. However, if the price falls below the firm’s minimum average variable cost at $5, the firm shuts down. Thus, the competitive firm’s short-run supply curve is its marginal cost curve above its minimum average variable cost.

The firm’s short-run supply curve, S, is a solid red line in the figure. At prices above $5, the short-run supply curve is the same as the marginal cost curve. The supply is zero when price is less than the minimum of the AVC curve of $5. (From now on, to keep the graphs as simple as possible, we will not show the supply curve at prices below the minimum AVC.)

FIGURE 8.3 How the Profit-Maximizing Quantity Varies with Price

p, $

p er

to n

q3 = 215 q4 = 285q1 = 50 q2 = 140

e1

e2

e3

e4

p2

p1

p3

p4

0

q, Thousand metric tons of lime per year

6

7

8

5

AVC

MC

AC

S As the market price incre ases, the lime manufacturing firm produces more output. The change in the price traces out the marginal cost (MC) curve of the firm. The firm’s short-run supply (S) curve is the MC curve above the mini- mum of its AVC curve (at e1).

When making shutdown decisions, good managers ignore unavoidable (sunk) fixed costs (Chapter 6). The manager of a competitive firm should continue oper- ating if price at least equals average variable cost even if revenue is not sufficient to fully cover the sunk fixed costs. As long as price exceeds average variable cost, the firm at least partially offsets the sunk fixed costs by operating instead of absorbing the entire amount as a loss.

Sunk Costs and the Shutdown Decision

Managerial Implication

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238 CHAPTER 8 Competitive Firms and Markets

The Short-Run Market Supply Curve The market supply curve is the horizontal sum of the supply curves of all the indi- vidual firms in the market. In the short run, the maximum number of firms in a market, n, is fixed because new firms need time to enter the market. If all the firms in a competitive market are identical, each firm’s costs are identical, so their supply curves are identical, and the market supply at any price is n times the supply of an individual firm. If the firms have different costs functions, their supply curves and shutdown points differ. Consequently, the market supply curve reflects a different number of firms operating at various prices even in the short run. We examine com- petitive markets first with firms that have identical costs and then with firms that have different costs.

Short-Run Market Supply with Identical Firms. To illustrate how to con- struct a short-run market supply curve, we suppose, for graphical simplicity, that the lime manufacturing market has n = 5 competitive firms with identical cost curves. Panel a of Figure 8.4 plots the short-run supply curve, S1, of a typical firm—the MC curve above the minimum AVC—where the horizontal axis shows the firm’s output, q, per year. Panel b illustrates the competitive market supply curve, the dark line S5, where the horizontal axis is market output, Q, per year. The price axis is the same in the two panels.

If the market price is less than $5 per ton, no firm supplies any output, so the market supply is zero. At $5, each firm is willing to supply q = 50 units, as in panel a. Consequently, the market supply is Q = 5q = 250 units in panel b. At $6 per ton, each firm supplies 140 units, so the market supply is 700 (= 5 * 140) units.

Suppose the market has fewer than five firms in the short run. The light-color lines in panel b show the market supply curves for various other numbers of firms.

FIGURE 8.4 Short-Run Market Supply with Five Identical Lime Firms

p, $

p er

to n

14050 175

q, Thousand metric tons of lime per year

6.476.47

6

7

p, $

p er

to n 7

5

0

AVC

(a) Firm

MC

200 150

100 70025050

Q, Thousand metric tons of lime per year

6

5

0

(b) Market

S3

S4

S5

S2S1 S1

(a) The short-run supply curve, S1, for a typical lime manufacturing firm is its MC above the minimum of its AVC. (b) The market supply curve, S5, is the horizon- tal sum of the supply curves of each of the five

identical firms. The curve S4 shows what the market supply curve would be with only four firms in the market.

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2398.2 Competition in the Short Run

The market supply curve is S1 if there is one price-taking firm, S2 with two firms, S3 with three firms, and S4 with four firms. The market supply curve flattens as the number of firms in the market increases because the market supply curve is the horizontal sum of more and more upward-sloping firm supply curves.8 Thus, the more identical firms producing at a given price, the f latter the short-run market supply curve at that price.

The flatter the supply curve is at a given quantity, the more elastic is the supply curve. As a result, the more firms in the market, the less the price has to increase for the short-run market supply to increase substantially. Consumers pay $6 per ton to obtain 700 units of lime if the market has five firms, but they must pay $6.47 per ton to obtain that much with only four firms. As the number of firms grows very large, the market supply curve approaches a horizontal line at $5.

Short-Run Market Supply with Firms That Differ. If the firms in a com- petitive market have different minimum average variable costs, then not all firms produce at every price, a situation that affects the shape of the short-run market supply curve. Suppose that the only two firms in the lime market are our typical lime firm with a supply curve of S1 and a second firm with a higher marginal and minimum average cost and the supply curve of S2 in Figure 8.5. The first firm pro- duces if the market price is at least $5, whereas the second firm does not produce unless the price is $6 or more. At $5, the first firm produces 50 units, so the quantity

8In the figure, if the price rises by ∆p = 47¢ from $6 to $6.47 per ton, each firm increases its output by ∆q = 35 tons, so the slope (measured in cents per ton) of its supply curve over that range is ∆p>∆q = 47>35 ≈ 1.34. With two firms, ∆q = 70, so the slope is 47>70 ≈ 0.67. Similarly, the slope is 47>105 ≈ 0.45 with three firms, 0.34 with four firms, and 0.27 with five firms. Although not shown in the figure, the slope is 0.13 with 10 firms and 0.013 with 100 firms.

FIGURE 8.5 Short-Run Market Supply with Two Different Lime Firms

p, $

p er

to n

45031521516514010025 50

S2 SS1

0

q, Q, Thousand metric tons of lime per year

6

7

8

5

The supply curve S1 is the same as for the typical lime firm in Figure 8.3. A second firm has an MC that lies to the left of the original firm’s cost curve and a higher minimum of its AVC. Thus, its supply curve, S2, lies above and to the left of the origi- nal firm’s supply curve, S1. The market supply curve, S, is the horizontal sum of the two supply curves. When price is $6 or higher, both firms produce, and the market supply curve is flat- ter than the supply curve of either individual firm.

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240 CHAPTER 8 Competitive Firms and Markets

on the market supply curve, S, is 50 units. Between $5 and $6, only the first firm produces, so the market supply, S, is the same as the first firm’s supply, S1. At and above $6, both firms produce, so the market supply curve is the horizontal sum- mation of their two individual supply curves. For example, at $7, the first firm produces 215 units, and the second firm supplies 100 units, so the market supply is 315 units.

As in a market with identical firms, where both firms are producing, the market supply curve is flatter than that of either firm. Because the second firm does not produce at as low a price as the first firm, the short-run market supply curve has a steeper slope (less elastic supply) at relatively low prices than it would if the firms were identical.

When the firms differ, only the low-cost firm supplies goods at relatively low prices. As the price rises, the other, higher-cost firm starts supplying, creating a stair- like market supply curve. The more suppliers with differing costs, the more steps in the market supply curve. As price rises and more firms supply the good, the market supply curve flattens, so it takes a smaller increase in price to increase supply by a given amount. Stated the other way, the more firms differ in costs, the steeper the market supply curve is at low prices. Differences in costs are one explanation for why some market supply curves are upward sloping.

Short-Run Competitive Equilibrium By combining the short-run market supply curve and the market demand curve, we can determine the short-run competitive equilibrium. We first show how to deter- mine the equilibrium in the lime market, and we then examine how taxes change the equilibrium.

Suppose the lime manufacturing market has five identical firms in the short-run equilibrium. Panel a of Figure 8.6 shows the short-run cost curves and the supply curve, S1, for a typical firm, and panel b shows the corresponding short-run competi- tive market supply curve, S.

In panel b, the initial demand curve D1 intersects the market supply curve at E1, the market equilibrium. The equilibrium quantity is Q1 = 1,075 units of lime per year, and the equilibrium market price is $7.

In panel a, each competitive firm faces a horizontal demand curve at the equilib- rium price of $7. Each price-taking firm chooses its output where its marginal cost curve intersects the horizontal demand curve at e1. Because each firm is maximizing its profit at e1, no firm wants to change its behavior, so e1 is the firm’s equilibrium. In panel a, each firm makes a short-run profit of area A + B = $172,000, which is the average profit per ton, p - AC = $7 - $6.20 = 80¢, times the firm’s out- put, q1 = 215 units. The equilibrium market output, Q1, is the number of firms, n, times the equilibrium output of each firm: Q1 = nq1 = 5 * 215 units = 1,075 units (panel b).

Now suppose that the demand curve shifts to D2. The new market equilibrium is E2, where the price is only $5. At that price, each firm produces q = 50 units, and mar- ket output is Q = 250 units. In panel a, each firm loses $98,500, area A + C, because it earns (p - AC) = ($5 - $6.97) = - $1.97 per unit and it sells q2 = 50 units. How- ever, such a firm does not shut down because price equals the firm’s average variable cost, so the firm is covering its out-of-pocket expenses.

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2418.3 Competition in the Long Run

8.3 Competition in the Long Run Originally one thought that if there were a half dozen large computers in this country, hidden away in research laboratories, this would take care of all requirements we had throughout the country. —Howard H. Aiken, a computer pioneer, 1952

In the long run, competitive firms can vary inputs that were fixed in the short run and firms can enter and exit the industry freely, so the long-run firm and market supply curves differ from the short-run curves. After briefly looking at how a firm determines its long-run supply curve to maximize its profit, we examine the rela- tionship between short-run and long-run market supply curves and competitive equilibria.

Long-Run Competitive Profit Maximization The firm’s two profit-maximizing decisions—how much to produce and whether to produce at all—are simpler in the long run than in the short run because, in the long run, all costs are avoidable.

FIGURE 8.6 Short-Run Competitive Equilibrium in the Lime Market

p, $

p er

to n

q1 = 215q2 = 50 Q1 = 1,075Q2 = 2500

q, Thousand metric tons of lime per year

Q, Thousand metric tons of lime per year

6.97

6.20 6

5

0

5

6

7

8

7

8

e2

e1

E2

S

E1p , $

p er

to n

(b) Market(a) Firm

AVC

AC

D 2

S1 D1

A

C

B

(a) The short-run supply curve is the marginal cost above the minimum average variable cost of $5. At a price of $5, each firm makes a short-run loss of (p - AC)q = ($5 - $6.97) * 50,000 = - $98,500, area A + C. At a price of $7, the short-run profit of a typical lime firm is (p - AC)q = ($7 - $6.20) * 215,000 = $172,000, area A + B.

(b) If the lime market has five firms in the short run so that the market supply is S and the mar- ket demand curve is D1, then the short-run equi- librium is E1, the market price is $7, and market output is Q1 = 1,075 units. If the demand curve shifts to D2, the market equilibrium is p = $5 and Q2 = 250 units.

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242 CHAPTER 8 Competitive Firms and Markets

The firm chooses the quantity that maximizes its profit using the same rules as in the short run. The firm picks the quantity that maximizes long-run profit, which is the dif- ference between revenue and long-run cost. Equivalently, it operates where long-run marginal profit is zero—where marginal revenue (price) equals long-run marginal cost.

After determining the output level, q*, that maximizes its profit or minimizes its loss, the firm decides whether to produce or shut down. The firm shuts down if its revenue is less than its avoidable cost. Because all costs are avoidable in the long run, the firm shuts down if it would make an economic loss by operating.

The Long-Run Firm Supply Curve A firm’s long-run supply curve is its long-run marginal cost curve above the mini- mum of its long-run average cost curve (because all costs are avoidable in the long run). The firm is free to choose its capital in the long run, so the firm’s long-run sup- ply curve may differ substantially from its short-run supply curve.

The firm chooses a plant size to maximize its long-run economic profit in light of its beliefs about the future. If its forecast is wrong, it may be stuck with a plant that is too small or too large for its level of production in the short run. The firm acts to correct this mistake in plant size in the long run.

The Long-Run Market Supply Curve The competitive market supply curve is the horizontal sum of the supply curves of the individual firms in both the short run and the long run. Because the maximum number of firms in the market is fixed in the short run, we add the supply curves of a known number of firms to obtain the short-run market supply curve. The only way for the market to supply more output in the short run is for existing firms to produce more.

However, in the long run, firms can enter or leave the market. Thus, before we can add all the relevant firm supply curves to obtain the long-run market supply curve, we need to determine how many firms are in the market at each possible market price.

We now look in detail at how market entry affects long-run market supply. To isolate the role of entry, we derive the long-run market supply curve, assuming that the price of inputs remains constant as market output increases.

Mini-Case When a large number of firms initially built ethanol processing plants, they built relatively small ones. When the ethanol market took off in the first few years of the twenty-first century, with the price reaching a peak of $4.23 a gallon in June 2006, many firms built larger plants or greatly increased their plant size. From 1999 to 2006, the number of plants nearly doubled and the average plant capacity nearly tripled (36 to 106 million gallons per year).

However, since then, the ethanol market price has collapsed. The price was generally below $3 and often below $1.50 from 2007 through 2018, hitting a low of $1.26 in January 2016. As a result, many firms closed plants or reduced their size. The average plant capacity fell by a third from 2006 to 2017 (106 to 78 million gallons per year).

The Size of Ethanol Processing Plants

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2438.3 Competition in the Long Run

Entry and Exit. The number of firms in a market in the long run is determined by the entry and exit of firms. In the long run, each firm decides whether to enter or exit depending on whether it can make a long-run profit.

In some markets, firms face significant costs to enter, such as large start-up costs, or barriers to entry, such as a government restriction. For example, many city gov- ernments limit the number of cabs, creating a barrier that prevents additional taxis from entering. Similarly, patent protection prevents new firms from producing the patented product until the patent expires.

However, in perfectly competitive markets, firms can enter and exit freely in the long run. For example, many construction firms that provide only labor services enter and exit a market several times a year. In the United States, an estimated 213,000 new firms began operations and 187,000 firms exited in the first quarter of 2014.9 The annual rates of entry and exit of such firms vary from year to year depending on the business cycle, but both normally exceed 10% of the underlying population of firms.

In such markets, a shift of the market demand curve to the right attracts firms to enter. For instance, without government regulations, the market for taxicabs would have free entry and exit. Car owners could enter or exit the market quickly. If the demand curve for cab rides shifted to the right, the market price would rise, and existing cab drivers would make unusually high profits in the short run. Seeing these profits, other car owners would enter the market, causing the market supply curve to shift to the right and the market price to fall. Entry would continue until the last firm to enter—the marginal firm—makes zero long-run profit.

Similarly, if the demand curve shifts to the left so that the market price drops, firms suffer losses. Firms with minimum average costs above the new, lower market price exit the market. Firms continue to leave the market until the next firm that considers leaving, the marginal firm, is again earning a zero long-run profit.

Thus, in a market with free entry and exit:

●● A firm enters the market if it can make a long-run profit, π 7 0. ●● A firm exits the market to avoid a long-run loss, π 6 0.

If firms in a market are making zero long-run profit, they are indifferent between staying in the market and exiting. We presume that if they are already in the market, they stay in the market when they are making zero long-run profit.

9Business Employment Dynamics, Bureau of Labor Statistics www.bls.gov/bdm/ (viewed August 9, 2015).

Mini-Case Firms can easily enter or exit most transportation markets unless governments regulate them. Trucking and shipping firms may serve a particular route, but entry is easy. Other firms quickly enter and serve a route as soon as a profit opportunity appears. Entrants shift their highly mobile equipment—trucks or ships—from less profitable routes to more profitable ones.

The annual entry and exit rates in construction were 10% in 2015. However, many construction firms enter and exit the market repeatedly over the year. When home construction booms during the spring and summer, the number of home construction firms in a market is large. During the slow winter months, many of these firms shut down, only to reenter the market when the weather improves.

Industries with High Entry and Exit Rates

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244 CHAPTER 8 Competitive Firms and Markets

Long-Run Market Supply with Identical Firms and Free Entry. The long-run market supply curve is flat at the minimum of long-run average cost if firms can freely enter and exit the market, an unlimited number of firms have identical costs, and input prices are constant. This result follows from our reasoning about the short-run supply curve, in which we showed that the market supply curve is flatter, the more firms in the market. With a large number of firms in the market in the long run, the market supply curve is effectively flat.

The long-run supply curve of a typical vegetable oil mill, S1 in panel a of Figure 8.7, is the long-run marginal cost curve above a minimum long-run average cost of $10. Because each firm shuts down if the market price is below $10, the long-run market supply curve is zero at a price below $10. If the price rises above $10, firms are making positive profits, so new firms enter, expanding market output until profits are driven to zero, where price is again $10. The long-run market supply curve in panel b is a horizontal line at the minimum long-run average cost of the typical firm, $10. At a price of $10, each firm produces q = 150 units (where one unit equals 100 metric tons). Thus, the total output produced by n firms in the market is Q = nq = n * 150 units. Extra market output is obtained by new firms entering the market.

In summary, the long-run market supply curve is horizontal if the market has free entry and exit, an unlimited number of firms have identical costs, and input prices are constant. As we show next, when these strong assumptions do not hold, the long-run market supply curve typically slopes upward but may slope downward. We examine two reasons why a long-run market supply curve is not flat: limited entry and differences in cost functions across firms. In addition, although we do not demonstrate this result, a third reason why long-run supply curves may slope up (or down) is that input prices rise (or fall) when output increases.

Long-Run Market Supply When Entry Is Limited. If the number of firms in a market is limited in the long run, the long-run market supply curve slopes upward. The number of firms is limited if the government restricts that number, if all firms need a scarce resource, or if entry is costly. An example of a

Even in agriculture, where it often takes firms substantial time to enter, about 7.5% of U.S. agricultural firms enter every year and about 8.5% exit. Solar energy firms rapidly entered and exited the California market (which has half of all solar energy systems). The number of firms went from 603 firms in 2008 to 1,057 in 2010 and 1,499 in 2018.

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2458.3 Competition in the Long Run

scarce resource is the limited number of lots in Miami on which a luxury beach- front hotel could be built. High entry costs restrict the number of firms in a market because firms enter only if the long-run economic profit is greater than the cost of entering.

The only way to get more output if the number of firms is limited is for existing firms to produce more. Because individual firms’ supply curves slope upward, the long-run market supply curve is also upward sloping. The reasoning is the same as in the short run, as panel b of Figure 8.4 illustrates, given that no more than five firms can enter. The market supply curve is the upward-sloping S5 curve, which is the horizontal sum of the five firms’ upward-sloping marginal cost curves above minimum average cost.

Long-Run Market Supply When Firms Differ. A second reason why some long-run market supply curves slope upward is that firms differ. Firms with rela- tively low minimum long-run average costs are willing to enter the market at lower prices than others, resulting in an upward-sloping long-run market supply curve (similar to the short-run example in Figure 8.5).

Suppose that a market has a number of low-cost firms and other higher-cost firms. If lower-cost firms can produce as much output as the market wants, only low-cost firms produce, and the long-run market supply curve is horizontal at the minimum of the low-cost firm’s average cost curve. The long-run supply curve is upward sloping only if lower-cost firms cannot produce as much output as the market demands because each of these firms has a limited capacity and the number of these firms is limited.

FIGURE 8.7 Long-Run Firm and Market Supply with Identical Vegetable Oil Firms

p, $

p er

u ni

t

150

LRAC

LRMC

(a) Firm

q, Hundred metric tons of oil per year

10

S1

0

p, $

p er

u ni

t

(b) Market

Q, Hundred metric tons of oil per year

Long-run market supply 10

0

(a) The long-run supply curve of a typical vegeta- ble oil mill, S1, is the long-run marginal cost curve above the minimum average cost of $10.

(b) The long-run market supply curve is horizontal at the minimum of the long-run minimum average cost of a typical firm. Each firm produces 150 units, so market output is 150n, where n is the number of firms.

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246 CHAPTER 8 Competitive Firms and Markets

Long-Run Competitive Equilibrium The intersection of the long-run market supply and demand curves determines the long-run competitive equilibrium. With identical firms, free entry and exit, and con- stant input prices, the long-run competitive market supply is horizontal at minimum long-run average cost, so the equilibrium price equals long-run average cost. A shift in the demand curve affects only the equilibrium quantity and not the equilibrium price, which remains constant at the minimum of long-run average cost. Because the market supply curve is different in the short run than in the long run, the long-run competitive equilibrium differs from the short-run equilibrium.

Mini-Case Many countries produce cotton. Production costs differ among countries because of differences in the quality of land, amount of rainfall, costs of irrigation, costs of labor, and other factors.

The length of each step-like segment of the long-run supply curve of cotton in the graph is the quantity produced by the labeled country. The amount that the low-cost countries can produce is limited, so we observe production by the higher-cost countries if the market price is sufficiently high.

The height of each segment of the supply curve is the typical minimum average cost of production in that country. The average cost of production in Pakistan is less than half that in Iran. The supply curve has a step-like appearance because we are assuming that average cost is constant within a given country, up to capacity.

As the market price rises, the number of countries producing increases. At market prices below $1.08 per kilogram, only Pakistan produces. If the market price is below $1.50, the United States and Iran do not produce. If the price increases to $1.56, the United States supplies a large amount of cotton. In this range of the supply curve, supply is elastic. For Iran to produce, the price has to rise to $1.71. Price increases in that range result in only a relatively small increase in supply. Thus, the supply curve is relatively inelastic at prices above $1.56.

An Upward-Sloping Long-Run Supply Curve for Cotton

0.71

P ric

e, $

p er

k g

0 1 2 3

Iran

United States

Nicaragua, Turkey

Brazil Australia

Argentina

Pakistan

4 5 6 6.8

Cotton, billion kg per year

1.08 1.15

1.27

1.43

1.56

1.71 S

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2478.4 Competition Maximizes Economic Well-Being

Zero Long-Run Profit with Free Entry The long-run supply curve is horizontal if firms are free to enter the market, firms have identical cost, and input prices are constant. All firms in the market are operat- ing at minimum long-run average cost. That is, they are indifferent between shutting down or not because they are earning zero economic profit.

In a competitive market with identical firms and free entry, if most firms are profit-maximizing, profits are driven to zero at the long-run equilibrium. Any firm that does not maximize profit—that is, any firm that sets its output so that the market price does not equal its marginal cost or does not use the most cost-efficient methods of production—loses money. Thus, to survive in a competitive market in the long run, a firm must maximize its profit. That only firms that maximize their profits operate is called the survivor principle (Chapter 7).

8.4 Competition Maximizes Economic Well-Being We have two main reasons to study competition in a managerial economics course. First, many sectors of the economy are highly competitive, including agriculture, parts of the construction industry, many labor markets, and much retail and whole- sale trade. Second, and perhaps more important, perfect competition serves as an ideal or benchmark for other industries. This benchmark is widely used by econo- mists and widely misused by politicians.

Most U.S. politicians have at one point or another in their careers stated (with a hand over their heart), “I believe in the free market.” While we’re not about to bash free markets, we find this statement to be, at best, mysterious. What do the politi- cians mean by “believe in” and “free market?” Hopefully they realize that whether

Q&A 8.3 A perfectly competitive industry is in long-run equilibrium. Each of the identical firms has a long-run cost function C = 100 + q2. As a result, a firm’s marginal cost function is MC = 2q. In the long-run competitive equilibrium, how much does the  firm produce, and what is the equilibrium price? If the market quantity demanded at the equilibrium price is Q = 2,500, how many firms are in the market?

Answer 1. Determine the AC curve. AC = C>q = 100>q + q. 2. Solve for the equilibrium quantity. Because a profit-maximizing firm operates

where p = MC and free entry by firms into the market ensures that p = AC, it follows that MC = AC. Therefore, MC = 2q = 100>q + q = AC. Simplifying yields q = 100>q or q2 = 100 so q = 10.

3. Use either the marginal cost curve or the average cost curve to determine the price. Substituting q = 10 into the marginal cost function, we know that p = MC = 2q = 20. Similarly, p = AC = 100>q + q = 20.

4. To obtain the number of firms, n, in the market, divide total output by the output per firm. Because total market output is 2,500, n = Q>q = 2,500>10 = 250.

Comment: Firms in this industry have fixed costs of 100 even in the long run. This cost is avoidable in the long run if a firm exits the industry but does not vary with output if the firm operates. An example is rent on a building.

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248 CHAPTER 8 Competitive Firms and Markets

a free market is desirable is a scientific question rather than one of belief. Possibly when they say they “believe in,” they are making some claim that free markets are desirable for some unspecified reason. By “free market,” they might mean a market without government regulation or intervention.

We believe that this statement is a bad summary of what is probably the most impor- tant theoretical result in economics: A perfectly competitive market maximizes an important measure of economic well-being. Adam Smith, the father of modern economics, in his book An Inquiry into the Nature and Causes of the Wealth of Nations, published in 1776, was the first to observe that firms and consumers acting independently in their own self- interest generate a desirable outcome. This insight is called the invisible hand theorem.10

Because a competitive market is desirable, government intervention in a perfectly competitive market reduces a society’s economic well-being. However, government intervention may increase economic well-being in markets that are not perfectly competitive, as with monopoly. In other words, freedom from government interven- tion does not guarantee that society’s well-being is maximized in markets that are not perfectly competitive. In the rest of this section, we first describe widely accepted measures of consumer well-being, consumer surplus, and producer well-being, pro- ducer surplus (a concept close to that of profit). Next, we define a measure of a soci- ety’s economic well-being, total surplus, as the sum of the consumer and producer measures of well-being. Then, we demonstrate why perfect competition maximizes total surplus. Finally, we discuss why a government action that causes a deviation from the perfectly competitive equilibrium reduces total surplus.

Consumer Surplus The monetary difference between what a consumer is willing to pay for the quantity of the good purchased and what the consumer actually pays is called consumer surplus (CS). Consumer surplus is a dollar-value measure of the extra economic benefit the consumer receives from a transaction over and above the good’s price. By measuring how much more a consumer is willing to pay than the consumer actually paid, we know how much the consumer gained from this transaction. For example, if Jane is willing to pay up to $500 for a ticket to a Bruno Mars concert, but only has to pay $150, her consumer surplus is $350.

We use this monetary measure to answer questions such as “What effect does a price increase have on consumers’ well-being?” or “How much does a government quota on the number of items each consumer may buy hurt consumers?” or “What is the harm to consumers from one firm monopolizing a market?”11

10The term invisible hand was coined by Smith. He expressed the basic theorem as “. . .every indi- vidual . . . intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. . . . By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it.” 11If we knew a consumer’s utility function (Chapter 4), we could directly answer the question of how an economic event, such as a price change, affects a consumer’s well-being. However, we do not know individual utility functions. Even if we did, we could not compare the utility levels of different individuals. If Mei says that she got 1,000 utils (units of utility) from watching a movie, while Alan reports that he got 872 utils, we would not know if Mei enjoyed the movie more than Alan. She might just be using a different subjective scale. Because of these and other difficulties in comparing consumers’ utilities, we use a monetary measure.

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2498.4 Competition Maximizes Economic Well-Being

Measuring Consumer Surplus Using a Demand Curve. Because con- sumer surplus is the difference between what a consumer is willing to pay for a unit of a good and the price of that good, it is a measure of what the consumer gains from trade: from exchanging money for the good. We can use the information stored in a demand curve and the market price to determine consumer surplus. The demand curve reflects a consumer’s marginal willingness to pay: the maximum amount a con- sumer will spend for an extra unit. The consumer’s marginal willingness to pay is the marginal value the consumer places on the last unit of output.

For example, David’s demand curve for magazines per week, panel a of Figure 8.8, indicates his marginal willingness to buy various numbers of magazines. David places a marginal value of $5 on the first magazine. As a result, if the price of a maga- zine is $5, David buys one magazine, point a on the demand curve. His marginal willingness to buy a second magazine is $4, so if the price falls to $4, he buys two magazines, b. His marginal willingness to buy three magazines is $3, so if the price of magazines is $3, he buys three magazines, c.

David’s consumer surplus from each additional magazine is his marginal willing- ness to pay minus what he pays to obtain the magazine. His marginal willingness to pay for the first magazine, $5, is area CS1 + E1. If the price is $3, his expenditure to obtain the magazine is area E1 = $3. Thus, his consumer surplus on the first maga- zine is area CS1 = (CS1 + E1) - E1 = $5 - $3 = $2. Because his marginal will- ingness to pay for the second magazine is $4, his consumer surplus for the second magazine is the smaller area CS2 = $1. His marginal willingness to pay for the third

FIGURE 8.8 Consumer Surplus

5

4

3

2

1

p1

543210

p, $

p er

tr ad

in g

ca rd

CS2 = $1CS1 = $2

E1 = $3 E2 = $3 E3 = $3

Price = $3

q1

a

b

c

q, Magazines per week q, Trading cards per year

Demand

Expenditure, E

Consumer surplus, CS

Marginal willingness to pay for the last unit of output

p, $

p er

m ag

az in

e

(a) David’s Consumer Surplus

Demand

(b) Steven’s Consumer Surplus

(a) David’s demand curve for magazines has a step-like shape. When the price is $3, he buys three magazines, point c. David’s marginal value for the first magazine is $5, areas CS1 + E1, and his expenditure is $3, area E1, so his consumer surplus is CS1 = $2. His consumer surplus is $1 for the second magazine, area CS2, and is $0 for the third (he is indifferent between

buying and not buying it). Thus, his total consumer surplus is the shaded area CS1 + CS2 = $3. (b) Steven’s willingness to pay for trading cards is the height of his smooth demand curve. At price p1, Steven’s expenditure is E (= p1q1), his consumer surplus is CS, and the total value he places on con- suming q1 trading cards per year is CS + E.

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250 CHAPTER 8 Competitive Firms and Markets

magazine is $3, which equals what he must pay to obtain it, so his consumer surplus is zero, CS3 = $0. He is indifferent between buying and not buying the third magazine.

At a price of $3, David buys three magazines. His total consumer surplus from the three magazines he buys is the sum of the consumer surplus he gets from each of these magazines: CS1 + CS2 + CS3 = $2 + $1 + $0 = $3. This total consumer surplus of $3 is the extra amount that David is willing to spend for the right to buy three magazines at $3 each. Thus, an individual’s consumer surplus is the area under the demand curve and above the market price up to the quantity the consumer buys.

David is unwilling to buy a fourth magazine unless the price drops to $2 or less. If David’s mother gives him a fourth magazine as a gift, the marginal value that David puts on that fourth magazine, $2, is less than what it cost his mother, $3.

We can determine consumer surplus for smooth demand curves in the same way as with David’s unusual stair-like demand curve. Steven has a smooth demand curve for baseball trading cards, panel b of Figure 8.8. The height of this demand curve measures his willingness to pay for one more card. This willingness varies with the number of cards he buys in a year. The total value he places on obtaining q1 cards per year is the area under the demand curve up to q1, the areas CS and E. Area E is his actual expenditure on q1 cards. Because the price is p1, his expenditure is p1q1. Steven’s consumer surplus from consuming q1 trading cards is the value of consum- ing those cards, areas CS and E, minus his actual expenditures E to obtain them, or CS. Thus, his consumer surplus, CS, is the area under the demand curve and above the horizontal line at the price p1 up to the quantity he buys, q1.

Just as we measure the consumer surplus for an individual using that individual’s demand curve, we measure the consumer surplus of all consumers in a market using the market demand curve. Market consumer surplus is the area under the market demand curve above the market price up to the quantity consumers buy.

To summarize, consumer surplus is a practical and convenient measure of con- sumers’ economic benefits from market transactions. Consumer surplus has two advantages over utility as a measure of economic benefit. First, we can easily com- pare or combine the dollar-denominated consumer surplus of several individuals, but not the utilities of various individuals. Second, we can relatively easily measure consumer surplus, but not utility directly. To calculate consumer surplus, all we have to do is measure the area under a demand curve.

For a product sold on eBay, a manager can use the information that eBay reports to quickly estimate the market demand curve for the product. People differ in their willingness to pay for a given item. We can determine individuals’ willing- ness to pay for an a.d. 238 Roman coin, a sesterce (originally equivalent in value to two and a half asses) of Emperor Balbinus, by how much they bid in an eBay auction.

On its website, eBay correctly argues (Chapter 12) that the best strategy for bidders is to bid their willingness to pay: the maximum value that they place on the item. If bidders follow this strategy, from what eBay reports, we know the maximum bid of each person except the winner because eBay uses a second-price auction, where the winner pays the second-highest amount bid (plus an incre- ment).12 The figure arranges the bids from highest to lowest. Because each bar on the graph indicates the bid for one coin, the figure shows how many units could

Willingness to Pay on eBay

Managerial Implication

have been sold to this group of bidders at various prices (assuming each bidder wants only one coin). That is, it is the market demand curve.

12The increment depends on the size of the bid. For example, it is $1 for bids between $25 and $99.99 and $25 for bids between $1,000 and $2,499.99.

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2518.4 Competition Maximizes Economic Well-Being

Effects of a Price Change on Consumer Surplus. If the supply curve shifts upward or a government imposes a new sales tax, the equilibrium price rises, causing the consumer surplus to fall. We illustrate the effect of a price increase on market consumer surplus using estimated supply and demand curves for sweetheart and hybrid tea roses sold in the United States.13 We then discuss which markets are likely to have the greatest loss of consumer surplus due to a price increase.

Suppose that the introduction of a new tax causes the wholesale price of roses to rise from the original equilibrium price of 30¢ to 32¢ per rose stem, a movement along the demand curve in Figure 8.9. The consumer surplus at the initial price of 30¢ is area A + B + C = $173.74 million per year.14 At a higher price of 32¢, the con- sumer surplus falls to area A = $149.64 million. Thus, the loss in consumer surplus from the increase in price is B + C = $24.1 million per year.

13We estimated this model using data from the Statistical Abstract of United States, Floriculture Crops, Floriculture and Environmental Horticulture Products, and usda.mannlib.cornell.edu. The prices are in real 1991 dollars. 14The height of triangle A is 25.8¢ = 57.8¢ - 32¢ per stem and the base is 1.16 billion stems per year, so its area is 12 * $0.258 * 1.16 billion = $149.64 million per year. Rectangle B is $0.02 * 1.16 billion = $23.2 million. Triangle C is 12 * $0.02 * 0.09 billion = $0.9 million.

have been sold to this group of bidders at various prices (assuming each bidder wants only one coin). That is, it is the market demand curve.

12The increment depends on the size of the bid. For example, it is $1 for bids between $25 and $99.99 and $25 for bids between $1,000 and $2,499.99.

$? $1,003 $950

$706

$600 $555

$166 $108

$50 $28

1 2 3 4 5 6 7 8 9 10

W ill

in gn

es s

to p

ay , $

b id

p er

c oi

n

Q, Number of coins

Mini-Case According to the U.S. Bureau of Economic Analysis, the information sector’s contribution to gross domestic product (GDP), the value of national output, of about 4% to 5% has not changed in the past 35 years. Part of the reason is that many information goods have zero prices, such as social networking sites, search engines, Spotify, YouTube, and Wikipedia, which contribute to consumer surplus but are not fully captured in GDP. When people went from buying music in the form of CDs, records, and other physical products to streaming songs digitally, the price associated with music dropped and hence its recorded contribution to GDP fell by 40% even though people listened to more music than ever. Con- sumer surplus rose despite the drop in contribution to GDP.

Digital Surplus

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252 CHAPTER 8 Competitive Firms and Markets

FIGURE 8.9 Fall in Consumer Surplus from Roses as Price Rises

p, ¢

p er

s te

m

Q, Billion rose stems per year

57.8

32 30

1.16 1.250

b

a

A = $149.64 million

B = $23.2 million

C = $0.9 million

Demand

As the price of roses rises 2¢ per stem from 30¢ to 32¢ per stem, the quantity demanded decreases from 1.25 to 1.16 billion stems per year. The loss in consumer surplus from the higher price, areas B and C, is $24.1 million per year.

Producer Surplus A supplier’s gain from participating in the market is measured by producer surplus (PS), which is the difference between the amount a good sells for and the minimum amount necessary for the producers to be willing to produce the good. The mini- mum amount a firm must receive to be willing to produce is the firm’s avoidable production cost. Therefore, producer surplus is a measure of what the firm gains from trade.

Measuring Producer Surplus Using a Supply Curve. To determine a competitive firm’s producer surplus, we use its supply curve: its marginal cost curve above its minimum average variable cost. The firm’s supply curve in panel a of Figure 8.10 looks like a staircase. The marginal cost of producing the first unit is MC1 = $1, which is the area under the marginal cost curve between 0 and 1. The marginal cost of producing the second unit is MC2 = $2, and so on. The variable cost, VC, of producing four units is the sum of the marginal costs for the first four units:

Nordhaus (2005) estimated that of the returns from technological advances made between 1948 and 2001, only 3.7% were retained by corporations and the remaining 96.3% went to consumers in the form of consumer surplus.

Brynjolfsson et al. (2018) used experiments to determine consumers’ willing- ness to pay for digital goods. A sample of Facebook users were asked whether they wanted to keep access to Facebook or give up access for a month in exchange for a certain amount of money. Brynjolfsson et al. estimated that the median Facebook user would have needed $37.76 to give up Facebook for a month in 2017. As Facebook is free to users, the estimated consumer surplus for the median Facebook consumer is $37.76 per month. Given that Facebook had 218 million U.S. users in 2018, it produces billions of dollars of consumer surplus.

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2538.4 Competition Maximizes Economic Well-Being

VC = MC1 + MC2 + MC3 + MC4 = $1 + $2 + $3 + $4 = $10.

If the market price, p, is $4, the firm’s revenue from the sale of the first unit exceeds its cost by PS1 = p - MC1 = $4 - $1 = $3, which is its producer surplus on the first unit. The firm’s producer surplus is $2 on the second unit and $1 on the third unit. On the fourth unit, the price equals marginal cost, so the firm just breaks even. As a result, the firm’s total producer surplus, PS, from selling four units at $4 each is the sum of its producer surplus on these four units:

PS = PS1 + PS2 + PS3 + PS4 = $3 + $2 + $1 + $0 = $6.

Graphically, the total producer surplus is the area above the supply curve and below the market price up to the quantity actually produced. This same reasoning holds when the firm’s supply curve is smooth.

A firm’s producer surplus is revenue, R, minus variable cost, VC:

PS = R-VC.

In panel a of Figure 8.10, revenue is $4 * 4 = $16 and variable cost is $10, so the firm’s producer surplus is $6.

FIGURE 8.10 Producer Surplus

4

3

2

1

43210

PS2 = $2 PS3 = $1PS1 = $3

MC2 = $2 MC3 = $3 MC4 = $4MC1 = $1

p

Supply

q, Units per week

p, $

p er

u ni

t

(a) A Firm’s Producer Surplus

p*

p, P

ric e

pe r

un it

Q*

Market supply curve

Q, Units per year

Market price

Variable cost, VC

Producer surplus, PS

(b) A Market’s Producer Surplus

(a) The firm’s producer surplus, $6, is the area below the market price, $4, and above the marginal cost (supply curve) up to the quantity sold, 4. The area under the marginal cost curve up to the number of units actually produced is the variable cost of production.

(b) The market producer surplus is the area above the supply curve and below the line at the mar- ket price, p*, up to the quantity produced, Q*. The area below the supply curve and to the left of the quantity produced by the market, Q*, is the vari- able cost of producing that level of output.

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254 CHAPTER 8 Competitive Firms and Markets

Using Producer Surplus. Even in the short run, we can use producer surplus to study the effects of a shock that affects the variable cost of production, such as a change in the price of a substitute or a variable input. Such shocks change profit by exactly the same amount as they change producer surplus because fixed costs do not change.

A major advantage of producer surplus is that we can use it to measure the effect of a shock on all the firms in a market without having to measure the profit of each firm in the market separately. We can calculate market producer surplus using the market supply curve in the same way as we calculate a firm’s producer surplus using its supply curve. The market producer surplus in panel b of Figure 8.10 is the area above the supply curve and below the market price, p*, up to the quantity sold, Q*. The market supply curve is the horizontal sum of the marginal cost curves of each of the firms. As a result, the variable cost for all the firms in the market of producing Q is the area under the supply curve between 0 and the market output, Q*.

Q&A 8.4 If a firm has unavoidable fixed costs of F, how is its producer surplus related to its profit?

Answer 1. Express the formula for profit in terms of variable and fixed cost. A firm’s profit is its

revenue, R, minus its total cost, C, which equals variable cost plus fixed cost, F:

π = R - C = R - (VC + F). 2. Take the difference between producer surplus and profit. The difference is

PS - π = (R - VC) - (R - VC - F) = F.

Thus, the difference between a firm’s producer surplus and profit is the fixed cost, F. If the fixed cost is zero (as often occurs in the long run), producer surplus equals profit.

Q&A 8.5 We estimated the supply curve for roses, which is the upward-sloping line in the following figure. How much producer surplus is lost if the price of roses falls from 30¢ to 21¢ per stem (so that the quantity sold falls from 1.25 billion to 1.16 billion rose stems per year)?

Answer 1. Draw the supply curve, and show the change in producer surplus caused by the price

change. The figure shows the estimated supply curve for roses. Point a indicates the quantity supplied at the original price, 30¢, and point b reflects the quantity supplied at the lower price, 21¢. The loss in producer surplus is the sum of rectangle D and triangle E.

2. Calculate the lost producer surplus by adding the areas of rectangle D and triangle E. The height of rectangle D is the difference between the original and the new price, 9¢, and its base is 1.16 billion stems per year, so the area of D (not all of which is shown in the figure because of the break in the quantity axis) is $0.09 per stem * 1.16 billion stems per year = $104.4 million per year. The height of triangle E is also 9¢, and its length is 90 million stems per year, so its area is 12 * $0.09 per stem * 90 million stems per year = $4.05 million per year. Thus, the loss in producer surplus from the drop in price is $108.45 mil- lion per year.

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2558.4 Competition Maximizes Economic Well-Being

Competition Maximizes Total Surplus One of the most important results in economics is that perfect competition maxi- mizes the sum of consumer surplus and producer surplus, which we call total sur- plus (TS):15

TS = CS + PS.

Total surplus is a measure of the total benefit to all market participants from market transactions, which are market participants’ gains from trade. Total surplus implic- itly weights the gains to consumers and producers equally. By using this measure to assess policies that affect market transactions, we are making a value judgment that the well-being of consumers and that of producers are equally important.

While most economists and many other people accept total surplus as a reason- able objective for society to try to maximize, not everyone agrees. Groups of produc- ers commonly argue for legislation that helps them even if it hurts consumers by more than the amount producers gain—as though only producer surplus matters. Similarly, some consumer advocates argue that we should care only about consum- ers, so social well-being should include only consumer surplus.

A demonstration that perfect competition maximizes total surplus requires show- ing that (1) producing less than the competitive output lowers economic benefit as measured by total surplus, and (2) producing more than the competitive output lowers total surplus.

15Many economists call this sum welfare. We do not use that term because it has many different meanings in common language.

Original Price, 30¢

Lower Price, 21¢

Change ($ millions)

Producer Surplus D + E + F F –(D + E) = –108.45

p, ¢

p er

s te

m

Q, Billion rose stems per year

30

21

1.251.160

Supply

b

a

D = $104.4 million

F

E = $4.05 million

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256 CHAPTER 8 Competitive Firms and Markets

We show that reducing output from the competitive level reduces consumer sur- plus, producer surplus, and total surplus. (In Question 4.5 at the end of the chapter, you are asked to use a similar analysis to show that producing more than the com- petitive equilibrium quantity reduces total surplus.)

At the competitive equilibrium in Figure 8.11, e1, where output is Q1 and price is p1, consumer surplus, CS1, equals areas A + B + C, producer surplus, PS1, is D + E, and the total surplus is TS1 = A + B + C + D + E. Now suppose that we reduce output slightly from the competitive equilibrium quantity Q1 to Q2. As a result, price rises to p2 at e2, consumer surplus falls to CS2 = A, producer surplus changes to PS2 = B + D, and total surplus falls to TS2 = A + B + D.

The change in consumer surplus is

∆CS = CS2 - CS1 = A - (A + B + C) = -B - C.

Consumers lose B because they have to pay p2 - p1 more than at the competitive price for the Q2 units they buy. Consumers lose C because they buy only Q2 rather than Q1 at the higher price.

FIGURE 8.11 Reducing Output from the Competitive Level Lowers Total Surplus

Competitive Output, Q1

(1)

Smaller Output, Q2

(2) Change (2) – (1)

Consumer Surplus, CS Producer Surplus, PS

Total Surplus, TS = CS + PS

A + B + C D + E

A + B + C + D + E

A B + D

A + B + D

–B – C = ∆CS B – E = ∆PS

–C – E = ∆TS = –DWL

p, $

p er

u ni

t

Q, Units per year

Supply

Demand

p2

MC1 = p1

Q2 Q1

e1

MC2

e2

C

E

B

D

A

F

Reducing output from the competitive level, Q1, to Q2 causes price to increase from p1 to p2. Con- sumers suffer: Consumer surplus is now A, a fall of ∆CS = -B - C. Producers may gain or lose: Producer

surplus is now B + D, a change of ∆PS = B - E. Over- all, the change in total surplus is ∆TS = -C - E, which is negative. Therefore, total surplus falls by C + E, which is a deadweight loss (DWL) to society.

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2578.4 Competition Maximizes Economic Well-Being

The change in producer surplus is

∆PS = PS2 - PS1 = (B + D) - (D + E) = B - E.

Producers gain B because they now sell Q2 units at p2 rather than p1. They lose E because they sell Q2 - Q1 fewer units.

The change in total surplus, ∆TS = TS2 - TS1, is16

∆TS = ∆CS + ∆PS = (-B - C) + (B - E) = -C - E.

The area B is a transfer from consumers to producers—the extra amount consum- ers pay for the Q2 units goes to the sellers—so it does not affect total surplus. Total surplus drops because the consumer loss of C and the producer loss of E benefit no one. This change in total surplus, ∆TS = -C - E, is a deadweight loss (DWL): the net reduction in total surplus from a loss of surplus by one group that is not offset by a gain to another group from an action that alters a market equilibrium.

The deadweight loss results because consumers value extra output by more than the mar- ginal cost of producing it. At each output between Q2 and Q1, consumers’ marginal willingness to pay for another unit—the height of the demand curve—is greater than the marginal cost of producing the next unit—the height of the supply curve. For example, at e2, consumers value the next unit of output at p2, which is much greater than the marginal cost, MC2, of producing it. Increasing output from Q2 to Q1 raises firms’ variable cost by area F, the area under the marginal cost (supply) curve between Q2 and Q1. Consumers value this extra output by the area under the demand curve between Q2 and Q1, area C + E + F. Thus, consumers value the extra output by C + E more than it costs to produce it.

Society would be better off producing and consuming extra units of this good than spending this amount on other goods. In short, the deadweight loss is the opportunity cost of giving up some of this good to buy more of another good.

16The change in total surplus is ∆TS = TS2 - TS1 = (CS2 + PS2) - (CS1 + PS1) = (CS2 - CS1) + (PS2 - PS1) = ∆CS + ∆PS.

Mini-Case Just how much did Nicholas enjoy the expensive lime green woolen socks with the dancing purple teddy bears that his Aunt Fern gave him for the holidays? Often the cost of a gift exceeds the value that the recipient places on it.

Until the advent of gift cards, only 10% to 15% of holiday gifts were mon- etary. A gift of cash typically gives at least as much pleasure to the recipient as a gift that costs the same. (So what if giving cash is tacky?) Of course, it’s possible that a gift can give more pleasure to the recipient than it cost the giver—but how often has that happened to you?

An efficient gift is one that the recipient values as much as the gift costs the giver, or more. The difference between the price of the gift and its value to the recipient is a deadweight loss. Joel Waldfogel (1993, 2009) asked Yale under- graduates just how large this deadweight loss is. He estimated that the dead- weight loss is between 10% and 33% of the value of gifts. Waldfogel (2005) found that consumers value their own purchases at 10% to 18% more, per dollar spent, than items received as gifts.

The Deadweight Loss of Holiday Gifts

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258 CHAPTER 8 Competitive Firms and Markets

Effects of Government Intervention A government policy that limits trade in a competitive market reduces total surplus. For example, in some markets the government imposes a price ceiling, which sets a limit on the highest price that a firm can legally charge. If the government sets the ceiling below the precontrol competitive price, consumers want to buy more than the precontrol equilibrium quantity, but firms supply less than that quantity. (For example, see Chapter 2’s Mini-Case “Disastrous Price Controls.”) Thus, due to the price ceiling, consumers can buy the good at a lower price but cannot buy as much of it as they’d like. Because less is sold than at the precontrol equilibrium, society suffers a deadweight loss: Consumers value the good more than the marginal cost of producing extra units. Producer surplus must fall because firms receive a lower price and sell fewer units.

Waldfogel found that gifts from friends and “significant others” are most efficient, while non- cash gifts from members of the extended family are least efficient (one-third of the value is lost).17 Luckily, grandparents, aunts, and uncles are most likely to give cash.

Waldfogel concluded that a conservative esti- mate of the deadweight loss of holidays with gift- giving rituals is about $12 billion. (And that’s not counting about 2.8 billion hours spent shopping.) However, if givers get pleasure from picking the “perfect” gift, accounting for that pleasure would reduce this estimated deadweight loss.

17People may deal with a disappointing present by “regifting” it. Some families have been passing the same fruitcake among family members for decades. According to one survey, 33% of women and 19% of men admitted that they pass on an unwanted gift (and 28% of respondents said that they would not admit it if asked whether they had done so).

Q&A 8.6 What is the effect on the equilibrium and consumer, producer, and total surplus if the government sets a price ceiling, p, below the unregulated competitive equi- librium price?

Answer 1. Show the initial unregulated equilibrium. The intersection of the demand curve

and the supply curve determines the unregulated, competitive equilibrium, e1, where the equilibrium quantity is Q1.

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2598.4 Competition Maximizes Economic Well-Being

2. Show how the equilibrium changes with the price ceiling. Because the price ceiling, p, is set below the equilibrium price of p1, the ceiling binds. At this lower price, the quantity consumers demand increases to Qd while the quantity firms are willing to supply falls to Qs, so only Qs = Q2 units are sold at the new equilib- rium, e2. Thus, the price control causes the equilibrium quantity and price to fall, but consumers have excess demand of Qd - Qs.

3. Describe the effects on consumer, producer, and total surplus. Because consumers are able to buy Qs units at a lower price than before the controls, they gain area D. Consumers lose consumer surplus of C, however, because they can purchase only Qs instead of Q1 units of output. Thus, consumers gain net con- sumer surplus of D - C. Because they sell fewer units at a lower price, firms lose producer surplus -D - E. Part of this loss, D, is transferred to consumers because of lower prices, but the rest, E, is a loss to society. The deadweight loss to society is at least C + E.

Comment: This measure of the deadweight loss may underestimate the true loss. Because consumers want to buy more units than are sold, they may spend time searching for a store that has units for sale. This unsuccessful search activity is wasteful and hence a deadweight loss to society. Another possible inefficiency is that consumers who buy the good may value it less than those who are unable to find a unit to purchase. For example, someone might purchase the good who values it at p2, while someone who values it at p3 cannot find any to buy.

No Ceiling Price Ceiling Change

A + B + D F

A + B + D + F

D – C = ∆CS –D – E = ∆PS

–C – E = ∆TS = –DWL

Consumer Surplus, CS Producer Surplus, PS

Total Surplus, TS = CS + PS

A + B + C D + E + F

A + B + C + D + E + F

p, $

p er

u ni

t

Q, Units per year

p3

p1

p2

Qs = Q2 QdQ1

e1

e2

D p, Price ceiling–

C

E

B

A

F

Supply

Demand

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260 CHAPTER 8 Competitive Firms and Markets

The Rising Cost of Keeping On Truckin’

Managerial Solut ion

We return to the Managerial Problem at the beginning of the chapter: What effect do the government’s higher annual fees and other lump-sum costs have on the trucking industry’s market price and quantity? Are individual firms providing more or fewer trucking services? Does the number of firms in the market rise or fall? Because firms may enter and exit this industry in the long run, such higher lump-sum costs can have a counterintuitive effect on the competitive equilibrium.

All trucks of a certain size are essentially identical, and trucks can easily enter and exit the industry (government regulations aside). Panel a of the figure shows a typical firm’s cost curves and panel b shows the market equilibrium.

The new, higher fees and other lump-sum costs raise the fixed cost of operat- ing by T. In panel a, a lump-sum, franchise tax shifts the typical firm’s average cost curve upward from AC1 to AC2 = AC1 + T>q, but does not affect the mar- ginal cost. As a result, the minimum average cost rises from e1 to e2.

Given that an unlimited number of identical truckers are willing to operate in this market, the long-run market supply is horizontal at minimum average cost. Thus, the market supply curve shifts upward in panel b by the same amount as the minimum average cost increases. Given a downward-sloping market demand curve D, the new equilibrium, E2, has a lower quantity, Q2 6 Q1, and higher price, p2 7 p1, than the original equilibrium, E1.

As the market price rises, the quantity that a firm produces rises from q1 to q2 in panel a. Because the marginal cost curve is upward sloping at the original equilibrium, when the average cost curve shifts up due to the higher fixed cost, the new minimum point on the average cost curve corresponds to a larger output than in the original equilibrium. Thus, any trucking firm still operating in the market produces at a larger volume.

Because the market quantity falls but each firm remaining in the market pro- duces more, the number of firms in the market must fall. At the initial equilibrium,

p, $

p er

u ni

t

q1 q2 Q1 = n1q1Q2 = n2q2q, Units per year Q, Units per year

p1

p2

p1

p2 e2

e1

E2 S2

S1

D

E1

p, $

p er

u ni

t

(a) Firm (b) Market

MC

AC1

AC 2 = AC1 + T/q

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261Summary

the number of firms was n1 = Q1>q1. The new equilibrium number of firms, n2 = Q2>q2, must be smaller than n1 because Q2 6 Q1 and q2 7 q1. Therefore, an increase in fixed cost causes the market price to rise and the total quantity and number of trucking firms to fall, as most people would have expected. However, it also has the surprising effect that it causes output per firm to increase for the firms that continue to produce.

SUMMARY

1. Perfect Competition. Perfect competition is a mar- ket structure in which buyers and sellers are price tak- ers. Each firm faces a horizontal demand curve. A firm’s demand curve is horizontal because perfectly competi- tive markets have five characteristics: the market has many small buyers and sellers, firms produce identical (homogeneous) products, buyers have full information about product prices and characteristics, transaction costs are negligible, and the market has free entry and exit in the long run. Many markets are highly competi- tive—firms are very close to being price takers—even if they do not strictly possess all five of the characteristics associated with perfect competition.

2. Competition in the Short Run. To maximize its profit, a competitive firm (like a firm in any other mar- ket structure) chooses its output level where marginal revenue equals marginal cost. Because a competitive firm is a price taker, its marginal revenue equals the market price, so it sets its output so that price equals marginal cost. New firms cannot enter in the short run. In addition, firms that are in the industry have some fixed inputs that cannot be changed and whose costs cannot be avoided. In this sense firms cannot exit the industry in the short run. However, a profit-maximiz- ing firm shuts down and produces no output if the market price is less than its minimum average variable cost. Thus, a competitive firm’s short-run supply curve is its marginal cost curve above its minimum average variable cost. The short-run market supply curve is the sum of the supply curves of the fixed number of firms producing in the short run. The short-run competitive equilibrium is determined by the intersection of the market demand curve and the short-run market sup- ply curve.

3. Competition in the Long Run. In the long run, a competitive firm sets its output where the market price equals its long-run marginal cost. It shuts down if the

market price is less than the minimum of its long-run average cost, because all costs are avoidable in the long run. Consequently, the competitive firm’s long- run supply curve is its long-run marginal cost above its minimum long-run average cost. The long-run sup- ply curve of a firm may have a different slope than the short-run curve because it can vary its fixed inputs in the long run. The long-run market supply curve is the horizontal sum of the supply curves of all the firms in the market. If all firms are identical, entry and exit are easy, and input prices are constant, then the long-run market supply curve is flat at minimum average cost. If firms differ, entry is difficult or costly, or input prices increase with output, the long-run market supply curve has an upward slope. The long-run market equilibrium price and quantity may be different from the short-run price and quantity.

4. Competition Maximizes Economic Well- Being. Perfect competition maximizes a commonly used measure of economic well-being, total surplus. Total surplus is the monetary value of the gain from trade. It is the sum of consumer surplus and producer surplus. Consumer surplus is the economic benefit or well-being obtained by a consumer in excess of the price paid. It equals the area under the consum- er’s demand curve above the market price up to the quantity that the consumer buys. Producer surplus is the amount producers are paid over and above the minimum amount needed to induce them to produce a given output level. A firm’s producer surplus is its revenue minus the variable cost of production. Thus, if a firm has no fixed costs, as often occurs in the long run, a firm’s producer surplus is the same as profit. In the short run, a firm’s producer surplus is greater than profit by an amount equal to unavoidable fixed cost. Producer surplus is the area below the price and above the supply curve up to the quantity that the firm sells.

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262 CHAPTER 8 Competitive Firms and Markets

QUESTIONS

1. Perfect Competition 1.1 According to Bustle.com, San Francisco has the most

coffee shops of any American city (as of April 2016) with 2,613, with new shops opening regularly as the population grows. Suppose the city decides to stop issuing new business licenses for coffee shops so that the industry is capped at its current number of establishments. Which characteristics of this market are consistent with perfect competition and which are not? Is the coffee shop market likely to be nearly perfectly competitive? Why or why not?

*1.2 Why would high transaction costs or imperfect information tend to prevent price-taking behavior?

1.3 Economists often use the model of perfect competi- tion to analyze the effect of economic shocks in par- ticular industries. Which of the following industries is best approximated by perfect competition: agri- culture, aircraft manufacturing, and social media (such as Facebook and Twitter)? Explain briefly.

2. Competition in the Short Run 2.1 A firm claims on its website that it has been in the

same location for over 50 years and has lower over- head than other firms because it bought the land 50 years ago when it was inexpensive. It also claims that it charges lower prices than competitors because of its lower overhead. Discuss the logic of these claims.

*2.2 Many marginal cost curves are U-shaped. As a result, it is possible that the MC curve hits the demand or price line at two output levels. Which is the profit- maximizing output? Why?

2.3 Initially, the market price was p = $50, and the com- petitive firm’s minimum average variable cost was $42 while is minimum average cost was $54. Should it shut down? Why or why not? Now suppose the firm’s average variable cost increases by $9 at every quantity, while other firms in the market are unaf- fected. What happens to its average cost? Should the firm shut down now? Why or why not?

2.4 Should a firm shut down if its revenue is R = $1,500 per week and:

a. its variable cost is VC = $1,100 and its sunk fixed cost is F = $800?

b. its variable cost is VC = $1,600 and its sunk fixed cost is F = $600?

c. its variable cost is VC = $1,100 and its fixed cost is F = $1000 ($800 of which is avoidable if it shuts down?

*2.5 The cost function for Acme Laundry is C(q) = 10 + 10q + q2, so its marginal cost function is MC = 10 + 2q, where q is tons of laundry cleaned. Derive the firm’s average cost and average variable cost curves. What q should the firm choose so as to maximize its profit if the market price is p? How much does it produce if the competitive market price is p = 50?

2.6 Beta Laundry’s cost function is C(q) = 50 + 10q + 2q2.

a. What quantity maximizes Beta’s profit if the market price is p? How much does it produce if p = $70?

b. If the government imposes a specific tax of t = $4, what quantity maximizes Beta’s after- tax profit? Does it operate or shut down? (Hint: See Q&A 8.1.) C

2.7 If the pre-tax cost function for John’s Shoe Repair is C(q) = 100 + 10q - q2 + 13 q3, and it faces a specific tax of t = 10, what is its profit-maximizing condi- tion if the market price is p? Can you solve for a single, profit-maximizing q in terms of p? (Hint: See Q&A 8.1.) C

2.8 If a specific subsidy (negative tax) of s is given to only one competitive firm, how should that firm change its output level to maximize its profit, and how does its maximum profit change? Use a graph to illustrate your answer. (Hint: See Q&A 8.1.)

2.9 In 2015, the average variable cost of producing wheat in Canada was close to $5.00 per bushel. Sup- pose that technological progress reduces the aver- age variable cost to $4.00 per bushel. Use a figure to show how this change affects the supply curve of a typical competitive firm and the supply curve of all the firms in the market.

2.10 Fierce storms in October 2004 caused TomatoFest Organic Heirlooms Farm to end its tomato harvest two weeks early. According to Gary Ibsen, a partner in this small business (Carolyn Said, “Tomatoes in Trou- ble,” San Francisco Chronicle, October 29, 2004, C1, C2), TomatoFest lost about 20,000 pounds of tomatoes that would have sold for about $38,000; however, because he did not have to hire pickers and rent trucks during these two weeks, his net loss was about $20,000. In calculating the revenue loss, he used the post-storm price, which was double the pre-storm price.

a. Draw a diagram for a typical firm next to one for the market to show what happened as a result of

All exercises are available on MyLab Economics; * = answer at the back of this book; C = use of calculus may be necessary; = this exercise is available in Excel Grader in MyLab Economics.

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263Questions

the storm. Assume that TomatoFest’s experience was typical of that of many small tomato farms.

b. Did TomatoFest suffer an economic loss? What extra information (if any) do you need to answer this question? How do you define “economic loss” in this situation?

2.11 The internet is affecting holiday shipping. In years past, the busiest shipping period was Thanksgiv- ing week. Now, as people have become comfortable with e-commerce, they purchase later in the year and are more likely to have gifts shipped (rather than purchasing locally). FedEx, along with Ama- zon and other e-commerce firms, hires extra workers during this period, and many regular workers log substantial overtime hours.

a. Are the marginal and average costs of inter- net retailers likely to rise or fall with this extra business? (Discuss economies of scale and the slopes of marginal and average cost curves.)

b. Use side-by-side firm-market diagrams to show the effects on the number of firms, equilibrium price and output, and profits of such a seasonal shift in demand for e-retailers in both the short run and the long run. Explain your reasoning.

2.12 What is the effect on the short-run equilibrium of a specific subsidy of s per unit that is given to all n firms in a market?

3. Competition in the Long Run 3.1 Customers at California grocery and drug stores

must pay an extra 10¢ for every paper bag the store provides (the store keeps this fee). Does such a charge affect the marginal cost of any particular good? If so, by how much? Is this fee likely to affect the overall amount that consumers pay for groceries?

*3.2 What are the short-run and long-run effects on firm and market equilibrium of the U.S. law requiring a firm to give its workers six months’ notice before it can shut down its plant?

3.3 The Mini-Case “An Upward-Sloping Long-Run Supply Curve for Cotton” shows a supply curve for cotton. Discuss the equilibrium if the world demand curve crosses this supply curve in either (a) a flat section labeled Brazil or (b) the vertical section that follows it. What do cotton farms in the United States do?

3.4 Chinese art factories are flooding the world’s generic art market (Keith Bradsher, “Own Original Chinese Copies of Real Western Art!” New York Times, July 15, 2005). The value of bulk shipments of Chinese paint- ings to the United States nearly tripled from slightly over $10 million in 1996 to $30.5 million in 2004 (and early 2005 sales were up 50% from the correspond- ing period in 2004). A typical artist earns less than

$200 a month, plus modest room and board, or $360 a month without food and housing. Using a step- like supply function (similar to the one in the Mini- Case “An Upward-Sloping Long-Run Supply Curve for Cotton”), show how the entry of the Chinese producers affects the world supply curve and how this change affects the equilibrium (including who produces art). Explain.

3.5 Oil spills such as BP’s huge 2010 oil spill in the Gulf of Mexico and the 2015 Plains All American Pipeline oil spill into the ocean near Santa Barbara, California, led to clean-up efforts that greatly increased purchases of boat services, various oil-absorbing materials, and other goods and services to minimize damage from the spill. Use side-by-side firm and market diagrams to show the effects (number of firms, price, output, profits) of such a shift in demand in one such indus- try, such as boat services, in both the short run and the long run. Explain how your answer depends on whether the shift in demand is expected to be tem- porary or permanent.

3.6 In late 2004 and early 2005, the price of raw coffee beans jumped as much as 50% from the previous year. In response, the price of roasted coffee rose about 14%. Similarly, in late 2014 and early 2015, the price of raw beans fell by about 25%, yet the price of roasted coffee fell by only a few percentage points. Why did the roasted coffee price change less than in proportion to the rise in the cost of raw beans?

3.7 When the voters of Oakland, California, passed a measure to tax medical marijuana, effectively legaliz- ing it, its City Council adopted regulations permitting industrial-scale marijuana farms with no size limits but requiring each to pay a $211,000 per year fee. One proposal called for a 100,000 square foot farm, the size of two football fields. Prior to this legalization, only individuals could grow marijuana. These small farm- ers complained bitterly, arguing that the large firms would drive them out of the industry they helped to build due to economies of scale. Draw a figure to illus- trate the situation. Under what conditions (concern- ing relative costs, characteristics of the demand curve, number of low-cost firms, or other) would the smaller, higher-cost growers be driven out of business?

3.8 A typical firm in long-run equilibrium in an indus- try with identical firms has a cost function given by C = 800 + 2q2 and has a marginal cost function of MC = 4q. The fixed cost of 800 is avoidable if the firm shuts down. What is the equilibrium price? (Hint: See Q&A 8.3.)

3.9 Given the cost information in the previous ques- tion and a demand function of Q = 2,400 - 5p, how many firms are in this industry in the long-run equilibrium?

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264 CHAPTER 8 Competitive Firms and Markets

4. Competition Maximizes Economic Well-Being 4.1 Using the information in panel a of Figure 8.8, deter-

mine what happens to David’s quantity demanded and consumer surplus if price falls to p = $1.

*4.2 If the inverse demand function for toasters is p = 60 - Q, what is the consumer surplus when the price is 30?

4.3 Access to Twitter is free, but Brynjolfsson et al. (2018) found that many Twitter users would be willing to pay for access. Draw a demand curve for Twitter. Show the consumer surplus at the current price of zero. (Hint: See the Mini-Case “Digital Surplus.”)

4.4 For a firm, how does the concept of producer surplus differ from that of profit if it has no fixed costs? (Hint: See Q&A 8.4.)

*4.5 Using a graph similar to Figure 8.11, show that increas- ing output beyond the competitive level decreases total surplus because the cost of producing this extra output exceeds the value consumers place on it.

4.6 If the supply function is Q = -50 + 5p, what is the producer surplus if the price is $40? (Hint: See Q&A 8.5.)

4.7 Nicholas owned no green sweaters, so his Aunt Fern gave him one for his 21st birthday. However, the market price of the sweater was higher than his will- ingness to pay for it. Draw a diagram showing Nich- olas’s demand curve for green sweaters and identify and explain the deadweight loss. (Hint: See the Mini- Case “The Deadweight Loss of Holiday Gifts.”)

4.8 The government sets a minimum wage above the current equilibrium wage. What effect does the minimum wage have on the market equilibrium? What are its effects on consumer surplus, producer surplus, and total surplus? Who are the consumers and who are the producers? (Hint: See Q&A 8.6.)

4.9 Suppose that the demand curve for wheat is Q = 100 - 10p and the supply curve is Q = 10p. The government imposes a price ceiling of p = 3. (Hint: See Q&A 8.6.)

a. Describe how the equilibrium changes.

b. What effect does this price ceiling have on con- sumer surplus, producer surplus, and dead- weight loss?

5. Managerial Problem 5.1 The North American Free Trade Agreement pro-

vides for two-way, long-haul trucking across the U.S.–Mexican border. U.S. truckers have objected,

arguing that the Mexican trucks don’t have to meet the same environmental and safety standards as U.S. trucks. They are concerned that the combination of these lower fixed costs and lower Mexican wages will result in Mexican drivers taking business from them. Their complaints have delayed implementa- tion of this agreement (except for a small pilot pro- gram during the Bush administration, which ended during the Obama administration). What would be the short-run and long-run effects of allowing entry of Mexican drivers on market price and quantity and on the number of U.S. truckers?

5.2 In the Managerial Solution, would it make a differ- ence to the analysis whether the government collects lump-sum costs such as registration fees annually or only once when the firm starts operation? How would each of these franchise taxes affect the firm’s long-run supply curve? Explain your answer.

5.3 Give an answer to the Managerial Problem for the short run rather than for the long run. (Hint: The answer depends on where the demand curve inter- sects the original short-run supply curve.)

5.4 In a perfectly competitive market, all firms are iden- tical, firms can freely enter and exit, and the mar- ket has an unlimited number of potential entrants. Now, the government starts collecting a specific tax t. What is the effect on the long-run equilibrium market quantity, market price, and the quantity for an individual firm?

6. MyLab Economics Spreadsheet Exercises18

6.1 A competitive firm’s cost of producing q units of output is C = 18 + 4q + q2. Its corresponding mar- ginal cost is MC = 4 + 2q.

a. The firm faces a market price p = $24. Create a spreadsheet with q = 0, 1, 2, … , 15, where the columns are q, R, C, VC, AVC, MC, and profit. Determine the profit-maximizing output for the firm and the corresponding profit. Should the firm produce this level of output or should it shut down? Explain briefly. (Hint: See Q&A 8.2.)

b. Suppose the competitive price declines to p = $12. Repeat the calculations of part a. Should the firm shut down?

6.2 The long-run average cost curve for a competitive firm is AC = 35 - 10q + q2.

a. Use the Excel Solver tool to find the cost- minimizing quantity. Enter the labels q and AC in cells A1 and B1. Enter the formula for AC in

18The spreadsheet exercises in this chapter are based largely on the work of Satyajit Ghosh, in cooperation with the authors. The answers are available on MyLab Economics.

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265Questions

cell B2. Select the Data tab, then select the Solver tool.19 A dialog box will appear. Enter B2 in the Set Objective row, select Min, and enter A2 in the “By Changing Variable Cells” row. Then select Solve. What is the cost-minimizing quantity? What is AC at this quantity?

b. This firm is one of many identical firms in a competitive industry that is in long run equi- librium. The market demand function for this industry is Q = 620 - 8p. Use Excel to deter- mine the industry quantity. (Hint: The long-run supply curve is horizontal at the minimum of the average cost of a typical firm.)

c. How many firms are in this industry in the long-run competitive equilibrium?

6.3 In a competitive market, the market demand curve is Q = 28 - 2p and the market supply curve is

19If you do not see the Solver tool, you need to load it first. Look up Solver in the Excel help facility for instructions.

Qs = -8 + 2p. Use a spreadsheet to answer the fol- lowing questions.

a. Determine the quantity demanded and quan- tity supplied for p = $4, 5, 6, … , 14. Determine the equilibrium quantity and price.

b. For prices p = $4, 5, 6, … , 14, determine the consumer surplus. How does an increase in price affect the consumer surplus?

c. For prices p = $4, 5, 6, … , 14, determine the producer surplus. How does an increase in price affect the producer surplus?

d. Suppose the government limits the quantity traded in the market to 6 units. Calculate the resulting deadweight loss.

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9 Monopoly Monopoly: one parrot.

A firm that creates a new drug may receive a patent that gives it the right to be the monopoly or sole producer of that drug for up to 20 years. As a result, the firm can charge a price much greater than its marginal cost of production. For example, one of the world’s best-selling drugs, the heart medication Plavix, sold for about $7 per pill, though it cost only about 3¢ per pill to produce. A new drug to treat hepatitis C, Harvoni, sells for over $1,000 a pill or over $84,000 for a 12-week course of treatment. In 2015, Martin Shkreli, then the head of Turing Pharmaceuticals, raised the price of Daraprim, used to treat infections that are common in HIV/AIDS patients, from $13.50 to $750 per pill. Its price rose to as high at $800 by 2018. Shkreli acknowledged that the drug costs “very little money” to make.

Every year, many pharmaceuticals lose their patent protection, as Plavix has. In 2018, patents for Apidra (diabetes), Ampyra (multiple sclerosis), Lyrica (nerve and muscle pain), and many other high-revenue drugs expired. In 2019, patent protec- tion for Avastin (cancer), Azasite (bacterial eye infections), Ranexa (heart disease),

and others end. Generally, when a patent for a highly prof-

itable drug expires, competing firms enter the market and sell generic (equivalent) versions of the brand-name drug. Generics’ share of all U.S. prescriptions rose from about 18% in 1984 to nearly 80% currently.

When the U.S. Congress originally passed a law permitting generic drugs to quickly enter a market after a patent expires, it expected that patent expiration would subsequently lead to sharp declines in drug prices.1 If consumers view the generic product and the brand-name product as perfect substitutes, both goods will sell for the same price, and entry by many firms will drive the price down to the competitive level. Even if consumers view the goods as imperfect substitutes, one might expect the price of the brand-name drug to fall.

1Under the 1984 Hatch-Waxman Act, the U.S. government allows a firm to sell a generic product after a brand-name drug’s patent expires if the generic-drug firm can prove that its product deliv- ers the same amount of active ingredient or drug to the body in the same way as the brand-name product. Sometimes the same firm manufactures both a brand-name drug and an equivalent generic drug, so the two have identical ingredients. Generics produced by other firms usually have a differ- ent appearance and name than the original product and may have different nonactive ingredients, but they have identical amounts of the active ingredients.

Brand-Name and Generic Drugs

Managerial Problem

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267CHAPTER 9 Monopoly

Why can a firm with a patent-based monopoly charge a high price? Why might a brand-name pharmaceutical’s price rise after its patent expires? To answer these questions, we need to understand the decision-making pro- cess for a monopoly: the sole supplier of a good that has no close substitute.3

Monopolies have been common since ancient times. In the fifth century b.c., the Greek philosopher Thales gained control of most of the olive presses during a year of exceptionally productive harvests. The ancient Egyptian pharaohs controlled the sale of food. In England, until Parliament limited the practice in 1624, kings granted monopoly rights called royal charters to court favorites. Particularly valuable royal charters went to companies that controlled trade with North America, the Hudson Bay Company, and with India, the British East India Company.

In modern times, government actions continue to play an important role in creat- ing monopolies. Governments grant patents that allow the inventor of a new prod- uct, such as a new drug, to be the sole supplier of that product for up to 20 years, and sometimes grant monopoly rights for other reasons as well. Many utilities— water, gas, and electricity—are government-owned or government-protected monopolies.4

Some firms are able to gain monopoly power without government help. When first introduced, Apple’s iPad had a near monopoly in the tablet market.

Unlike a competitive firm, which is a price taker (Chapter 8), a monopoly can set its price. A monopoly’s output is the market output, and the demand curve a monopoly faces is the market demand curve. Because the market demand curve is downward sloping, the monopoly (unlike a competitive firm) doesn’t lose all its sales if it raises its price. As a consequence, a profit-maximizing monopoly sets its price above marginal cost, the price that would prevail in a competitive market. Consumers buy less at this relatively high monopoly price than they would at the competitive price.

3Analogously, a monopsony is the only buyer of a good in a given market. 4Whether the law views a firm as a monopoly depends on how broadly the market is defined. Is the market limited to a particular drug or the pharmaceutical industry as a whole? The manufacturer of the drug is a monopoly in the former case, but just one of many firms in the latter case. Thus, defining a market is critical in legal cases. A market definition depends on whether other products are good substitutes for those in that market.

However, the prices of many brand-name drugs have increased after their pat- ents expired and generics entered the market. The generic drugs are relatively inexpensive, but the brand-name drugs often continue to enjoy a significant market share and sell for high prices. Regan (2008) studied the effects of generic entry on post-patent price competition for 18 prescription drugs, and found an average 2% increase in brand-name prices. Studies based on older data have found up to a 7% average increase. Why do some brand-name prices rise after the entry of generic drugs?2

2The sources for this Challenge and the Applications in this chapter are listed at the end of this chapter.

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268 CHAPTER 9 Monopoly

9.1 Monopoly Profit Maximization All firms, including competitive firms and monopolies, maximize their profits by setting quantity such that marginal revenue equals marginal cost (Chapter 7). Chapter 6 demonstrates how to derive a marginal cost curve. We now derive the monopoly’s marginal revenue curve and then use the marginal revenue and marginal cost curves to examine how the manager of a monopoly sets quantity to maximize profit.

Marginal Revenue A firm’s marginal revenue curve depends on its demand curve. We will show that a monopoly’s marginal revenue curve lies below its demand curve at any positive quantity because its demand curve is downward sloping.

Marginal Revenue and Price. A firm’s demand curve shows the price, p, it receives for selling a given quantity, q. The price is the average revenue the firm receives, so a firm’s revenue is R = pq.

A firm’s marginal revenue, MR, is the change in its revenue from selling one more unit. A firm that earns ∆R more revenue when it sells ∆q extra units of output has a marginal revenue of

MR = ∆R ∆q

.

If the firm sells exactly one more unit ( ∆q = 1), then its marginal revenue, MR, is ∆R( = ∆R>1).

The marginal revenue of a monopoly differs from that of a competitive firm because the monopoly faces a downward-sloping demand curve, unlike the com- petitive firm. The competitive firm in panel a of Figure 9.1 faces a horizontal demand curve at the market price, p1. Because its demand curve is horizontal, the competi- tive firm can sell another unit of output without reducing its price. As a result, the marginal revenue it receives from selling the last (and every) unit of output is the market price.

Initially, the competitive firm sells q units of output at the market price of p1, so its revenue, R1, is area A, which is a rectangle that is p1 * q. If the firm sells one more unit, its revenue is R2 = A + B, where area B is p1 * 1 = p1. The competitive firm’s marginal revenue equals the market price:

∆R = R2 - R1 = (A + B) - A = B = p1.

Learning Objectives

1. Show how a monopoly chooses an output level to maximize its profit.

2. Calculate the extent of a monopoly’s market power.

3. Describe how monopoly causes a market failure.

4. List the causes of monopoly.

5. Explain how a monopoly uses advertising to increase its profit.

6. Discuss the sources of market power for internet firms.

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2699.1 Monopoly Profit Maximization

A monopoly faces a downward-sloping market demand curve, as in panel b of Figure 9.1. So far, we have used q to represent the output of a single firm and Q to represent the combined market output of all firms in a market. Because a monopoly is the only firm in the market, q and Q are identical, so we use Q to describe both the firm’s output and market output.

The monopoly, which initially sells Q units at p1, can sell one extra unit only if it lowers its price to p2 on all units. The monopoly’s initial revenue, p1 * Q, is R1 = A + C. When it sells the extra unit, its revenue, p2 * (Q + 1), is R2 = A + B. Thus, its marginal revenue is

∆R = R2 - R1 = (A + B) - (A + C) = B - C.

The monopoly sells the extra unit of output at the new price, p2, so its extra rev- enue is B = p2 * 1 = p2. The monopoly loses the difference between the original price and the new lower price, ∆p = (p1 - p2), on the Q units it originally sold: C = ∆p * Q. Therefore the monopoly’s marginal revenue, B - C = p2 - C, is less than the price it charges by an amount equal to area C.

Because the competitive firm in panel a can sell as many units as it wants at the market price, it does not have to cut its price to sell an extra unit, so it does not have to give up revenue such as area C in panel b. It is the downward slope of the monopoly’s demand curve that causes its marginal revenue to be less than its price. For a monopoly to sell one more unit in a given period, it must lower the price on all

FIGURE 9.1 Average and Marginal Revenue

p , $

p er

u ni

t

q q + 1 q, Units per year

p1

(a) Competitive Firm

Demand curve

A B

Q Q + 1 Q, Units per year

p1

p2

p, $

p er

u ni

t

(b) Monopoly

Demand curve

A B

C

Revenue with One More Unit,

R2 Initial Revenue,

R1 Marginal Revenue,

R2 – R1

Competition A A + B B = p1 Monopoly A + C A + B B – C = p2 − C

The demand curve shows the average revenue or price per unit of output sold. (a) The competitive firm’s marginal revenue, area B, equals the market price, p1.

(b) The monopoly’s marginal revenue is less than the price p2 by area C, the revenue lost due to a lower price on the Q units originally sold.

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270 CHAPTER 9 Monopoly

the units it sells that period, so its marginal revenue is less than the price obtained for the extra unit. The marginal revenue is this new price minus the loss in revenue arising from charging a lower price for all other units sold.

The Marginal Revenue Curve. Thus, the monopoly’s marginal revenue curve lies below a downward-sloping demand curve at every positive quantity. The relation- ship between the marginal revenue and demand curves depends on the shape of the demand curve.

For linear demand curves, the marginal revenue curve is a straight line that starts at the same point on the vertical (price) axis as the demand curve but has twice the slope. Therefore, the marginal revenue curve hits the horizontal (quantity) axis at half the quantity at which the demand curve hits the quantity axis. In Figure 9.2, the demand curve has a slope of -1 and hits the horizontal axis at 24 units, while the marginal revenue curve has a slope of -2 and hits the horizontal axis at 12 units.

We now derive an equation for the monopoly’s marginal revenue curve. For a monopoly to increase its output by one unit, the monopoly lowers its price per unit by an amount indicated by the demand curve, as panel b of Figure 9.1 illustrates. Specifically, output demanded rises by one unit if price falls by the slope of the demand curve, ∆p>∆Q. By lowering its price, the monopoly loses ( ∆p>∆Q) * Q on the units it originally sold at the higher price (area C), but it earns an additional p on the extra output it now sells (area B). Thus, the monopoly’s marginal revenue is

MR = p + ∆p ∆Q

Q. (9.1)

FIGURE 9.2 Elasticity of Demand and Total, Average, and Marginal Revenue

p, $

p er

u ni

t

Demand (p = 24 – Q )

Perfectly elastic, « –`

Perfectly inelastic, « = 0

Elastic, « < –1

Inelastic, –1 < « < 0

« = –1

Dp = –1

DQ = 1DQ = 1

DMR = –2

Q, Units per day

24

12

0 12 24

Marginal Revenue (MR = 24 – 2Q )

The demand curve (or average revenue curve), p = 24 - Q, lies above the marginal revenue curve, MR = 24 - 2Q. Where the marginal revenue equals

zero, Q = 12, the elasticity of demand is e = -1. For larger quantities, the marginal revenue is negative, so the MR curve is below the horizontal axis.

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2719.1 Monopoly Profit Maximization

Because the slope of the monopoly’s demand curve, ∆p>∆Q, is negative, the last term in Equation 9.1, ( ∆p>∆Q)Q, is negative. Equation 9.1 confirms that the price the monopoly charges is greater than the marginal revenue, which equals p plus a negative term and must therefore be less than the price.

We now use Equation 9.1 to derive the marginal revenue curve when the monop- oly faces the linear inverse demand function (Chapter 3)

p = 24 - Q (9.2)

that Figure 9.2 illustrates. Equation 9.2 shows that the price consumers are willing to pay falls $1 if quantity increases by one unit. More generally, if quantity increases by ∆Q, price falls by ∆p = - ∆Q. Thus, the slope of the demand curve is ∆p>∆Q = -1.

We obtain the marginal revenue function for this monopoly by substituting into Equation 9.1 the actual slope of the demand function, ∆p>∆Q = -1, and replacing p with 24 - Q (using Equation 9.2):

MR = p + ∆p ∆Q

Q = (24 - Q) + ( -1)Q = 24 - 2Q. (9.3)

Figure 9.2 shows a plot of Equation 9.3. The slope of this marginal revenue curve is ∆MR>∆Q = -2, so the marginal revenue curve is twice as steep as the demand curve.

Deriving a Monopoly’s Marginal Revenue Function

Using Calculus Using calculus, if a firm’s revenue function is R(Q), then its marginal revenue function is

MR(Q) = dR(Q)

dQ .

For our example, where the inverse demand function is p(Q) = 24 - Q, the revenue function is

R(Q) = p(Q)Q = (24 - Q)Q = 24Q - Q2. (9.4)

By differentiating Equation 9.4 with respect to Q, we obtain the marginal revenue function, MR(Q) = dR(Q) >dQ = 24 - 2Q, which is the same as Equation 9.3.

Q&A 9.1 Given a general linear inverse demand function p(Q) = a - bQ, where a and b are positive constants, use calculus to show that the marginal revenue curve is twice as steeply sloped as the demand curve. (Hint: Recall that this linear inverse demand function corresponds to a linear demand curve with a price intercept a and a slope equal to the derivative of the inverse demand function with respect to quantity.)

Answer 1. Differentiate the inverse linear demand function with respect to Q to determine its

derivative, which is the slope of the demand curve. The derivative of the linear inverse demand function with respect to Q is

dp(Q)

dQ =

d(a - bQ) dQ

= -b.

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272 CHAPTER 9 Monopoly

Marginal Revenue and Price Elasticity of Demand. The marginal revenue at any given quantity depends on the demand curve’s height (the price) and shape. The shape of the demand curve at a particular quantity is described by the price elasticity of demand (Chapter 3), e = ( ∆Q>Q) > ( ∆p>p) 6 0, which tells us the percentage by which quantity demanded falls as the price increases by 1%.

At a given quantity, the marginal revenue equals the price times a term involving the elasticity of demand (Chapter 3):5

MR = pa1 + 1 e b . (9.5)

According to Equation 9.5, marginal revenue is closer to price as demand becomes more elastic. Where the demand curve hits the price axis (Q = 0), the demand curve is perfectly elastic, so the marginal revenue equals price: MR = p.6 Where the demand elasticity is unitary, e = -1, marginal revenue is zero: MR = p[1 + 1> ( -1)] = 0. Marginal revenue is negative where the demand curve is inelastic, -1 6 e … 0.

With the inverse demand function in Equation 9.2, ∆Q>∆p = -1, so the elas- ticity of demand is e = ( ∆Q>∆p) (p>Q) = -p>Q. Table 9.1 shows the relationship among quantity, price, marginal revenue, and elasticity of demand for this linear example. As Q approaches 24, e approaches 0, and marginal revenue is negative. As Q approaches zero, the demand becomes increasingly elastic, and marginal revenue approaches the price.

5By multiplying the last term in Equation 9.1 by p>p ( = 1) and using algebra, we can rewrite the expression as

MR = p + p ∆p ∆Q

Q p

= p c 1 + 1 ( ∆Q > ∆p) (p>Q) d .

The last term in this expression is 1>e, because e = ( ∆Q>∆p) (p>Q). 6As e approaches -∞ (perfectly elastic demand), the 1>e term approaches zero, so MR = p (1 + 1>e) approaches p.

2. Differentiate the monopoly’s revenue function with respect to Q to obtain the marginal revenue function; then differentiate the marginal revenue function with respect to Q to determine its slope. The monopoly’s revenue function is R(Q) = p(Q)Q = (a - bQ)Q = aQ - bQ2. Differentiating the revenue func- tion with respect to quantity, we find that the marginal revenue function is linear,

MR(Q) = dR(Q) >dQ = a - 2bQ. The marginal revenue curve that corresponds to this marginal revenue func- tion has a slope of

dMR(Q) dQ

= -2b,

which is twice the slope of the demand curve, dp>dQ = -b. Comment: Note that the vertical axis intercept is a for both the demand curve and the MR curve and that the marginal revenue curve, like the demand curve, is linear. The marginal revenue curve is twice as steep as the demand curve.

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2739.1 Monopoly Profit Maximization

Choosing Price or Quantity Any firm maximizes its profit by operating where its marginal revenue equals its marginal cost. Unlike a competitive firm, a monopoly can adjust its price, so it has a choice of setting its price or its quantity to maximize its profit. (A competitive firm sets its quantity to maximize profit because it cannot affect the market price.)

Whether the monopoly sets its price or its quantity, the other variable is deter- mined by the market demand curve. Because the demand curve slopes down, the monopoly faces a trade-off between a higher price and a lower quantity or a lower price and a higher quantity. A profit-maximizing monopoly chooses the point on the demand curve that maximizes its profit. Unfortunately for the monopoly, it can- not set both its quantity and its price, such as at a point that lies above its demand curve. If it could do so, the monopoly would choose an extremely high price and an extremely large output and would earn a very high profit. However, the monopoly cannot choose a point that lies above the demand curve.

If the monopoly sets its price, the demand curve determines how much output it sells. If the monopoly picks an output level, the demand curve determines the price. Because the monopoly wants to operate at the price and output at which its profit is maximized, it chooses the same profit-maximizing solution whether it sets the price or quantity. Thus, setting price and setting quantity are equivalent for a monopoly. In the following discussion, we assume that the monopoly sets quantity.

Quantity, Q Price, p Marginal Revenue,

MR Elasticity of Demand,

� = −p>Q 0 24 24 - ∞

m or

e el

as ti

c

c 1 23 22 -23

2 22 20 -11

3 21 18 -7

4 20 16 -5

5 19 14 -3.8

6 18 12 -3

7 17 10 -2.43

8 16 8 -2

T

le ss

e la

st ic

9 15 6 -1.67

10 14 4 -1.4

11 13 2 -1.18

12 12 0 −1

13 11 -2 -0.85 f f f f

23 1 -22 -0.043

24 0 -24 0

TABLE 9.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Function p = 24 − Q

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274 CHAPTER 9 Monopoly

Two Steps to Maximizing Profit All profit-maximizing firms, including monopolies, use a two-step analysis to deter- mine the output level that maximizes their profit (Chapter 7). First, the firm deter- mines the output, Q*, at which it makes the highest possible profit (or minimizes its loss). Second, the firm decides whether to produce Q* or shut down.

Profit-Maximizing Output. In Chapter 7, we saw that profit is maximized where marginal profit equals zero. Equivalently, because marginal profit equals marginal revenue minus marginal cost (Chapter 7), marginal profit is zero where marginal revenue equals marginal cost.

To illustrate how a monopoly chooses its output to maximize its profit, we use the same linear demand and marginal revenue curves as above and add a linear marginal cost curve in panel a of Figure 9.3. Panel b shows the corresponding profit curve.

The marginal revenue curve, MR, intersects the marginal cost curve, MC, at 6 units in panel a. The corresponding price, 18, is the height of the demand curve, point e, at 6 units. The profit, π, is the gold rectangle. The height of this rectangle is the average profit per unit, p - AC = 18 - 8 = 10. The length of the rectangle is 6 units. Thus, the area of the rectangle is the average profit per unit times the number of units, which is the profit, π = 60.

FIGURE 9.3 Maximizing Profit

12

18

24

8

6

60

60 12 24

p , $

0 126

AC

AVC e

Demand

p = 60

MC

MR

Q, Units per day

Profit, p

Q, Units per day

p, $

p er

u ni

t

(a) Monopolized Market

(b) Profit

(a) At Q = 6, where marginal revenue, MR, equals marginal cost, MC, profit is maximized. The rectangle shows that the profit is $60, where the height of the rectangle is the average profit per unit, p - AC = $18 - $8 = $10, and the length is the number of units, 6. (b) Profit is maximized at Q = 6 (where marginal revenue equals marginal cost).

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2759.1 Monopoly Profit Maximization

The profit at 6 units is the maximum possible profit: The profit curve in panel b reaches its peak, 60, at 6 units. At the peak of the profit curve, the marginal profit is zero, which is consistent with the marginal revenue equaling the marginal cost.

Why does the monopoly maximize its profit by producing where its marginal revenue equals its marginal cost? At smaller quantities, the monopoly’s marginal revenue is greater than its marginal cost, so its marginal profit is positive—the profit curve is upward sloping. By increasing its output, the monopoly raises its profit. Similarly, at quantities greater than 6 units, the monopoly’s marginal cost is greater than its marginal revenue, so its marginal profit is negative, and the monopoly can increase its profit by reducing its output.

As Figure 9.2 illustrates, the marginal revenue curve is positive where the elastic- ity of demand is elastic, is zero at the quantity where the demand curve has a unitary elasticity, and is negative at larger quantities where the demand curve is inelastic. Because the marginal cost curve is never negative, the marginal revenue curve can only intersect the marginal cost curve where the marginal revenue curve is positive, in the range in which the demand curve is elastic. That is, a monopoly’s profit is maxi- mized in the elastic portion of the demand curve. In our example, profit is maximized at Q = 6, where the elasticity of demand is -3. A profit-maximizing monopoly never operates in the inelastic portion of its demand curve.

The Shutdown Decision. A monopoly shuts down to avoid making a loss in the short run if its price is below its average variable cost at its profit-maximizing (or loss-minimizing) quantity (Chapter 7). In the long run, the monopoly shuts down if the price is less than its average cost.

In the short-run example in Figure 9.3, the average variable cost, AVC = 6, is less than the price, p = 18, at the profit-maximizing output, Q = 6, so the monopoly chooses to produce. Because the price is also above the average cost at Q = 6, the average profit per unit, p - AC, (the height of the gold profit rectangle), is positive, so the monopoly makes a positive profit.

Solving for the Profit-Maximizing Output

Using Calculus We can also solve for the profit-maximizing quantity mathematically. We already know the demand and marginal revenue functions for this monopoly. We need to determine its cost curves.

The monopoly’s cost is a function of its output, C(Q). In Figure 9.3, we assume that the monopoly faces a short-run cost function of C(Q) = 12 + Q2, (9.6)

where Q2 is the monopoly’s variable cost as a function of output and 12 is its fixed cost. Given this cost function, Equation 9.6, the monopoly’s marginal cost function is

dC(Q)

dQ = MC(Q) = 2Q. (9.7)

This marginal cost curve in panel a is an upward sloping straight line through the origin with a slope of 2. The average variable cost is AVC = Q2>Q = Q, so it is an upward sloping straight line through the origin with a slope of 1. The average cost is AC = C>Q = (12 + Q2) >Q = 12>Q + Q, which is U-shaped.

Using Equations 9.4 and 9.6, we can write the monopoly’s profit as

π(Q) = R(Q) - C(Q) = (24Q - Q2) - (12 + Q2).

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276 CHAPTER 9 Monopoly

By setting the derivative of this monopoly’s profit function with respect to Q equal to zero, we have an equation that determines the profit-maximizing output:

dπ(Q)

dQ =

dR(Q) dQ

- dC(Q)

dQ = MR - MC

= (24 - 2Q) - 2Q = 0.

Thus, MR = 24 - 2Q = 2Q = MC. To determine the profit-maximizing output, we solve this equation and find that Q = 6. Substituting Q = 6 into the inverse demand function (Equation 9.2), we learn that the profit-maximizing price is

p = 24 - Q = 24 - 6 = 18.

Q&A 9.2 When the iPad was introduced, Apple’s constant marginal cost of producing its top-of-the-line iPad was about $220, its fixed cost was $2,000 million (= $2  billion), and we estimate that its inverse demand function was p = 770 - 11Q, where Q is the millions of iPads purchased.7 What was Apple’s average cost function? What was its marginal revenue function? What were its profit-maximizing price and quantity? What was its profit? Show Apple’s profit-maximizing solution in a figure.

7See the Mini-Case “Apple’s iPad” in the Sources at the end of this book for details on these estimates.

Mini-Case

Apple’s iPad

Apple’s iPad was the first commercially successful tablet. Users interact with the iPad using Apple’s multi-touch, finger-sensitive touchscreen (rather than the pressure-triggered stylus that most previous tablets used) and a virtual onscreen keyboard (rather than a physical one). Most importantly, the iPad offers an intui-

tive interface and is well integrated with Apple’s iTunes, eBooks, and various application programs.

People loved the original iPad. Even at $499 for the basic model, Apple had a virtual monopoly in its first year in 2010, with 87% of the tablet market. Moreover, the other tablets available in 2010 were not viewed by most consumers as close substi- tutes. Apple reported that it sold 25 million iPads worldwide in its first full year.

Unfortunately for Apple, its monopoly was short lived. Within a year of the iPad’s introduc- tion, over a hundred iPad want-to-be tablets were available. Apple’s share of the tablet market fell to 29% by early 2018.

JEFFREY M. PERLOFF JAMES A. BRANDER

T H

IR D

E D

IT IO

N

MANAGERIAL ECONOMICS AND STRATEGY

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2779.1 Monopoly Profit Maximization

Effects of a Shift of the Demand Curve Shifts of the demand curve or marginal cost curve affect the profit-maximizing monopoly price and quantity and can have a wider variety of effects with a monop- oly than with a competitive market. In a competitive market, the effect of a shift in demand on a competitive firm’s output depends only on the shape of the mar- ginal cost curve. In contrast, the effect of a shift in demand on a monopoly’s output depends on the shapes of both the marginal cost curve and the demand curve.

As we saw in Chapter 8, a competitive firm’s marginal cost curve tells us every- thing we need to know about the amount that the firm is willing to supply at any given market price. The competitive firm’s supply curve is its upward-sloping

Answer 1. Derive the average cost function using the information about Apple’s marginal and

fixed costs. Given that Apple’s marginal cost was constant, its average variable cost, AVC, equaled its marginal cost, $220. Its average fixed cost, AFC, was its fixed cost divided by the quantity produced, 2,000>Q. Thus, its average cost was AC = AVC + AFC = 220 + 2,000>Q.

2. Derive Apple’s marginal revenue function using the information about its demand function. Given that Apple’s inverse demand function is linear, p = 770 - 11Q, its marginal revenue function has the same intercept and twice the slope: MR = 770 - 22Q.8

3. Derive Apple’s profit-maximizing quantity and price by equating the marginal rev- enue and marginal cost functions and solving. Apple maximized its profit where MR = MC:

770 - 22Q = 220. Solving this equation for the profit- maximizing output, we find that Q = 25 million iPads. By substituting this quan- tity into the inverse demand function, we determine that the profit-maximizing price was p = $495 per unit as the figure shows.

4. Calculate Apple’s profit using the profit- maximizing price and quantity and the aver- age cost. At Q = 25, the firm’s average cost was AC = 220 + 2,000>25 = $300. The firm’s profit was π = (p - AC)Q= (495 - 300)25 =$4,875 million. The figure shows that the profit is a rectangle with a height of (p - AC) = $195 and a length of Q = 25 million.

8Alternatively, we can use calculus to derive the marginal revenue curve. We multiply the inverse demand function by Q to obtain Apple’s revenue function, R = 770Q - 11Q2. Then, we derive the marginal revenue function by differentiating the revenue function with respect to quantity: MR = dR>dQ = 770 - 22Q.

p, $

p er

iP ad

Q, Millions of iPads per year

770

220

495

300 AC

MC

MR Demand

0 25 35

p = 4.875

70

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278 CHAPTER 9 Monopoly

marginal cost curve above its minimum average variable cost. A competitive firm’s supply behavior does not depend on the shape of the market demand curve because it always faces a horizontal demand curve at the market price. Thus, if we know a competitive firm’s marginal cost curve, we can predict how much that firm will produce at any given market price.

In contrast, a monopoly’s output decision depends on the shapes of its marginal cost curve and its demand curve. Unlike a competitive firm, a monopoly does not have a supply curve. Knowing the monopoly’s marginal cost curve is not enough for us to predict how much a monopoly will sell at any given price.

Figure 9.4 illustrates that the relationship between price and quantity is unique in a competitive market but not in a monopolistic market. If the market is competitive, the initial equilibrium is e1 in panel a, where the original demand curve D1 intersects the supply curve, MC, which is the sum of the marginal cost curves of a large number of competitive firms. When the demand curve shifts to D2, the new competitive equi- librium, e2, has a higher price and quantity. A shift of the demand curve maps out competitive equilibria along the marginal cost curve, so every equilibrium quantity has a single corresponding equilibrium price.

For the monopoly in panel b, as the demand curve shifts from D1 to D2, the profit- maximizing monopoly outcome shifts from E1 to E2, so the price rises but the quan- tity stays constant, Q1 = Q2. Thus, a given quantity can correspond to more than one profit-maximizing price, depending on the position of the demand curve. A shift in the demand curve may cause the profit-maximizing price to stay constant while the quantity changes. More commonly, both the profit-maximizing price and quantity change.

FIGURE 9.4 Effects of a Shift of the Demand Curve

p, $

p er

u ni

t

Q, Units per year

p1 p2

Q2Q1

(a) Competition

MC, Supply curve

e2

e1

D1D2

Q, Units per year

p1

p2

Q2Q1=

p, $

p er

u ni

t

(b) Monopoly

MC

D1D2

MR1

E2

E1

MR2

(a) A shift of the demand curve from D1 to D2 causes the competitive equilibrium to move from e1 to e2 along the supply curve (which is the hori- zontal sum of the marginal cost curves of all the competitive firms). Because the competitive equi- librium lies on the supply curve, each quantity (such as Q1 and Q2) corresponds to only one pos- sible equilibrium price.

(b) With a monopoly, this same shift of demand causes the monopoly optimum to change from E1 to E2. The monopoly quantity stays the same, but the monopoly price rises. Thus, a shift in demand does not map out a unique relationship between price and quantity in a monopolized market. The same quantity, Q1 = Q2, is associated with two dif- ferent prices, p1 and p2.

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2799.1 Monopoly Profit Maximization

Q&A 9.3 A monopoly faces an inverse demand function p = 40 - 2Q and has a cost func- tion C(Q) = 12 + 10Q + Q2. It follows that MR = 40 - 4Q and MC = 10 + 2Q. The price elasticity of demand is -0.5p>Q (see Equation 3.6 in Chapter 3). Use an Excel spreadsheet to calculate revenue, cost, profit, marginal revenue, marginal cost, and the demand elasticity for each quantity from 1 through 11 in one-unit increments. Find the profit-maximizing quantity and price. Verify that MR = MC at this quantity. What quantity and price maximize revenue? What is the profit at the revenue-maximizing quantity? What are the price elasticities of demand at the profit-maximizing and revenue-maximizing quantities?

Answer 1. Open an Excel spreadsheet; put the titles Quantity, Price, Revenue, Cost, Profit,

MR, MC, and Elasticity in cells A1 through H1 and list the quantities in the first column. Enter the quantities 1 through 11 in one-unit increments in cells A2 through A12.

2. Fill in the correct formulas in cells B2 through H2. Enter “= 40-2*A2” in cell B2, “=A2*B2” in cell C2, “=12+10*A2+A2^2” in cell D2, “=C2-D2” in cell E2, “=40-4*A2” in cell F2, “=10+2*A2” in cell G2, and “= -0.5*B2>A2” in cell H2.

3. Copy the formulas in row 2 and paste them into rows 3 through 12. Copy cell B2 and paste it into cells B3 through B12, then do the same for each column from C2 through H2. Format column H to show two digits after the decimal point.

4. Find the quantity and price where profit is greatest. Scan the profit column to find the largest profit. This maximum profit of 63 is highlighted in yellow. The profit-maximizing quantity is 5 and the corresponding price is 30.

5. Check whether marginal revenue equals marginal cost at the profit-maximizing quan- tity. At the profit-maximizing quantity, 5, the marginal revenue and marginal cost are both 20.

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280 CHAPTER 9 Monopoly

6. Through inspection, show that the profit maximum occurs at a smaller quantity than the revenue maximum. The revenue maximum occurs at a quantity of 10, while the profit maximum occurs at a quantity of 5. We have highlighted the maxi- mum revenue in blue.

7. Determine the profit at the revenue maximum. The profit is -12 at the revenue- maximizing output, so maximizing revenue does not maximize profit.

8. Determine the elasticities where profit and revenue reach their maximums. At the profit maximum, where quantity is five, the demand curve is elastic, with an elasticity of -3. Revenue always reaches its maximum at a price elasticity of demand of -1.0. We have highlighted these elasticities in green.

Mini-Case Taylor Swift’s 2015 concert tour was a huge success, breaking the Rolling Stones’ North American tour revenue record. Her 2018 “Reputation” tour is poised to be even more successful, opening to rave reviews and enthusiastic crowds. But not all her 2018 concerts are selling out. Why would the exceptionally popular pop music icon have empty seats at her concerts?

The main reason for the empty seats is high prices. Ms. Swift can earn more profit by charging high prices and selling fewer tickets. We examine why in the following Q&A.

Taylor Swift Concert Pricing

Q&A 9.4 Illustrate why charging a higher price, p1, than the price that causes the concert to sell out, p2, increases profit. For simplicity, assume that the marginal cost of selling tickets is constant at m until the stadium’s capacity is reached, and that fixed cost is zero. Explain why setting a price high enough that the show does not sell out increases profit.

Answer 1. Draw the marginal cost curve and explain its shape. The marginal cost curve is

horizontal at m until capacity is reached at Q2. Because no more than Q2 seats are available, the marginal cost of providing an additional seat becomes infi- nite at Q2. That is, the marginal cost curve is vertical at Q2.

2. Add the demand curve and marginal revenue curve to the diagram, and show the profit-maximizing price and quantity. The intersection of the marginal revenue

and marginal cost curve determines the profit- maximizing quantity, Q1. The corresponding price on the demand curve at point a is p1. 3. Show the profit at Q1. Without a fixed cost, the

average cost equals the marginal cost, m. Thus the profit is π1 = (p1 - m)Q1, which is area A + B.

4. Show the price such that ticket sales reach full capacity and the corresponding profit. To reach capacity by selling Q2 tickets, the price must fall to p2 at point b on the demand curve. The corresponding profit is π2 = (p2 - m)Q2, which is area B + C.

p, $

p er

ti ck

et

Q, Tickets

MC MR

Demand

A

B C m

p1

Q1 Q2

p2

a

b

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2819.2 Market Power

9.2 Market Power A monopoly has market power, which is the ability to significantly affect the market price. In contrast, no single competitive firm can significantly affect the market price.

A profit-maximizing monopoly charges a price that exceeds its marginal cost. The extent to which the monopoly price exceeds marginal cost depends on the shape of the demand curve.

Many people falsely believe that the biggest monopolies have the most power over prices:

Size doesn’t matter. Rather, a profit-maximizing monopoly marks up price over marginal cost more if consumers are less sensitive to price (the demand curve is less elastic). For example, some of the drugs mentioned in the Managerial Problem at the beginning of the chapter do not have a large volume of sales but have extremely high prices because they are crucial for a small segment of the population.

Market Power and the Shape of the Demand Curve If the monopoly faces a highly elastic—nearly flat—demand curve at the profit- maximizing quantity, it would lose substantial sales if it raised its price by even a small amount. Conversely, if the demand curve is not very elastic (if it is relatively steep) at that quantity, the monopoly would lose fewer sales from raising its price by the same amount.

We can derive the relationship between the markup of price over marginal cost and the elasticity of demand at the profit-maximizing quantity using the expression for marginal revenue in Equation 9.5 and the firm’s profit-maximizing condition that marginal revenue equals marginal cost:

MR = p a1 + 1 e b = MC. (9.8)

By rearranging terms, we see that a profit-maximizing manager chooses quantity such that

p

MC =

1 1 + (1 > e) . (9.9)

5. Explain why not selling out the show is profit maximizing. By charging a higher price and selling fewer tickets, Ms. Swift earns a higher profit: π1 7 π2. We know that profit is maximized where marginal revenue equals marginal cost. To sell each additional seat, she has to lower the price by enough that the mar- ginal revenue is less than the marginal cost, which reduces profit.

Common Confusion The larger the monopoly, the more it can mark up its price over its cost.

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282 CHAPTER 9 Monopoly

In our linear demand example in panel a of Figure 9.3, the elasticity of demand is e = -3 at the monopoly optimum where Q = 6. As a result, the ratio of price to mar- ginal cost is p>MC = 1>[1 + 1> ( -3)] = 1.5, or p = 1.5MC. The profit-maximizing price, $18, in panel a is 1.5 times the marginal cost of $12.

Table 9.2 illustrates how the ratio of price to marginal cost varies with the elasticity of demand. When the elasticity is -1.01, only slightly elastic, the monopoly’s profit- maximizing price is 101 times larger than its marginal cost: p>MC =1>[1 + 1> ( -1.01)] ≈ 101. As the elasticity of demand approaches negative infinity (becomes perfectly elastic), the ratio of price to marginal cost shrinks to p>MC = 1.9 Thus, even in the absence of rivals, the shape of the demand curve constrains the monopolist’s ability to exercise market power.

9As the elasticity approaches negative infinity, 1>e approaches zero, so 1> (1 + 1>e) approaches 1>1 = 1.

Elasticity of Demand, e Price/Marginal Cost Ratio,

p>MC = 1>[1 + (1>e)] Lerner Index,

(p - MC) >p = -1>e

le ss

e la

st ic

c -1.01 101 0.99

-1.1 11 0.91

-2 2 0.5

-3 1.5 0.33

T

m or

e el

as ti

c -5 1.25 0.2

-10 1.11 0.1

-100 1.01 0.01

- ∞ 1 0

TABLE 9.2 Elasticity of Demand, Price, and Marginal Cost

A manager can use this last result to determine whether the firm is maximizing its profit. Typically, a monopoly knows its costs accurately, but is somewhat uncertain about the demand curve it faces and hence what price (or quantity) to set. Many private firms—such as ACNielsen, IRI, and IMS Health—and industry groups collect data on quantities and prices in a wide variety of industries includ- ing automobiles, foods and beverages, drugs, and many services. Firms can use these data to estimate the firm’s demand curve (Chapter 3). More commonly, firms hire consulting firms (often the same firms that collect data) to estimate the elasticity of demand for their products.

A manager can use the estimated elasticity of demand to check whether the firm is maximizing profit. If the p>MC ratio does not approximately equal 1> (1 + 1>e), as required by Equation 9.9, then the manager knows that the firm is not setting its price to maximize its profit. Of course, the manager can also check whether the firm is maximizing profit by varying its price or quantity. However, often such experiments may be more costly than using statistical techniques to estimate the elasticity of demand.

Checking Whether the Firm Is Maximizing Profit

Managerial Implication

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2839.2 Market Power

The Lerner Index Another way to show how the elasticity of demand affects a monopoly’s price rela- tive to its marginal cost is to look at the firm’s Lerner Index (or price markup)—the ratio of the difference between price and marginal cost to the price: (p - MC) >p. This index can be calculated for any firm, regardless of whether the firm is a monopoly. The Lerner Index is zero for a competitive firm because a competitive firm produces where marginal cost equals price. The Lerner Index measures a firm’s market power: The larger the difference between price and marginal cost, the larger the Lerner Index and the firm’s market power.

If the firm is maximizing its profit, we can express the Lerner Index in terms of the elasticity of demand by rearranging Equation 9.9:10

p - MC

p = -

1 e . (9.10)

The Lerner Index ranges between 0 and 1 for a profit-maximizing monopoly.11 Equa- tion 9.10 confirms that a competitive firm has a Lerner Index of zero because its demand curve is perfectly elastic.12

As Table 9.2 illustrates, the monopoly’s Lerner Index is greater, the less elastic is the demand curve. If e = -5, the monopoly’s markup (Lerner Index) is 1>5 = 0.2; if e = -2, the markup is 1>2 = 0.5; and if e = -1.01, the markup is 0.99. Monopolies that face demand curves that are only slightly elastic set prices that are multiples of their marginal cost and have Lerner Indexes close to 1.

10Equation 9.9 can be rewritten as p (1 + 1>e) = MC or p - MC = -p>e . Dividing both sides of this equation by p produces Equation 9.10. 11For the Lerner Index to be above 1 in Equation 9.10, e would have to be a negative fraction, indicat- ing that the demand curve was inelastic at the monopoly’s output choice. However, as we’ve already seen, a profit-maximizing monopoly never operates in the inelastic portion of its demand curve. 12As the elasticity of demand approaches negative infinity, the Lerner Index, -1>e, approaches zero.

Q&A 9.5 The EpiPen is a small portable device that can quickly deliver the drug epineph- rine to stop a potentially life-threatening allergic reaction. The manufacturer of the EpiPen faces virtually no competition from other firms. The price for a pair of EpiPens is $630 for people without insurance, while two industry experts esti- mate that its marginal cost is $30.13 What is its Lerner Index? If the firm is maxi- mizing its short-run profit, what is its elasticity of demand?

Answer 1. Determine the Lerner Index by substituting the price and marginal cost into the Lerner

definition. The EpiPen’s Lerner Index is

p - MC p

= 630 - 30

630 ≈ 0.952.

2. Use Equation 9.10 to infer the elasticity. According to that equation, a profit- maximizing monopoly operates where (p - MC) >p = -1>e. Combining that equation with the Lerner Index from the previous step, we learn that 0.952 = -1>e, or e ≈ -1.05.

13www.nbcnews.com/business/consumer/industry-insiders-estimate-epipen-costs-no-more -30-n642091.

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284 CHAPTER 9 Monopoly

Sources of Market Power What factors cause a monopoly to face a relatively elastic demand curve and hence have little market power? Ultimately, the elasticity of demand of the market demand curve depends on consumers’ tastes and options. The more consumers want a good—the more willing they are to pay “virtually anything” for it—the less elastic is the demand curve.

Other things equal, the demand curve a firm (not necessarily a monopoly) faces becomes more elastic as (1) better substitutes for the firm’s product are introduced, (2) more firms enter the market selling the same product, or (3) firms that provide the same service locate closer to this firm. The demand curves for Xerox, the U.S. Postal Service, and McDonald’s have become more elastic in recent decades for these three reasons.

When Xerox started selling its plain-paper copier, no other firm sold a close sub- stitute. Other companies’ machines produced copies on special heat-sensitive paper that yellowed quickly. As other firms developed plain-paper copiers, the demand curve that Xerox faced became more elastic.

The U.S. Postal Service (USPS) has a legal monopoly in its core business of first- class mail delivery. However, FedEx, United Parcel Service, and many other courier firms are allowed to deliver urgent mail, and internet communication has also become an important alternative to regular mail. Because of increasing competition from courier ser- vices and the internet, the demand curve for first- class mail has shifted downward and become flatter. USPS delivers much less mail now than in the past, down from 104 billion pieces of first-class mail in 2001, to only about 59 billion pieces in 2017.14

As you drive down a highway, you may notice that McDonald’s restaurants are located miles apart. The purpose of this spacing is to reduce the likeli- hood that two McDonald’s outlets will compete for the same customer. Although McDonald’s can pre- vent its own restaurants from competing with each other, it cannot prevent Wendy’s or Burger King from locating near its restaurants. As other fast-food restaurants open near a McDonald’s, that restau- rant faces a more elastic demand. What happens as a profit-maximizing monopoly faces more elastic demand? It has to lower its price.

14about.usps.com/who-we-are/postal-history/first-class-mail-since-1926.htm.

9.3 Market Failure Due to Monopoly Pricing A profit-maximizing monopoly is economically inefficient because it wastes potential surplus, resulting in a deadweight loss. In contrast, perfect com- petition achieves economic efficiency because it maximizes total surplus, TS (= consumer surplus + producer surplus = CS + PS). The inefficiency of monop- oly pricing is an example of a market failure: a non-optimal allocation of goods and services such that a market does not achieve economic efficiency. Market failure

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2859.3 Market Failure Due to Monopoly Pricing

often occurs because the price differs from the marginal cost, as with a monopoly. This economic inefficiency creates a rationale for governments to intervene, which we discuss in Chapter 16.

Total surplus (Chapter 8) is lower under monopoly than under competition. That is, monopoly destroys some of the potential gains from trade. Chapter 8 showed that competition maximizes total surplus because price equals marginal cost. By setting its price above its marginal cost, a monopoly causes consumers to buy less than the competitive level of the good, so society suffers a deadweight loss.

If the monopoly were to act like a competitive market, it would produce where the marginal cost curve cuts the demand curve—the output where price equals marginal cost. For example, using the demand curve given by Equation 9.2 and the marginal cost curve given by Equation 9.7,

p = 24 - Q = 2Q = MC.

Solving this equation, we find that the competitive quantity, Qc, would be 8 units and the price would be $16, as Figure 9.5 shows. At this competitive price, consumer surplus is area A + B + C and producer surplus is D + E.

FIGURE 9.5 Deadweight Loss of Monopoly

p, $

p er

u ni

t

Demand

Q, Units per day

MR

MC

pc = 16 B = $12

D = $60

C = $2

MR = MC = 12

pm = 18

24

Qm = 6 Qc = 8 240

em

ec

Competition Monopoly Change

Consumer Surplus, CS A + B + C –B – C = ΔCS Producer Surplus, PS D + E B – E = ΔPS

A + B + C + D + E

A B + D

A + B + D –C – E = ΔTS = –DWL

A = $18

E = $4

12

Total Surplus, TS = CS + PS

A competitive market would produce Qc = 8 at pc = $16, where the demand curve intersects the marginal cost (supply) curve. A monopoly produces only Qm = 6 at pm = $18, where the marginal

revenue curve intersects the marginal cost curve. Under monopoly, consumer surplus is A, producer surplus is B + D, and the inefficiency or deadweight loss of monopoly is C + E.

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286 CHAPTER 9 Monopoly

If instead the firm acts like a profit-maximizing monopoly and operates where its marginal revenue equals its marginal cost, the monopoly output, Qm, is only 6 units and the monopoly price is $18. Consumer surplus is only A. Part of the lost consumer surplus, B, goes to the monopoly, but the rest, C, is lost. The benefit of being a monopoly is that it allows the firm to extract some consumer surplus from consumers and convert it to profit.

By charging the monopoly price of $18 instead of the competitive price of $16, the monopoly receives $2 more per unit and earns extra profit (and extra producer sur- plus) of area B = $12 on the Qm = 6 units it sells. The monopoly loses area E, how- ever, because it sells less than the competitive output. Consequently, the monopoly’s producer surplus increases by B - E over the competitive level. Monopoly pricing increases producer surplus relative to competition.

Total surplus is less under monopoly than under competition. The change in total surplus is -C - E. Thus, the deadweight loss of monopoly is C + E, which repre- sents the potential surplus that is wasted because less than the competitive output is produced. The deadweight loss is due to the gap between price and marginal cost at the monopoly output. At Qm = 6, the price, $18, is above the marginal cost, $12, so consumers are willing to pay more for the last unit of output than it costs to produce it.

Q&A 9.6 In the linear example in panel a of Figure 9.3, how does charging the monopoly a specific tax of t = $8 per unit affect the profit-maximizing price and quantity and the well-being of consumers, the monopoly, and society (where total surplus includes the tax revenue)? What is the tax incidence on consumers (the increase in the price they pay as a fraction of the tax)?

Answer 1. Determine how imposing the tax affects the monopoly price and quantity. In the

accompanying graph, the intersection of the marginal revenue curve, MR, and the before-tax marginal cost curve, MC1, determines the monopoly quantity, Q1 = 6. At the before-tax solution, e1, the price is p1 = 18. The specific tax causes the monopoly’s before-tax marginal cost curve, MC1 = 2Q, to shift upward by 8 to MC2 = MC1 + 8 = 2Q + 8. After the tax is applied, the monopoly oper- ates where MR = 24 - 2Q = 2Q + 8 = MC2. In the after-tax monopoly solu- tion, e2, the quantity is Q2 = 4 and the price is p2 = 20. Thus, output falls by ∆Q = 6 - 4 = 2 units and the price increases by ∆p = 20 - 18 = 2.

2. Calculate the change in the various surplus measures. The graph shows how the surplus measures change. Area G is the tax revenue collected by the govern- ment, tQ = 32, because its height is the distance between the two marginal cost curves, t = 8, and its width is the output the monopoly produces after the tax is imposed, Q = 4. The tax reduces consumer and producer surplus and increases the deadweight loss. We know that producer surplus falls because (a) the monopoly could have produced this reduced output level in the absence of the tax but did not because it was not the profit-maximizing output, so its before-tax profit falls, and (b) the monopoly must now pay taxes. Before the tax, the change in total surplus due to monopoly is -F, so the deadweight loss is F. After the tax, the deadweight loss is C + E + F. Thus, the increase in deadweight loss due to the tax is C + E. The table below the graph shows that consumer surplus changes by -B - C and producer surplus by B - E - G.

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2879.4 Causes of Monopoly

9.4 Causes of Monopoly Why are some markets monopolized? The two most important reasons are cost con- siderations and government policy.15

15In later chapters, we discuss other means by which monopolies are created. One method is the merger of several firms into a single firm. This method creates a monopoly if new firms fail to enter the market. A second method is for a monopoly to use strategies that discourage other firms from entering the market. A third possibility is that firms coordinate their activities and set their prices as a monopoly would. Firms that act collectively in this way are called a cartel rather than a monopoly.

3. Calculate the incidence of the tax on consumers. Because the tax goes from 0 to 8, the change in the tax is ∆t = 8. Because the change in the price that the consumer pays is ∆p = 2, the share of the tax paid by consumers is ∆p>∆t = 2>8 = 14. Thus, the monopoly absorbs $6 of the tax and passes on only $2.

p, $

p er

u ni

t

Demand

Q, Units per day

MR

MC1 (before tax)

MC2 (after tax)

p1 = 18

D E

C

F

G

B

A t = $8

0

8

p2 = 20

24

Q2 = 4 Q1 = 6 2412

e1

e2

Monopoly Before Tax Monopoly After Tax Change

Consumer Surplus, CS A + B + C A –B – C = ΔCS Producer Surplus, PS D + E + G B + D B – E – G = ΔPS Tax Revenues, T = tQ 0 G G = ΔT

A + B + C + D + E + G A + B + D + G –C – E = ΔTS Deadweight Loss, DWL F C + E + F C + E = ΔDWL Total Surplus, TS = CS + PS + T

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288 CHAPTER 9 Monopoly

Cost-Based Monopoly Certain cost structures may facilitate the creation of a monopoly. One possibility is that a firm may have substantially lower costs than potential rivals. A second pos- sibility is that the firms in an industry have cost functions such that one firm can produce any given output at a lower cost than two or more firms can.

Cost Advantages. If a low-cost firm profitably sells at a price so low that other potential competitors with higher costs would lose money, no other firms enter the market. Thus, the low-cost firm is a monopoly. A firm can have a cost advantage over potential rivals for several reasons. It may have a superior technology or a better way of organizing production.16 For example, Henry Ford’s methods of organizing produc- tion using assembly lines and standardization allowed him to produce cars at substan- tially lower cost than rival firms until they copied his organizational techniques.

If a firm controls an essential facility or a scarce resource that is needed to produce a particular output, no other firm can produce at all—at least not at a reasonable cost. For example, a firm that owns the only gravel quarry in a region is the only firm that can profitably sell gravel to local construction firms.

Natural Monopoly. A market has a natural monopoly if one firm can produce the total output of the market at lower cost than two or more firms could. A firm can be a natural monopoly even if it does not have a cost advantage over rivals, provided that average cost is lower if only one firm operates. Specifically, if the cost for any firm to produce q is C(q), the condition for a natural monopoly is

C(Q) 6 C(q1) + C(q2) + g + C(qn), (9.11)

where Q = q1 + q2 + g + qn is the sum of the output of any n firms where n Ú 2. If a firm has economies of scale at all levels of output, its average cost curve falls

as output increases for any observed level of output. If all potential firms have the same strictly declining average cost curve, this market is a natural monopoly, as we now illustrate.17

A company that supplies water to homes incurs a high fixed cost, F, to build a plant and connect houses to the plant. The firm’s marginal cost, m, of supply- ing water is constant, so its marginal cost curve is horizontal and its average cost, AC = m + F>Q, declines as output rises. (This cost curve is similar to that of the iPad example in Q&A 9.2.)

Figure 9.6 shows such marginal and average cost curves where m = 10 and F = 60. If the market output is 12 units per day, one firm produces that output at an average cost of 15, or a total cost of 180 ( = 15 * 12). If two firms each produce 6 units, the average cost is 20 and the cost of producing the market output is 240 ( = 20 * 12), which is greater than the cost with a single firm.

If the two firms divided total production in any other way, their cost of production would still exceed the cost of a single firm (as the following Q&A asks you to prove).

16When a firm develops a better production method that provides it with a cost advantage, it is important for the firm to either keep the information secret or obtain a patent, so that it can legally prevent anyone from imitating the firm’s innovation. Thus, both secrecy and patents facilitate cost-based monopolies. 17A firm may be a natural monopoly even if its cost curve does not fall at all levels of output. If a U-shaped average cost curve reaches its minimum at 100 units of output, it may be less costly for only one firm to produce an output of 101 units even though average cost is rising at that output. Thus, a cost function with economies of scale everywhere is a sufficient but not a necessary condi- tion for a natural monopoly.

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2899.4 Causes of Monopoly

The reason is that the marginal cost per unit is the same no matter how many firms produce, but each additional firm adds a fixed cost, which raises the cost of produc- ing a given quantity. If only one firm provides water, the cost of building a second plant and a second set of pipes is avoided.

In an industry with a natural monopoly cost structure, having just one firm is the cheapest way to produce any given output level. Governments often use a natural monopoly argument to justify their granting monopoly rights to public utilities, which provide essential goods or services such as water, gas, electric power, or mail delivery.

FIGURE 9.6 Natural Monopoly

15

20

40

10

60 12 15

AC = 10 + 60/Q

MC = 10

Q, Units per day A

C , M

C , $

p er

u ni

tThis natural monopoly has a strictly declining average cost, AC = 10 + 60>Q.

Government Creation of Monopoly Governments have created many monopolies. Sometimes governments own and manage such monopolies. In the United States, as in most countries, first-class mail delivery is a government monopoly. Many local governments own and operate

Q&A 9.7 A firm that delivers Q units of water to households has a total cost of C(Q) = mQ + F. If any entrant would have the same cost, does this market have a natural monopoly?

Answer Determine whether costs rise if two firms produce a given quantity. Let q1 be the output of Firm 1 and q2 be the output of Firm 2. The combined cost of these two firms producing Q = q1 + q2 is

C(q1) + C(q2) = (mq1 + F) + (mq2 + F) = m(q1 + q2) + 2F = mQ + 2F.

If a single firm produces Q, its cost is C(Q) = mQ + F. Thus, the cost of pro- ducing any given Q is greater with two firms than with one firm (the condition in Equation 9.11), so this market is a natural monopoly.

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290 CHAPTER 9 Monopoly

public utility monopolies that provide garbage collection, electricity, water, gas, phone services, and other utilities.

Barriers to Entry. Frequently, governments create monopolies by preventing competing firms from entering a market occupied by an existing incumbent firm. Several countries, such as China, maintain a tobacco monopoly. Similarly, most gov- ernments grant patents that limit entry and allow the patent-holding firm to earn a monopoly profit from an invention—a reward for developing the new product that acts as an incentive for research and development.

By preventing other firms from entering a market, governments create monopo- lies. Typically, governments create monopolies either by making it difficult for new firms to obtain a license to operate or by explicitly granting a monopoly right to one firm, thereby excluding other firms. By auctioning a monopoly to a private firm, a government can capture the future value of monopoly earnings.18

Frequently, firms need government licenses to operate. If one initial incumbent has a license and governments make it difficult for new firms to obtain licenses, the incumbent firm may maintain its monopoly for a substantial period. Until recently, many U.S. cities required that new hospitals or other inpatient facilities demonstrate the need for a new facility in order to obtain a certificate of need, which allowed them to enter the market.

Government grants of monopoly rights have been common for public utilities. Instead of running a public utility itself, a government might give a private sector company the monopoly rights to operate the utility. A government may capture some of the monopoly profits by charging the firm in some way for its monopoly rights. In many countries or other political jurisdictions, such a system is an induce- ment to corruption, as firms seeking monopoly privileges may bribe public officials to obtain the monopoly rights.

Governments around the world have privatized many state-owned monopolies in the past several decades. By selling cable television, garbage collection, phone service, towing, and other monopolies to private firms, a government can capture the value of future monopoly earnings today. However, for political or other reasons, governments frequently sell at a lower price that does not capture all future profits.

18Alternatively, a government could auction the rights to the firm that offers to charge the lowest price, so as to maximize total surplus.

Mini-Case The Canadian government created a medical marijuana monopoly by issuing only one license allowing a firm to operate. For 13 years, Prairie Plant Systems Inc. was the sole supplier of medical marijuana to Health Canada, which is the Canadian government agency that oversees the program.

The government then eliminated the monopoly, creating a competitive market. The licensing law changed in 2014, when other firms could receive licenses and start providing medical marijuana. By early 2015, Health Canada had received more than 1,200 applications for licenses. While many applications were unsuccessful, significant entry occurred rapidly. The industry changed from being a monopoly to being competitive within a year. By early 2018, more than 100 licensed producers of medical marijuana had entered the market. Additional producers of marijuana were poised to enter after the Canadian government passed legislation to legalize recreational marijuana in 2018.

The Canadian Medical Marijuana Market

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2919.4 Causes of Monopoly

Patents. If an innovating firm cannot prevent imitation by keeping its discover- ies secret, it may try to obtain government protection to prevent other firms from duplicating its innovations and entering the market. Most countries provide such protection through patents. A patent is an exclusive right granted to the inventor of a new and useful product, process, substance, or design for a specified length of time. Most patents in the United States and other major jurisdictions last for up to 20 years from the application date.

This right allows the patent holder to be the exclusive seller or user of the new invention.19 Patents often give rise to monopoly, but not always. For example, although a patent may grant a firm the exclusive right to use a particular process in making a product, other firms may be able to make the same product using different processes. In Chapter 16, we discuss the reasons why governments grant patents.

19Owners of patents may sell or grant the right to use a patented process or produce a patented product to other firms. This practice is called licensing.

Mini-Case Ophthalmologist Dr. Alan Scott turned the deadly poison botulinum toxin into a miracle drug to treat two eye conditions: strabismus, a condition in which the eyes are not properly aligned, and blepharospasm, an uncontrollable closure of the eyes. Strabismus affects about 4% of children and blepharospasm left about 25,000 Americans functionally blind before Scott’s discovery. His patented drug for treating these condition, Botox, is sold by Allergan, Inc.

Dr. Scott has been amused to see several of the unintended beneficiaries of his research at the Academy Awards. Even before it was explicitly approved for cosmetic use, many doctors were injecting Botox into the facial muscles of actors, models, and others to smooth out their wrinkles. (The drug paralyzes the muscles, so those injected with it also lose the ability to frown or smile—and, some would say, act.) The treatment is only temporary, lasting up to 120 days, so repeated injections are necessary.

Allergan has a near-monopoly in the treatment of wrinkles, although plastic surgery and collagen, Restylane, hyaluronic acids, and other filler injections provide limited competition. However, 54% of Botox sales are now for other uses, including as a treatment for chronic migraine and overactive bladder.

Allergan had Botox sales of $800 million in 2004 and about $2.8 billion in 2016. Indeed, Botox’s value continues to increase as Allergan finds new uses for Botox. According to one forecast, Botox’s global sales will reach $3.2 billion by the end of 2018 and $4.3 billion by 2022.

Dr. Scott can produce a vial of Botox in his lab for about $25. Allergan sells the potion to doctors for about $400. Assuming that the firm is setting its price to maximize its short-run profit, we can rearrange Equation 9.10 to determine the elasticity of demand for Botox:

e = - p

p - MC = -

400 400 - 25

≈ -1.067.

Thus, the demand that Allergan faces is only slightly elastic: A 1% increase in price causes quantity to fall by slightly more than 1%.

Botox

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292 CHAPTER 9 Monopoly

If the demand curve is linear and the elasticity of demand is -1.067 at the 2002 monopoly optimum, em (1 million vials sold at $400 each, producing rev- enue of $400 million), then Allergan’s inverse demand function is20

p = 775 - 375Q. This demand curve (see the graph) has a slope of -375 and hits the price

axis at $775 and the quantity axis at about 2.07 million vials per year. Thus, its revenue is R = 775Q - 375Q2, so its marginal revenue curve is

MR = dR>dQ = 775 - 750Q. The MR curve strikes the price axis at $775 and has twice the slope, -750, of the demand curve.

The intersection of the marginal revenue and marginal cost curves,

MR = 775 - 750Q = 25 = MC, determines the monopoly equilibrium at the profit-maximizing quantity of 1 million vials per year and a price of $400 per vial.

Were the company to sell Botox at a price equal to its marginal cost of $25 (as a competitive industry would), consumer surplus would equal

area A + B + C. The height of triangle A + B + C is $750 = $775 - $25, and its length is 2 million vials, so its area is $750 (= 12 * 750 * 2) million. At the higher monop- oly price of $400, the con- sumer surplus is A = $187.5 million. Compared to the competitive solution, ec, buy- ers lose consumer surplus of B + C = $562.5 million per year. Part of this loss, B = $375 million per year, is transferred from consum- ers to Allergan. The rest, C = $187.5 million per year, is the deadweight loss from monopoly pricing. Allergan’s profit is its producer surplus, B, minus its fixed costs.

20The graph shows a linear demand curve with algebraic form p = a - bQ. Such a linear demand curve has an elasticity of e = - (1>b) (p>Q). Given that the elasticity of demand is -400>375 = - (1>b) (400>1), where Q is measured in millions of vials, then b = 375. Solving p = 400 = a - 375, we find that a = 775.

p, $

p er

v ia

l

2.07

A ≈ $187.5 million

C ≈ $187.5 million

B ≈ $375 million Demand

Q, Million vials of Botox per year

400

25

0

em

ec MC = AVC MR

775

1

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2939.5 Advertising

9.5 Advertising You can fool all the people all the time if you have a big enough advertising budget.

In addition to setting prices or quantities and choosing investments, firms engage in many other strategic actions to boost their profits. One of the most important is advertis- ing.21 By advertising, a monopoly can shift its demand curve, which may allow it to sell more units at a higher price. In contrast, a competitive firm has no incentive to advertise, as it can sell as many units as it wants at the going price without advertising.

Advertising is only one way to promote a product. Other promotional activities include providing free samples and using sales agents. Some promotional tactics are subtle. For example, grocery stores place sugary breakfast cereals on lower shelves so that they are at children’s eye level. According to a survey of 27 supermarkets nationwide by the Center for Science in the Public Interest, the average position of 10 child-appealing brands (44% sugar) was on the next-to-bottom shelf, while the average position of 10 adult brands (10% sugar) was on the next-to-top shelf.

A firm advertises to raise its profit. A successful advertising campaign shifts the market demand curve by changing consumers’ tastes or informing them about new products. The firm may be able to change the tastes of some consumers by telling them that a famous athlete or performer uses the product. Children and teenagers are frequently the targets of such advertising. If the advertising convinces some consumers that they can’t live without the product, the monopoly’s demand curve may shift outward and become less elastic at the new equilibrium, at which the firm charges a higher price for its product.

If a firm informs potential consumers about a new use for the product, the demand curve shifts to the right. For example, a 1927 Heinz advertisement suggested that putting its baked beans on toast was a good way to eat beans for breakfast as well as dinner. By so doing, it created a British national dish and shifted the demand curve for its product to the right.

Deciding Whether to Advertise Japanese space startup, iSpace Technologies, raised $90 million to launch a spacecraft into lunar orbit so that it can offer a “projection mapping service” to advertise on the moon’s surface.22

Even if advertising succeeds in shifting demand, it may not pay for the firm to adver- tise. If advertising shifts demand outward or makes it less elastic, the firm’s gross profit, ignoring the cost of advertising, must rise. The firm undertakes this advertis- ing campaign, however, only if it expects its net profit (gross profit minus the cost of advertising) to increase.

We illustrate a monopoly’s decision making about advertising in Figure 9.7. If the monopoly does not advertise, it faces the demand curve D1. If it advertises, its demand curve shifts from D1 to D2.

21For example, Ford spends more on advertising, $4.1 billion in 2017, than anything except R&D (John D. Stoll, “Behind Ford’s New Approach to Advertising,” Wall Street Journal, May 21, 2018). 22www.slate.com/articles/health_and_science/science/2017/12/ispace_wants_to_advertise_on_ the_moon_is_that_legal.html.

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FIGURE 9.7 Advertising

p ,

$ pe

r un

it

B

Q, Units per yearQ2Q1

MR1 MR2 D2D1

p2 p1

e2

e1

p1

MC = AC

If the monopoly does not advertise, its demand curve is D1. At its actual level of advertising, its demand curve is D2. Advertising increases the monopoly’s gross profit (ignoring the cost of

advertising) from π1 to π2 = π1 + B. Thus, if the cost of advertising is less than the benefits from advertis- ing, B, the monopoly’s net profit (gross profit minus the cost of advertising) rises.

The monopoly’s marginal cost, MC, is constant and equals its average cost, AC. Before advertising, the monopoly chooses its output, Q1, where its marginal cost curve intersects its marginal revenue curve, MR1, which corresponds to demand curve, D1. The profit-maximizing equilibrium is e1, and the monopoly charges a price of p1. The monopoly’s profit, π1, is a box whose height is the difference between the price and the average cost and whose length is the quantity, Q1.

After its advertising campaign shifts its demand curve to D2, the monopoly chooses a higher quantity, Q2( 7 Q1), where the MR2 and MC curves intersect. In this new equilibrium, e2, the monopoly charges p2. Despite this higher price, the monopoly sells more units after advertising because of the outward shift of its demand curve.

As a consequence, the monopoly’s gross profit rises. Its new gross profit is the rectangle π1 + B, where the height of the rectangle is the new price minus the aver- age cost, and the length is the quantity, Q2. Thus, the benefit, B, to the monopoly from advertising at this level is the increase in its gross profit. If its cost of advertising is less than B, its net profit rises, and it pays for the monopoly to advertise at this level rather than not to advertise at all.

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2959.5 Advertising

How Much to Advertise The firm that stops advertising to save money is like the person who stops the clock to save time.

How much should a monopoly advertise to maximize its net profit? The rule for set- ting the profit-maximizing amount of advertising is the same as that for setting the profit-maximizing amount of output: Set advertising or quantity where the marginal benefit (the extra gross profit from one more unit of advertising or the marginal revenue from one more unit of output) equals its marginal cost.

Consider what happens if the monopoly raises or lowers its advertising expen- ditures by $1, which is its marginal cost of an additional unit of advertising. If a monopoly spends one more dollar on advertising—its marginal cost of advertising— and its gross profit rises by more than $1, its net profit rises, so the extra advertising pays. A profit-maximizing monopoly keeps increasing its advertising until the last dollar of advertising raises its gross profit by exactly $1. If it were to advertise more, its profit would fall.

Optimal Advertising

Using Calculus We can derive this marginal rule for optimal advertising using calculus. A monopoly’s inverse demand function is p = p(Q, A), which says that the price it must charge to clear the market depends on the number of units it chooses to sell, Q, and on the level of its advertising, A. As a result, the firm’s revenue func- tion is R(Q, A) = p(Q, A)Q. The firm’s cost function is C(Q) + A, where C(Q) is the cost of manufacturing Q units and A is the cost of advertising, because each unit of advertising costs $1 (by choosing the units of measure appropriately). The monopoly’s profit is π(Q, A) = R(Q, A) - C(Q) - A. (9.12)

The monopoly maximizes its profit by choosing Q and A. Its first-order con- ditions to maximize its profit are found by partially differentiating the profit function in Equation 9.12 with respect to Q and A in turn:

0π(Q, A)

0Q =

0R(Q, A) 0Q

- dC(Q)

dQ = 0, (9.13)

0π(Q, A)

0A =

0R(Q, A) 0A

- 1 = 0. (9.14)

The profit-maximizing output and advertising levels are the Q and A that simul- taneously satisfy Equations 9.13 and 9.14. Equation 9.13 says that the monopoly should set its output so that the marginal revenue from one more unit of output, 0R>0Q, equals the marginal cost, dC>dQ, which is the same condition that we previously derived before considering advertising. According to Equation 9.14, the monopoly should advertise to the point where its marginal revenue or mar- ginal benefit from the last unit of advertising, 0R>0A, equals the marginal cost of the last unit of advertising, $1.

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296 CHAPTER 9 Monopoly

Q&A 9.8 A monopoly’s inverse demand function is p = 800 - 4Q + 0.2A 0.5, where Q is

its quantity, p is its price, and A is the level of advertising. Its marginal cost of production is 2, and its cost of a unit of advertising is 1. What are the firm’s profit- maximizing price, quantity, and level of advertising?

Answer 1. Write the firm’s profit function using its inverse demand function. The monopoly’s

profit is π = (800 - 4Q + 0.2A0.5)Q - 2Q - A

= 798Q - 4Q2 + 0.2A0.5Q - A. (9.15)

2. Set the partial derivatives of the profit function in Equation 9.15 with respect to Q and A to zero to obtain the equations that determine the profit-maximizing levels, as in Equations 9.13 and 9.14. The first-order conditions are

0π 0Q

= 798 - 8Q + 0.2A0.5 = 0, (9.16)

0π 0A

= 0.1A-0.5Q - 1 = 0. (9.17)

3. Solve Equations 9.16 and 9.17 for the profit-maximizing levels of Q and A. We can rearrange Equation 9.17 to show that A0.5 = 0.1Q. Substituting this expres- sion into Equation 9.16, we find that 798 - 8Q + 0.02Q = 0, or Q = 100. As a result, A0.5 = 0.1Q = 10. Squaring both sides of this equation, we find that A = 100.

Mini-Case Super Bowl commercials are the most expensive commercials on U.S. television. A 30-second spot during the Super Bowl averaged more than $5 million in 2018. A high price for these commercials is not surprising because the cost of com- mercials generally increases with the number of viewers (eyeballs in industry jargon), and the Super Bowl is the most widely watched show, with 103 million viewers in 2018. Super Bowl advertising costs 2.5 times as much per viewer as other TV commercials.

However, a Super Bowl commercial is much more likely to influence viewers than commercials on other shows. The Super Bowl is not only a premier sports event; it also showcases the most memorable commercials of the year, such as Apple’s classic 1984 Macintosh ad, which is still discussed today. Indeed, many Super Bowl viewers are not even football fans—they watch to see these superior ads. Moreover, Super Bowl commercials receive extra exposure because these ads often go viral on the internet.

Given that Super Bowl ads are more likely to be remembered by viewers, are these commercials worth the extra price? Obviously, many advertisers believe so, as their demand for these ads has bid up the price. Kim, Freling, and Grisaffe (2013) found that immediately after a Super Bowl commercial airs, the advertis- ing firm’s stock value rises. Thus, investors apparently believe that Super Bowl commercials raise a firm’s profits despite the high cost of the commercial. Ho,

Super Bowl Commercials

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2979.6 Internet Monopolies: Network Effects and Scale Economies

9.6 Internet Monopolies: Network Effects and Scale Economies

A number of technology giants, such as Facebook (95% of young adults on the inter- net use one of its services), Google (89% of internet searches), and Amazon (75% of electronic book sales), have such large shares of their markets that they are nearly monopolies.23 Why are they dominant? Two important reasons concern networks and natural monopoly.

The demand for many goods and services depends on who else consumes them. In such cases, consumers form a network: an interconnected group of people or things. Facebook, LinkedIn, and Twitter users form networks, as no one would be interested in such internet social media services unless others also used them.

Another characteristic that is more common on the internet than elsewhere in the economy is a cost structure with low or zero marginal cost and high fixed cost. For example, your online search using the Google search engine has a negligible marginal cost for Google. However, to provide this service, Google incurs a large fixed cost for programmers and infrastructure. As a result, its average cost curve is downward sloping, which is a condition that can lead to natural monopoly.

Network Externalities A good has a network externality if one person’s demand depends on the consump- tion of a good by others.24 If a good has a positive network externality, its value to a consumer grows as the number of units sold increases. Network externalities are an important source of monopoly power. They arise in many parts of the economy but are particularly important on the internet.

When a firm introduces a new good with a network externality, it faces a chicken- and-egg problem: Ali won’t buy the good unless Shan buys it, and Shan won’t buy it unless Ali does. The firm wants its customers to coordinate or to make their purchase decisions simultaneously.

The telephone provides a classic example of a positive network externality. When the phone was introduced, potential adopters had no reason to subscribe for phone service unless their family and friends did. Why pay for phone service if you have no one to call? For Bell’s phone network to succeed, it had to achieve a critical mass of users—enough adopters so that others wanted to join. Had it failed to achieve this critical mass, demand would have withered and the network would have died.

23www.wsj.com/articles/the-antitrust-case-against-facebook-google-amazon-and-apple- 1516121561. 24 In Chapter 16, we discuss the more general case of an externality, which occurs when a person’s well-being or a firm’s production capability is directly affected by the actions of other consumers or firms rather than indirectly through changes in prices.

Dhar, and Weinberg (2009) found that for the typical movie with a substantial advertising budget, a Super Bowl commercial advertising the movie raises the- ater revenues by more than the same expenditure on other television advertis- ing. They also concluded that movie firms’ advertising during the Super Bowl was at (or close to) the profit-maximizing amount.

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298 CHAPTER 9 Monopoly

Behavioral Network Externalities Network externalities depend on the size of the network because customers want to interact with each other. However, sometimes consumers’ behavior depends on beliefs or tastes that can be explained by psychological and sociological theories, which economists study in behavioral economics (Chapter 4).

One such explanation for a network externality effect is based on consumer atti- tudes toward other consumers. Harvey Leibenstein (1950) suggested that consumers sometimes want a good because “everyone else has it.” A fad or other popularity- based explanation for a positive network externality is called a bandwagon effect: A person places greater value on a good as more and more people possess it.26 The  continued dominance of the iPad today may be partially due to its early popularity.

26Jargon alert: Some economists use bandwagon effect to mean any positive network externality—not just those that are based on popularity.

Managers of firms that want to sell goods and services with network externalities often initially sell them at a low introductory price to obtain a critical mass. By doing so, the manager maximizes long-run profit but not short-run profit.

Suppose that a monopoly sells its good—root-beer-scented sandals—for only two periods (after that, the demand goes to zero as a new craze hits the market). If the monopoly sells less than a critical quantity of output, Q, in the first period, then its second-period demand curve lies close to the price axis. However, if the good is a success in the first period—at least Q units are sold—the second-period demand curve shifts substantially to the right.

If the monopoly maximizes its short-run profit in the first period, it charges p* and sells Q* units, which is fewer than Q. To sell Q units, it would have to lower its first-period price below p*, which would reduce its first-period profit from π* to π.

In the second period, the monopoly maximizes its profit given its second- period demand curve. If the monopoly sold only Q* units in the first period, it earns a relatively low second-period profit of πl. However, if it sells Q units in the first period, it makes a relatively high second-period profit, πh.

Should the monopoly charge a low introductory price in the first period? Its objective is to maximize its long-run profit: the sum of its profit in the two peri- ods.25 If the firm has a critical mass in the second period, its extra profit is πh - πl. To obtain this critical mass by charging a low introductory price in the first period, it lowers its first-period profit by π* - π. Thus, a manager should charge a low introductory price in the first period if the reduction in first-period profit is less than the extra profit in the second period.

This policy is profitable for many firms. A 2018 Google search found over a million web pages touting an introductory price.

A closely related strategy used for many internet services is to start by offer- ing a free version, then, after creating a large enough user base, offer a premium version at a positive (and profitable) price, like Yahoo! mail.

25Firms place lower value on profit in the future than profit today (Chapter 7). However, for simplic- ity, we assume that the monopoly places equal value on profit in either period.

Introductory Prices

Managerial Implication

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2999.6 Internet Monopolies: Network Effects and Scale Economies

The opposite, negative network externality is called a snob effect: A person places greater value on a good as fewer and fewer people possess it. Some people prefer an original painting by an unknown artist to a lithograph by a star because no one else can possess that painting. (As Yogi Berra is reported to have said, “Nobody goes there anymore; it’s too crowded.”)

Two-Sided Markets A two-sided market or two-sided network is an economic platform that has two or more user groups that provide each other with network externalities. Two common types of economic platforms are online matchmakers and innovation platforms.

Economic platforms such as Airbnb (short-term rentals), Lyft (driver service), and Monster.com (an employment site) match sellers with buyers. If more drivers are available on Lyft, more customers will want to use the service, which is a net- work externality. Similarly, if more customers use Lyft, more drivers will want to drive for it.

An innovation platform provides a technology upon which other firms can build and customers use. Google’s Android operating system for cell phones is an innovation platform. Developers produce apps that function on this operat- ing system. The more apps, the more users. The more users, the more developers producing apps.

The internet itself is an innovation platform. In the early days of the internet, connecting to it over phone lines was slow and costly. Because the internet had rela- tively little content, many people found that the cost of connecting to the internet and using it exceeded the benefit. But, once a large enough number of customers had internet service, more suppliers found it profitable to provide internet content such as news media and downloadable music, movies, and computer software. As content increased, more people used the internet. And, with more customers, more firms started selling on the internet.

Many non-internet industries also have two-sided networks. Both cardholders and merchants use credit cards. Gamers and game developers link using video-game consoles. Doctors and patients connect through health maintenance organizations and hospitals.

Natural Monopoly on the Internet Many internet services require a large up-front fixed cost—primarily for develop- ment and promotion—but have a low marginal cost, sometimes nearly zero. As a result, such firms have downward-sloping average cost curves, reflecting economies of scale. Under such a cost structure, a monopoly or near-monopoly may emerge after a brief period of internet competition.27

27If internet sites provide differentiated products, then several sites may coexist even though aver- age costs are strictly decreasing. In 2007, commentators were predicting the emergence of monopo- lies in social networks such as MySpace, an early social networking site. MySpace lost dominance to Facebook. In turn, Facebook may eventually lose ground to a similar site; to newer variants, such as Twitter, Snapchat, and Instagram; or to sites that cater to specialized audiences such as LinkedIn.

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300 CHAPTER 9 Monopoly

Disruptive Technologies The internet facilitates the introduction of disruptive technologies (see Disruptive Innovations and the Evolution of Market Structure in Chapter 7) with strong net- work externalities and economies of scale. Because these new internet technologies have network externalities, low marginal costs, and decreasing average cost curves, they often can drive out existing technologies.

Amazon started by selling books over the internet. The ease of finding and pur- chasing books that way attracted many consumers. Moreover, Amazon has much lower marginal and average costs than traditional brick-and-mortar bookstores. Its Kindle reader provides a two-sided market for online books. For all these reasons, Amazon is driving many traditional bookstores out of business.

Online news is driving print newspapers out of business. Streaming movies killed off most of the movie videotape/CD/Blu-ray rental stores. Streaming music has largely eliminated record-CD sales.

Google is an example of such a natural monopoly. It has high fixed costs, but it incurs virtually zero marginal cost when someone uses its search engine. It can there- fore easily accommodate more users. And because Google offers this service free to users, a potential competitor providing an identical service cannot undercut Google, short of offering a subsidy, and would struggle to cover its fixed costs. Google is able to cover its fixed costs because its large user base is attractive to advertisers. It earns large advertising revenues and has substantial profits even after covering its fixed costs.

Some firms, such as Facebook, benefit from both a natural monopoly cost struc- ture and network externalities. Like Google, Facebook has high fixed costs and can add users at negligible marginal cost. It continuously expands its user base by offer- ing free use of its service. In addition, because of network externalities, users increas- ingly want to join Facebook as its network becomes larger, further enhancing the value of Facebook to advertisers.

Mini-Case In the early years of the internet, eBay’s online auction site, which started in 1995, faced competition from a variety of other internet sites including Yahoo! Auctions that the then mighty Yahoo! created in 1998. At the time, many com- mentators correctly predicted that whichever auction site first achieved a criti- cal mass of users would drive the other sites out of business. Indeed, most of these alternative sites died or faded into obscurity. For example, Yahoo! Auctions closed its U.S. and Canada sections of the site in 2007 (although its Hong Kong, Taiwanese, and Japanese sites continue to operate).

Sellers value having a reputation system, based on feedback from many buy- ers, and one site where virtually all buyers and sellers congregate, which lowers buyers’ search costs (Brown and Morgan, 2006). Apparently, these advantages more than compensate sellers for the lack of competition in sellers’ fees. Brown and Morgan (2009) found that, prior to the demise of the Yahoo! Auction site, the same type of items attracted an average of two additional bidders on eBay and, consequently, the prices on eBay were consistently 20% to 70% percent higher than Yahoo! Auction prices.

Critical Mass and eBay

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3019.6 Internet Monopolies: Network Effects and Scale Economies

Brand-Name and Generic Drugs

Managerial Solut ion

When generic drugs enter the market after the patent on a brand-name drug expires, the demand curve facing the brand-name firm shifts to the left. Why do many brand-name drug companies raise their prices after generic rivals enter the market? The reason is that the demand curve not only shifts to the left but also rotates so that it is less elastic at the original price.

The price the brand-name firm sets depends on the elasticity of demand. When the firm has a patent monopoly, it faces the linear demand curve D1 in the figure. The intersection of the corresponding marginal revenue curve MR1 and the marginal cost curve determines the monopoly optimum, e1. (Because MR1 is twice as steeply sloped as D1, it intersects the MC curve at Q1, while the demand curve D1 intersects the MC curve at 2Q1.) The monopoly sells the Q1 units at a price of p1.

After the generic drugs enter the market, the linear demand curve facing the original patent holder shifts leftward to D2 and becomes steeper and less elastic at the original price. The firm now maximizes its profit at e2, where the quantity, Q2, is smaller than Q1 because D2 lies to the left of D1. However, the new price, p2, is higher than the initial price, p1, because the D2 demand curve is less elastic at the new optimum quantity Q2 than is the D1 curve at Q1.

Why might the demand curve rotate and become less elastic at the initial price? One explanation is that the brand-name firm has two types of consumers with different elasticities of demand who differ in their willingness to switch to a generic. One group of consumers is relatively price sensitive and switches to the lower-priced generics. However, the brand-name drug continues to be the monopoly supplier to the remaining brand-loyal customers whose demand is less elastic than that of the price-sensitive consumers. These loyal customers prefer the brand-name drug because they are more comfortable with a familiar product, worry that new products may be substandard, or fear that differences in the inactive ingredients might affect them.

Older customers are less likely to switch brands than younger people. A sur- vey by the American Association of Retired Persons found that people aged 65

p, $

p er

u ni

t

D1

Q, Units per day

MR1 D 2

e2 e1p1

p2

MC

MR 2

Q1Q2 2Q2 2Q1

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302 CHAPTER 9 Monopoly

and older were 15% less likely than people aged 45 to 64 to request generic ver- sions of a drug from their doctor or pharmacist. Similarly, patients with generous insurance plans may be more likely to pay for expensive drugs (if their insurer permits) than customers with more limited insurance policies.

SUMMARY

1. Monopoly Profit Maximization. Like any firm, a monopoly—a single seller—maximizes its profit by set- ting its output so that its marginal revenue equals its marginal cost. The monopoly makes a positive profit if its average cost is less than the price at the profit- maximizing output.

2. Market Power. Market power is the ability of a firm to significantly affect the market price. The extent of a firm’s market power depends on the shape of the demand curve. The more elastic the demand curve at the point where the firm is producing, the lower the markup of price over marginal cost.

3. Market Failure Due to Monopoly Pricing. Because a monopoly’s price is above its marginal cost, too little output is produced, and society suffers a deadweight loss. The monopoly makes higher profit than it would if it acted as a price taker. Consumers are worse off, buying less output at a higher price.

4. Causes of Monopoly. A firm may be a monopoly if it has lower operating costs than rivals, due to reasons such as superior knowledge or control of a key input. A market may also have a natural monopoly if one firm can produce the market output at lower average cost than can a larger number of firms (even if all firms have the same cost function). Many, if not most, monopolies

are created by governments, which prevent other firms from entering the markets. One important barrier to entry is a patent, which gives the inventor of a new product or process the exclusive right to sell the prod- uct or use the process for 20 years in most countries.

5. Advertising. A monopoly advertises or engages in other promotional activity to shift its demand curve to the right or make it less elastic so as to raise its profit net of its advertising expenses.

6. Internet Monopolies: Network Effects and Scale Economies. One important reason for the emergence of near-monopoly firms on the internet is network externalities. For products with network externalities, the value to one user increases with the number of other users. Behavioral economics pro- vides an explanation for some network externalities, such as bandwagon effects and snob effects. Many of these firms operate in a two-sided market, serving as a platform for sellers and buyers. The more buyers or sellers, the greater the network externalities. Many internet products also have high fixed costs and very low marginal costs, leading to economies of scale. The combination of network externalities and economies of scale may allow a firm that first establishes critical mass to become a monopoly.

QUESTIONS

1. Monopoly Profit Maximization 1.1 If the inverse demand function is p = 800 - 4Q,

what is the marginal revenue function? Draw the demand and marginal revenue curves. At what quantities do the demand and marginal revenue curves hit the quantity axis? (Hint: See Q&A 9.1.)

1.2 If the inverse demand function a monopoly faces is p = 50Q-0.5, what is the firm’s marginal revenue function? (Hint: See Q&A 9.1.) C

*1.3 If the inverse demand function is p = 500 - 10Q, what is the revenue and the elasticity of demand at Q = 10?

1.4 Is a monopoly’s profit affected by whether it chooses price or quantity (assuming it chooses them opti- mally)? Why can’t a monopoly choose both price and quantity?

1.5 For the monopoly in Figure 9.3, at what quantity is its revenue maximized? (Hint: At the quantity where the revenue function reaches its peak, the slope of the revenue function is zero. That is, MR = 0. See Q&A 9.3.) Why is revenue maximized at a larger quantity than profit? Modify panel b of Figure 9.3 to show the revenue curve.

All exercises are available on MyLab Economics; * = answer at the back of this book; C = use of calculus may be necessary; = this exercise is available in Excel Grader in MyLab Economics.

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1.6 Are Major League Baseball clubs profit-maximizing monopolies? Some observers of this market have contended that baseball club owners want to maxi- mize attendance or revenue. Alexander (2001) says that one test of whether a firm is a profit- maximizing monopoly is to check whether the firm is operating in the elastic portion of its demand curve (which he finds is true). Why is that a relevant test? What would the elasticity be if a baseball club were maxi- mizing revenue? (Hint: See Q&A 9.3.)

1.7 Using a graph, show under what condition the monopoly operates—does not shut down—in the long run. Discuss your result in terms of the demand curve and the average cost curve at the profit- maximizing quantity.

1.8 Why might a monopoly operate in any part (down- ward sloping, flat, upward sloping) of its long-run average cost curve, but a competitive firm will operate only at the bottom or in the upward-sloping section?

1.9 AT&T Inc., the large U.S. phone company and the one-time monopoly, left the payphone business at the beginning of 2009 because people were switch- ing to wireless phones. U.S. consumers owning cellphones reached 80% by 2007 and 95% by 2018 according to the Pew Research Center. Consequently, the number of payphones fell from 2.6 million at the peak in 1998 to only about 100,000 in 2018 (money. cnn.com/2018/03/19/news/companies/pay-phones/ index.html). Use graphs to explain why a monopoly may exit a market when its demand curve shifts to the left.

*1.10 The inverse demand function a monopoly faces is p = 100 - Q. The firm’s cost curve is C (Q) = 10 + 5Q. What is the profit- maximizing solution? How does your answer change if C (Q) = 100 + 5Q? (Hint: See  “Using Calculus: Solving for the Profit-Maximizing Output” and Q&A 9.2.) C

1.11 The inverse demand function a monopoly faces is p = 50Q-0.5 (Hint: See Question 1.2). The firm’s cost curve is C (Q) = 5Q. What is the profit-maximizing solution? (Hint: See “Using Calculus: Solving for the Profit-Maximizing Output” and Q&A 9.2.) C

1.12 Show that after a shift in the demand curve, a monopoly’s price may remain constant but its out- put may rise.

2. Market Power 2.1 Why is the ratio of the monopoly’s price to its mar-

ginal cost, p>MC, larger if the demand curve is less elastic at the optimum quantity? Can the demand curve be inelastic at that quantity?

2.2 When will a monopoly set its price equal to its mar- ginal cost?

2.3 The U.S. Postal Service (USPS) has a constitution- ally guaranteed monopoly on first-class mail. In 2018, it charged 50¢ for a stamp, which was not the profit-maximizing price–the USPS goal, alleg- edly, is to break even rather than to turn a profit. Following the postal services in Australia, Brit- ain, Canada, Switzerland, and Ireland, the USPS allowed Stamps.com to sell a sheet of twenty 50¢ stamps with a photo of your dog, your mommy, or whatever image you want for $23.99 (that’s $1.20 per stamp, or a 240% markup). Stamps.com keeps the extra beyond the 50¢ it pays the USPS. What is the firm’s Lerner Index? If Stamps.com is a profit- maximizing monopoly, what elasticity of demand does it face for a customized stamp? (Hint: See Q&A 9.5.)

2.4 According to the California Nurses Association, Tenet Healthcare hospitals marked up drugs sub- stantially. At Tenet’s Sierra Vista Regional Medical Center, drug prices were 1,840.80% of the hospi- tal’s costs (Chuck Squatriglia and Tyche Hendricks, “Tenet Hiked Drug Prices, Study Finds More Than Double U.S. Average,” San Francisco Chronicle, November 24, 2002: A1, A10). Assuming Tenet was maximizing its profit, what was the elasticity of demand that Tenet believed it faced? What was its Lerner Index for drugs? (Hint: See Q&A 9.5.) C

2.5 In 2015, Apple introduced the Apple Watch. Accord- ing to market research firm IHS, the cost of produc- ing the 38 mm Apple Watch Sport was $84. The price was $349. What was Apple’s price/marginal cost ratio? What was its Lerner Index? If Apple is a short- run profit-maximizing monopoly, what elasticity of demand did Apple believe it faced? (Hint: See Q&A 9.5.) C

*2.6 In 2009, the price of Amazon’s Kindle 2 was $359, while iSuppli estimated that its marginal cost was $159. What was Amazon’s Lerner Index? What elas- ticity of demand did it face if it was engaging in short- run profit maximization? (Hint: See Q&A 9.5.) C

2.7 When Apple introduced its first portable media player, the iPod, its constant marginal cost of pro- ducing the top-of-the-line model was $200 (iSup- pli), its fixed cost was approximately $736 million, and we estimate that its inverse demand function was p = 600 - 25Q, where Q is units measured in millions. What was Apple’s average cost function? Assuming that Apple was maximizing its short-run monopoly profit, what was its marginal revenue function? What were its profit-maximizing price and quantity, profit, and Lerner Index? What was the elasticity of demand at the profit-maximizing level? Show Apple’s profit-maximizing solution in a figure. (Hint: See Q&A 9.2 and Q&A 9.5.) C

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2.8 Xerox, the U.S. Postal Service, and McDonald’s have enjoyed significant market power in the past. List and explain three major factors that have eroded this market power.

2.9 Q&A 9.4 shows that a concert’s profit-maximizing price may exceed the price that allows the concert to sell out. Redraw the figure if the concert requires a large fixed cost (lighting, the stage’s appearance, and so forth). Indicate the profit areas if Ms. Swift sets a price such that (a) marginal revenue equals marginal cost or (b) the concert sells out. How do we know that the first profit area is greater than the second one?

3. Market Failure Due to Monopoly Pricing 3.1 A monopoly has a constant marginal cost of pro-

duction of $1 per unit and a fixed cost of $10. Draw the firm’s MC, AVC, and AC curves. Add a down- ward-sloping demand curve, and show the profit- maximizing quantity and price. Indicate the profit as an area on your diagram. Show the deadweight loss.

3.2 A monopoly has an inverse demand function given by p = 480 - 4Q and a constant marginal cost of 40. Calculate the deadweight loss if the monopoly charges the profit-maximizing price.

3.3 A monopoly’s inverse demand function is p = 160 - 2Q, and it has no fixed cost. Initially, its marginal cost is 12. Now, the firm makes a process innovation that reduces its marginal cost to 4. Deter- mine the price, quantity, consumer surplus, profit, total surplus, and deadweight loss before and after the innovation. What share of the increased total surplus goes to consumers?

3.4 What is the effect of a lump-sum tax (which is like an additional fixed cost) on a monopoly? (Hint: Con- sider the possibility that the firm may shut down, and see Q&A 9.6.)

3.5 If the inverse demand function is p = 200 - 2Q and the marginal cost is constant at $20, how does charging the monopoly a specific tax of t = $20 per unit affect price and quantity and the surplus of con- sumers, the monopoly, and society (where society’s surplus includes the tax revenue)? What is the inci- dence of the tax on consumers? (Hint: See Q&A 9.6.)

*3.6 Show mathematically that a monopoly may raise the price to consumers by more than a specific tax imposed on it. (Hint: Consider a monopoly facing a constant-elasticity demand function Q = Ape where e is a negative constant greater than 1 in abso- lute value, and with a constant marginal cost, m.) C

3.7 Q&A 9.6 illustrates the effect of imposing a specific tax of $8 per unit of a monopoly’s output. Suppose that instead of charging a specific tax, the government

charges a profit tax of 10%. How does this profit tax affect the equilibrium price and quantity, consumer surplus, producer surplus, and total surplus?

4. Causes of Monopoly *4.1 Can a firm be a natural monopoly if it has a U-shaped

average cost curve? Why or why not? (Hint: See Q&A 9.7.)

*4.2 Can a firm operating in the upward-sloping portion of its average cost curve be a natural monopoly? Explain. (Hint: See Q&A 9.7.)

4.3 Figure 9.6 shows that two firms producing 6 units each have a higher total cost than one firm produc- ing 12 units. Given the cost function underlying Figure 9.6, would two firms each producing output Q ( 7 0) always incur more total cost than one firm producing 2Q? (Hint: See Q&A 9.7.)

4.4 Once the copyright runs out on a book or a piece of music, it can legally be placed on the internet for anyone to download. In 1998 the U.S. Congress extended the copyright law to 95 years after the orig- inal publication. But the copyright holds for only 50 years in Australia and 70 years in the European Union. Thus, an Australian website could post Gone with the Wind, a 1936 novel, or Elvis Presley’s 1954 single “That’s All Right,” while a U.S. site could not. Obviously, this legal nicety won’t stop U.S. fans from downloading from Australian or European sites. Discuss how limiting the length of a copyright would affect the pricing used by the publisher of a novel.

4.5 In the Mini-Case “Botox,” consumer surplus, trian- gle A, equals the deadweight loss, triangle C. Show that this equality is a result of the linear demand and constant marginal cost assumptions.

5. Advertising 5.1 Using a graph, explain why a firm might not want

to spend money on advertising, even if such an expenditure would shift the firm’s demand curve to the right.

*5.2 A monopoly’s inverse demand function is p = 100 - Q + (5A - A2) >Q, where Q is its quan- tity, p is its price, and A is the level of advertising. Its marginal cost of production is constant at 10, and its cost of a unit of advertising is 1. What are the firm’s profit-maximizing price, quantity, and level of advertising? (Hint: See Q&A 9.8.) C

5.3 A monopoly’s inverse demand function is p = Q-0.25A0.5, where Q is its quantity, p is its price, and A is the level of advertising. Its constant mar- ginal and average cost of production is 6, and its cost of a unit of advertising is 0.25. What are the

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firm’s profit-maximizing price, quantity, and level of advertising? (Hint: See Q&A 9.8.) C

5.4 Canada subsidizes Canadian magazines to offset the invasion of foreign (primarily U.S.) magazines, which take 90% of the country’s sales. The Canada Magazine Fund provides a lump-sum subsidy to various magazines to “maintain a Canadian presence against the overwhelming presence of foreign maga- zines.” Eligibility is based on high levels of invest- ment in Canadian editorial content and reliance on advertising revenues. What effect will a lump-sum subsidy have on the number of subscriptions sold?

5.5 Use a diagram similar to Figure 9.7 to illustrate the effect of social media on the demand for Super Bowl commercials. (Hint: See the Mini-Case “Super Bowl Commercials.”)

6. Internet Monopolies: Network Effects and Scale Economies

6.1 A monopoly chocolate manufacturer faces two types of consumers. The larger group, the hoi polloi, loves desserts and has a relatively flat, linear demand curve for chocolate. The smaller group, the snobs, is interested in buying chocolate only if the hoi polloi do not buy it. Given that the hoi polloi do not buy the chocolate, the snobs have a relatively steep, lin- ear demand curve. Show the monopoly’s possible outcomes—high price, low quantity; low price, high quantity—and explain the condition under which the monopoly chooses to cater to the snobs rather than to the hoi polloi.

*6.2 A monopoly produces a good with a network exter- nality at a constant marginal and average cost of 2. In the first period, its inverse demand function is p = 10 - Q. In the second period, its demand is p = 10 - Q unless it sells at least Q = 8 units in the first period. If it meets or exceeds this target, then the demand curve rotates out by v (it sells v times as many units for any given price), so that its inverse demand function is p = 10 - Q>v. The monopoly knows that it can sell no output after the second period. The monopoly’s objective is to maximize the sum of its profits over the two periods. In the first period, should the monopoly set the output that maximizes its profit in that period? How does your answer depend on v? C (Hint: See the Managerial Implication “Introductory Prices”.)

6.3 What are the main factors that have created positive network externalities for eBay? (Hint: See the Mini- Case “eBay’s Critical Mass.”)

6.4 In the past, Games Unlimited sold copies of its trademark computer game on DVD. It faced inverse demand function p = 60 - Q and had cost func- tion C = 100 + 20Q. It recently switched to sell- ing its game online via the internet. Demand was unchanged, but its cost function changed as fixed costs rose to 500 but marginal cost dropped to zero: C = 500. Assuming that Games Unlimited maxi- mizes profit, what effect did moving from DVD to internet distribution have on price, quantity, con- sumer surplus, and profit?

7. Managerial Problem 7.1 Under what circumstances will a drug company

charge more for its drug after its patent expires?

7.2 Does the Managerial Solution change if the entry of the generic causes a parallel shift to the left of the patent monopoly’s linear demand curve?

7.3 Some people propose reducing the number of years that a drug patent lasts, but their critics argue that such a change would result in even higher prices dur- ing the patent period as companies would need to recover drug development costs more quickly. Is this argument valid if drug companies maximize profit?

8. MyLab Economics Spreadsheet Exercises28

8.1 A monopoly faces the inverse demand function: p = 100 - 2Q, with the corresponding marginal revenue function, MR = 100 - 4Q. The firm’s total cost of production is C = 50 + 10Q + 3Q2, with a corresponding marginal cost of MC = 10 + 6Q.

a. Create a spreadsheet for Q = 1, 2, 3, .  .  .  , 15. Using the MR = MC rule, determine the profit- maximizing output and price for the firm and the consequent level of profit.

b. Calculate the Lerner Index of monopoly power for each output level and verify its relationship with the value of the price elasticity of demand (e) at the profit-maximizing level of output.

c. Now suppose that a specific tax of 5 per unit is imposed on the monopoly. What is the effect on the monopoly’s profit-maximizing price?

8.2 A monopoly faces the demand function Q = 30 - p. Its inverse demand function is therefore p = 30 - Q, so its marginal revenue function is MR = 30 - 2Q. The firm’s cost function is C = 6Q + Q2, so its mar- ginal cost is MC = 6 + 2Q. The monopoly sets its price. Its quantity is determined by the demand function.

28The spreadsheet exercises in this chapter are based largely on the work of Satyajit Ghosh, in cooperation with the authors. The answers are available on MyLab Economics.

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a. Create a spreadsheet with headings Price, Quan- tity, Revenue, Cost, Profit, Marginal Revenue, and Marginal Cost. Enter prices ranging from 15 to 30 in increments of one in Column A (the price column). Enter the appropriate formulas in the other cells in the spreadsheet to calculate the values of the other variables for each price. For example, the price of 15 goes in cell A2, the quantity demanded at that price goes in cell B2, the resulting revenue at that price and quantity goes in cell C2, and so on. Find the price that maximizes profit and verify that MR = MC at this price. (Hint: See Q&A 9.3.)

b. Add columns for consumer surplus and total surplus in your spreadsheet. The formula for consumer surplus is CS = 0.5(30 - p)Q. The firm’s producer surplus equals its profit because it has no fixed cost. Total surplus is the sum of the consumer surplus and the pro- ducer surplus. Find the price that maximizes

total surplus and verify that p = MC at this price. If the profit-maximizing monopoly price is charged instead of the price that maximizes total surplus, what is the deadweight loss?

c. In addition to using the method described in parts a and b, use Excel’s Solver tool to find the price that maximizes profit and the price that maximizes consumer surplus. (Hint: See the instructions for using Solver in Question 6.2 of Chapter 8 or use Excel’s Help feature.)

8.3 A firm’s demand function is Q = 110 - p + 2A0.5, where A is the amount of advertising undertaken by the firm and the price of advertising is one. The firm’s cost of production is C = 50 + 10Q + 2Q2. The government imposes a binding price control at $135. Use Excel to determine the profit-maximizing level of advertising. (Hint: Try advertising levels that vary in hundreds from 0 to $1,000. Select the most profitable range and try smaller increments within that range.)

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Sales are not the only means that firms use to charge customers different prices. Why are airline fares often substantially less if you book in advance? Why do the spiritualists who live at the Wonewoc Spiritualist Camp give readings for $60 for half an hour, but charge seniors only $50 on Wednesdays?1 Why are some goods, including computers and software, combined and sold as a bundle? To answer these questions, we need to examine how monopolies and other noncompeti- tive firms set prices.

In Chapter 9, we examined how a monopoly maximizes its profit when it uses uni- form pricing: charging the same price for every unit sold of a particular good. However, a monopoly can increase its profit if it can use nonuniform pricing, charging consumers different prices for the same product or charging a single customer a price that depends on the number of units the customer buys. In this chapter, we analyze nonuniform pricing for monopolies, but similar principles apply to any firm with market power.

1www.campwonewoc.org/index.html, July 24, 2018.

10 Pricing with Market Power Everything is worth what its purchaser will pay for it.

—Publilius Syrus (first century b.c.)

Because many retail managers use sales—temporarily setting the price below the usual price—some customers pay lower prices than others over time. Grocery stores are particularly likely to put products on sale frequently. In large U.S. supermarkets, a soft drink brand is on sale 94% of the time. Either Coke or Pepsi is on sale half the weeks in a year.

Heinz ketchup controls about 60% of the U.S. ketchup market, 70% of the Canadian market and 80% of the market in the U.K. The Kraft Heinz company sells hundreds of millions of bottles of Heinz ketchup per year in more than 140 countries. Approximately 200 million U.S. consumers used Heinz ketchup in 2018. When Heinz ketchup goes on sale, switchers— ketchup customers who normally buy whichever brand is least expensive—purchase Heinz rather than the low-price generic ketchup. How can Heinz’s managers design a pattern of sales that maximizes profit by obtaining extra sales from switchers without losing substantial sums by selling to its loyal custom- ers at a discount price? Under what conditions does it pay for Heinz to have a policy of periodic sales?

Sale Prices

Managerial Problem

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As we saw in Chapter 9, a monopoly that sets a uniform price sells only to custom- ers who value the good enough to buy it at the monopoly price, and those custom- ers receive some consumer surplus. The monopoly does not sell the good to other customers who value the good at less than the single price, even if those consumers would be willing to pay more than the marginal cost of production. These lost sales cause deadweight loss, which is the foregone value of these potential sales in excess of the cost of producing the good.

A firm with market power can earn a higher profit using nonuniform pricing than by setting a uniform price for two reasons. First, the firm captures some or all of the single-price consumer surplus. Second, the firm converts at least some of the single- price deadweight loss into profit by charging a price below the uniform price (but above the firm’s marginal cost) to some customers who would not purchase at the single-price level. A monopoly that uses nonuniform pricing can lower the price to these otherwise excluded consumers without lowering the price to consumers who are willing to pay higher prices.

In this chapter, we examine several types of nonuniform pricing including price discrimination, two-part pricing, bundling, and peak-load pricing. The most common form of nonuniform pricing is price discrimination: charging consumers different prices for the same good based on individual characteristics of consumers, on mem- bership in an identifiable subgroup of consumers, or on the quantity purchased by the consumers. For example, regular subscribers to the Wall Street Journal Classic package of print and online access pay $222 annually, while students, who are price sensitive, are offered the same product for only about 22% of that price, $49 for the year.

Some firms with market power use other forms of nonuniform pricing to increase profits. A firm may use two-part pricing, charging a customer one fee for the right to buy the good and an additional fee for each unit purchased. For example, members of health or golf clubs typically pay an annual fee to belong to the club and then pay an additional amount each time they use the facilities. Similarly, cable television companies often charge a monthly fee for basic service and an additional fee (pay- per-view) for certain shows.

Another type of nonuniform pricing is called bundling, where several products are sold together as a package. For example, many restaurants provide full-course dinners for a fixed price that is less than the sum of the prices charged if the items (appetizer, main dish, and dessert) are ordered separately (à la carte).

Finally, some firms use peak-load pricing: charging higher prices in periods of peak demand than at other times. For example, ticket prices for flights from cold northern cities to Hawaii are higher in the winter months, when demand is higher than in the summer.

Learning Objectives

1. List the conditions necessary to price discriminate.

2. Show how perfect price discrimination extracts all surplus from consumers.

3. Describe how a firm sets different prices for various consumer groups to raise its profit.

4. Demonstrate how a firm can increase its profit by charging prices based on the quantities consumers buy.

5. Illustrate how a firm may raise its profit by charging an access fee and a per-unit price.

6. Determine when a firm can increase its profit by selling related products in a bundle.

7. Explain why firms charge higher prices in periods of peak demand.

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30910.1 Conditions for Price Discrimination

10.1 Conditions for Price Discrimination We start by studying the most common form of nonuniform pricing, price discrimina- tion, where a firm charges various consumers different prices for a good.2 Many people complain that price discrimination is irrational:

2Price discrimination is generally legal in the United States unless it harms competition between firms, as specified in the Robinson-Patman Act of 1936.

However, many (but not all) firms can profit by price discriminating.

Why Price Discrimination Pays For almost any good or service, some consumers are willing to pay more than oth- ers. A firm that sets a single price faces a trade-off between charging consumers with a high willingness to pay a high price and charging a low enough price to sell to other customers with a lower willingness to pay. As a result, a single-price firm sets an intermediate price. By price discriminating, a firm can partially or entirely avoid this trade-off.

As with any kind of nonuniform pricing, price discrimination increases profit above the uniform pricing level through two channels. Price discrimination can extract additional consumer surplus from consumers who place a high value on the good and can simultaneously sell to new customers who would not be willing to pay the profit-maximizing uniform price. We use a pair of extreme examples to illustrate these two benefits of price discrimination to firms—capturing more of the consumer surplus and selling to more customers.

Suppose that the only movie theater in town has two types of patrons: college students and senior citizens. College students see the Saturday night movie if the price is $20 or less, and senior citizens attend if the price is $10 or less. Thus, col- lege students have a willingness to pay $20 and senior citizens have a willingness to pay $10. For simplicity, we assume that the theater incurs no cost when showing the movie, so profit is the same as revenue. We also assume that the theater is large enough to hold all potential customers, so the marginal cost of admitting one more customer is zero. Table 10.1 shows how pricing affects the theater’s profit.

In panel a, the theater potentially has 10 college student and 20 senior citizen cus- tomers. If the theater charges everyone $10, its profit is $300 because all 30 potential customers buy a ticket. If it charges $20, the senior citizens do not go to the movie, so the theater makes only $200, receiving $20 each from the 10 college students. Thus, if the theater charges everyone the same price, it maximizes its profit by setting the price at $10. The theater does not want to charge less than $10 because the same number of people go to the movie as when $10 is charged. Charging between $10 and $20 is less profitable than charging $20 because no extra seniors go and the col- lege students are willing to pay $20. Charging more than $20 results in no customers.

Common Confusion It can’t pay for a firm to charge some consumers a differ- ent price than others.

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If the price is $10, the seniors have no consumer surplus: They pay exactly what seeing the movie is worth to them. Seeing the movie is worth $20 to the college students so, if the price is only $10, each has a consumer surplus of $10, and their combined consumer surplus is $100.

If the theater can price discriminate by charging senior citizens $10 and college students $20, its profit increases to $400. Its profit rises because the theater makes $200 from the seniors (the same amount as when it was selling all tickets for $10) but gets an extra $100 from the college students ($10 more from each of the 10 students). By price discriminating, the theater sells the same number of seats but makes more money from the college students, capturing all the consumer surplus they had under uniform pricing. Neither group of customers has any consumer surplus if the theater price discriminates.

In panel b, the theater potentially has 10 college student and 5 senior citizen cus- tomers. If the theater must charge a single price, it charges $20. Only college students see the movie, so the theater’s profit is $200. (If it charges $10, both students and seniors go to the theater, but its profit is only $150.) If the theater can price discrimi- nate and charge seniors $10 and college students $20, its profit increases to $250. Here the gain from price discrimination comes from selling more tickets (those sold to seniors) and not from making more money on the same number of tickets, as in panel a. With price discrimination the theater earns as much from the students as without price discrimination, and makes more from the seniors. Neither customer group enjoys any consumer surplus.

These examples illustrate the two channels through which price discrimination can increase profit: charging some existing customers more or selling extra units. Leslie (1997) found that Broadway theaters in New York increase their profits 5% by price discriminating rather than using uniform prices.

In the examples just considered, the movie theater’s ability to increase its profits by price discrimination arises from its ability to segment the market into two groups, students and senior citizens, with different levels of willingness to pay.

(a) No Extra Customers from Price Discrimination

Pricing Profit from 10 College

Students Profit from 20 Senior

Citizens Total Profit

Uniform, $10 $100 $200 $300

Uniform, $20 $200 $0 $200

Price discrimination* $200 $200 $400

(b) Extra Customers from Price Discrimination

Pricing Profit from 10 College

Students Profit from 5 Senior

Citizens Total Profit

Uniform, $10 $100 $50 $150

Uniform, $20 $200 $0 $200

Price discrimination* $200 $50 $250

*The theater price discriminates by charging college students $20 and senior citizens $10. Notes: College students go to the theater if they are charged no more than $20. Senior citizens are willing to pay up to $10. The theater’s marginal cost for an extra customer is zero.

TABLE 10.1 Theater Profits Based on the Pricing Method Used

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31110.1 Conditions for Price Discrimination

Which Firms Can Price Discriminate For a firm to price discriminate profitably, it must meet three conditions.

First, a firm must have market power to price discriminate profitably. Without mar- ket power, a firm cannot charge any consumer more than the competitive price. A monopoly, an oligopoly firm, or a monopolistically competitive firm might be able to price discriminate. However, a perfectly competitive firm cannot price discrimi- nate because it must sell its product at the given market price.

Second, for a firm to price discriminate profitably, groups of consumers or individual consumers must have demand curves that differ, and the firm must be able to identify how its consumers’ demand curves differ. The movie theater knows that college students and senior citizens differ in their willingness to pay for a ticket, and Disneyland knows that tourists and local residents differ in their willingness to pay for admission. In both cases, the firms can identify members of these two groups by using driver’s licenses or other forms of identification. Similarly, if a firm knows that each indi- vidual’s demand curve slopes downward, it may charge each customer a higher price for the first unit of a good than for subsequent units.

Mini-Case Disneyland, in southern California, is a well-run operation that rarely misses a trick when it comes to increasing its profit. (Indeed, Disneyland prints its own money: When you enter the park, you can exchange U.S. currency for Disney dollars, which can be spent only in the park.)3

For part of 2018, Disneyland offered local, Southern Californians two-day and three-day theme park tickets at a 25% discount. This policy of charging locals a discounted price makes sense if out-of-town visitors are willing to pay more than locals and if Disneyland can prevent locals from selling discounted tickets to non-

locals. Imagine a Midwesterner who’s never been to Disneyland and wants to visit. Travel accounts for most of the trip’s cost, so spending a few extra dol- lars to enter the park makes little percentage differ- ence in the total cost of the visit and hence does not greatly affect that person’s decision about visiting Disneyland. In contrast, for a local who has been to Disneyland many times and for whom the entrance price is a larger share of the total cost, a slightly higher entrance fee might prevent a visit.4

Charging both groups the same price is not in Disney’s best interest. If Disney were to charge the higher price to everyone, many locals wouldn’t visit the park. If Disney were to use the lower price for everyone, it would be charging nonresidents much less than they are willing to pay.

3According to www.babycenter.com/cost-of-raising-child-calculator, it costs an average U.S. fam- ily $334,860 to raise a child from cradle through college. Parents can cut that total in half, however: They don’t have to take their kids to Disneyland. 4In 2012, a Southern Californian couple, Jeff Reitz and Tonya Mickesh, were out of work, so they decided to cheer themselves up by using their annual passes to visit Disneyland 366 days that year (a leap year).

Disneyland Pricing

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312 CHAPTER 10 Pricing with Market Power

Third, a firm must be able to prevent or limit resale to price discriminate. The price- discriminating firm must be able to prevent consumers who buy the good at low prices from reselling the good to customers who would otherwise pay high prices. Price discrimination doesn’t work if resale is easy because the firm would be able to make only low-price sales. A movie theater can charge different prices for different groups of customers because those customers normally enter the theater as soon as they buy their tickets, and therefore they do not have time to resell them. For events that sell tickets in advance, other methods can be used to prevent resale, such as having different colors for children’s tickets and adults’ tickets.

The first two conditions—market power and the ability to identify groups with different price sensitivities—are present in many markets. Usually, the biggest obsta- cle to price discrimination is a firm’s inability to prevent resale.

Preventing resale is easier in certain industries than in others. In industries where resale is initially easy, managers can act to make resale more costly.

Resale is difficult or impossible for most services. If a plumber charges you less than your neighbor for fixing a clogged water pipe, you cannot make a deal with your neighbor to resell this service. Even for physical goods, resale is difficult when transaction costs are high. The higher the transaction costs a consumer must incur to resell a good, the less likely resale becomes. Suppose that you are able to buy a 50-pound bag of cement (which, in addition to being heavy, is also dusty) for $1 less than the usual price. Would you take the time and trouble to buy the cement and seek a buyer willing to pay an extra dollar, or would the transaction costs be prohibitive? The more valuable and widely consumed a product is, the more likely it is that transaction costs are low enough to allow resale.

Some firms act to raise transaction costs or otherwise make resale difficult. If your college requires that someone with a student ticket to a sporting event show a student identification card containing a photo, it will be difficult to resell your low-price tickets to nonstudents, who pay higher prices. When students at some universities buy computers at lower-than-usual prices, they must sign a contract that forbids resale of the computer. Disney prevents resale by locals, who can buy a ticket at a lower price, by checking driver’s licenses and requiring that the ticket be used for same-day entrance.

Governments frequently aid price discrimination by preventing resale. Gov- ernment tariffs (taxes on imports) limit resale by making it expensive to buy a branded good in a low-price country and resell it in a high-price country. Under U.S. trade laws, certain brand-name perfumes may not be sold in the United States except by their manufacturers. Similarly, if the countries have very different safety rules, a product sold in one country might not be legally sold in another.

However, resale is legal for many products. Imported goods that go through legal but unofficial channels that are unauthorized by the original manufacturer are said to sell in a gray market or parallel market. To make such a transaction unat- tractive, Nikon provides a warranty on its cameras that is only applicable in the country in which the good is supposed to be sold.

Preventing Resale

Managerial Implication

Mini-Case During the holiday season, stores often limit how many of the hottest items— such as this year’s best-selling toy—a customer can buy. But it may surprise you that websites of luxury-goods retailers such as Saks Fifth Avenue, Neiman Marcus, and Bergdorf Goodman limit how many designer handbags one can

Preventing Resale of Designer Bags

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31310.2 Perfect Price Discrimination

Not All Price Differences Are Price Discrimination Not every seller who charges consumers different prices is price discriminating. A seller price discriminates by charging different prices for units of a good that cost the same to produce. In contrast, e-book and hardcopy versions of the same book sell for different prices in large part because these different versions have different costs.

The Andrew Sean Greer novel Less, the winner of the 2018 Pulitzer Prize for fic- tion, sold on Amazon in July 2018 for $9.88 as a Kindle e-book and for $17.68 in hardcover. This price difference reflects the lower marginal cost of selling an e-book and is therefore not due purely to price discrimination by the publisher.

Types of Price Discrimination Traditionally, economists focus on three types of price discrimination: perfect price discrimination, group price discrimination, and nonlinear price discrimination. With perfect price discrimination—also called first-degree price discrimination—the firm sells each unit at the maximum amount any customer is willing to pay. Under perfect price discrimination, the price differs across consumers and a given consumer may pay higher prices for some units than for others.

With group price discrimination—also called third-degree price discrimination—the firm charges each group of customers a different price, but it does not charge dif- ferent prices within the group. The price that a firm charges a consumer depends on that consumer’s membership in a particular group. Thus, not all customers pay different prices: The firm sets different prices only for a few groups of customers. Group price discrimination is the most common type of price discrimination.

A firm engages in nonlinear price discrimination (also called second-degree price discrimination) when it charges a different price for large purchases than for small quan- tities, so that the price paid varies according to the quantity purchased. With pure non- linear price discrimination, all customers who buy a given quantity pay the same price; however, firms can combine nonlinear price discrimination with group price discrimi- nation, setting different nonlinear price schedules for different groups of consumers.

10.2 Perfect Price Discrimination A firm with market power that knows exactly how much each customer is willing to pay for each unit of its good and is able to prevent resale can charge each person his or her reservation price: the maximum amount a person is willing to pay for a

buy. For example, the Bergdorf Goodman site won’t let you order more than one Prada Lizard Trimmed Nylon Shoulder Bag at $4,190 (darn!).

Some websites explain that they impose limits due to “popular demand.” The more plausible explanation is that the restriction facilitates international price discrimination. The handbag manufacturers force U.S. retailers to limit the number one person can buy to prevent people from buying large numbers of bags and reselling them in Europe or Asia where the same items in Prada and Gucci stores often cost 20% to 40% more. By purchasing from Prada’s U.S. online site, one must agree that the purchase is solely for private household use, that commercial resale or sale outside the United States is not authorized, and that the company reserves the right to reject orders and to limit order quantities.

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unit of output. Such an all-knowing firm can perfectly price discriminate. By selling each unit of its output to the customer who values it the most at the maximum price that person is willing to pay, the perfectly price-discriminating monopoly captures all possible consumer surplus.

Perfect price discrimination is rare because firms do not have perfect information about their customers. Nevertheless, it is useful to examine perfect price discrimi- nation because it is the most efficient form of price discrimination and provides a benchmark against which we can compare other types of nonuniform pricing.

We now show how a firm with full information about consumer reservation prices can use that information to perfectly price discriminate. Next, we compare the mar- ket outcomes (price, quantity, surplus) of a perfectly price-discriminating monopoly to those of perfectly competitive and uniform-price monopoly firms.

How a Firm Perfectly Price Discriminates A firm with market power that can prevent resale and has full information about its customers’ willingness-to-pay price discriminates by selling each unit at its reserva- tion price—the maximum amount any consumer would pay for it. The maximum price for any unit of output is given by the height of the demand curve at that output level. In the demand curve facing a monopoly in Figure 10.1, the first customer is willing to pay $6 for a unit, the next is willing to pay $5, and so forth. A perfectly price-discriminating firm sells its first unit of output for $6. Having sold the first unit, the firm can get at most $5 for its second unit. The firm must drop its price by $1 for each successive unit it sells.

FIGURE 10.1 Perfect Price Discrimination

The monopoly can charge $6 for the first unit, $5 for the sec- ond, and $4 for the third, as the demand curve shows. Its mar- ginal revenue is MR1 = $6 for the first unit, MR2 = $5 for the second unit, and MR3 = $4 for the third unit. Thus, the demand curve is also the marginal rev- enue curve. Because the firm’s marginal and average cost is $3 per unit, it is unwilling to sell at a price below $3, so it sells 4 units, point e, and breaks even on the last unit. MR4 = $3

p, $

p er

u ni

t

6

5

4

3

2

1

Q, Units per day

6543210

MC e

Demand, Marginal revenue

MR1 = $6 MR2 = $5 MR3 = $4

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31510.2 Perfect Price Discrimination

A perfectly price-discriminating firm’s marginal revenue is the same as its price. As the figure shows, the firm’s marginal revenue is MR1 = $6 on the first unit, MR2 = $5 on the second unit, and MR3 = $4 on the third unit. As a result, if it can perfectly price discriminate, a firm’s marginal revenue curve is the same as its demand curve.

This firm has a constant marginal cost of $3 per unit. It pays for the firm to pro- duce the first unit because the firm sells that unit for $6, so its marginal revenue exceeds its marginal cost by $3. Similarly, the firm sells the second unit for $5 and the third unit for $4. The firm breaks even when it sells the fourth unit for $3. The firm is unwilling to sell more than four units because its marginal cost would exceed its marginal revenue on all successive units. Thus, like any profit-maximizing firm, a perfectly price-discriminating firm produces at point e, where its marginal revenue curve intersects its marginal cost curve.

A firm’s revenue is the sum of the marginal revenues for each unit sold. There- fore, this perfectly price-discriminating firm’s revenue is MR1 + MR2 + MR3 + MR4 = $6 + $5 + $4 + $3 = $18, which is the area under its marginal revenue curve up to the number of units, four, it sells. If the firm has no fixed cost, its cost of producing four units is $12 = $3 * 4, so its profit is $6.

Perfect Price Discrimination Is Efficient but Harms Some Consumers Perfect price discrimination is efficient: It maximizes the sum of consumer surplus and producer surplus. Therefore, both perfect competition and perfect price dis- crimination maximize total surplus. However, the entire surplus goes to the firm with perfect price discrimination, whereas consumers obtain some surplus under competition.

If the market illustrated in Figure 10.2 is competitive, the intersection of the demand curve and the marginal cost curve, MC, determines the competitive equi- librium at ec, where price is pc and quantity is Qc. Consumer surplus is A + B + C, producer surplus is D + E, and society suffers no deadweight loss. The market is efficient because the price, pc, equals the marginal cost, MCc. With a single-price monopoly (which charges all its customers the same price), the intersection of the MC curve and the single-price monopoly’s marginal revenue curve, MRs, determines the output, Qs.5 The monopoly operates at es, where it charges ps. The deadweight loss from monopoly is C + E. This efficiency loss is due to charging a price, ps, above marginal cost, MCs, so less is sold than in a competitive market.

A perfectly price-discriminating firm sells each unit at its reservation price, which is the height of the demand curve. As a result, the firm’s price-discrimination marginal revenue curve, MRd, is the same as its demand curve. It sells the Qd unit for pc, where its marginal revenue curve, MRd, intersects the marginal cost curve, MC, so it just covers its marginal cost on the last unit. The firm is unwilling to sell additional units because its marginal revenue would be less than the marginal cost of producing them.

A perfectly price-discriminating firm’s producer surplus from the Qd units it sells is the area below its demand curve and above its marginal cost curve, A + B + C + D + E. Its profit is the producer surplus minus its fixed cost, if any. Consumers receive no consumer surplus because each consumer pays his or her res- ervation price. The perfectly price-discriminating firm’s profit-maximizing solution

5We assume that if we convert a monopoly into a competitive industry, the industry’s marginal cost curve—the lowest cost at which an additional unit can be produced by any firm—is the same as the monopoly MC curve. The industry MC curve is the industry supply curve (Chapter 8).

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316 CHAPTER 10 Pricing with Market Power

has no deadweight loss because the last unit is sold at a price, pc, that equals the mar- ginal cost, MCc, as in a competitive market. Thus, both a perfect price discrimination outcome and a competitive equilibrium are efficient.

The perfect price discrimination solution differs from the competitive equilibrium in two important ways. First, in the competitive equilibrium, everyone is charged a price equal to the equilibrium marginal cost, pc = MCc; however, in the perfect price discrimination equilibrium, only the last unit is sold at that price. The other units are sold at customers’ reservation prices, which are greater than pc. Second, consumers receive some net benefit (consumer surplus, A + B + C) in a competitive market, whereas a perfectly price-discriminating monopoly captures all the surplus or potential gains from trade. Thus, perfect price discrimination does not reduce efficiency—both output and total surplus are the same as under competition—but it does redistribute income away from consumers. Consumers are much better off under competition.

FIGURE 10.2 Competitive, Single-Price, and Perfect Price Discrimination Outcomes

Monopoly

Perfect Price Competition Single Price Discrimination

Consumer Surplus, CS 0

Producer Surplus, PS

A + B + C

D + E

A

B + D A + B + C + D + E

Total Surplus, TS = CS + PS A + B + C + D + E

Deadweight Loss

EA + B + C + D +

0

A + B + D

C + E 0

p, $

p er

u ni

t

E

D

C B

A

Q, Units per dayQs Qc = Qd

MCs

Demand, MRd

MRs

pc = MCc ec

esps

MC

In the competitive market equilibrium, ec, price is pc, quantity is Qc, consumer surplus is A + B + C, producer surplus is D + E, and society has no dead- weight loss. In the single-price monopoly equilibrium, es, price is ps, quantity is Qs, consumer surplus falls to A, producer surplus is B + D, and deadweight loss

is C + E. In the perfect price discrimination equilib- rium, the monopoly sells each unit at the customer’s reservation price on the demand curve. It sells Qd (= Qc) units, where the last unit is sold at its mar- ginal cost. Customers have no consumer surplus, but society has no deadweight loss.

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31710.2 Perfect Price Discrimination

Is a single-price or a perfectly price-discriminating monopoly better for con- sumers? The perfect price discrimination equilibrium is more efficient than the single-price monopoly equilibrium because more output is produced. A single-price monopoly, however, takes less consumer surplus from consumers than a perfectly price-discriminating monopoly. Consumers who put a relatively high value on the good are better off under single-price monopoly, where they have consumer surplus, than with perfect price discrimination, where they have none. Consumers with lower reservation prices who purchase from the perfectly price-discriminating monopoly but not from the single-price monopoly have no consumer surplus in either case. All the social gain from the extra output goes to the seller under perfect price dis- crimination. Consumer surplus is greatest with competition, lower with single-price monopoly, and eliminated by perfect price discrimination.

Mini-Case To show how perfect price discrimination differs from competition and single- price monopoly, we revisit the Mini-Case on Allergan’s Botox from Chapter 9. The graph shows our estimated linear demand curve for Botox and a constant marginal cost (and average variable cost) of $25 per vial. If the market were competitive (so that price equals marginal cost at ec), consumer surplus would be the triangle A + B + C = $750 million per year, and there would have been

Botox Revisited

Monopoly

Perfect Price Competition Single Price Discrimination

Consumer Surplus, CS A 0

Producer Surplus, PS

A + B + C

0 B A + B + C

A + B + CA + B + C A + B

Deadweight Loss 0 C 0

Total Surplus, TS = CS + PS

p, $

p er

v ia

l

2 2.07

A ≈ $187.5 million

C ≈ $187.5 million

B ≈ $375 million Demand

Q, Million vials of Botox per year

400

25

0

es

ec MC = AVC MR

775

1

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318 CHAPTER 10 Pricing with Market Power

Individual Price Discrimination Perfect price discrimination is rarely fully achieved in practice because firms lack full information about individuals’ reservation prices. For example, a coffee shop would have to know that Yi Lin is willing to pay $4 for her first cup of coffee, $3 for her second, and so on and then actually charge these amounts. We use the

no producer surplus or deadweight loss. In the (actual) single-price monopoly equilibrium, es, the Botox vials sell for $400 each, and one million vials are sold. The corresponding consumer surplus is triangle A = $187.5 million per year, producer surplus is rectangle B = $375 million, and the deadweight loss is tri- angle C = $187.5 million.

If Allergan could perfectly price discriminate, its producer surplus would double to A + B + C = $750 million per year, and consumers would obtain no consumer surplus. The marginal consumer would pay a price equal to the marginal cost of $25, just as in a competitive market.

Allergan’s inability to perfectly price discriminate costs the company dearly. Its producer surplus as a single-price monopoly is $375 million per year, which is lower than what it could earn if it perfectly price discriminated, A + B + C = $750 million per year. Society’s total surplus under single-price monopoly is lower than under perfect price discrimination by the deadweight loss, C, of $187.5 million per year, whereas consumers have no surplus with perfect price discrimination.

Q&A 10.1 How does total surplus change if the movie theater described in Table 10.1 goes from charging a single price to perfectly price discriminating?

Answer 1. Calculate and compare the total surplus for panel a (a) if the theater sets a single price

or (b) if it perfectly price discriminates. (a) If the theater sets the profit-maximizing single price of $10, it sells 30 tickets and makes a profit of $300. The 20 senior citizen customers are paying their reservation price, so they have no consumer surplus. The 10 college students have reservation prices of $20, so they have consumer surplus of $10 each for a total of $100. Thus, total surplus is $400: the sum of the producer surplus (which equals profit in this case) of $300, and the consumer surplus of $100. (b) If the firm perfectly price discriminates, it charges seniors $10 and college students $20. Because the theater is charging all customers their reservation prices, they have no consumer surplus. The firm’s profit rises to $400. Thus, total surplus is the same ($400) under both pricing systems because output stays the same.

2. Calculate and compare the total surplus for panel b (a) if the theater sets a single price or (b) if it perfectly price discriminates. (a) If the theater sets the profit-maximizing single price of $20, only college students attend and they receive no consumer surplus. The theater’s profit (producer surplus) is $200, so total surplus is $200. (b) With perfect price discrimination, consumers have no consumer surplus, but profit increases to $250, so total surplus rises to $250. Thus, total surplus is greater with perfect price discrimination and output is greater. (The result that total surplus increases if and only if output rises holds generally.)

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31910.2 Perfect Price Discrimination

term individual price discrimination to refer to a situation in which a firm charges individual-specific prices to different consumers, which may or may not exactly equal consumers’ reservation prices. Even if firms cannot achieve perfect price discrimina- tion, imperfect individual price discrimination can increase their profits significantly.

Some firms do a good job of estimating each person’s reservation price. At most car dealerships, a salesperson negotiates with potential buyers. During the discus- sions, the salesperson tries to determine each individual’s reservation price from the buyer’s comments and appearance. Is the potential buyer a local? Is the buyer wearing expensive clothing? Does the buyer claim to own other expensive cars? The salesperson uses this information to estimate the buyer’s reservation price and offers to sell the car at that price. As a result, prices vary across consumers for a given car. Similarly, the managers of the Suez Canal set tolls on an individual ship- by-ship basis, taking into account many factors such as weather and each ship’s alternative routes.

Private colleges request and receive financial information from students, which allows the schools to apply individual price discrimination. The schools give partial scholarships as a means of reducing the tuition for relatively poor students, who pre- sumably have lower willingness to pay than wealthier students. Epple et al. (2017) estimated that private schools raise tuition by an average of $210 to $510 for every $10,000 increase in family income.

Transaction costs are a major reason why these firms do not perfectly price dis- criminate: It is often too difficult or too costly to gather information about each customer’s reservation price for each unit of the product. However, recent advances in computer technologies have lowered these transaction costs, causing hotels, car and truck rental companies, cruise lines, airlines, and other firms to increasingly use individual price discrimination, as the following Mini-Case illustrates.

Mini-Case The ads that appear next to your Google search results depend on the terms in your search. That is, Google allows advertisers to contextually target people who search for particular phrases (Goldfarb, 2014). By making searches easy and fast with targeted ads, Google helps advertisers reach hard-to-find potential custom- ers. For example, a lawyer specializing in toxic mold lawsuits can place an ad that appears only when someone searches for “toxic mold lawyer.”

Google uses auctions to price ads. Advertisers place higher bids for the first listing on Google’s search page. Goldfarb and Tucker (2011) found that the amount lawyers are willing to pay for context-based ads depends on the dif- ficulty of making a match. The fewer the number of self-identified potential customers (the fewer people searching for a particular topic), the more lawyers are willing to pay per search request to advertise.

They also found that lawyers bid more when other methods of reaching potential clients are limited. Some states have anti-ambulance-chaser regula- tions, which prohibit personal injury lawyers from directly contacting potential clients by snail mail, phone, or e-mail for a few months after an accident. Search engine advertising prices per click are 5%–7% higher in those states than in others.

By taking advantage of advertisers’ desire to reach small, targeted segments of the population and varying the price according to advertisers’ willingness to pay using auctions, Google is achieving the equivalent of individual price discrimination.

Google Uses Bidding for Ads to Price Discriminate

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10.3 Group Price Discrimination Most firms have no practical way to estimate the reservation price for each of their customers. But many of these firms know which groups of customers are likely to have higher reservation prices on average than others. A firm engages in group price discrimination by dividing potential customers into two or more groups and setting different prices for each group. Consumer groups may differ by age (such as adults and children), by location (such as by country), or in other ways. All units of the good sold to customers within a group are sold at a single price. As with individual price discrimination, to engage in group price discrimination, a firm must have market power, be able to identify groups with different reservation prices, and prevent resale.

For example, first-run movie theaters with market power charge seniors a lower ticket price than they charge younger adults because typically older adults are unwilling to pay as much to see a movie. By admitting seniors immediately after they prove their age and buy tickets, the theater prevents resale.

Group Price Discrimination with Two Groups How does a firm set its prices if it sells to two (or more) groups of consumers with different demand curves and if resale between the two groups is impossible? We explain the process in the following example, which looks at a firm that sells to groups of consumers in different areas.

A patent gives Tesla the legal monopoly to produce and sell the Tesla S electric car. When Tesla started selling the Model S in 2012, it was the only luxury electric car. Even by 2018, it faced little competition from all-electric luxury cars. Tesla engages in group price discrimination by charging different prices in various countries. Resale is not a problem because Tesla honors its warranty only in the region or country where the car is sold.

A Graphical Approach. How should Tesla set its prices or equivalently its quantities in the United States and in Europe to maximize its total profit? Because Tesla currently manufactures in a single plant, its marginal cost is the same for all customers. A group price-discriminating monopoly with a constant marginal cost maximizes its total profit by maximizing its profit from each group separately, as a single-price monopoly would. Tesla sets its quantities so that the marginal revenue for each group equals the common marginal cost, m, which is about $30,000 per car.6 In 2017, American consumers bought about QA = 30 thousand cars at pA = $80 thousand. Europeans bought QE = 16 thousand cars at pE = $130 thousand (€110,000).7

Figure 10.3 shows our estimates of the linear demand curves in the two areas. In panel a, Tesla maximizes its U.S. profit by selling QA = 30 thousand cars, where its

6Reportedly according to Elon Musk, the CEO of Tesla: www.inverse.com/article/31597-tesla- secret-profit. The shipping cost to Europe is sufficiently low that including it would not change our calculations. 7The source of the price information for the Tesla Model S D100 is www.tesla.com. Prices vary somewhat across European countries. We are using the price for the Netherlands. We are not includ- ing government subsidies or taxes. The 2017 quantity data (rounded) come from http://europe .autonews.com/article/20180220/ANE/180219831/tesla-model-s-outsells-german-luxury-flagships- in-europe (viewed July 6, 2018). We estimated the linear demand curves using these data based on the assumption that Tesla is maximizing its profit.

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32110.3 Group Price Discrimination

marginal revenue equals its marginal cost MRA = m = $30 thousand (Chapter 9), and charging pA = $80 thousand. Similarly, in panel b, Tesla maximizes its European profit by selling QE = 16 thousand cars, where MRE = m = $30,000, at pB = $130 thousand.

Because the price-discriminating firm maximizes its profit by operating where its marginal revenue for each country equals its common marginal cost, m = $30 thousand, the marginal revenues in the two countries are equal:

MRA = m = MRE. (10.1)

FIGURE 10.3 Group Pricing of the Tesla S Car

p A , $

th ou

sa nd

p er

c ar

Q A , Thousand cars per year

π A

130

(a) United States

30 m

DWL A

30

80 CS

A

DA

π E

Q E

, Thousand cars per year

MRE

DWL E

p E , $

th ou

sa nd

s pe

r ca

r

(b) Europe

30 m

16

130

DEMRA

36.8

CS E

78

230

Tesla, the monopoly producer of the Model S all- electric car, charges more in Europe, pE = $130 thousand (€110,000), than in the United States, pA = $80 thousand, because demand is more elastic in the United States. Tesla sets the quan- tity independently in each country. It maximizes

profit by operating where its marginal revenue for each area equals its common, constant mar- ginal cost, m = $30 thousand. Consequently, the marginal revenues in the two countries are equal: MRA = m = MRE.

Maximizing Profit for a Group Discriminating Monopoly

Using Calculus We can also derive these results using calculus. The group discriminating monopo-ly’s total profit, π, is the sum of its American profit, πA, and its European profit, πE: π(QA, QE) = πA (QA) + πE (QE) = [RA (QA) - mQA] + [RE (QE) - mQE],

where RA (QA) = pA (QA)QA is the revenue function in the United States, pA (QA) is the U.S. inverse demand function, and RE (QE) and pE (QE) are similarly defined for Europe. Again, because of the constant marginal cost of production,

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322 CHAPTER 10 Pricing with Market Power

Prices and Elasticities. We can use Equation 10.1, MRA = m = MRE, to deter- mine how the prices in the two countries vary with the price elasticities of demand at the profit-maximizing outputs. Each country’s marginal revenue is a function of its price and the price elasticity of demand (Chapter 9). The U.S. marginal revenue is MRA = pA (1 + 1>eA), where eA is the price elasticity of demand for U.S. consumers, and the European marginal revenue is MRE = pE (1 + 1>eE), where eE is the price elasticity of demand for European consumers.

Rewriting Equation 10.1 using these expressions for marginal revenue, we find that

MRA = pAa1 + 1eA b = m = pE a1 + 1 eE b = MRE. (10.4)

Equation 10.4 implies that eA = pA> (m - pA).9 As m = $30 thousand, pA = $80 thousand, and pE = $130 thousand, Tesla must believe that eA = pA>[m - pA] = 80>[30 - 80] = -1.6. Similarly, it believes that eE = pE>[m - pE] = 130>[30 - 130] = -1.3.

We can rearrange Equation 10.4 to show that the ratio of prices in the two coun- tries is a function solely of the demand elasticities in those countries:

pE pA

= 1 + 1 > eA 1 + 1 > eE . (10.5)

9We can rewrite the equality pA(1 + (1>eA)) = m (Equation 10.4) as pA + pA>eA = m, which implies that pA>eA = m - pA or eA = pA> (m - pA).

the firm’s profit in either country depends only on the quantity that it sells in that country.8

To find the QA and QE that maximize Tesla’s total profit, we can maximize its profit in each country separately, as we did in the graphical approach. However, here we solve for the optimal quantities simultaneously (which we would have to do if the marginal cost were not constant). We differentiate the monopoly’s profit function with respect to each quantity, holding the other quantity fixed, and set these derivatives equal to zero:

0π(QA, QE)

0QA =

dRA (QA) dQA

- m = 0, (10.2)

0π(QA, QE)

0QE =

dRE (QE) dQE

- m = 0. (10.3)

According to Equation 10.2, the monopoly sets the marginal revenue in the United States, MRA = dRA>dQA, equal to its constant marginal cost, m. Similarly, Equation 10.3 says the marginal revenue in Europe, MRE = dRE>dQE, equals the marginal cost, m. Consequently, Equation 10.1 holds: MRA = m = MRE.

8For a more general cost function, C (QA, QB), Tesla’s profit in each country would depend on the amount it sold in both countries.

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32310.3 Group Price Discrimination

Substituting the prices and the demand elasticities into Equation 10.5, we deter- mine that

pE pA

= $130 $80

= 1.625 = 1 + 1 > ( -1.6) 1 + 1 > ( -1.3) =

1 + 1 > eA 1 + 1 > eE .

Thus, Tesla apparently believes that the European demand curve is less elastic at its profit-maximizing price than is the U.S. demand curve. Specifically, eE = -1.3 is closer to zero than is eA = -1.6. Consequently, Tesla charges European consumers 62.5% more than it charges U.S. customers.

Mini-Case Under U.S. federal law, firms may price discriminate between people except if based on race, religion, nationality, or gender. Firms often discriminate based on age.

You’ve probably noticed that movie theaters offer discount admission to chil- dren and senior citizens. Thus, it was probably a large shock to Tinder, an online dating app, when it was sued for price discriminating based on age.

Allan Candelore filed a class-action lawsuit on behalf of himself and others over the age of 30 who had to pay $19.99 a month to use the app’s premium service, Tinder Plus, while those under 30 paid only $9.99 to $14.99. In a ruling that, under California state law, Tinder was unlawfully discriminating against users over 30, a California state appeals court said that “we swipe left, and reverse,” using Tinder’s terminology to express disapproval.10

10 Individual states may impose stricter restrictions on price discrimination than under federal law.

Age Discrimination

Q&A 10.2 Greyhound Lines is the monopoly long-distance bus line on many routes in North America, especially those connecting small towns. Greyhound offers a senior discount to passengers aged 62 or older. Suppose that for a particular route Greyhound faces an hourly linear inverse demand function of p1 = 60 - 5Q1 for seniors and p2 = 90 - 10Q2 for other passengers (“adults”). The marginal cost of an extra passenger is 10. What price would a profit-maximizing monopoly charge for each age group if it is allowed to price discriminate? What price would it charge if price discrimination by age is prohibited?

MC MR1 D1

p 1 , $

p er

ti ck

et

Q1, Tickets per hour

10

35

60

5 12

(a) Seniors

MC MR

p, $

p er

ti ck

et

Q, Tickets per hour

10

90

60

40

3 9 21

(c) Single-Price Monopoly

MC D2MR2

p 2 , $

p er

ti ck

et

Q2, Tickets per hour

10

90

50

4 9

(b) Adults

D

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324 CHAPTER 10 Pricing with Market Power

Answer If price discrimination by age is legal: 1. Determine the profit-maximizing quantity and price that the bus line sets for each

age group by setting the relevant marginal revenue equal to the marginal cost. If Greyhound can price discriminate, it sets a monopoly price independently for each group. The marginal revenue curve is twice as steeply sloped as is the linear inverse demand function (see Q&A 9.1), so the marginal revenue function for seniors is MR1 = 60 - 10Q1, as panel a of the figure shows. Grey- hound maximizes its profit where its marginal revenue function equals its marginal cost, MR1 = 60 - 10Q1 = 10 = MC. Solving this equation, we find that its profit-maximizing output is Q1 = 5. Substituting this expression back into the inverse demand function, we learn that the profit-maximizing price is p1 = 60 - 25 = 35, as panel a illustrates. Because the inverse demand function for adults is p2 = 90 - 10Q2, the bus line chooses Q2 such that MR2 = 90 - 20Q2 = 10 = MC. Thus, it maximizes its profit where Q2 = 4 and p2 = 50, as panel b shows.

If price discrimination by age is not legal: 2. Derive the total demand curve. If Greyhound cannot price discriminate, it charges

the same price, p, to all users. The company faces the total demand curve in panel c, which is the horizontal sum of the demand curves for each of the two age groups in panels a and b (Chapter 2). If the price is between 60 and 90, the quantity demanded is positive only for the adults, so the total demand curve (panel c) is the just the adults’ demand curve (panel b). If the price is less than 60, then both groups demand a positive quantity, and the total demand curve in panel c is the horizontal sum of the two age groups’ demand curves (panels a and b).11 As panel c shows, the total demand curve has a kink at p = 60, because the quantity demanded by seniors is positive only at lower prices.

3. Determine the marginal revenue curve corresponding to the total demand curve. Because the total demand curve has a kink at p = 60, the corresponding marginal revenue curve has two sections. At prices greater than 60, the marginal revenue curve is that of the adult group. At prices less than 60, the inverse total demand function is p = 70 - (1>0.3)Q, so the marginal revenue function has twice the slope: MR = 70 - (2>0.3)Q. Panel c shows that the marginal revenue curve jumps—is discontinuous—at the quantity where the total demand curve has a kink.

4. Solve for the single-price monopoly solution. Greyhound maximizes its profit where its marginal revenue equals its marginal cost. From inspecting panel c, we learn that the intersection occurs in the section where both age groups have positive demand, so that MR = 70 - (2>0.3)Q = 10 = MC. Solving this equation, we find that the profit-maximizing output is Q = 9. Substituting that quantity into the inverse total demand function, we learn that Greyhound charges p = 40. Thus, a single-price monopoly would charge a price of 40, which lies between the two prices it would charge if it could price discriminate: 35 6 40 6 50.

11Rearranging the inverse demand functions, we find that the seniors’ demand function is Q1 = 12 - 0.2p1 and the adults’ demand function is Q2 = 90 - 0.1p2. As a result for a price less than 60, the total demand function is Q = (12 - 0.2p) + (9 - 0.1p) = 21 - 0.3p, where Q = Q1 + Q2 is the total quantity that the monopoly sells and p is the common price. Therefore the inverse demand function is p = 70 - ( 10.3)Q for prices less than 60.

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32510.3 Group Price Discrimination

Identifying Groups Firms use two main approaches to divide customers into groups. One method is to divide buyers into groups based on observable characteristics of consumers that the firm believes are associated with unusually high or low reservation prices or demand elasticities. For example, age is often used as a basis for price discrimination and is often easy to check, as at a movie theater or buying a ticket from Greyhound. Similarly, as with Tesla, some firms charge customers higher prices in one country than another.

The second approach is to identify and divide consumers on the basis of their actions: The firm allows consumers to self-select the group to which they belong. For example, customers may be identified by their willingness to spend time to buy a good at a lower price or to order goods and services in advance of delivery.

Firms use differences in the value customers place on their time to discriminate by using queues (making people wait in line) and other time- intensive methods of selling goods. Store managers who believe that high-wage people are unwilling to “waste their time shopping” may have sales that require consumers to visit the store and pick up the good themselves, while consumers who order over the phone or online pay a higher price. This type of price discrimination increases profit if people who put a high value on their time also have less elastic demand for the good.

Early adopters of a new product are often very enthusiastic and will pay premium prices. Firms can take advantage of early adopters by charging a high initial price for a new product and then lowering the price after the initial sales are made.

To make sure that price discrimination pays, managers should not offer dis- counts to all their customers. Rather, they should only give discounts to those consumers who are willing to incur a cost, such as their time, to obtain the dis- count. Consumers willing to spend extra time to obtain a discount are typically more price sensitive than others. Skilled managers use a variety of methods to induce customers to self-identify as being price sensitive by incurring a cost.

Coupons

Many firms use discount coupons to group price discrimi- nate. Through this device, firms divide customers into two groups, charging coupon clippers less than nonclippers. Offering coupons makes sense if the people who do not clip coupons are less price sensitive on average than those who do. People who are willing to spend their time clipping cou- pons buy cereals and other goods at lower prices than those who value their time more. In the first half of 2018, firms dis- tributed 143 billion print and digital coupons for packaged goods, of which 925 million (about 0.6%) were redeemed. The introduction of digital coupons (for example, EverSave.com) has made it easier for firms to target appropriate groups, but has lowered consumers’ costs of using them.

Airline Tickets

By choosing between two different types of tickets, airline customers indicate whether they are likely to be business travelers or vacationers. Airlines give

Discounts

Managerial Implication

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