Macro econonomics.

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MACROECONOMICS

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N. GREGORY MANKIW Harvard University

Worth Publishers

EIGHTH EDITION

MACROECONOMICS

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Senior Vice President, Editorial and Production: Catherine Woods

Publisher: Charles Linsmeier

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Composition: MPS Limited

Printing and Binding: Quad/Graphics

Cover Art: Jylian Gustlin, Fibonacci 48

Library of Congress Control Number: 2012933861

ISBN-13: 978-1-4292-4002-4

ISBN-10: 1-4292-4002-4

© 2013, 2010, 2007, 2003 by Worth Publishers

All rights reserved.

Printed in the United States of America

First printing 2012

Worth Publishers

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New York, NY 10010

www.worthpublishers.com

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about the author

P h

o to

b y

Jo rd

i C

ab ré

N. Gregory Mankiw is the Robert M. Beren Professor of Economics at

Harvard University. He began his study of economics at Princeton University,

where he received an A.B. in 1980. After earning a Ph.D. in economics from

MIT, he began teaching at Harvard in 1985 and was promoted to full professor

in 1987. Today, he regularly teaches both undergraduate and graduate courses

in macroeconomics. He is also author of the best-selling introductory textbook

Principles of Economics (Cengage Learning).

Professor Mankiw is a regular participant in academic and policy debates. His

research ranges across macroeconomics and includes work on price adjustment,

consumer behavior, financial markets, monetary and fiscal policy, and economic

growth. In addition to his duties at Harvard, he has been a research associate of

the National Bureau of Economic Research, a member of the Brookings Panel

on Economic Activity, and an adviser to Congressional Budget Office and the

Federal Reserve Banks of Boston and New York. From 2003 to 2005 he was

chairman of the President’s Council of Economic Advisers.

Professor Mankiw lives in Wellesley, Massachusetts, with his wife, Deborah;

children, Catherine, Nicholas, and Peter; and their border terrier, Tobin.

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To Deborah

Mankiw_Macro_FM.indd viMankiw_Macro_FM.indd vi 04/19/12 6:47 PM04/19/12 6:47 PM

Those branches of politics, or of the laws of social life, on which there exists a collection of facts sufficiently sifted and methodized to form the beginning of a science should be taught ex professo. Among the chief of these is Political Economy, the sources and conditions of wealth and

material prosperity for aggregate bodies of human beings. . . .

The same persons who cry down Logic will generally warn you against

Political Economy. It is unfeeling, they will tell you. It recognises unpleasant

facts. For my part, the most unfeeling thing I know of is the law of gravitation:

it breaks the neck of the best and most amiable person without scruple, if he

forgets for a single moment to give heed to it. The winds and waves too are very

unfeeling. Would you advise those who go to sea to deny the winds and waves –

or to make use of them, and find the means of guarding against their dangers?

My advice to you is to study the great writers on Political Economy, and hold

firmly by whatever in them you find true; and depend upon it that if you are not

selfish or hardhearted already, Political Economy will not make you so.

John Stuart Mill, 1867

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viii |

Preface xxiii Supplements and Media xxxii

part I Introduction 1 Chapter 1 The Science of Macroeconomics 3 Chapter 2 The Data of Macroeconomics 17

part II Classical Theory: The Economy in the Long Run 45 Chapter 3 National Income: Where It Comes

From and Where It Goes 47

Chapter 4 The Monetary System: What It Is and How It Works 81

Chapter 5 Inflation: Its Causes, Effects, and Social Costs 101

Chapter 6 The Open Economy 133 Chapter 7 Unemployment 177

part III Growth Theory: The Economy in the Very Long Run 203 Chapter 8 Economic Growth I: Capital

Accumulation and Population Growth 205

Chapter 9 Economic Growth II: Technology, Empirics, and Policy 235

part IV Business Cycle Theory: The Economy in the Short Run 271 Chapter 10 Introduction to Economic

Fluctuations 273

Chapter 11 Aggregate Demand I: Building the IS–LM Model 303

Chapter 12 Aggregate Demand II: Applying the IS–LM Model 327

Chapter 13 The Open Economy Revisited: The Mundell–Fleming Model and the Exchange-Rate Regime 355

Chapter 14 Aggregate Supply and the Short- Run Tradeoff Between Inflation and Unemployment 397

part V Topics in Macroeconomic Theory 427 Chapter 15 A Dynamic Model of Aggregate

Demand and Aggregate Supply 429

Chapter 16 Understanding Consumer Behavior 465

Chapter 17 The Theory of Investment 497

part VI Topics in Macroeconomic Policy 519 Chapter 18 Alternative Perspectives on

Stabilization Policy 521

Chapter 19 Government Debt and Budget Deficits 543

Chapter 20 The Financial System: Opportunities and Dangers 569

Epilogue What We Know, What We Don’t 593

Glossary 601 Index 611

brief contents

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Preface xxiii Supplements and Media xxxii

part I Introduction 1

Chapter 1 The Science of Macroeconomics 3

1-1 What Macroeconomists Study 3 � CASE STUDY The Historical Performance of the U.S. Economy 5

1-2 How Economists Think 7 Theory as Model Building 8

� FYI Using Functions to Express Relationships Among Variables 11 The Use of Multiple Models 12

Prices: Flexible Versus Sticky 12

Microeconomic Thinking and Macroeconomic Models 13

� FYI Nobel Macroeconomists 14

1-3 How This Book Proceeds 15

Chapter 2 The Data of Macroeconomics 17

2-1 Measuring the Value of Economic Activity: Gross Domestic Product 18 Income, Expenditure, and the Circular Flow 18

� FYI Stocks and Flows 20 Rules for Computing GDP 20

Real GDP Versus Nominal GDP 23

The GDP Deflator 25

Chain-Weighted Measures of Real GDP 25

� FYI Two Arithmetic Tricks for Working With Percentage Changes 26 The Components of Expenditure 27

� FYI What Is Investment? 28 � CASE STUDY GDP and Its Components 28 Other Measures of Income 29

Seasonal Adjustment 31

2-2 Measuring the Cost of Living: The Consumer Price Index 32 The Price of a Basket of Goods 32

The CPI Versus the GDP Deflator 33

Does the CPI Overstate Inflation? 35

� CASE STUDY The Billion Prices Project 36

contents

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2-3 Measuring Joblessness: The Unemployment Rate 36 The Household Survey 37

� CASE STUDY Trends in Labor-Force Participation 38 The Establishment Survey 40

2-4 Conclusion: From Economic Statistics to Economic Models 41

part II Classical Theory: The Economy in the Long Run 45

Chapter 3 National Income: Where It Comes From and Where It Goes 47

3-1 What Determines the Total Production of Goods and Services? 49 The Factors of Production 49

The Production Function 50

The Supply of Goods and Services 50

3-2 How Is National Income Distributed to the Factors of Production? 51 Factor Prices 51

The Decisions Facing a Competitive Firm 52

The Firm’s Demand for Factors 53

The Division of National Income 56

� CASE STUDY The Black Death and Factor Prices 58 The Cobb—Douglas Production Function 58

� FYI The Growing Gap Between Rich and Poor 62 � CASE STUDY Labor Productivity as the Key Determinant of Real Wages 62

3-3 What Determines the Demand for Goods and Services? 63 Consumption 64

Investment 65

� FYI The Many Different Interest Rates 67 Government Purchases 67

3-4 What Brings the Supply and Demand for Goods and Services Into Equilibrium? 68 Equilibrium in the Market for Goods and Services: The Supply and Demand

for the Economy’s Output 69

Equilibrium in the Financial Markets: The Supply and Demand for Loanable Funds 70

Changes in Saving: The Effects of Fiscal Policy 72

� CASE STUDY Wars and Interest Rates in the United Kingdom, 1730–1920 73 Changes in Investment Demand 74

3-5 Conclusion 76

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Chapter 4 The Monetary System: What It Is and How It Works 81

4-1 What Is Money? 81 The Functions of Money 82

The Types of Money 82

� CASE STUDY Money in a POW Camp 83 The Development of Fiat Money 84

� CASE STUDY Money and Social Conventions on the Island of Yap 84 How the Quantity of Money Is Controlled 85

How the Quantity of Money Is Measured 85

� FYI How Do Credit Cards and Debit Cards Fit Into the Monetary System? 87

4-2 The Role of Banks in the Monetary System 87 100-Percent-Reserve Banking 88

Fractional-Reserve Banking 88

Bank Capital, Leverage, and Capital Requirements 90

4-3 How Central Banks Influence the Money Supply 92 A Model of the Money Supply 92

The Instruments of Monetary Policy 94

� CASE STUDY Quantitative Easing and the Exploding Monetary Base 95 Problems in Monetary Control 96

� CASE STUDY Bank Failures and the Money Supply in the 1930s 97

4-4 Conclusion 98

Chapter 5 Inflation: Its Causes, Effects, and Social Costs 101

5-1 The Quantity Theory of Money 102 Transactions and the Quantity Equation 102

From Transactions to Income 103

The Money Demand Function and the Quantity Equation 104

The Assumption of Constant Velocity 105

Money, Prices, and Inflation 106

� CASE STUDY Inflation and Money Growth 106

5-2 Seigniorage: The Revenue From Printing Money 109 � CASE STUDY Paying for the American Revolution 109

5-3 Inflation and Interest Rates 110 Two Interest Rates: Real and Nominal 110

The Fisher Effect 110

� CASE STUDY Inflation and Nominal Interest Rates 111 Two Real Interest Rates: Ex Ante and Ex Post 112

� CASE STUDY Nominal Interest Rates in the Nineteenth Century 113

5-4 The Nominal Interest Rate and the Demand for Money 114 The Cost of Holding Money 114

Future Money and Current Prices 114

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5-5 The Social Costs of Inflation 116 The Layman’s View and the Classical Response 116

� CASE STUDY What Economists and the Public Say About Inflation 117

The Costs of Expected Inflation 117

The Costs of Unexpected Inflation 119

� CASE STUDY The Free Silver Movement, the Election of 1896, and The Wizard of Oz 120

One Benefit of Inflation 121

5-6 Hyperinflation 121 The Costs of Hyperinflation 122

The Causes of Hyperinflation 122

� CASE STUDY Hyperinflation in Interwar Germany 123 � CASE STUDY Hyperinflation in Zimbabwe 125

5-7 Conclusion: The Classical Dichotomy 126 Appendix: The Cagan Model: How Current and Future Money Affect the Price Level 130

Chapter 6 The Open Economy 133

6-1 The International Flows of Capital and Goods 134 The Role of Net Exports 134

International Capital Flows and the Trade Balance 136

International Flows of Goods and Capital: An Example 138

� FYI The Irrelevance of Bilateral Trade Balances 139

6-2 Saving and Investment in a Small Open Economy 139 Capital Mobility and the World Interest Rate 139

Why Assume a Small Open Economy? 140

The Model 141

How Policies Influence the Trade Balance 142

Evaluating Economic Policy 144

� CASE STUDY The U.S. Trade Deficit 146 � CASE STUDY Why Doesn’t Capital Flow to Poor Countries? 148

6-3 Exchange Rates 149 Nominal and Real Exchange Rates 149

The Real Exchange Rate and the Trade Balance 151

The Determinants of the Real Exchange Rate 151

How Policies Influence the Real Exchange Rate 153

The Effects of Trade Policies 154

The Determinants of the Nominal Exchange Rate 156

� CASE STUDY Inflation and Nominal Exchange Rates 157 The Special Case of Purchasing-Power Parity 159

� CASE STUDY The Big Mac Around the World 160

6-4 Conclusion: The United States as a Large Open Economy 162 Appendix: The Large Open Economy 166

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Net Capital Outflow 166

The Model 168

Policies in the Large Open Economy 170

Conclusion 174

Chapter 7 Unemployment 177

7-1 Job Loss, Job Finding, and the Natural Rate of Unemployment 178 7-2 Job Search and Frictional Unemployment 180

Causes of Frictional Unemployment 181

Public Policy and Frictional Unemployment 181

� CASE STUDY Unemployment Insurance and the Rate of Job Finding 182

7-3 Real-Wage Rigidity and Structural Unemployment 183 Minimum-Wage Laws 184

� CASE STUDY The Characteristics of Minimum-Wage Workers 185 Unions and Collective Bargaining 186

Efficiency Wages 187

� CASE STUDY Henry Ford’s $5 Workday 188

7-4 Labor-Market Experience: The United States 189 The Duration of Unemployment 189

� CASE STUDY The Increase in U.S. Long-Term Unemployment and the Debate Over Unemployment Insurance 190

Variation in the Unemployment Rate Across Demographic Groups 192

Transitions Into and Out of the Labor Force 193

7-5 Labor-Market Experience: Europe 194 The Rise in European Unemployment 194

Unemployment Variation Within Europe 196

� CASE STUDY The Secrets to Happiness 197 The Rise of European Leisure 198

7-6 Conclusion 200

part III Growth Theory: The Economy in the Very Long Run 203

Chapter 8 Economic Growth I: Capital Accumulation and Population Growth 205

8-1 The Accumulation of Capital 206 The Supply and Demand for Goods 206

Growth in the Capital Stock and the Steady State 209

Approaching the Steady State: A Numerical Example 211

� CASE STUDY The Miracle of Japanese and German Growth 213 How Saving Affects Growth 214

� CASE STUDY Saving and Investment Around the World 215

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8-2 The Golden Rule Level of Capital 217 Comparing Steady States 217

Finding the Golden Rule Steady State: A Numerical Example 220

The Transition to the Golden Rule Steady State 222

8-3 Population Growth 224 The Steady State With Population Growth 225

The Effects of Population Growth 226

� CASE STUDY Population Growth Around the World 228 Alternative Perspectives on Population Growth 229

8-4 Conclusion 231

Chapter 9 Economic Growth II: Technology, Empirics, and Policy 235

9-1 Technological Progress in the Solow Model 236 The Efficiency of Labor 236

The Steady State With Technological Progress 237

The Effects of Technological Progress 238

9-2 From Growth Theory to Growth Empirics 239 Balanced Growth 239

Convergence 240

Factor Accumulation Versus Production Efficiency 241

� CASE STUDY Is Free Trade Good for Economic Growth? 242

9-3 Policies to Promote Growth 243 Evaluating the Rate of Saving 244

Changing the Rate of Saving 245

Allocating the Economy’s Investment 246

� CASE STUDY Industrial Policy in Practice 247 Establishing the Right Institutions 248

� CASE STUDY The Colonial Origins of Modern Institutions 249 Encouraging Technological Progress 250

� CASE STUDY The Worldwide Slowdown in Economic Growth 251

9-4 Beyond the Solow Model: Endogenous Growth Theory 253 The Basic Model 254

A Two-Sector Model 255

The Microeconomics of Research and Development 256

The Process of Creative Destruction 257

9-5 Conclusion 258 Appendix: Accounting for the Sources of Economic Growth 262 Increases in the Factors of Production 262

Technological Progress 264

The Sources of Growth in the United States 265

� CASE STUDY Growth in the East Asian Tigers 266 The Solow Residual in the Short Run 267

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part IV Business Cycle Theory: The Economy in the Short Run 271

Chapter 10 Introduction to Economic Fluctuations 273

10-1 The Facts About the Business Cycle 274 GDP and Its Components 274

Unemployment and Okun’s Law 277

Leading Economic Indicators 279

10-2 Time Horizons in Macroeconomics 281 How the Short Run and Long Run Differ 281

� CASE STUDY If You Want to Know Why Firms Have Sticky Prices, Ask Them 282 The Model of Aggregate Supply and Aggregate Demand 284

10-3 Aggregate Demand 285 The Quantity Equation as Aggregate Demand 285

Why the Aggregate Demand Curve Slopes Downward 286

Shifts in the Aggregate Demand Curve 287

10-4 Aggregate Supply 288 The Long Run: The Vertical Aggregate Supply Curve 288

The Short Run: The Horizontal Aggregate Supply Curve 290

From the Short Run to the Long Run 291

� CASE STUDY A Monetary Lesson From French History 293 � FYI David Hume on the Real Effects of Money 294

10-5 Stabilization Policy 294 Shocks to Aggregate Demand 295

Shocks to Aggregate Supply 296

� CASE STUDY How OPEC Helped Cause Stagflation in the 1970s and Euphoria in the 1980s 298

10-6 Conclusion 299

Chapter 11 Aggregate Demand I: Building the IS–LM Model 303

11-1 The Goods Market and the IS Curve 305 The Keynesian Cross 305

� CASE STUDY Cutting Taxes to Stimulate the Economy: The Kennedy and Bush Tax Cuts 312

� CASE STUDY Increasing Government Purchases to Stimulate the Economy: The Obama Spending Plan 313

The Interest Rate, Investment, and the IS Curve 314

How Fiscal Policy Shifts the IS Curve 316

11-2 The Money Market and the LM Curve 317 The Theory of Liquidity Preference 317

� CASE STUDY Does a Monetary Tightening Raise or Lower Interest Rates? 319 Income, Money Demand, and the LM Curve 320

How Monetary Policy Shifts the LM Curve 321

11-3 Conclusion: The Short-Run Equilibrium 322

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Chapter 12 Aggregate Demand II: Applying the IS–LM Model 327

12-1 Explaining Fluctuations With the IS–LM Model 328 How Fiscal Policy Shifts the IS Curve and Changes the Short-Run

Equilibrium 328

How Monetary Policy Shifts the LM Curve and Changes the Short-Run Equilibrium 329

The Interaction Between Monetary and Fiscal Policy 331

� CASE STUDY Policy Analysis With Macroeconometric Models 333 Shocks in the IS–LM Model 334

� CASE STUDY The U.S. Recession of 2001 335 What Is the Fed’s Policy Instrument—The Money Supply

or the Interest Rate? 336

12-2 IS–LM as a Theory of Aggregate Demand 337 From the IS–LM Model to the Aggregate Demand Curve 337

The IS–LM Model in the Short Run and Long Run 340

12-3 The Great Depression 342 The Spending Hypothesis: Shocks to the IS Curve 343

The Money Hypothesis: A Shock to the LM Curve 344

The Money Hypothesis Again: The Effects of Falling Prices 345

Could the Depression Happen Again? 347

� CASE STUDY The Financial Crisis and Economic Downturn of 2008 and 2009 348

� FYI The Liquidity Trap (Also Known as the Zero Lower Bound) 350

12-4 Conclusion 351

Chapter 13 The Open Economy Revisited: The Mundell–Fleming Model and the Exchange-Rate Regime 355

13-1 The Mundell–Fleming Model 357 The Key Assumption: Small Open Economy With Perfect Capital Mobility 357

The Goods Market and the IS* Curve 358

The Money Market and the LM* Curve 358

Putting the Pieces Together 360

13-2 The Small Open Economy Under Floating Exchange Rates 361 Fiscal Policy 362

Monetary Policy 363

Trade Policy 364

13-3 The Small Open Economy Under Fixed Exchange Rates 365 How a Fixed-Exchange-Rate System Works 366

� CASE STUDY The International Gold Standard 367 Fiscal Policy 368

Monetary Policy 368

� CASE STUDY Devaluation and the Recovery From the Great Depression 370

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Trade Policy 370

Policy in the Mundell–Fleming Model: A Summary 371

13-4 Interest Rate Differentials 372 Country Risk and Exchange-Rate Expectations 372

Differentials in the Mundell–Fleming Model 373

� CASE STUDY International Financial Crisis: Mexico 1994–1995 375 � CASE STUDY International Financial Crisis: Asia 1997–1998 376

13-5 Should Exchange Rates Be Floating or Fixed? 377 Pros and Cons of Different Exchange-Rate Systems 377

� CASE STUDY The Debate Over the Euro 378 Speculative Attacks, Currency Boards, and Dollarization 380

The Impossible Trinity 381

� CASE STUDY The Chinese Currency Controversy 382

13-6 From the Short Run to the Long Run: The Mundell–Fleming Model With a Changing Price Level 383

13-7 A Concluding Reminder 386 Appendix: A Short-Run Model of the Large Open Economy 390 Fiscal Policy 392

Monetary Policy 393

A Rule of Thumb 394

Chapter 14 Aggregate Supply and the Short-Run Tradeoff Between Inflation and Unemployment 397

14-1 The Basic Theory of Aggregate Supply 398 The Sticky-Price Model 399

An Alternative Theory: The Imperfect-Information Model 401

� CASE STUDY International Differences in the Aggregate Supply Curve 403 Implications 404

14-2 Inflation, Unemployment, and the Phillips Curve 406 Deriving the Phillips Curve From the Aggregate Supply Curve 406

� FYI The History of the Modern Phillips Curve 408 Adaptive Expectations and Inflation Inertia 408

Two Causes of Rising and Falling Inflation 409

� CASE STUDY Inflation and Unemployment in the United States 409 The Short-Run Tradeoff Between Inflation and Unemployment 412

� FYI How Precise Are Estimates of the Natural Rate of Unemployment? 413 Disinflation and the Sacrifice Ratio 414

Rational Expectations and the Possibility of Painless Disinflation 414

� CASE STUDY The Sacrifice Ratio in Practice 416 Hysteresis and the Challenge to the Natural-Rate Hypothesis 417

14-3 Conclusion 419 Appendix: The Mother of All Models 422

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part V Topics in Macroeconomic Theory 427

Chapter 15 A Dynamic Model of Aggregate Demand and Aggregate Supply 429

15-1 Elements of the Model 430 Output: The Demand for Goods and Services 430

The Real Interest Rate: The Fisher Equation 431

Inflation: The Phillips Curve 432

Expected Inflation: Adaptive Expectations 433

The Nominal Interest Rate: The Monetary-Policy Rule 434

� CASE STUDY The Taylor Rule 435

15-2 Solving the Model 437 The Long-Run Equilibrium 437

The Dynamic Aggregate Supply Curve 439

The Dynamic Aggregate Demand Curve 440

The Short-Run Equilibrium 442

15-3 Using the Model 443 Long-Run Growth 444

A Shock to Aggregate Supply 444

� FYI The Numerical Calibration and Simulation 447 A Shock to Aggregate Demand 448

A Shift in Monetary Policy 449

15-4 Two Applications: Lessons for Monetary Policy 453 The Tradeoff Between Output Variability and Inflation

Variability 453

� CASE STUDY The Fed Versus the European Central Bank 455 The Taylor Principle 456

� CASE STUDY What Caused the Great Inflation? 459

15-5 Conclusion: Toward DSGE Models 460

Chapter 16 Understanding Consumer Behavior 465

16-1 John Maynard Keynes and the Consumption Function 466 Keynes’s Conjectures 466

The Early Empirical Successes 467

Secular Stagnation, Simon Kuznets, and the Consumption Puzzle 468

16-2 Irving Fisher and Intertemporal Choice 470 The Intertemporal Budget Constraint 470

� FYI Present Value, or Why a $1,000,000 Prize Is Worth Only $623,000 472 Consumer Preferences 473

Optimization 474

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How Changes in Income Affect Consumption 475

How Changes in the Real Interest Rate Affect Consumption 476

Constraints on Borrowing 477

16-3 Franco Modigliani and the Life-Cycle Hypothesis 479 The Hypothesis 480

Implications 481

� CASE STUDY The Consumption and Saving of the Elderly 483

16-4 Milton Friedman and the Permanent-Income Hypothesis 484 The Hypothesis 484

Implications 485

� CASE STUDY The 1964 Tax Cut and the 1968 Tax Surcharge 486 � CASE STUDY The Tax Rebates of 2008 486

16-5 Robert Hall and the Random-Walk Hypothesis 487 The Hypothesis 488

Implications 488

� CASE STUDY Do Predictable Changes in Income Lead to Predictable Changes in Consumption? 489

16-6 David Laibson and the Pull of Instant Gratification 490 � CASE STUDY How to Get People to Save More 491

16-7 Conclusion 492

Chapter 17 The Theory of Investment 497

17-1 Business Fixed Investment 498 The Rental Price of Capital 499

The Cost of Capital 500

The Determinants of Investment 502

Taxes and Investment 504

The Stock Market and Tobin’s q 505

� CASE STUDY The Stock Market as an Economic Indicator 506 Alternative Views of the Stock Market: The Efficient Markets Hypothesis Versus

Keynes’s Beauty Contest 507

Financing Constraints 509

17-2 Residential Investment 510 The Stock Equilibrium and the Flow Supply 510

Changes in Housing Demand 511

17-3 Inventory Investment 514 Reasons for Holding Inventories 514

How the Real Interest Rate and Credit Conditions Affect Inventory Investment 515

17-4 Conclusion 515

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part VI Topics in Macroeconomic Policy 519

Chapter 18 Alternative Perspectives on Stabilization Policy 521

18-1 Should Policy Be Active or Passive? 522 Lags in the Implementation and Effects of Policies 522

The Difficult Job of Economic Forecasting 524

� CASE STUDY Mistakes in Forecasting 524 Ignorance, Expectations, and the Lucas Critique 526

The Historical Record 527

� CASE STUDY Is the Stabilization of the Economy a Figment of the Data? 528

18-2 Should Policy Be Conducted by Rule or by Discretion? 529 Distrust of Policymakers and the Political Process 529

The Time Inconsistency of Discretionary Policy 530

� CASE STUDY Alexander Hamilton Versus Time Inconsistency 532 Rules for Monetary Policy 532

� CASE STUDY Inflation Targeting: Rule or Constrained Discretion? 533 � CASE STUDY Central-Bank Independence 534

18-3 Conclusion: Making Policy in an Uncertain World 536 Appendix: Time Inconsistency and the Tradeoff Between Inflation and Unemployment 539

Chapter 19 Government Debt and Budget Deficits 543

19-1 The Size of the Government Debt 544 � CASE STUDY The Troubling Long-Term Outlook for Fiscal Policy 547

19-2 Problems in Measurement 548 Measurement Problem 1: Inflation 549

Measurement Problem 2: Capital Assets 549

Measurement Problem 3: Uncounted Liabilities 550

Measurement Problem 4: The Business Cycle 551

Summing Up 551

19-3 The Traditional View of Government Debt 552 � FYI Taxes and Incentives 554

19-4 The Ricardian View of Government Debt 554 The Basic Logic of Ricardian Equivalence 555

Consumers and Future Taxes 556

� CASE STUDY George Bush’s Withholding Experiment 557 � CASE STUDY Why Do Parents Leave Bequests? 559 Making a Choice 559

� FYI Ricardo on Ricardian Equivalence 560

19-5 Other Perspectives on Government Debt 561 Balanced Budgets Versus Optimal Fiscal Policy 561

Fiscal Effects on Monetary Policy 562

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Debt and the Political Process 563

International Dimensions 563

� CASE STUDY The Benefits of Indexed Bonds 564

19-6 Conclusion 565

Chapter 20 The Financial System: Opportunities and Dangers 569

20-1 What Does the Financial System Do? 570 Financing Investment 570

Sharing Risk 571

Dealing With Asymmetric Information 572

Fostering Economic Growth 573

� CASE STUDY Microfinance: Professor Yunus’s Profound Idea 574

20-2 Financial Crises 575 The Anatomy of a Crisis 576

� FYI The TED Spread 578 � CASE STUDY Who Should Be Blamed for the Financial Crisis

of 2008–2009? 580 Policy Responses to a Crisis 581

Policies to Prevent Crises 585

� FYI CoCo Bonds 586 � CASE STUDY The European Sovereign Debt Crisis 587

20-3 Conclusion 588

Epilogue What We Know, What We Don’t 593

The Four Most Important Lessons of Macroeconomics 593 Lesson 1: In the long run, a country’s capacity to produce goods and services

determines the standard of living of its citizens. 594

Lesson 2: In the short run, aggregate demand influences the amount of goods and services that a country produces. 594

Lesson 3: In the long run, the rate of money growth determines the rate of inflation, but it does not affect the rate of unemployment. 595

Lesson 4: In the short run, policymakers who control monetary and fiscal policy face a tradeoff between inflation and unemployment. 595

The Four Most Important Unresolved Questions of Macroeconomics 596 Question 1: How should policymakers try to promote growth in the economy’s

natural level of output? 596

Question 2: Should policymakers try to stabilize the economy? If so, how? 597

Question 3: How costly is inflation, and how costly is reducing inflation? 598

Question 4: How big a problem are government budget deficits? 599

Conclusion 600

Glossary 601

Index 611

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An economist must be “mathematician, historian, statesman, philosopher, in some degree . . . as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.” So remarked John Maynard Keynes, the great British economist who, as much as anyone, could be called the father of macroeconomics. No single statement summarizes better what it means to be an economist.

As Keynes’s assessment suggests, students who aim to learn economics need to draw on many disparate talents. The job of helping students find and develop these talents falls to instructors and textbook authors. When writing this textbook for intermediate-level courses in macroeconomics, my goal was to make macroeco- nomics understandable, relevant, and (believe it or not) fun. Those of us who have chosen to be professional macroeconomists have done so because we are fasci- nated by the field. More important, we believe that the study of macroeconomics can illuminate much about the world and that the lessons learned, if properly applied, can make the world a better place. I hope this book conveys not only our profession’s accumulated wisdom but also its enthusiasm and sense of purpose.

This Book’s Approach

Macroeconomists share a common body of knowledge, but they do not all have the same perspective on how that knowledge is best taught. Let me begin this new edition by recapping four of my objectives, which together define this book’s approach to the field.

First, I try to offer a balance between short-run and long-run issues in macro- economics. All economists agree that public policies and other events influence the economy over different time horizons. We live in our own short run, but we also live in the long run that our parents bequeathed us. As a result, courses in macroeconomics need to cover both short-run topics, such as the business cycle and stabilization policy, and long-run topics, such as economic growth, the natural rate of unemployment, persistent inflation, and the effects of government debt. Neither time horizon trumps the other.

Second, I integrate the insights of Keynesian and classical theories. Although Keynes’s General Theory provides the foundation for much of our current under- standing of economic fluctuations, it is important to remember that classical economics provides the right answers to many fundamental questions. In this book I incorporate many of the contributions of the classical economists before Keynes and the new classical economists of the past several decades. Substantial coverage is given, for example, to the loanable-funds theory of the interest rate, the quantity theory of money, and the problem of time inconsistency. At the same time, I recognize that many of the ideas of Keynes and the new Keynesians are necessary for understanding economic fluctuations. Substantial coverage is given

preface

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also to the IS –LM model of aggregate demand, the short-run tradeoff between inflation and unemployment, and modern models of business cycle dynamics.

Third, I present macroeconomics using a variety of simple models. Instead of pretending that there is one model that is complete enough to explain all facets of the economy, I encourage students to learn how to use and compare a set of prominent models. This approach has the pedagogical value that each model can be kept relatively simple and presented within one or two chapters. More important, this approach asks students to think like economists, who always keep various models in mind when analyzing economic events or public policies.

Fourth, I emphasize that macroeconomics is an empirical discipline, moti- vated and guided by a wide array of experience. This book contains numerous Case Studies that use macroeconomic theory to shed light on real-world data or events. To highlight the broad applicability of the basic theory, I have drawn the Case Studies both from current issues facing the world’s economies and from dramatic historical episodes. The Case Studies analyze the policies of Alexander Hamilton, Henry Ford, George Bush (both of them!), and Barack Obama. They teach the reader how to apply economic principles to issues from fourteenth- century Europe, the island of Yap, the land of Oz, and today’s newspaper.

What’s New in the Eighth Edition?

Economics instructors are vigilant in keeping their lectures up to date as the economic landscape changes. Textbook authors cannot be less so. This book is therefore updated about every three years. Each revision reflects new events in the economy as well as new research about the best way to understand macro- economic developments.

One significant change in this edition is that some of the existing material has been reorganized. Over the past several years, monetary policymakers at the Federal Reserve have engaged in a variety of unconventional measures to prop up a weak banking system and promote recovery from a deep recession. Understanding these policies requires a strong background in the details of the monetary system. As a result, this edition covers the topic earlier in the book than did previous editions. A complete treatment of the monetary system and the tools of monetary policy can now be found in Chapter 4.

The biggest change in the book, however, is the addition of Chapter 20, “The Financial System: Opportunities and Dangers.” Over the past several years, in the aftermath of the financial crisis and economic downturn of 2008 and 2009, econ- omists have developed a renewed appreciation of the crucial linkages between the financial system and the broader economy. Chapter 20 gives students a deeper look at this topic. It begins by discussing the functions of the financial system. It then discusses the causes and effects of financial crises, as well as the government policies that aim to deal with crises and to prevent future ones.

All the other chapters in the book have been updated to incorporate the latest data and recent events. Here are some of the noteworthy additions:

� Chapter 2 has a new Case Study on the Billion Prices Project, which uses data found on the internet to monitor inflation trends.

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� Chapter 3 has a new FYI box on the growing gap between rich and poor.

� Chapter 4 has a new Case Study on quantitative easing and the recent explosion in the monetary base.

� Chapter 7 has a new Case Study on the recent increase in long-term unemployment and the debate over unemployment insurance.

� Chapter 9 has a new Case Study about industrial policy in practice.

� Chapter 16 has a new Case Study about new research that studies the tax rebates of 2008.

As always, all the changes that I made, and the many others that I considered, were evaluated keeping in mind the benefits of brevity. From my own experience as a student, I know that long books are less likely to be read. My goal in this book is to offer the clearest, most up-to-date, most accessible course in macro- economics in the fewest words possible.

The Arrangement of Topics

My strategy for teaching macroeconomics is first to examine the long run when prices are flexible and then to examine the short run when prices are sticky. This approach has several advantages. First, because the classical dichotomy per- mits the separation of real and monetary issues, the long-run material is easier for students to understand. Second, when students begin studying short-run fluctuations, they understand fully the long-run equilibrium around which the economy is fluctuating. Third, beginning with market-clearing models makes clearer the link between macroeconomics and microeconomics. Fourth, students learn first the material that is less controversial among macroeconomists. For all these reasons, the strategy of beginning with long-run classical models simplifies the teaching of macroeconomics.

Let’s now move from strategy to tactics. What follows is a whirlwind tour of the book.

Part One, Introduction

The introductory material in Part One is brief so that students can get to the core topics quickly. Chapter l discusses the broad questions that mac- roeconomists address and the economist’s approach of building models to explain the world. Chapter 2 introduces the key data of macroeconomics, emphasizing gross domestic product, the consumer price index, and the unemployment rate.

Part Two, Classical Theory: The Economy in the Long Run

Part Two examines the long run over which prices are flexible. Chapter 3 pres- ents the basic classical model of national income. In this model, the factors of production and the production technology determine the level of income, and the marginal products of the factors determine its distribution to households. In addition, the model shows how fiscal policy influences the allocation of the

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economy’s resources among consumption, investment, and government pur- chases, and it highlights how the real interest rate equilibrates the supply and demand for goods and services.

Money and the price level are introduced next. Chapter 4 examines the mon- etary system and the tools of monetary policy. Chapter 5 begins the discussion of the effects of monetary policy. Because prices are assumed to be fully flexible, the chapter presents the prominent ideas of classical monetary theory: the quantity theory of money, the inflation tax, the Fisher effect, the social costs of inflation, and the causes and costs of hyperinflation.

The study of open-economy macroeconomics begins in Chapter 6. Maintaining the assumption of full employment, this chapter presents models to explain the trade balance and the exchange rate. Various policy issues are addressed: the relationship between the budget deficit and the trade deficit, the macroeconomic impact of protectionist trade policies, and the effect of monetary policy on the value of a currency in the market for foreign exchange.

Chapter 7 relaxes the assumption of full employment by discussing the dynamics of the labor market and the natural rate of unemployment. It examines various causes of unemployment, including job search, minimum-wage laws, union power, and efficiency wages. It also presents some important facts about patterns of unemployment.

Part Three, Growth Theory: The Economy in the Very Long Run

Part Three makes the classical analysis of the economy dynamic by developing the tools of modern growth theory. Chapter 8 introduces the Solow growth model as a description of how the economy evolves over time. This chapter emphasizes the roles of capital accumulation and population growth. Chapter 9 then adds technological progress to the Solow model. It uses the model to discuss growth experiences around the world as well as public policies that influence the level and growth of the standard of living. Finally, Chapter 9 introduces students to the modern theories of endogenous growth.

Part Four, Business Cycle Theory: The Economy in the Short Run

Part Four examines the short run when prices are sticky. It begins in Chapter 10 by examining some of the key facts that describe short-run fluctuations in eco- nomic activity. The chapter then introduces the model of aggregate supply and aggregate demand as well as the role of stabilization policy. Subsequent chapters refine the ideas introduced in this chapter.

Chapters 11 and 12 look more closely at aggregate demand. Chapter 11 pres- ents the Keynesian cross and the theory of liquidity preference and uses these models as building blocks for developing the IS –LM model. Chapter 12 uses the IS –LM model to explain economic fluctuations and the aggregate demand curve. It concludes with an extended case study of the Great Depression.

The study of short-run fluctuations continues in Chapter 13, which focuses on aggregate demand in an open economy. This chapter presents the Mundell– Fleming model and shows how monetary and fiscal policies affect the economy

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under floating and fixed exchange-rate systems. It also discusses the debate over whether exchange rates should be floating or fixed.

Chapter 14 looks more closely at aggregate supply. It examines various approaches to explaining the short-run aggregate supply curve and discusses the short-run tradeoff between inflation and unemployment.

Part Five, Topics in Macroeconomic Theory

After developing basic theories to explain the economy in the long run and in the short run, the book turns to several topics that refine our understanding of the economy. Part Five focuses on theoretical topics, while Part Six focuses on policy topics. These chapters are written to be used flexibly, so instructors can pick and choose which topics to cover. Some of these chapters can also be cov- ered earlier in the course, depending on the instructor’s preferences.

Chapter 15 develops a dynamic model of aggregate demand and aggregate sup- ply. It builds on ideas that students have already encountered and uses those ideas as stepping-stones to take the student close to the frontier of knowledge concerning short-run economic fluctuations. The model presented here is a simplified version of modern dynamic, stochastic, general equilibrium (DSGE) models.

The next two chapters analyze more fully some of the microeconomic deci- sions behind macroeconomic phenomena. Chapter 16 presents the various theories of consumer behavior, including the Keynesian consumption func- tion, Fisher’s model of intertemporal choice, Modigliani’s life-cycle hypothesis, Friedman’s permanent-income hypothesis, Hall’s random-walk hypothesis, and Laibson’s model of instant gratification. Chapter 17 examines the theory behind the investment function.

Part Six, Topics in Macroeconomic Policy

Once the student has solid command of standard macroeconomic models, the book uses these models as the foundation for discussing some of the key debates over economic policy. Chapter 18 considers the debate over how policymakers should respond to short-run economic fluctuations. It emphasizes two broad questions: Should monetary and fiscal policy be active or passive? Should policy be conducted by rule or by discretion? The chapter presents arguments on both sides of these questions.

Chapter 19 focuses on the various debates over government debt and budget deficits. It gives a broad picture about the magnitude of government indebted- ness, discusses why measuring budget deficits is not always straightforward, recaps the traditional view of the effects of government debt, presents Ricardian equiva- lence as an alternative view, and discusses various other perspectives on govern- ment debt. As in the previous chapter, students are not handed conclusions but are given the tools to evaluate the alternative viewpoints on their own.

Chapter 20 discusses the financial system and its linkages to the overall economy. It begins by examining what the financial system does: financing investment, sharing risk, dealing with asymmetric information, and foster- ing economic growth. It then discusses the causes of financial crises, their

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macroeconomic impact, and the policies that might mitigate their effects and reduce their likelihood.

Epilogue

The book ends with a brief epilogue that reviews the broad lessons about which most macroeconomists agree and discusses some of the most important open questions. Regardless of which chapters an instructor chooses to cover, this capstone chapter can be used to remind students how the many models and themes of macroeconomics relate to one another. Here and throughout the book, I emphasize that despite the disagreements among macroeconomists, there is much that we know about how the economy works.

Alternative Routes Through the Text

Although I have organized the material in the way that I prefer to teach intermediate-level macroeconomics, I understand that other instructors have different preferences. I tried to keep this in mind as I wrote the book so that it would offer a degree of flexibility. Here are a few ways that instructors might consider rearranging the material:

� Some instructors are eager to cover short-run economic fluctuations. For such a course, I recommend covering Chapters 1 through 5 so stu- dents are grounded in the basics of classical theory and then jumping to Chapters 10, 11, 12, 14, and 15 to cover the model of aggregate demand and aggregate supply.

� Some instructors are eager to cover long-run economic growth. These instructors can cover Chapters 8 and 9 immediately after Chapter 3.

� An instructor who wants to defer (or even skip) open-economy macro- economics can put off Chapters 6 and 13 without loss of continuity.

� An instructor who wants to emphasize economic policy can skip Chapters 8, 9, 15, 16, and 17 in order to get to Chapters 18, 19, and 20 more quickly.

Experience with previous editions suggests this text complements well a variety of approaches to the field.

Learning Tools

I am pleased that students have found the previous editions of this book user- friendly. I have tried to make this eighth edition even more so.

Case Studies

Economics comes to life when it is applied to understanding actual events. Therefore, the numerous Case Studies (many new or revised in this edition) are an important learning tool, integrated closely with the theoretical material presented in each

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chapter. The frequency with which these Case Studies occur ensures that a student does not have to grapple with an overdose of theory before seeing the theory applied. Students report that the Case Studies are their favorite part of the book.

FYI Boxes

These boxes present ancillary material “for your information.” I use these boxes to clarify difficult concepts, to provide additional information about the tools of economics, and to show how economics relates to our daily lives. Several are new or revised in this edition.

Graphs

Understanding graphical analysis is a key part of learning macroeconomics, and I have worked hard to make the figures easy to follow. I often use comment boxes within figures that describe briefly and draw attention to the important points that the figures illustrate. They should help students both learn and review the material.

Mathematical Notes

I use occasional mathematical footnotes to keep more difficult material out of the body of the text. These notes make an argument more rigorous or present a proof of a mathematical result. They can easily be skipped by those students who have not been introduced to the necessary mathematical tools.

Chapter Summaries

Every chapter ends with a brief, nontechnical summary of its major lessons. Students can use the summaries to place the material in perspective and to review for exams.

Key Concepts

Learning the language of a field is a major part of any course. Within the chapter, each key concept is in boldface when it is introduced. At the end of the chapter, the key concepts are listed for review.

Questions for Review

After studying a chapter, students can immediately test their understanding of its basic lessons by answering the Questions for Review.

Problems and Applications

Every chapter includes Problems and Applications designed for homework assignments. Some of these are numerical applications of the theory in the chap- ter. Others encourage the student to go beyond the material in the chapter by addressing new issues that are closely related to the chapter topics.

Chapter Appendices

Several chapters include appendices that offer additional material, sometimes at a higher level of mathematical sophistication. These are designed so that

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instructors can cover certain topics in greater depth if they wish. The appendices can be skipped altogether without loss of continuity.

Glossary

To help students become familiar with the language of macroeconomics, a glossary of more than 250 terms is provided at the back of the book.

Translations The English-language version of this book has been used in dozens of countries. To make the book more accessible for students around the world, editions are (or will soon be) available in 15 other languages: Armenian, Chinese, French, German, Greek, Hungarian, Indonesian, Italian, Japanese, Korean, Portuguese, Romanian, Russian, Spanish, and Ukrainian. In addition, a Canadian adapta- tion coauthored with William Scarth (McMaster University) and a European adaptation coauthored with Mark Taylor (University of Warwick) are available. Instructors who would like information about these versions of the book should contact Worth Publishers.

Acknowledgments

Since I started writing the first edition of this book more than two decades ago, I have benefited from the input of many reviewers and colleagues in the econom- ics profession. Now that the book is in its eighth edition, these individuals are too numerous to list in their entirety. However, I continue to be grateful for their willingness to have given up their scarce time to help me improve the economics and pedagogy of this text. Their advice has made this book a better teaching tool for hundreds of thousands of students around the world.

I would like to mention those instructors whose recent input shaped this new edition:

Mohsen Bahmani- Oskooee University of Wisconsin– Milwaukee

Quentin Duroy Denison University

John W. Graham Rutgers University at Newark

Denise Hazlett Whitman College

Nancy Jianakoplos Colorado State University

Roger Kaufman Smith College

Carlos F. Liard-Muriente Central Connecticut State University

Robert G. Murphy Boston College

Ebere Oriaku Elizabeth City State University

Andrew Paizis New York University

Brian P. Rosario American River College and California State University

Thomas Scheiding University of Wisconsin–Stout

David E. Spencer Brigham Young University

Henry Terrell George Washington University

Bill Yang Georgia Southern University

Nora Underwood University of Central Florida

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In addition, I am grateful to Yang Du, a student at Harvard, who helped me update the data, refine my prose, and proofread the entire book.

The people at Worth Publishers have continued to be congenial and dedicated. I would like to thank Catherine Woods, Senior Vice President, Editorial and Production; Charles Linsmeier, Publisher; Sarah Dorger, Senior Acquisitions Editor; Scott Guile, Executive Marketing Manager; Julie Tompkins, Marketing Assistant; Paul Shensa, Consulting Editor; Tom Acox, Digital Solutions Coordinator; Lukia Kliossis, Associate Media Editor; Mary Melis, Assistant Editor; Lisa Kinne, Associate Managing Editor; Tracey Kuehn, Director of Print and Digital Development, Worth; Barbara Seixas, Production Manager; Kevin Kall, Designer; Karen Osborne, Copy Editor; Edgar Bonilla, Supplements Project Editor; and Stacey Alexander, Supplements Manager.

Many other people made valuable contributions as well. Most important, Jane Tufts, freelance developmental editor, worked her magic on this book once again, confirming that she’s the best in the business. Alexandra Nickerson did a great job preparing the index. Deborah Mankiw, my wife and in-house editor, continued to be the first reader of new material, providing the right mix of criti- cism and encouragement.

Finally, I would like to thank my three children, Catherine, Nicholas, and Peter. They helped immensely with this revision—both by providing a pleas- ant distraction and by reminding me that textbooks are written for the next generation.

Cambridge, Massachusetts May 2012

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xxxii |

Supplements

Worth Publishers has worked closely with Greg Mankiw and a team of talented economics instructors to put together a variety of supplements to aid instructors and students. We have been delighted at the positive feedback we have received on these supplements. Here is a summary of the resources available.

For Instructors

Instructor’s Resources

Robert G. Murphy (Boston College) has revised the impressive resource manual for instructors to appear on the Instructor’s Web site. For each chapter of this book, the manual contains notes to the instructor, a detailed lecture outline, additional Case Studies, and coverage of advanced topics. Instructors can use the manual to prepare their lectures, and they can reproduce whatever pages they choose as handouts for students. Each chapter also contains a Dismal Scientist Activity (www.dismalscientist.com), which challenges students to combine the chapter knowledge with a high-powered business database and analysis service that offers real-time monitoring of the global economy.

Solutions Manual

Nora Underwood (University of Central Florida) has updated the Solutions Manual for all of the Questions for Review and Problems and Applications. The manual also contains the answers to selected questions from the Student Guide and Workbook.

Test Bank

Nancy Jianakoplos (Colorado State University) has updated and revised the Test Bank so that it now includes over 2,500 multiple-choice questions, numerical problems, and short-answer graphical questions to accompany each chapter of the text. The Test Bank is available both as a printed book and on a CD-ROM. The CD includes our flexible test-generating software, which instructors can use to easily write and edit questions as well as create and print tests.

PowerPoint Slides

Ron Cronovich (Carthage College) has revised his PowerPoint presentations of the material in each chapter. They feature animated graphs with careful explana- tions and additional case studies, data, and helpful notes to the instructor. Designed to be customized or used “as is,” they include easy instructions for those who have little experience with PowerPoint. They are available on the Web site (www. worthpublishers.com/mankiw).

supplements and media

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For Students

Student Guide and Workbook

Roger Kaufman (Smith College) has revised his superb study guide for students. This guide offers various ways for students to learn the material in the text and assess their understanding.

� Fill-In Questions give students the opportunity to review and check their knowledge of the key terms and concepts in the chapter.

� Multiple-Choice Questions allow students to test themselves on the chapter material.

� Exercises guide students step by step through the various models using graphs and numerical examples.

� Problems ask students to apply the models on their own.

� Questions to Think About require critical thinking as well as economic analysis.

� Data Questions ask students to obtain and learn about readily available economic data.

Online Offerings

FOR MACROECONOMICS www.youreconportal .com

With EconPortal (available Spring 2013) instructors get a complete learning management system, ready to use without hours of prepwork. Students get easy access to learning resources specific to the course and the textbook. And virtually every aspect of EconPortal is customizable.

New to EconPortal � LearningCurve Formative Quizzing Engine bringing adaptive question

selection, personalized study plans, and state-of-the-art question analysis to game-like activities that keep students engaged.

Also Featuring:

� The Eighth Edition Test Bank, with questions sortable by level, skill, for- mat, and topic.

� All end-of-chapter problems easily assignable and automatically gradable.

� Student self-assessment resources tied specifically to the book.

� An HTML-based eBook that allows for note-taking (both public and private), custom syllabi (chapters and sections), highlighting, instructor– student communication, and more! Also available stand-alone as a low- cost text purchase option.

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Companion Web Site for Students and Instructors (www.worthpublishers. com/mankiw)

For each chapter in the textbook, the tools on the companion Web site include the following:

� Self-Tests. Students can test their knowledge of the material in the book by taking multiple-choice tests on any chapter. After the student responds, the program explains the answer and directs the student to specific sections in the book for additional study. Students may also test their knowledge of key terms using the flashcards.

� Web Links. Students can access real-world information via specifically chosen hyperlinks relating to chapter content.

� Sample Essays. Students can view chapter-specific essay questions followed by sample essay answers.

� Data Plotter. Originally created by David Weil, Brown University. Students can explore macroeconomic data with time-series graphs and scatterplots.

� Macro Models. These modules provide simulations of the models presented in the book. Students can change the exogenous variables and see the outcomes in terms of shifting curves and recalculated numerical values of the endogenous variables. Each module contains exercises that instructors can assign as homework.

� A Game for Macroeconomists. Also originally created by David Weil, Brown University, the game allows students to become president of the United States in the year 2017 and to make macroeconomic policy decisions based on news events, economic statistics, and approval ratings. It gives students a sense of the complex interconnections that influence the econ- omy. It is also fun to play.

� Flashcards. Students can test their knowledge of the definitions in the glossary with these virtual flashcards.

Along with the Instructor’s Resources (see p. xxxii), the following additional instructor support material is available:

� PowerPoint Lecture Presentations. These customizable PowerPoint slides, prepared by Ronald Cronovich (Carthage College), are designed to assist instructors with lecture preparation and presentations.

� Images from the Textbook. Instructors have access to a complete set of fig- ures and tables from the textbook in high-res and low-res JPEG formats. The textbook art has been processed for “high-resolution” (150 dpi). These figures and photographs have been especially formatted for maxi- mum readability in large lecture halls and follow standards that were set and tested in a real university auditorium.

� Solutions Manual. Instructors have access to detailed solutions to the Questions for Review and Problems and Applications.

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The Aplia/Worth partnership combines Worth texts and eBooks with Aplia’s interactive problem sets, news analyses, tutorials, and economic experiments—all in a format that saves professors time while encouraging students.

Aplia for Macroeconomics Features: � Homework sets correlated to the text that can be assigned and graded

online. An easy-to-use gradebook tracks results.

� Multiple purchase options. Students can access Aplia free for the first two weeks of the course, then decide if they want to purchase an eBook or a text package. Students purchasing an eBook can also purchase a physical text directly from Aplia at about half off the retail price.

� Algorithmic problem sets. Students can take the tests up to three times with new iterations of the problems each time.

eBook Students who purchase the eBook have access to these interactive features:

� Quick, intuitive navigation

� Customizable note-taking

� Highlighting

� Searchable glossary

With the eBook, instructors can do the following:

� Focus only on the chapters they want to use. Instructors can assign the entire text or a custom version with only the chapters that correspond to their syllabus. Students see the customized version, with selected chapters only.

� Annotate any page of the text. Instructors’ notes can include text, Web links, and even photos and images from the book’s media or other sources. Students can get an eBook annotated just for them, customized for the course.

WebCT The Mankiw WebCT e-pack enables instructors to create a thorough online course or a course Web site. The e-pack contains online materials that facilitate critical thinking and learning, including preprogrammed quizzes and tests that are fully functional in the WebCT environment.

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BlackBoard The Mankiw BlackBoard course cartridge makes it possible to combine Black- Board’s popular tools and easy-to-use interface with the text’s Web content, includ- ing preprogrammed quizzes and tests. The result is an interactive, comprehensive online course that allows for effortless implementation, management, and use. The files are organized and prebuilt to work within the BlackBoard software.

Additional Offerings

i-clicker Developed by a team of University of Illinois physicists, i-clicker is the most flexible and most reliable classroom response system available. It is the only solution created for educators, by educators—with continuous product improve- ments made through direct classroom testing and faculty feedback. No matter their level of technical expertise, instructors will appreciate the i-clicker because the focus remains on teaching, not the technology. To learn more about packaging i-clicker with this textbook, please contact your local sales representative or visit www.iclicker.com.

Dismal Scientist A high-powered business database and analysis service comes to the classroom! Dismal Scientist offers real-time monitoring of the global economy, produced locally by economists and other professionals at Moody’s Economy.com around the world. Dismal Scientist is free when packaged with this text. Please contact your local sales representative or go to www.dismalscientist.com.

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MACROECONOMICS

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P A R T I

Introduction

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3

The Science of Macroeconomics

1C H A P T E R

The whole of science is nothing more than the refi nement of everyday thinking.

—Albert Einstein

When Albert Einstein made the above observation about the nature of science, he was probably referring to physics, chemistry, and other natural sciences. But the statement is equally true when applied to social sciences like economics. As a participant in the economy, and as a citizen in a democracy, you cannot help but think about economic issues as you go about your life or when you enter the voting booth. But if you are like most people, your everyday thinking about economics has probably been casual rather than rigorous (or at least it was before you took your fi rst economics course). The goal of studying economics is to refi ne that thinking. This book aims to help you in that endeavor, focusing on the part of the fi eld called macroeconomics, which studies the forces that infl uence the economy as a whole.

1-1 What Macroeconomists Study

Why have some countries experienced rapid growth in incomes over the past century while others stay mired in poverty? Why do some countries have high rates of infl ation while others maintain stable prices? Why do all countries experience recessions and depressions—recurrent periods of falling incomes and rising unemployment—and how can government policy reduce the frequency and severity of these episodes? Macroeconomics attempts to answer these and many related questions.

To appreciate the importance of macroeconomics, you need only read the newspaper or listen to the news. Every day you can see headlines such as INCOME GROWTH REBOUNDS, FED MOVES TO COMBAT INFLA- TION, or STOCKS FALL AMID RECESSION FEARS. These macroeconomic events may seem abstract, but they touch all of our lives. Business executives forecasting the demand for their products must guess how fast consumers’ incomes will grow. Senior citizens living on fi xed incomes wonder how fast prices will rise. Recent college graduates looking for jobs hope that the economy will boom and that fi rms will be hiring.

Because the state of the economy affects everyone, macroeconomic issues play a central role in national political debates. Voters are aware of how the economy

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4 | P A R T I Introduction

is doing, and they know that government policy can affect the economy in pow- erful ways. As a result, the popularity of an incumbent president often rises when the economy is doing well and falls when it is doing poorly.

Macroeconomic issues are also central to world politics, and the international news is fi lled with macroeconomic questions. Was it a good move for much of Europe to adopt a common currency? Should China maintain a fi xed exchange rate against the U.S. dollar? Why is the United States running large trade defi cits? How can poor nations raise their standards of living? When world leaders meet, these topics are often high on their agenda.

Although the job of making economic policy belongs to world leaders, the job of explaining the workings of the economy as a whole falls to macroeconomists. Toward this end, macroeconomists collect data on incomes, prices, unemployment, and many other variables from different time periods and different countries. They then attempt to formulate general theories to explain these data. Like astronomers studying the evolution of stars or biologists studying the evolution of species, macroeconomists cannot conduct controlled experiments in a laboratory. Instead, they must make use of the data that history gives them. Macroeconomists observe that economies differ across countries and that they change over time. These observations provide both the motivation for developing macroeconomic theories and the data for testing them.

To be sure, macroeconomics is a young and imperfect science. The macroecon- omist’s ability to predict the future course of economic events is no better than the meteorologist’s ability to predict next month’s weather. But, as you will see, macroeconomists know quite a lot about how economies work. This knowledge is useful both for explaining economic events and for formulating economic policy.

Every era has its own economic problems. In the 1970s, Presidents Richard Nixon, Gerald Ford, and Jimmy Carter all wrestled in vain with a rising rate of infl ation. In the 1980s, infl ation subsided, but Presidents Ronald Reagan and George H. W. Bush presided over large federal budget defi cits. In the 1990s, with President Bill Clinton in the Oval Offi ce, the economy and stock market enjoyed a remarkable boom, and the federal budget turned from defi cit to surplus. As Clinton left offi ce, however, the stock market was in retreat, and the economy was heading into recession. In 2001 President George W. Bush reduced taxes to help end the recession, but the tax cuts contributed to a reemergence of budget defi cits.

President Barack Obama moved into the White House in 2009 during a peri- od of heightened economic turbulence. The economy was reeling from a fi nancial crisis, driven by a large drop in housing prices, a steep rise in mortgage defaults, and the bankruptcy or near-bankruptcy of many fi nancial institutions. As the fi nancial crisis spread, it raised the specter of the Great Depression of the 1930s, when in its worst year one out of four Americans who wanted to work could not fi nd a job. In 2008 and 2009, offi cials in the Treasury, Federal Reserve, and other parts of government acted vigorously to prevent a recurrence of that outcome. And while they succeeded—the unemployment rate peaked at 10.1 percent—the downturn was nonetheless severe, the subsequent recovery was painfully slow, and the policies enacted left a legacy of greatly expanded government debt.

Macroeconomic history is not a simple story, but it provides a rich motivation for macroeconomic theory. While the basic principles of macroeconomics do not change from decade to decade, the macroeconomist must apply these principles with fl exibility and creativity to meet changing circumstances.

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C H A P T E R 1 The Science of Macroeconomics | 5

The Historical Performance of the U.S. Economy

Economists use many types of data to measure the performance of an economy. Three macroeconomic variables are especially important: real gross domestic product (GDP), the infl ation rate, and the unemployment rate. Real GDP measures the total income of everyone in the economy (adjusted for the level of prices). The infl ation rate measures how fast prices are rising. The unemploy- ment rate measures the fraction of the labor force that is out of work. Mac- roeconomists study how these variables are determined, why they change over time, and how they interact with one another.

Figure 1-1 shows real GDP per person in the United States. Two aspects of this fi gure are noteworthy. First, real GDP grows over time. Real GDP per person today is about eight times higher than it was in 1900. This growth in average income allows us to enjoy a much higher standard of living than our great- grandparents did. Second, although real GDP rises in most years, this growth

CASE STUDY

FIGURE 1-1

World War I

Great Depression

World War II

Korean War

Vietnam War

First oil-price shock Second oil-price

shock

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

50,000

10,000

5,000

40,000

Year 2000 2010

Real GDP per person (2005 dollars)

9/11 terrorist attack

Financial crisis

20,000

Real GDP per Person in the U.S. Economy Real GDP measures the total income of everyone in the economy, and real GDP per person measures the income of the average person in the economy. This fi gure shows that real GDP per person tends to grow over time and that this normal growth is sometimes interrupted by periods of declining income, called recessions or depressions.

Note: Real GDP is plotted here on a logarithmic scale. On such a scale, equal distances on the vertical axis represent equal percentage changes. Thus, the distance between $5,000 and $10,000 (a 100 percent change) is the same as the distance between $10,000 and $20,000 (a 100 percent change). Source: U.S. Department of Commerce and Economic History Services.

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6 | P A R T I Introduction

is not steady. There are repeated periods during which real GDP falls, the most dramatic instance being the early 1930s. Such periods are called recessions if they are mild and depressions if they are more severe. Not surprisingly, periods of declining income are associated with substantial economic hardship.

Figure 1-2 shows the U.S. infl ation rate. You can see that infl ation varies substan- tially over time. In the fi rst half of the twentieth century, the infl ation rate averaged only slightly above zero. Periods of falling prices, called defl ation, were almost as common as periods of rising prices. By contrast, infl ation has been the norm dur- ing the past half century. Infl ation became most severe during the late 1970s, when prices rose at a rate of almost 10 percent per year. In recent years, the infl ation rate has been about 2 or 3 percent per year, indicating that prices have been fairly stable.

Figure 1-3 shows the U.S. unemployment rate. Notice that there is always some unemployment in the economy. In addition, although the unemployment rate has no long-term trend, it varies substantially from year to year. Recessions and depressions are associated with unusually high unemployment. The highest rates of unemployment were reached during the Great Depression of the 1930s. The

1-2FIGURE

1900

30

25

20

15

10

5

0

−5

−10

−15

−20

Percent

Inflation

Deflation

1910

World War I

Great Depression

World War II

Korean War

Vietnam War

First oil-price shock Second oil-price shock

1920 1930 1940 Year

1950 1960 1970 1980 1990 2000 2010

9/11 terrorist attack

Financial crisis

The Infl ation Rate in the U.S. Economy The infl ation rate measures the percent- age change in the average level of prices from the year before. When the infl ation rate is above zero, prices are rising. When it is below zero, prices are falling. If the infl ation rate declines but remains positive, prices are rising but at a slower rate.

Note: The infl ation rate is measured here using the GDP defl ator. Source: U.S. Department of Commerce and Economic History Services.

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C H A P T E R 1 The Science of Macroeconomics | 7

worst economic downturn since the Great Depression occurred in the aftermath of the fi nancial crisis of 2008–2009, when unemployment rose substantially.

These three fi gures offer a glimpse at the history of the U.S. economy. In the chapters that follow, we fi rst discuss how these variables are measured and then develop theories to explain how they behave. ■

1-3FIGURE

1900

25

Percent unemployed

1910

World War I

Great Depression

World War II

Korean War

Vietnam War

First oil-price shock Second oil-price shock

1920 1930 1940 Year

1950 1960 1970 1980 1990 2000

9/11 terrorist attack

Financial crisis

2010

20

15

10

5

0

The Unemployment Rate in the U.S. Economy The unemployment rate measures the percentage of people in the labor force who do not have jobs. This fi gure shows that the economy always has some unemployment and that the amount fl uctuates from year to year.

Source: U.S. Department of Labor and U.S. Bureau of the Census (Historical Statistics of the United States: Colonial Times to 1970).

1-2 How Economists Think

Economists often study politically charged issues, but they try to address these issues with a scientist’s objectivity. Like any science, economics has its own set of tools—terminology, data, and a way of thinking—that can seem foreign and arcane to the layman. The best way to become familiar with these tools is to practice using them, and this book affords you ample opportunity to do so. To make these tools less forbidding, however, let’s discuss a few of them here.

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8 | P A R T I Introduction

Theory as Model Building

Young children learn much about the world around them by playing with toy versions of real objects. For instance, they often put together models of cars, trains, or planes. These models are far from realistic, but the model-builder learns a lot from them nonetheless. The model illustrates the essence of the real object it is designed to resemble. (In addition, for many children, building models is fun.)

Economists also use models to understand the world, but an economist’s model is more likely to be made of symbols and equations than plastic and glue. Economists build their “toy economies” to help explain economic variables, such as GDP, infl ation, and unemployment. Economic models illustrate, often in mathematical terms, the relationships among the variables. Models are useful because they help us dispense with irrelevant details and focus on underlying connections. (In addition, for many economists, building models is fun.)

Models have two kinds of variables: endogenous variables and exogenous vari- ables. Endogenous variables are those variables that a model tries to explain. Exogenous variables are those variables that a model takes as given. The pur- pose of a model is to show how the exogenous variables affect the endogenous variables. In other words, as Figure 1-4 illustrates, exogenous variables come from outside the model and serve as the model’s input, whereas endogenous variables are determined within the model and are the model’s output.

To make these ideas more concrete, let’s review the most celebrated of all economic models—the model of supply and demand. Imagine that an economist wants to fi gure out what factors infl uence the price of pizza and the quantity of pizza sold. He or she would develop a model that described the behavior of pizza buyers, the behavior of pizza sellers, and their interaction in the market for pizza. For example, the economist supposes that the quantity of pizza demanded by consumers Qd depends on the price of pizza P and on aggregate income Y. This relationship is expressed in the equation

Qd = D(P, Y ),

where D( ) represents the demand function. Similarly, the economist supposes that the quantity of pizza supplied by pizzerias Qs depends on the price of

1-4FIGURE

Endogenous VariablesModelExogenous Variables

How Models Work Models are simplifi ed theories that show the key relationships among economic variables. The exogenous variables are those that come from outside the model. The endogenous variables are those that the model explains. The model shows how changes in the exogenous variables affect the endogenous variables.

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C H A P T E R 1 The Science of Macroeconomics | 9

pizza P and on the price of materials Pm, such as cheese, tomatoes, fl our, and anchovies. This relationship is expressed as

Qs = S(P, Pm),

where S( ) represents the supply function. Finally, the economist assumes that the price of pizza adjusts to bring the quantity supplied and quantity demanded into balance:

Qs = Qd.

These three equations compose a model of the market for pizza. The economist illustrates the model with a supply-and-demand diagram, as in

Figure 1-5. The demand curve shows the relationship between the quantity of pizza demanded and the price of pizza, holding aggregate income constant. The demand curve slopes downward because a higher price of pizza encourages con- sumers to switch to other foods and buy less pizza. The supply curve shows the relationship between the quantity of pizza supplied and the price of pizza, holding the price of materials constant. The supply curve slopes upward because a higher price of pizza makes selling pizza more profi table, which encourages pizzerias to produce more of it. The equilibrium for the market is the price and quantity at which the supply and demand curves intersect. At the equilibrium price, consum- ers choose to buy the amount of pizza that pizzerias choose to produce.

This model of the pizza market has two exogenous variables and two endog- enous variables. The exogenous variables are aggregate income and the price of materials. The model does not attempt to explain them but instead takes them as

1-5FIGURE

Supply

Demand

Price of pizza, P

Quantity of pizza, Q

Equilibrium price

Equilibrium quantity

Market equilibrium

The Model of Supply and Demand The most famous economic model is that of supply and demand for a good or service—in this case, pizza. The demand curve is a downward-sloping curve relating the price of pizza to the quantity of pizza that con- sumers demand. The supply curve is an upward-sloping curve relating the price of pizza to the quantity of pizza that pizzerias supply. The price of pizza adjusts until the quantity supplied equals the quantity demanded. The point where the two curves cross is the market equilib- rium, which shows the equi- librium price of pizza and the equilibrium quantity of pizza.

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10 | P A R T I Introduction

given (perhaps to be explained by another model). The endogenous variables are the price of pizza and the quantity of pizza exchanged. These are the variables that the model attempts to explain.

The model can be used to show how a change in one of the exogenous variables affects both endogenous variables. For example, if aggregate income increases, then the demand for pizza increases, as in panel (a) of Figure 1-6. The model shows that both the equilibrium price and the equilibrium quantity of pizza rise. Similarly, if the price of materials increases, then the supply of pizza decreases, as in panel (b) of Figure 1-6. The model shows that in this case the equilibrium price of pizza rises and the equilibrium quantity of pizza falls.

1-6FIGURE

Price of pizza, P

D2

D1

Q1 Q2

P1

P2

S

Quantity of pizza, Q

S2

S1

Q1 Q2

P2

P1

D

Price of pizza, P

Quantity of pizza, Q

(a) A Shift in Demand

(b) A Shift in Supply

Changes in Equilibrium In panel (a), a rise in aggregate income causes the demand for pizza to increase: at any given price, consumers now want to buy more pizza. This is represented by a rightward shift in the demand curve from D1 to D2. The market moves to the new intersec- tion of supply and demand. The equilibrium price rises from P1 to P2, and the equi- librium quantity of pizza rises from Q1 to Q2. In panel (b), a rise in the price of materi- als decreases the supply of pizza: at any given price, pizzerias fi nd that the sale of pizza is less profi table and therefore choose to produce less pizza. This is represented by a leftward shift in the sup- ply curve from S1 to S2. The market moves to the new intersection of supply and demand. The equilibrium price rises from P1 to P2, and the equilibrium quantity falls from Q1 to Q2.

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C H A P T E R 1 The Science of Macroeconomics | 11

Thus, the model shows how changes either in aggregate income or in the price of materials affect price and quantity in the market for pizza.

Like all models, this model of the pizza market makes simplifying assumptions. The model does not take into account, for example, that every pizzeria is in a different location. For each customer, one pizzeria is more convenient than the others, and thus pizzerias have some ability to set their own prices. The model assumes that there is a single price for pizza, but in fact there could be a different price at every pizzeria.

How should we react to the model’s lack of realism? Should we discard the simple model of pizza supply and demand? Should we attempt to build a more complex model that allows for diverse pizza prices? The answers to these ques- tions depend on our purpose. If our goal is to explain how the price of cheese affects the average price of pizza and the amount of pizza sold, then the diversity of pizza prices is probably not important. The simple model of the pizza market does a good job of addressing that issue. Yet if our goal is to explain why towns with ten pizzerias have lower pizza prices than towns with two, the simple model is less useful.

All economic models express relationships among economic variables. Often, these relationships are expressed as functions. A function is a math- ematical concept that shows how one variable depends on a set of other variables. For example, in the model of the pizza market, we said that the quantity of pizza demanded depends on the price of pizza and on aggregate income. To express this, we use functional notation to write

Qd = D(P, Y ).

This equation says that the quantity of pizza demanded Qd is a function of the price of pizza P and aggregate income Y. In functional notation, the variable preceding the parentheses denotes the function. In this case, D( ) is the function expressing how the variables in parentheses deter- mine the quantity of pizza demanded.

If we knew more about the pizza market, we could give a numerical formula for the quantity of pizza demanded. For example, we might be able to write

Qd = 60 − 10P + 2Y.

Using Functions to Express Relationships Among Variables

In this case, the demand function is

D(P, Y ) = 60 − 10P + 2Y.

For any price of pizza and aggregate income, this function gives the corresponding quantity of pizza demanded. For example, if aggregate income is $10 and the price of pizza is $2, then the quantity of pizza demanded is 60 pies; if the price of pizza rises to $3, the quantity of pizza demanded falls to 50 pies.

Functional notation allows us to express the general idea that variables are related, even when we do not have enough information to indicate the precise numerical relationship. For example, we might know that the quantity of pizza demanded falls when the price rises from $2 to $3, but we might not know by how much it falls. In this case, functional notation is useful: as long as we know that a relationship among the variables exists, we can express that relationship using functional notation.

F Y I

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12 | P A R T I Introduction

The art in economics lies in judging when a simplifying assumption (such as assuming a single price of pizza) clarifi es our thinking and when it misleads us. Simplifi cation is a necessary part of building a useful model: any model constructed to be completely realistic would be too complicated for anyone to understand. Yet models lead to incorrect conclusions if they assume away features of the economy that are crucial to the issue at hand. Economic modeling there- fore requires care and common sense.

The Use of Multiple Models

Macroeconomists study many facets of the economy. For example, they examine the role of saving in economic growth, the impact of minimum-wage laws on unemployment, the effect of infl ation on interest rates, and the infl uence of trade policy on the trade balance and exchange rate.

Economists use models to address all of these issues, but no single model can answer every question. Just as carpenters use different tools for different tasks, economists use different models to explain different economic phenom- ena. Students of macroeconomics therefore must keep in mind that there is no single “correct’’ model that is always applicable. Instead, there are many models, each of which is useful for shedding light on a different facet of the economy. The fi eld of macroeconomics is like a Swiss army knife—a set of comple- mentary but distinct tools that can be applied in different ways in different circumstances.

This book presents many different models that address different questions and make different assumptions. Remember that a model is only as good as its assumptions and that an assumption that is useful for some purposes may be misleading for others. When using a model to address a question, the economist must keep in mind the underlying assumptions and judge whether they are rea- sonable for studying the matter at hand.

Prices: Flexible Versus Sticky

Throughout this book, one group of assumptions will prove especially important— those concerning the speed at which wages and prices adjust to changing economic conditions. Economists normally presume that the price of a good or a service moves quickly to bring quantity supplied and quantity demanded into balance. In other words, they assume that markets are normally in equilibrium, so the price of any good or service is found where the supply and demand curves intersect. This assumption, called market clearing, is central to the model of the pizza market discussed earlier. For answering most questions, economists use market-clearing models.

Yet the assumption of continuous market clearing is not entirely realistic. For markets to clear continuously, prices must adjust instantly to changes in supply and demand. In fact, many wages and prices adjust slowly. Labor contracts often set wages for up to three years. Many fi rms leave their product prices the same for long periods of time—for example, magazine publishers typically change

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C H A P T E R 1 The Science of Macroeconomics | 13

their newsstand prices only every three or four years. Although market-clearing models assume that all wages and prices are fl exible, in the real world some wages and prices are sticky.

The apparent stickiness of prices does not make market-clearing models use- less. After all, prices are not stuck forever; eventually, they adjust to changes in supply and demand. Market-clearing models might not describe the economy at every instant, but they do describe the equilibrium toward which the economy gravitates. Therefore, most macroeconomists believe that price fl exibility is a good assumption for studying long-run issues, such as the growth in real GDP that we observe from decade to decade.

For studying short-run issues, such as year-to-year fl uctuations in real GDP and unemployment, the assumption of price fl exibility is less plausible. Over short periods, many prices in the economy are fi xed at predetermined levels. Therefore, most macroeconomists believe that price stickiness is a better assump- tion for studying the short-run behavior of the economy.

Microeconomic Thinking and Macroeconomic Models

Microeconomics is the study of how households and fi rms make decisions and how these decisionmakers interact in the marketplace. A central principle of microeconomics is that households and fi rms optimize—they do the best they can for themselves given their objectives and the constraints they face. In micro- economic models, households choose their purchases to maximize their level of satisfaction, which economists call utility, and fi rms make production decisions to maximize their profi ts.

Because economy-wide events arise from the interaction of many households and fi rms, macroeconomics and microeconomics are inextricably linked. When we study the economy as a whole, we must consider the decisions of individual economic actors. For example, to understand what determines total consumer spending, we must think about a family deciding how much to spend today and how much to save for the future. To understand what determines total investment spending, we must think about a fi rm deciding whether to build a new factory. Because aggregate variables are the sum of the variables describing many indi- vidual decisions, macroeconomic theory rests on a microeconomic foundation.

Although microeconomic decisions underlie all economic models, in many models the optimizing behavior of households and fi rms is implicit rather than explicit. The model of the pizza market we discussed earlier is an example. Households’ decisions about how much pizza to buy underlie the demand for pizza, and pizzerias’ decisions about how much pizza to produce underlie the supply of pizza. Presumably, households make their decisions to maximize util- ity, and pizzerias make their decisions to maximize profi t. Yet the model does not focus on how these microeconomic decisions are made; instead, it leaves these decisions in the background. Similarly, although microeconomic decisions underlie macroeconomic phenomena, macroeconomic models do not necessar- ily focus on the optimizing behavior of households and fi rms; again, they some- times leave that behavior in the background.

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14 | P A R T I Introduction

The winner of the Nobel Prize in economics is announced every October. Many winners have been macroeconomists whose work we study in this book. Here are a few of them, along with some of their own words about how they chose their fi eld of study:

Milton Friedman (Nobel 1976): “I graduated from college in 1932, when the United States was at the bottom of the deepest depression in its history before or since. The dominant problem of the time was economics. How to get out of the depression? How to reduce unemployment? What explained the paradox of great need on the one hand and unused resources on the other? Under the circumstances, becoming an economist seemed more relevant to the burning issues of the day than becoming an applied mathematician or an actuary.”

James Tobin (Nobel 1981): “I was attracted to the fi eld for two reasons. One was that economic theory is a fascinating intellectual challenge, on the order of mathematics or chess. I liked analytics and logical argument. . . . The other reason was the obvious relevance of economics to understanding and perhaps overcoming the Great Depression.”

Franco Modigliani (Nobel 1985): “For awhile it was thought that I should study medicine because my father was a physician. . . . I went to the regis- tration window to sign up for medicine, but then I closed my eyes and thought of blood! I got pale just thinking about blood and decided under those con- ditions I had better keep away from medicine. . . . Casting about for something to do, I happened to get into some economics activities. I knew some German and was asked to translate from German into Italian some articles for one of the trade associ- ations. Thus I began to be exposed to the economic problems that were in the German literature.”

Robert Solow (Nobel 1987): “I came back [to college after being in the army] and, almost without thinking about it, signed up to fi nish my undergraduate degree as an economics major. The time was such that I had to make a decision in a hurry. No doubt I acted as if I were maximizing

Nobel Macroeconomists an infi nite discounted sum of one-period utilities, but you couldn’t prove it by me. To me it felt as if I were saying to myself: ‘What the hell.’”

Robert Lucas (Nobel 1995): “In public school sci- ence was an unending and not very well organized list of things other people had discovered long ago. In college, I learned something about the process of scientifi c discovery, but what I learned did not attract me as a career possibility. . . . What I liked thinking about were politics and social issues.”

George Akerlof (Nobel 2001): “When I went to Yale, I was convinced that I wanted to be either an economist or an historian. Really, for me it was a distinction without a difference. If I was going to be an historian, then I would be an economic historian. And if I was to be an economist I would consider history as the basis for my economics.”

Edward Prescott (Nobel 2004): “Through discus- sion with [my father], I learned a lot about the way businesses operated. This was one reason why I liked my microeconomics course so much in my fi rst year at Swarthmore College. The price theory that I learned in that course rationalized what I had learned from him about the way businesses operate. The other reason was the textbook used in that course, Paul A. Samuelson’s Principles of Economics. I loved the way Samuelson laid out the theory in his textbook, so simply and clearly.”

Edmund Phelps (Nobel 2006): “Like most Ameri- cans entering college, I started at Amherst College without a predetermined course of study or without even a career goal. My tacit assumption was that I would drift into the world of business—of money, doing something terribly smart. In the fi rst year, though, I was awestruck by Plato, Hume and James. I would probably have gone into philosophy were it not that my father cajoled and pleaded with me to try a course in economics, which I did the second year. . . . I was hugely impressed to see that it was possible to subject the events in those newspapers I had read about to a formal sort of analysis.”

If you want to learn more about the Nobel Prize and its winners, go to www.nobelprize.org.1

F Y I

1The fi rst fi ve quotations are from William Breit and Barry T. Hirsch, eds., Lives of the Laureates, 4th ed. (Cambridge, Mass.: MIT Press, 2004). The next two are from the Nobel Web site. The last one is from Arnold Heertje, ed., The Makers of Modern Economics, vol. II (Aldershot, U.K.: Edward Elgar Publishing, 1995).

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C H A P T E R 1 The Science of Macroeconomics | 15

1-3 How This Book Proceeds

This book has six parts. This chapter and the next make up Part One, the “Intro- duction.” Chapter 2 discusses how economists measure economic variables, such as aggregate income, the infl ation rate, and the unemployment rate.

Part Two, “Classical Theory: The Economy in the Long Run,” presents the classical model of how the economy works. The key assumption of the classical model is that prices are fl exible. That is, with rare exceptions, the classical model assumes that markets clear. The assumption of price fl exibility greatly simplifi es the analysis, which is why we start with it. Yet because this assumption accurately describes the economy only in the long run, classical theory is best suited for analyzing a time horizon of at least several years.

Part Three, “Growth Theory: The Economy in the Very Long Run,” builds on the classical model. It maintains the assumptions of price fl exibility and market clearing but adds a new emphasis on growth in the capital stock, the labor force, and technological knowledge. Growth theory is designed to explain how the economy evolves over a period of several decades.

Part Four, “Business Cycle Theory: The Economy in the Short Run,” exam- ines the behavior of the economy when prices are sticky. The non-market- clearing model developed here is designed to analyze short-run issues, such as the reasons for economic fl uctuations and the infl uence of government policy on those fl uctuations. It is best suited for analyzing the changes in the economy we observe from month to month or from year to year.

The last two parts of the book cover various topics to supplement, reinforce, and refi ne our long-run and short-run analysis. Part Five, “Topics in Macroeco- nomic Theory,” presents advanced material of a somewhat theoretical nature, including macroeconomic dynamics, models of consumer behavior, and theories of fi rms’ investment decisions. Part Six, “Topics in Macroeconomic Policy,” con- siders what role the government should have in the economy. It discusses the policy debates over stabilization policy, government debt, and fi nancial crises.

Summary

1. Macroeconomics is the study of the economy as a whole, including growth in incomes, changes in prices, and the rate of unemployment. Macroecono- mists attempt both to explain economic events and to devise policies to improve economic performance.

2. To understand the economy, economists use models—theories that simplify reality in order to reveal how exogenous variables infl uence endogenous variables. The art in the science of economics lies in judging whether a model captures the important economic relationships for the matter at hand. Because no single model can answer all questions, macroeconomists use different models to look at different issues.

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16 | P A R T I Introduction

3. A key feature of a macroeconomic model is whether it assumes that prices are fl exible or sticky. According to most macroeconomists, models with fl exible prices describe the economy in the long run, whereas models with sticky prices offer a better description of the economy in the short run.

4. Microeconomics is the study of how fi rms and individuals make decisions and how these decisionmakers interact. Because macroeconomic events arise from many microeconomic interactions, all macroeconomic models must be consistent with microeconomic foundations, even if those founda- tions are only implicit.

K E Y C O N C E P T S

Macroeconomics

Real GDP

Infl ation and defl ation

Unemployment

Recession

Depression

Models

Endogenous variables

Exogenous variables

Market clearing

Flexible and sticky prices

Microeconomics

1. Explain the difference between macroeconomics and microeconomics. How are these two fi elds related?

2. Why do economists build models?

Q U E S T I O N S F O R R E V I E W

3. What is a market-clearing model? When is it appropriate to assume that markets clear?

P R O B L E M S A N D A P P L I C A T I O N S

1. What macroeconomic issues have been in the news lately?

2. What do you think are the defi ning characteris- tics of a science? Does the study of the economy have these characteristics? Do you think macro- economics should be called a science? Why or why not?

3. Use the model of supply and demand to explain how a fall in the price of frozen yogurt would

affect the price of ice cream and the quantity of ice cream sold. In your explanation, identify the exogenous and endogenous variables.

4. How often does the price you pay for a haircut change? What does your answer imply about the usefulness of market-clearing models for analyz- ing the market for haircuts?

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17

The Data of Macroeconomics

2C H A P T E R

It is a capital mistake to theorize before one has data. Insensibly one begins to

twist facts to suit theories, instead of theories to fi t facts.

—Sherlock Holmes

Scientists, economists, and detectives have much in common: they all want to fi gure out what’s going on in the world around them. To do this, they rely on theory and observation. They build theories in an attempt to make sense of what they see happening. They then turn to more systematic observation to evaluate the theories’ validity. Only when theory and evidence come into line do they feel they understand the situation. This chapter discusses the types of observation that economists use to develop and test their theories.

Casual observation is one source of information about what’s happening in the economy. When you go shopping, you notice whether prices are rising, fall- ing, or staying the same. When you look for a job, you learn whether fi rms are hiring. Every day, as we go about our lives, we participate in some aspect of the economy and get some sense of economic conditions.

A century ago, economists monitoring the economy had little more to go on than such casual observations. Such fragmentary information made economic policymaking diffi cult. One person’s anecdote would suggest the economy was moving in one direction, while a different person’s anecdote would suggest oth- erwise. Economists needed some way to combine many individual experiences into a coherent whole. There was an obvious solution: as the old quip goes, the plural of “anecdote” is “data.”

Today, economic data offer a systematic and objective source of infor- mation, and almost every day the newspaper has a story about some newly released statistic. Most of these statistics are produced by the government. Various government agencies survey households and firms to learn about their economic activity—how much they are earning, what they are buying, what prices they are charging, how much they are producing, whether they have a job or are looking for work, and so on. From these surveys, various statistics are computed that summarize the state of the economy. Economists use these statistics to study the economy; policymakers use them to monitor developments and formulate policies.

This chapter focuses on the three statistics that economists and policymak- ers use most often. Gross domestic product, or GDP, tells us the nation’s total

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18 | P A R T I Introduction

income and the total expenditure on its output of goods and services. The consumer price index, or CPI, measures the level of prices. The unemployment rate tells us the fraction of workers who are unemployed. In the following pages, we see how these statistics are computed and what they tell us about the economy.

2-1 Measuring the Value of Economic Activity: Gross Domestic Product

Gross domestic product, or GDP, is often considered the best measure of how well the economy is performing. This statistic is computed every three months by the Bureau of Economic Analysis, a part of the U.S. Department of Commerce, from a large number of primary data sources. These primary sources include both administrative data, which are byproducts of government functions such as tax collection, education programs, defense, and regulation, and statistical data, which come from government surveys of, for example, retail establishments, manufacturing fi rms, and farms. The purpose of GDP is to summarize all these data with a single number representing the dollar value of economic activity in a given period of time.

There are two ways to view this statistic. One way to view GDP is as the total income of everyone in the economy; another way is as the total expenditure on the economy’s output of goods and services. From either viewpoint, it is clear why GDP is a gauge of economic performance. GDP measures something people care about—their incomes. Similarly, an economy with a large output of goods and services can better satisfy the demands of households, fi rms, and the government.

How can GDP measure both the economy’s income and its expenditure on output? The reason is that these two quantities are really the same: for the economy as a whole, income must equal expenditure. That fact, in turn, follows from an even more fundamental one: because every transaction has a buyer and a seller, every dollar of expenditure by a buyer must become a dollar of income to a seller. When Joe paints Jane’s house for $1,000, that $1,000 is income to Joe and expenditure by Jane. The transaction contributes $1,000 to GDP, regardless of whether we are adding up all income or all expenditure.

To understand the meaning of GDP more fully, we turn to national income accounting, the accounting system used to measure GDP and many related statistics.

Income, Expenditure, and the Circular Flow

Imagine an economy that produces a single good, bread, from a single input, labor. Figure 2-1 illustrates all the economic transactions that occur between households and fi rms in this economy.

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C H A P T E R 2 The Data of Macroeconomics | 19

The inner loop in Figure 2-1 represents the fl ows of bread and labor. The households sell their labor to the fi rms. The fi rms use the labor of their workers to produce bread, which the fi rms in turn sell to the households. Hence, labor fl ows from households to fi rms, and bread fl ows from fi rms to households.

The outer loop in Figure 2-1 represents the corresponding fl ow of dollars. The households buy bread from the fi rms. The fi rms use some of the revenue from these sales to pay the wages of their workers, and the remainder is the profi t belonging to the owners of the fi rms (who themselves are part of the house- hold sector). Hence, expenditure on bread fl ows from households to fi rms, and income in the form of wages and profi t fl ows from fi rms to households.

GDP measures the fl ow of dollars in this economy. We can compute it in two ways. GDP is the total income from the production of bread, which equals the sum of wages and profi t—the top half of the circular fl ow of dollars. GDP is also the total expenditure on purchases of bread—the bottom half of the circular fl ow of dollars. To compute GDP, we can look at either the fl ow of dollars from fi rms to households or the fl ow of dollars from households to fi rms.

These two ways of computing GDP must be equal because, by the rules of accounting, the expenditure of buyers on products is income to the sellers of those products. Every transaction that affects expenditure must affect income, and every transaction that affects income must affect expenditure. For example, sup- pose that a fi rm produces and sells one more loaf of bread to a household. Clearly this transaction raises total expenditure on bread, but it also has an equal effect on

2-1FIGURE

Income ($)

Labor

Goods (bread)

Expenditure ($)

Households Firms

The Circular Flow This fi gure illustrates the fl ows between fi rms and house- holds in an economy that produces one good, bread, from one input, labor. The inner loop represents the fl ows of labor and bread: house- holds sell their labor to fi rms, and the fi rms sell the bread they produce to households. The outer loop represents the cor- responding fl ows of dol- lars: households pay the fi rms for the bread, and the fi rms pay wages and profi t to the households. In this economy, GDP is both the total expen- diture on bread and the total income from the production of bread.

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20 | P A R T I Introduction

total income. If the fi rm produces the extra loaf without hiring any more labor (such as by making the production process more effi cient), then profi t increases. If the fi rm produces the extra loaf by hiring more labor, then wages increase. In both cases, expenditure and income increase equally.

Rules for Computing GDP

In an economy that produces only bread, we can compute GDP by adding up the total expenditure on bread. Real economies, however, include the produc- tion and sale of a vast number of goods and services. To compute GDP for such a complex economy, it will be helpful to have a more precise defi nition: Gross

Many economic variables measure a quantity of something—a quantity of money, a quan- tity of goods, and so on. Economists distinguish between two types of quantity variables: stocks and fl ows. A stock is a quantity measured at a given point in time, whereas a fl ow is a quantity measured per unit of time.

A bathtub, shown in Figure 2-2, is the classic example used to illustrate stocks and fl ows. The amount of water in the tub is a stock: it is the quantity of water in the tub at a given point in time. The amount of water coming out of the faucet is a fl ow: it is the quantity of water being added to the tub per unit of time. Note that we measure stocks and fl ows in different units. We say that the bathtub contains 50 gallons of water

Figure 2-2 Stocks and Flows The amount of water in a bathtub is a stock: it is a quantity measured at a given moment in time. The amount of water coming out of the faucet is a fl ow: it is a quantity measured per unit of time.

Flow Stock

Stocks and Flows but that water is coming out of the faucet at 5 gallons per minute.

GDP is probably the most important fl ow variable in economics: it tells us how many dol- lars are fl owing around the economy’s circular fl ow per unit of time. When someone says that the U.S. GDP is $14 trillion, this means that it is $14 trillion per year. (Equivalently, we could say that U.S. GDP is $444,000 per second.)

Stocks and fl ows are often related. In the bathtub example, these relationships are clear. the stock of water in the tub represents the accu- mulation of the fl ow out of the faucet, and the fl ow of water represents the change in the stock. When building theories to explain economic variables, it is often useful to determine whether the variables are stocks or fl ows and whether any relationships link them.

Here are some examples of related stocks and fl ows that we study in future chapters:

■ A person’s wealth is a stock; his income and expenditure are fl ows.

■ The number of unemployed people is a stock; the number of people losing their jobs is a fl ow.

■ The amount of capital in the economy is a stock; the amount of investment is a fl ow.

■ The government debt is a stock; the government budget defi cit is a fl ow.

F Y I

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C H A P T E R 2 The Data of Macroeconomics | 21

domestic product (GDP) is the market value of all fi nal goods and services produced within an economy in a given period of time. To see how this defi nition is applied, let’s discuss some of the rules that economists follow in constructing this statistic.

Adding Apples and Oranges The U.S. economy produces many differ- ent goods and services—hamburgers, haircuts, cars, computers, and so on. GDP combines the value of these goods and services into a single measure. The diver- sity of products in the economy complicates the calculation of GDP because different products have different values.

Suppose, for example, that the economy produces four apples and three oranges. How do we compute GDP? We could simply add apples and oranges and conclude that GDP equals seven pieces of fruit. But this makes sense only if we think apples and oranges have equal value, which is generally not true. (This would be even clearer if the economy produces four watermelons and three grapes.)

To compute the total value of different goods and services, the national income accounts use market prices because these prices refl ect how much people are willing to pay for a good or service. Thus, if apples cost $0.50 each and oranges cost $1.00 each, GDP would be

GDP = (Price of Apples × Quantity of Apples) + (Price of Oranges × Quantity of Oranges)

= ($0.50 × 4) + ($1.00 × 3)

= $5.00.

GDP equals $5.00—the value of all the apples, $2.00, plus the value of all the oranges, $3.00.

Used Goods When the Topps Company makes a pack of baseball cards and sells it for $2, that $2 is added to the nation’s GDP. But when a collector sells a rare Mickey Mantle card to another collector for $500, that $500 is not part of GDP. GDP measures the value of currently produced goods and services. The sale of the Mickey Mantle card refl ects the transfer of an asset, not an addition to the economy’s income. Thus, the sale of used goods is not included as part of GDP.

The Treatment of Inventories Imagine that a bakery hires workers to produce more bread, pays their wages, and then fails to sell the additional bread. How does this transaction affect GDP?

The answer depends on what happens to the unsold bread. Let’s fi rst suppose that the bread spoils. In this case, the fi rm has paid more in wages but has not received any additional revenue, so the fi rm’s profi t is reduced by the amount that wages have increased. Total expenditure in the economy hasn’t changed because no one buys the bread. Total income hasn’t changed either—although more is distributed as wages and less as profi t. Because the transaction affects neither expenditure nor income, it does not alter GDP.

Now suppose, instead, that the bread is put into inventory (perhaps as frozen dough) to be sold later. In this case, the national income accounts treat the

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22 | P A R T I Introduction

transaction differently. The owners of the fi rm are assumed to have “purchased’’ the bread for the fi rm’s inventory, and the fi rm’s profi t is not reduced by the additional wages it has paid. Because the higher wages paid to the fi rm’s workers raise total income, and the greater spending by the fi rm’s owners on inventory raises total expenditure, the economy’s GDP rises.

What happens later when the fi rm sells the bread out of inventory? This case is much like the sale of a used good. There is spending by bread consumers, but there is inventory disinvestment by the fi rm. This negative spending by the fi rm offsets the positive spending by consumers, so the sale out of inventory does not affect GDP.

The general rule is that when a fi rm increases its inventory of goods, this investment in inventory is counted as an expenditure by the fi rm owners. Thus, production for inventory increases GDP just as much as does production for fi nal sale. A sale out of inventory, however, is a combination of positive spending (the purchase) and negative spending (inventory disinvestment), so it does not infl u- ence GDP. This treatment of inventories ensures that GDP refl ects the economy’s current production of goods and services.

Intermediate Goods and Value Added Many goods are produced in stages: raw materials are processed into intermediate goods by one fi rm and then sold to another fi rm for fi nal processing. How should we treat such products when computing GDP? For example, suppose a cattle rancher sells one-quarter pound of meat to McDonald’s for $1, and then McDonald’s sells you a hamburger for $3. Should GDP include both the meat and the hamburger (a total of $4) or just the hamburger ($3)?

The answer is that GDP includes only the value of fi nal goods. Thus, the hamburger is included in GDP but the meat is not: GDP increases by $3, not by $4. The reason is that the value of intermediate goods is already included as part of the market price of the fi nal goods in which they are used. To add the intermediate goods to the fi nal goods would be double counting—that is, the meat would be counted twice. Hence, GDP is the total value of fi nal goods and services produced.

One way to compute the value of all fi nal goods and services is to sum the value added at each stage of production. The value added of a fi rm equals the value of the fi rm’s output less the value of the intermediate goods that the fi rm purchases. In the case of the hamburger, the value added of the rancher is $1 (assuming that the rancher bought no intermediate goods), and the value added of McDonald’s is $3 – $1, or $2. Total value added is $1 + $2, which equals $3. For the economy as a whole, the sum of all value added must equal the value of all fi nal goods and services. Hence, GDP is also the total value added of all fi rms in the economy.

Housing Services and Other Imputations Although most goods and services are valued at their market prices when computing GDP, some are not sold in the marketplace and therefore do not have market prices. If GDP is to include the value of these goods and services, we must use an estimate of their value. Such an estimate is called an imputed value.

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C H A P T E R 2 The Data of Macroeconomics | 23

Imputations are especially important for determining the value of housing. A person who rents a house is buying housing services and providing income for the landlord; the rent is part of GDP, both as expenditure by the renter and as income for the landlord. Many people, however, own their own homes. Although they do not pay rent to a landlord, they are enjoying housing services similar to those that renters purchase. To take account of the housing services enjoyed by homeowners, GDP includes the “rent” that these homeowners “pay” to themselves. Of course, homeowners do not in fact pay themselves this rent. The Department of Com- merce estimates what the market rent for a house would be if it were rented and includes that imputed rent as part of GDP. This imputed rent is included both in the homeowner’s expenditure and in the homeowner’s income.

Imputations also arise in valuing government services. For example, police offi cers, fi refi ghters, and senators provide services to the public. Assigning a value to these services is diffi cult because they are not sold in a marketplace and there- fore do not have a market price. The national income accounts include these services in GDP by valuing them at their cost. That is, the wages of these public servants are used as a measure of the value of their output.

In many cases, an imputation is called for in principle but, to keep things simple, is not made in practice. Because GDP includes the imputed rent on owner-occupied houses, one might expect it also to include the imputed rent on cars, lawn mowers, jewelry, and other durable goods owned by households. Yet the value of these rental services is left out of GDP. In addition, some of the output of the economy is produced and consumed at home and never enters the marketplace. For example, meals cooked at home are similar to meals cooked at a restaurant, yet the value added when a person prepares a meal at home is left out of GDP.

Finally, no imputation is made for the value of goods and services sold in the underground economy. The underground economy is the part of the economy that people hide from the government either because they wish to evade taxation or because the activity is illegal. Examples include domestic workers paid “off the books” and the illegal drug trade. The size of the underground economy varies widely from country to country. In the United States, the underground economy is estimated to be less than 10 percent of the offi cial economy, whereas in some developing nations, such as Thailand, Nigeria, and Egypt, the underground economy is almost as large as the offi cial one.

Because the imputations necessary for computing GDP are only approximate, and because the value of many goods and services is left out altogether, GDP is an imperfect measure of economic activity. These imperfections are most prob- lematic when comparing standards of living across countries. Yet as long as the magnitude of these imperfections remains fairly constant over time, GDP is use- ful for comparing economic activity from year to year.

Real GDP Versus Nominal GDP

Economists use the rules just described to compute GDP, which values the economy’s total output of goods and services. But is GDP a good measure of

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24 | P A R T I Introduction

economic well-being? Consider once again the economy that produces only apples and oranges. In this economy, GDP is the sum of the value of all the apples produced and the value of all the oranges produced. That is,

GDP = (Price of Apples × Quantity of Apples) + (Price of Oranges × Quantity of Oranges).

Economists call the value of goods and services measured at current prices nominal GDP. Notice that nominal GDP can increase either because prices rise or because quantities rise.

It is easy to see that GDP computed this way is not a good gauge of eco- nomic well-being. That is, this measure does not accurately refl ect how well the economy can satisfy the demands of households, fi rms, and the government. If all prices doubled without any change in quantities, nominal GDP would double. Yet it would be misleading to say that the economy’s ability to satisfy demands has doubled because the quantity of every good produced remains the same.

A better measure of economic well-being would tally the economy’s output of goods and services without being infl uenced by changes in prices. For this purpose, economists use real GDP, which is the value of goods and services measured using a constant set of prices. That is, real GDP shows what would have happened to expenditure on output if quantities had changed but prices had not.

To see how real GDP is computed, imagine we want to compare output in 2011 with output in subsequent years for our apple-and-orange economy. We could begin by choosing a set of prices, called base-year prices, such as the prices that prevailed in 2011. Goods and services are then added up using these base-year prices to value the different goods in each year. Real GDP for 2011 would be

Real GDP = (2011 Price of Apples × 2011 Quantity of Apples) + (2011 Price of Oranges × 2011 Quantity of Oranges).

Similarly, real GDP in 2012 would be

Real GDP = (2011 Price of Apples × 2012 Quantity of Apples) + (2011 Price of Oranges × 2012 Quantity of Oranges).

And real GDP in 2013 would be

Real GDP = (2011 Price of Apples × 2013 Quantity of Apples) + (2011 Price of Oranges × 2013 Quantity of Oranges).

Notice that 2011 prices are used to compute real GDP for all three years. Because the prices are held constant, real GDP varies from year to year only if the quantities produced vary. Because a society’s ability to provide economic satisfaction for its members ultimately depends on the quantities of goods and services produced, real GDP provides a better measure of economic well-being than does nominal GDP.

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C H A P T E R 2 The Data of Macroeconomics | 25

The GDP Deflator

From nominal GDP and real GDP we can compute a third statistic: the GDP defl ator. The GDP defl ator, also called the implicit price defl ator for GDP, is the ratio of nominal GDP to real GDP:

Nominal GDP GDP Defl ator = ——––––——. Real GDP

The GDP defl ator refl ects what’s happening to the overall level of prices in the economy.

To better understand this, consider again an economy with only one good, bread. If P is the price of bread and Q is the quantity sold, then nominal GDP is the total number of dollars spent on bread in that year, P × Q. Real GDP is the number of loaves of bread produced in that year times the price of bread in some base year, Pbase × Q. The GDP defl ator is the price of bread in that year relative to the price of bread in the base year, P/Pbase.

The defi nition of the GDP defl ator allows us to separate nominal GDP into two parts: one part measures quantities (real GDP) and the other measures prices (the GDP defl ator). That is,

Nominal GDP = Real GDP × GDP Defl ator.

Nominal GDP measures the current dollar value of the output of the economy. Real GDP measures output valued at constant prices. The GDP defl ator measures the price of output relative to its price in the base year. We can also write this equation as

Nominal GDP Real GDP = ——————. GDP Defl ator

In this form, you can see how the defl ator earns its name: it is used to defl ate (that is, take infl ation out of) nominal GDP to yield real GDP.

Chain-Weighted Measures of Real GDP

We have been discussing real GDP as if the prices used to compute this measure never change from their base-year values. If this were truly the case, over time the prices would become more and more dated. For instance, the price of computers has fallen substantially in recent years, while the price of a year at college has risen. When valuing the production of computers and edu- cation, it would be misleading to use the prices that prevailed ten or twenty years ago.

To solve this problem, the Bureau of Economic Analysis used to periodically update the prices used to compute real GDP. About every fi ve years, a new base year was chosen. The prices were then held fi xed and used to measure year-to- year changes in the production of goods and services until the base year was updated once again.

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26 | P A R T I Introduction

In 1995, the Bureau announced a new policy for dealing with changes in the base year. In particular, it now uses chain-weighted measures of real GDP. With these new measures, the base year changes continuously over time. In essence, average prices in 2011 and 2012 are used to measure real growth from 2011 to 2012, average prices in 2012 and 2013 are used to measure real growth from 2012 to 2013, and so on. These various year-to-year growth rates are then put together to form a “chain” that can be used to compare the output of goods and services between any two dates.

This new chain-weighted measure of real GDP is better than the more tra- ditional measure because it ensures that the prices used to compute real GDP are never far out of date. For most purposes, however, the differences are not signifi cant. It turns out that the two measures of real GDP are highly correlated with each other. As a practical matter, both measures of real GDP refl ect the same thing: economy-wide changes in the production of goods and services.

For manipulating many relationships in econom- ics, there is an arithmetic trick that is useful to know: The percentage change of a product of two vari- ables is approximately the sum of the percentage changes in each of the variables.

To see how this trick works, consider an example. Let P denote the GDP defl ator and Y denote real GDP. Nominal GDP is P × Y. The trick states that

Percentage Change in (P × Y) ≈ (Percentage Change in P) + (Percentage Change in Y).

For instance, suppose that in one year, real GDP is 100 and the GDP defl ator is 2; the next year, real GDP is 103 and the GDP defl ator is 2.1. We can calculate that real GDP rose by 3 percent and that the GDP defl ator rose by 5 percent. Nominal GDP rose from 200 the fi rst year to 216.3 the second year, an increase of 8.15 percent. Notice that the growth in nominal GDP (8.15 percent) is

Two Arithmetic Tricks for Working With Percentage Changes

approximately the sum of the growth in the GDP defl ator (5 percent) and the growth in real GDP (3 percent).1

A second arithmetic trick follows as a corol- lary to the fi rst: The percentage change of a ratio is approximately the percentage change in the numera- tor minus the percentage change in the denominator. Again, consider an example. Let Y denote GDP and L denote the population, so that Y/L is GDP per person. The second trick states that

Percentage Change in (Y/L) ≈ (Percentage Change in Y ) − (Percentage Change in L).

For instance, suppose that in the fi rst year, Y is 100,000 and L is 100, so Y/L is 1,000; in the second year, Y is 110,000 and L is 103, so Y/L is 1,068. Notice that the growth in GDP per person (6.8 percent) is approximately the growth in income (10 percent) minus the growth in popu- lation (3 percent).

F Y I

1Mathematical note: The proof that this trick works begins with the product rule from calculus: d(PY ) = Y dP + P dY.

Now divide both sides of this equation by PY to obtain: d(PY )/(PY ) = dP/P + dY/Y.

Notice that all three terms in this equation are percentage changes.

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C H A P T E R 2 The Data of Macroeconomics | 27

The Components of Expenditure

Economists and policymakers care not only about the economy’s total output of goods and services but also about the allocation of this output among alterna- tive uses. The national income accounts divide GDP into four broad categories of spending:

■ Consumption (C )

■ Investment (I )

■ Government purchases (G)

■ Net exports (NX ).

Thus, letting Y stand for GDP,

Y = C + I + G + NX.

GDP is the sum of consumption, investment, government purchases, and net exports. Each dollar of GDP falls into one of these categories. This equation is an identity—an equation that must hold because of the way the variables are defi ned. It is called the national income accounts identity.

Consumption consists of the goods and services bought by households. It is divided into three subcategories: nondurable goods, durable goods, and services. Nondurable goods are goods that last only a short time, such as food and cloth- ing. Durable goods are goods that last a long time, such as cars and TVs. Services include various intangible items purchased by consumers, such as haircuts and doctor visits.

Investment consists of goods bought for future use. Investment is also divided into three subcategories: business fi xed investment, residential fi xed investment, and inventory investment. Business fi xed investment is the purchase of new plant and equipment by fi rms. Residential investment is the purchase of new housing by households and landlords. Inventory investment is the increase in fi rms’ inventories of goods (if inventories are falling, inventory investment is negative).

Government purchases are the goods and services bought by federal, state, and local governments. This category includes such items as military equipment, highways, and the services provided by government workers. It does not include transfer payments to individuals, such as Social Security and welfare. Because transfer payments reallocate existing income and are not made in exchange for goods and services, they are not part of GDP.

The last category, net exports, accounts for trade with other countries. Net exports are the value of goods and services sold to other countries (exports) minus the value of goods and services that foreigners sell us (imports). Net exports are positive when the value of our exports is greater than the value of our imports and negative when the value of our imports is greater than the value of our exports. Net exports represent the net expenditure from abroad on our goods and services, which provides income for domestic producers.

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28 | P A R T I Introduction

Newcomers to macroeconomics are sometimes confused by how macroeconomists use familiar words in new and specifi c ways. One example is the term “investment.” The confusion arises because what looks like investment for an indi- vidual may not be investment for the economy as a whole. The general rule is that the economy’s investment does not include purchases that merely reallocate existing assets among different individu- als. Investment, as macroeconomists use the term, creates a new physical asset, called capital, which can be used in future production.

Let’s consider some examples. Suppose we observe these two events:

■ Smith buys himself a 100-year-old Victorian house.

■ Jones builds herself a brand-new contempo- rary house.

What is total investment here? Two houses, one house, or zero?

A macroeconomist seeing these two transac- tions counts only the Jones house as investment.

What Is Investment? Smith’s transaction has not created new hous- ing for the economy; it has merely reallocated existing housing. Smith’s purchase is investment for Smith, but it is disinvestment for the person selling the house. By contrast, Jones has added new housing to the economy; her new house is counted as investment.

Similarly, consider these two events:

■ Gates buys $5 million in IBM stock from Buffett on the New York Stock Exchange.

■ General Motors sells $10 million in stock to the public and uses the proceeds to build a new car factory.

Here, investment is $10 million. In the fi rst transaction, Gates is investing in IBM stock, and Buffett is disinvesting; there is no invest- ment for the economy. By contrast, General Motors is using some of the economy’s output of goods and services to add to its stock of capital; hence, its new factory is counted as investment.

F Y I

GDP and Its Components

In 2010, the GDP of the United States totaled about $14.5 trillion. This number is so large that it is almost impossible to comprehend. We can make it easier to understand by dividing it by the 2010 U.S. population of 309 million. In this way, we obtain GDP per person—the amount of expenditure for the average American—which equaled $47,050 in 2010.

How did this GDP get used? Table 2-1 shows that about two-thirds of it, or $33,184 per person, was spent on consumption. Investment was $5,814 per per- son. Government purchases were $9,726 per person, $2,653 of which was spent by the federal government on national defense.

The average American bought $7,633 of goods imported from abroad and produced $5,959 of goods that were exported to other countries. Because the average American imported more than he exported, net exports were negative. Furthermore, because the average American earned less from selling to foreigners than he spent on foreign goods, he must have fi nanced the difference by taking

CASE STUDY

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C H A P T E R 2 The Data of Macroeconomics | 29

out loans from foreigners (or, equivalently, by selling them some of his assets). Thus, the average American borrowed $1,674 from abroad in 2010. ■

Other Measures of Income

The national income accounts include other measures of income that differ slightly in defi nition from GDP. It is important to be aware of the various mea- sures, because economists and the press often refer to them.

To see how the alternative measures of income relate to one another, we start with GDP and modify it in various ways. To obtain gross national product (GNP), we add to GDP receipts of factor income (wages, profi t, and rent) from the rest of the world and subtract payments of factor income to the rest of the world:

GNP = GDP + Factor Payments from Abroad – Factor Payments to Abroad.

Whereas GDP measures the total income produced domestically, GNP measures the total income earned by nationals (residents of a nation). For instance, if a Japanese resident owns an apartment building in New York, the rental income he earns is part of U.S. GDP because it is earned in the United States. But because this rental income is a factor payment to abroad, it is not part of U.S. GNP. In

Total Per Person (billions of dollars) (dollars)

Gross Domestic Product 14,527 47,050

Consumption 10,246 33,184 Nondurable goods 2,302 7,454 Durable goods 1,086 3,516 Services 6,859 22,214

Investment 1,795 5,814 Nonresidential fi xed investment 1,390 4,502 Residential fi xed investment 338 1,095 Inventory investment 67 217

Government Purchases 3,003 9,726 Federal 1,223 3,961 Defense 819 2,653 Nondefense 404 1,307 State and Local 1,780 5,765

Net Exports −517 −1,674 Exports 1,840 5,959 Imports 2,357 7,633

Source: U.S. Department of Commerce.

GDP and the Components of Expenditure: 2010

TABLE 2-1

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30 | P A R T I Introduction

the United States, factor payments from abroad and factor payments to abroad are similar in size—each representing about 3 percent of GDP—so GDP and GNP are quite close.

To obtain net national product (NNP), we subtract from GNP the depreciation of capital—the amount of the economy’s stock of plants, equipment, and resi- dential structures that wears out during the year:

NNP = GNP – Depreciation.

In the national income accounts, depreciation is called the consumption of fi xed capital. It equals about 10 percent of GNP. Because the depreciation of capital is a cost of producing the output of the economy, subtracting depreciation shows the net result of economic activity.

Net national product is approximately equal to another measure called national income. The two differ by a small correction called the statistical discrepancy, which arises because different data sources may not be completely consistent. National income measures how much everyone in the economy has earned.

The national income accounts divide national income into six components, depending on who earns the income. The six categories, and the percentage of national income paid in each category, are the following:

■ Compensation of employees (63%). The wages and fringe benefi ts earned by workers.

■ Proprietors’ income (8%). The income of noncorporate businesses, such as small farms, mom-and-pop stores, and law partnerships.

■ Rental income (3%). The income that landlords receive, including the imputed rent that homeowners “pay” to themselves, less expenses, such as depreciation.

■ Corporate profi ts (14%). The income of corporations after payments to their workers and creditors.

■ Net interest (4%). The interest domestic businesses pay minus the interest they receive, plus interest earned from foreigners.

■ Indirect business taxes (8%). Certain taxes on businesses, such as sales taxes, less offsetting business subsidies. These taxes place a wedge between the price that consumers pay for a good and the price that fi rms receive.

A series of adjustments take us from national income to personal income, the amount of income that households and noncorporate businesses receive. Four of these adjustments are most important. First, we subtract indirect business taxes because these taxes never enter anyone’s income. Second, we reduce national income by the amount that corporations earn but do not pay out, either because the corporations are retaining earnings or because they are paying taxes to the government. This adjustment is made by subtracting corporate profi ts (which equal the sum of corporate taxes, dividends, and retained earnings) and adding back dividends. Third, we increase national income by the net amount the gov- ernment pays out in transfer payments. This adjustment equals government trans- fers to individuals minus social insurance contributions paid to the government.

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C H A P T E R 2 The Data of Macroeconomics | 31

Fourth, we adjust national income to include the interest that households earn rather than the interest that businesses pay. This adjustment is made by adding personal interest income and subtracting net interest. (The difference between personal interest and net interest arises in part because interest on the govern- ment debt is part of the interest that households earn but is not part of the inter- est that businesses pay out.) Thus,

Personal Income = National Income − Indirect Business Taxes − Corporate Profi ts − Social Insurance Contributions − Net Interest + Dividends + Government Transfers to Individuals + Personal Interest Income.

Next, if we subtract personal tax payments and certain nontax payments to the government (such as parking tickets), we obtain disposable personal income:

Disposable Personal Income = Personal Income – Personal Tax and Nontax Payments.

We are interested in disposable personal income because it is the amount house- holds and noncorporate businesses have available to spend after satisfying their tax obligations to the government.

Seasonal Adjustment

Because real GDP and the other measures of income refl ect how well the econ- omy is performing, economists are interested in studying the quarter-to-quarter fl uctuations in these variables. Yet when we start to do so, one fact leaps out: all these measures of income exhibit a regular seasonal pattern. The output of the economy rises during the year, reaching a peak in the fourth quarter (October, November, and December) and then falling in the fi rst quarter (January, February, and March) of the next year. These regular seasonal changes are substantial. From the fourth quarter to the fi rst quarter, real GDP falls on average about 8 percent.2

It is not surprising that real GDP follows a seasonal cycle. Some of these changes are attributable to changes in our ability to produce: for example, build- ing homes is more diffi cult during the cold weather of winter than during other seasons. In addition, people have seasonal tastes: they have preferred times for such activities as vacations and Christmas shopping.

When economists study fl uctuations in real GDP and other economic vari- ables, they often want to eliminate the portion of fl uctuations due to predictable

2Robert B. Barsky and Jeffrey A. Miron, “The Seasonal Cycle and the Business Cycle,’’ Journal of Political Economy 97 (June 1989): 503–534.

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32 | P A R T I Introduction

seasonal changes. You will fi nd that most of the economic statistics reported in the newspaper are seasonally adjusted. This means that the data have been adjusted to remove the regular seasonal fl uctuations. (The precise statistical procedures used are too elaborate to discuss here, but in essence they involve subtracting those changes in income that are predictable just from the change in season.) Therefore, when you observe a rise or fall in real GDP or any other data series, you must look beyond the seasonal cycle for the explanation.

2-2 Measuring the Cost of Living: The Consumer Price Index

A dollar today doesn’t buy as much as it did twenty years ago. The cost of almost everything has gone up. This increase in the overall level of prices, called infl ation, is one of the primary concerns of economists and policymakers. In later chapters we examine in detail the causes and effects of infl ation. Here we discuss how economists measure changes in the cost of living.

The Price of a Basket of Goods

The most commonly used measure of the level of prices is the consumer price index (CPI). The Bureau of Labor Statistics, which is part of the U.S. Depart- ment of Labor, has the job of computing the CPI. It begins by collecting the prices of thousands of goods and services. Just as GDP turns the quantities of many goods and services into a single number measuring the value of produc- tion, the CPI turns the prices of many goods and services into a single index measuring the overall level of prices.

How should economists aggregate the many prices in the economy into a sin- gle index that reliably measures the price level? They could simply compute an average of all prices. But this approach would treat all goods and services equally. Because people buy more chicken than caviar, the price of chicken should have a greater weight in the CPI than the price of caviar. The Bureau of Labor Statistics weights different items by computing the price of a basket of goods and services purchased by a typical consumer. The CPI is the price of this basket of goods and services relative to the price of the same basket in some base year.

For example, suppose that the typical consumer buys 5 apples and 2 oranges every month. Then the basket of goods consists of 5 apples and 2 oranges, and the CPI is

(5 × Current Price of Apples) + (2 × Current Price of Oranges) CPI = . (5 × 2011 Price of Apples) + (2 × 2011 Price of Oranges)

In this CPI, 2011 is the base year. The index tells us how much it costs now to buy 5 apples and 2 oranges relative to how much it cost to buy the same basket of fruit in 2011.

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The consumer price index is the most closely watched index of prices, but it is not the only such index. Another is the producer price index, which measures the price of a typical basket of goods bought by fi rms rather than consumers. In addition to these overall price indexes, the Bureau of Labor Statistics computes price indexes for specifi c types of goods, such as food, housing, and energy. Another statistic, sometimes called core infl ation, measures the increase in price of a consumer basket that excludes food and energy products. Because food and energy prices exhibit substantial short-run volatility, core infl ation is sometimes viewed as a better gauge of ongoing infl ation trends.

The CPI Versus the GDP Deflator

Earlier in this chapter we saw another measure of prices—the implicit price defl ator for GDP, which is the ratio of nominal GDP to real GDP. The GDP defl ator and the CPI give somewhat different information about what’s happen- ing to the overall level of prices in the economy. There are three key differences between the two measures.

The fi rst difference is that the GDP defl ator measures the prices of all goods and services produced, whereas the CPI measures the prices of only the goods and services bought by consumers. Thus, an increase in the price of goods bought only by fi rms or the government will show up in the GDP defl ator but not in the CPI.

The second difference is that the GDP defl ator includes only those goods pro- duced domestically. Imported goods are not part of GDP and do not show up in the GDP defl ator. Hence, an increase in the price of Toyotas made in Japan and sold in this country affects the CPI, because the Toyotas are bought by consum- ers, but it does not affect the GDP defl ator.

The third and most subtle difference results from the way the two measures aggregate the many prices in the economy. The CPI assigns fi xed weights to the prices of different goods, whereas the GDP defl ator assigns changing weights. In other words, the CPI is computed using a fi xed basket of goods, whereas the GDP defl ator allows the basket of goods to change over time as the composi- tion of GDP changes. The following example shows how these approaches dif- fer. Suppose that major frosts destroy the nation’s orange crop. The quantity of oranges produced falls to zero, and the price of the few oranges that remain on grocers’ shelves is driven sky-high. Because oranges are no longer part of GDP, the increase in the price of oranges does not show up in the GDP defl ator. But because the CPI is computed with a fi xed basket of goods that includes oranges, the increase in the price of oranges causes a substantial rise in the CPI.

Economists call a price index with a fi xed basket of goods a Laspeyres index and a price index with a changing basket a Paasche index. Economic theorists have studied the properties of these different types of price indexes to determine which is a better measure of the cost of living. The answer, it turns out, is that neither is clearly superior. When prices of different goods are changing by different amounts, a Laspeyres (fi xed basket) index tends to overstate the increase in the cost of living because it does not take into account the fact that consumers have the opportunity

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34 | P A R T I Introduction

to substitute less expensive goods for more expensive ones. By contrast, a Paasche (changing basket) index tends to understate the increase in the cost of living. Although it accounts for the substitution of alternative goods, it does not refl ect the reduction in consumers’ welfare that may result from such substitutions.

The example of the destroyed orange crop shows the problems with Laspeyres and Paasche price indexes. Because the CPI is a Laspeyres index, it overstates the impact of the increase in orange prices on consumers: by using a fi xed basket of goods, it ignores consumers’ ability to substitute apples for oranges. By contrast, because the GDP defl ator is a Paasche index, it understates the impact on con- sumers: the GDP defl ator shows no rise in prices, yet surely the higher price of oranges makes consumers worse off.3

Luckily, the difference between the GDP defl ator and the CPI is usually not large in practice. Figure 2-3 shows the percentage change in the GDP defl ator and the percentage change in the CPI for each year from 1948 to 2010. Both measures usually tell the same story about how quickly prices are rising.

3Because a Laspeyres index overstates infl ation and a Paasche index understates it, one might strike a compromise by taking an average of the two measured rates of infl ation. This is the approach taken by another type of index, called a Fisher index.

2-3FIGURE

16

GDP deflator

Year 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

CPI14

12

10

8

6

4

2

0

–2

Percentage change

The GDP Defl ator and the CPI This fi gure shows the percentage change in the GDP defl ator and in the CPI for every year from 1948 to 2010. Although these two measures of prices diverge at times, they usually tell the same story about how quickly prices are rising. Both the CPI and the GDP defl ator show that prices rose slowly in most of the 1950s and 1960s, that they rose much more quickly in the 1970s, and that they have risen slowly again since the mid-1980s.

Source: U.S. Department of Commerce, U.S. Department of Labor.

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C H A P T E R 2 The Data of Macroeconomics | 35

Does the CPI Overstate Inflation?

The consumer price index is a closely watched measure of infl ation. Policymak- ers in the Federal Reserve monitor the CPI when determining monetary policy. In addition, many laws and private contracts have cost-of-living allowances, called COLAs, which use the CPI to adjust for changes in the price level. For instance, Social Security benefi ts are adjusted automatically every year so that infl ation will not erode the living standard of the elderly.

Because so much depends on the CPI, it is important to ensure that this mea- sure of the price level is accurate. Many economists believe that, for a number of reasons, the CPI tends to overstate infl ation.

One problem is the substitution bias we have already discussed. Because the CPI measures the price of a fi xed basket of goods, it does not refl ect the ability of consumers to substitute toward goods whose relative prices have fallen. Thus, when relative prices change, the true cost of living rises less rapidly than does the CPI.

A second problem is the introduction of new goods. When a new good is introduced into the marketplace, consumers are better off because they have more products from which to choose. In effect, the introduction of new goods increases the real value of the dollar. Yet this increase in the purchasing power of the dollar is not refl ected in a lower CPI.

A third problem is unmeasured changes in quality. When a fi rm changes the quality of a good it sells, not all of the good’s price change refl ects a change in the cost of living. The Bureau of Labor Statistics does its best to account for changes in the quality of goods over time. For example, if Ford increases the horsepower of a particular car model from one year to the next, the CPI will refl ect the change: the quality-adjusted price of the car will not rise as fast as the unadjusted price. Yet many changes in quality, such as comfort or safety, are hard to measure. If unmeasured quality improvement (rather than unmea- sured quality deterioration) is typical, then the measured CPI rises faster than it should.

Because of these measurement problems, some economists have suggested revising laws to reduce the degree of indexation. For example, Social Security benefi ts could be indexed to CPI infl ation minus 1 percent. Such a change would provide a rough way of offsetting these measurement problems. At the same time, it would automatically slow the growth in government spending.

In 1995, the Senate Finance Committee appointed a panel of economists to study the magnitude of the measurement error in the CPI. The panel con- cluded that the CPI was biased upward by 0.8 to 1.6 percentage points per year, with their “best estimate” being 1.1 percentage points. This report led to some changes in the way the CPI is calculated, so the bias is now thought to be under 1 percentage point. The CPI still overstates infl ation, but not by as much as it once did.4

4For further discussion of these issues, see Matthew Shapiro and David Wilcox, “Mismeasurement in the Consumer Price Index: An Evaluation,” NBER Macroeconomics Annual, 1996, and the symposium on “Measuring the CPI” in the Winter 1998 issue of The Journal of Economic Perspectives.

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36 | P A R T I Introduction

2-3 Measuring Joblessness: The Unemployment Rate

One aspect of economic performance is how well an economy uses its resources. Because an economy’s workers are its chief resource, keeping workers employed is a paramount concern of economic policymakers. The unemployment rate is the statistic that measures the percentage of those people wanting to work who

The Billion Prices Project

The consumer price index is a single number that measures the overall cost of living, but it is based on thousands of prices for individual goods and ser- vices. To collect the raw data with which the index is constructed, hundreds of government workers go store to store every month. They check prices, write them down, and then send their reports into a central offi ce, where the CPI is computed. Recently, a couple of MIT economists—Alberto Cavallo and Roberto Rigobon—have suggested another way to accomplish this task using the resources of the Internet.

In their research, called the Billion Prices Project, Cavallo and Rigobon col- lect data on the prices charged by online retailers. From their offi ces in Cam- bridge, Massachusetts, they track about 5 million items sold in 70 countries by 300 online retailers. They then use these online prices to compute overall price indexes for these 70 economies.

There are pros and cons to this approach. One problem is that not all goods and services are sold online, so these new price indexes are not as comprehen- sive as the CPI. Yet there are also some signifi cant advantages. Because the data collection occurs automatically by computer, rather than relying on numerous government workers, it can be done quickly. For the U.S. economy, Cavallo and Rigobon publish a daily price index. As a result, their approach can pick up changes in infl ation more quickly than can the CPI, which is published only monthly and with a delay of several weeks. More timely data should, in principle, lead to better economic policy.

What have we learned from this new data source? So far, Cavallo and Rigobon have found that their daily price index for the United States tracks the CPI fairly well. That is, they seem to be picking up the same trends as the offi cial data but more quickly. For Argentina, by contrast, these new data have shown signifi cantly more infl ation than do the offi cial statistics. Some observers have suggested that the Argentine government manipulates the infl ation statistics in order to pay less to holders of infl ation-indexed bonds, an accusation that the president of the nation has denied. These new online price indexes cannot prove manipulation of the offi cial statistics, but they do provide some suggestive evidence.5 ■

CASE STUDY

5To learn more about the Billion Prices Project, go to http://bpp.mit.edu/.

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do not have jobs. Every month, the U.S. Bureau of Labor Statistics computes the unemployment rate and many other statistics that economists and policymakers use to monitor developments in the labor market.

The Household Survey

The unemployment rate comes from a survey of about 60,000 households called the Current Population Survey. Based on the responses to survey ques- tions, each adult (age 16 and older) in each household is placed into one of three categories:

■ Employed. This category includes those who at the time of the survey worked as paid employees, worked in their own business, or worked as unpaid workers in a family member’s business. It also includes those who were not working but who had jobs from which they were temporarily absent because of, for example, vacation, illness, or bad weather.

■ Unemployed. This category includes those who were not employed, were available for work, and had tried to fi nd employment during the previ- ous four weeks. It also includes those waiting to be recalled to a job from which they had been laid off.

■ Not in the labor force. This category includes those who fi t neither of the fi rst two categories, such as a full-time student, homemaker, or retiree.

Notice that a person who wants a job but has given up looking—a discouraged worker—is counted as not being in the labor force.

The labor force is defi ned as the sum of the employed and unemployed, and the unemployment rate is defi ned as the percentage of the labor force that is unemployed. That is,

Labor Force = Number of Employed + Number of Unemployed

and

Number of UnemployedUnemployment Rate = × 100. Labor Force

A related statistic is the labor-force participation rate, the percentage of the adult population that is in the labor force:

Labor ForceLabor-Force Participation Rate = × 100. Adult Population

The Bureau of Labor Statistics computes these statistics for the overall popula- tion and for groups within the population: men and women, whites and blacks, teenagers and prime-age workers.

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38 | P A R T I Introduction

Figure 2-4 shows the breakdown of the population into the three categories for August 2011. The statistics broke down as follows:

Labor Force = 139.6 + 14.0 = 153.6 million.

Unemployment Rate = (14.0/153.6) × 100 = 9.1%.

Labor-Force Participation Rate = (153.6/239.9) × 100 = 64.0%.

Hence, about two-thirds of the adult population was in the labor force and about 9.1 percent of those in the labor force did not have a job.

Trends in Labor-Force Participation

The data on the labor market collected by the Bureau of Labor Statistics refl ect not only economic developments, such as the booms and busts of the business cycle, but also a variety of social changes. Longer-term social changes in the roles of men and women in society, for example, are evident in the data on labor-force participation.

Figure 2-5 shows the labor-force participation rates of men and women in the United States from 1950 to 2010. Just after World War II, men and women had very different economic roles. Only 33 percent of women were work- ing or looking for work, in contrast to 87 percent of men. Since then, the difference between the participation rates of men and women has gradually

CASE STUDY

2-4FIGURE

Labor force 153.6 million

Unemployed: 14.0 million

Employed: 139.6 million

Not in labor force: 86.3 million

Population: 239.9 million (16 years and older)

The Three Groups of the Population When the Bureau of Labor Statistics surveys the population, it places all adults into one of three categories: employed, unemployed, or not in the labor force. This fi gure shows the number of people in each category in August 2011.

Source: U.S. Department of Labor.

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C H A P T E R 2 The Data of Macroeconomics | 39

diminished, as growing numbers of women have entered the labor force and some men have left it. Data for 2010 show that close to 59 percent of women were in the labor force, in contrast to 71 percent of men. As measured by labor-force participation, men and women are now playing a more equal role in the economy.

There are many reasons for this change. In part, it is due to new technologies, such as the washing machine, clothes dryer, refrigerator, freezer, and dishwasher, which have reduced the amount of time required to complete routine household tasks. In part, it is due to improved birth control, which has reduced the number of children born to the typical family. And in part, this change in women’s role is due to changing political and social attitudes. Together, these developments have had a profound impact, as demonstrated by these data.

Although the increase in women’s labor-force participation is easily explained, the fall in men’s participation may seem puzzling. There are several developments at work. First, young men now stay in school longer than their fathers and grand- fathers did. Second, older men now retire earlier and live longer. Third, with more women employed, more fathers now stay at home to raise their children. Full-time students, retirees, and stay-at-home fathers are all counted as out of the labor force.

Looking ahead, many economists believe that labor-force participation for both men and women may gradually decline over the next several decades.

2-5FIGURE

Labor force participation rates

Year

100

Men

Women

1960 197019551950 19801965 1975 1985 1990 1995 2000 2005 2010

90

80

70

60

50

40

30

20

10

0

Labor-Force Participation Over the past several decades, the labor-force participation rate for women has risen, while the rate for men has declined.

Source: U.S. Department of Labor.

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40 | P A R T I Introduction

The reason is demographic. People today are living longer and having fewer children than did their counterparts in previous generations. As a result, the elderly represent an increasing share of the population. Because they are more often retired and thus less often members of the labor force, their ris- ing share of the population will tend to reduce the economy’s labor-force participation rate. ■

The Establishment Survey

When the Bureau of Labor Statistics (BLS) reports the unemployment rate every month, it also reports a variety of other statistics describing conditions in the labor market. Some of these statistics, such as the labor-force participation rate, are derived from the Current Population Survey. Other statistics come from a separate survey of about 160,000 business establishments that employ over 40 million workers. When you read a headline that says the economy created a certain number of jobs last month, that statistic is the change in the number of workers that businesses report having on their payrolls.

Because the BLS conducts two surveys of labor-market conditions, it pro- duces two measures of total employment. From the household survey, it obtains an estimate of the number of people who say they are working. From the estab- lishment survey, it obtains an estimate of the number of workers fi rms have on their payrolls.

One might expect these two measures of employment to be identical, but that is not the case. Although they are positively correlated, the two measures can diverge, especially over short periods of time. A particularly large divergence occurred in the early 2000s, as the economy recovered from the recession of 2001. From November 2001 to August 2003, the establishment survey showed a decline in employment of 1.0 million, while the household survey showed an increase of 1.4 million. Some commentators said the economy was experiencing a “jobless recovery,” but this description applied only to the establishment data, not to the household data.

Why might these two measures of employment diverge? Part of the expla- nation is that the surveys measure different things. For example, a person who runs his or her own business is self-employed. The household survey counts that person as working, whereas the establishment survey does not because that per- son does not show up on any fi rm’s payroll. As another example, a person who holds two jobs is counted as one employed person in the household survey but is counted twice in the establishment survey because that person would show up on the payroll of two fi rms.

Another part of the explanation for the divergence is that surveys are imper- fect. For example, when new fi rms start up, it may take some time before those fi rms are included in the establishment survey. The BLS tries to estimate employment at start-ups, but the model it uses to produce these estimates is one possible source of error. A different problem arises from how the household survey extrapolates employment among the surveyed households to the entire population. If the BLS uses incorrect estimates of the size of the population, these

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C H A P T E R 2 The Data of Macroeconomics | 41

errors will be refl ected in its estimates of household employment. One possible source of incorrect population estimates is changes in the rate of immigration, both legal and illegal.

In the end, the divergence between the household and establishment surveys from 2001 to 2003 remains a mystery. Some economists believe that the establishment survey is the more accurate one because it has a larger sample. Yet one recent study suggests that the best measure of employment is an average of the two surveys.6

More important than the specifi cs of these surveys or this particular episode when they diverged is the broader lesson: all economic statistics are imperfect. Although they contain valuable information about what is happening in the economy, each one should be interpreted with a healthy dose of caution and a bit of skepticism.

2-4 Conclusion: From Economic Statistics to Economic Models

The three statistics discussed in this chapter—gross domestic product, the consumer price index, and the unemployment rate—quantify the perfor- mance of the economy. Public and private decisionmakers use these statistics to monitor changes in the economy and to formulate appropriate policies. Economists use these statistics to develop and test theories about how the economy works.

In the chapters that follow, we examine some of these theories. That is, we build models that explain how these variables are determined and how economic policy affects them. Having learned how to measure economic performance, we are now ready to learn how to explain it.

Summary

1. Gross domestic product (GDP) measures the income of everyone in the economy and, equivalently, the total expenditure on the economy’s output of goods and services.

2. Nominal GDP values goods and services at current prices. Real GDP values goods and services at constant prices. Real GDP rises only when the amount of goods and services has increased, whereas nominal GDP can rise either because output has increased or because prices have increased.

3. GDP is the sum of four categories of expenditure: consumption, invest- ment, government purchases, and net exports. This relationship is called the national income accounts identity.

6George Perry, “Gauging Employment: Is the Professional Wisdom Wrong?,” Brookings Papers on Economic Activity (2005): 2.

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42 | P A R T I Introduction

K E Y C O N C E P T S

Gross domestic product (GDP)

National income accounting

Stocks and fl ows

Value added

Imputed value

Nominal versus real GDP

GDP defl ator

National income accounts identity

Consumption

Investment

Government purchases

Net exports

Consumer price index (CPI)

Labor force

Unemployment rate

Labor-force participation rate

1. List the two things that GDP measures. How can GDP measure two things at once?

2. What does the consumer price index measure? How is it different from the GDP defl ator?

3. List the three categories used by the Bureau of Labor Statistics to classify everyone in the

Q U E S T I O N S F O R R E V I E W

economy. How does the Bureau compute the unemployment rate?

4. Describe the two ways the Bureau of Labor Sta- tistics measures total employment.

P R O B L E M S A N D A P P L I C A T I O N S

1. Look at the newspapers for the past few days. What new economic statistics have been released? How do you interpret these statistics?

2. A farmer grows a bushel of wheat and sells it to a miller for $1. The miller turns the wheat into fl our and then sells the fl our to a baker for $3. The baker uses the fl our to make bread and sells the bread to an engineer for $6. The engineer eats the bread. What is the value added by each person? What is the bread’s contribu- tion to GDP?

3. Suppose a woman marries her butler. After they are married, her husband continues to wait on her as before, and she continues to support him as before (but as a husband rather than as an employee). How does the marriage affect GDP? How do you think it should affect GDP?

4. Place each of the following transactions in one of the four components of expenditure: con- sumption, investment, government purchases, and net exports.

a. Boeing sells an airplane to the Air Force.

b. Boeing sells an airplane to American Airlines.

4. The consumer price index (CPI) measures the price of a fi xed basket of goods and services purchased by a typical consumer relative to the same basket in a base year. Like the GDP defl ator, which is the ratio of nominal GDP to real GDP, the CPI measures the overall level of prices.

5. The labor-force participation rate shows the fraction of adults who are working or want to work. The unemployment rate shows what fraction of those who would like to work do not have a job.

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C H A P T E R 2 The Data of Macroeconomics | 43

c. Boeing sells an airplane to Air France.

d. Boeing sells an airplane to Amelia Earhart.

e. Boeing builds an airplane to be sold next year.

5. Find data on GDP and its components, and compute the percentage of GDP for the follow- ing components for 1950, 1980, and the most recent year available.

a. Personal consumption expenditures

b. Gross private domestic investment

c. Government purchases

d. Net exports

e. National defense purchases

f. Imports

Do you see any stable relationships in the data? Do you see any trends? (Hint: You can fi nd the data at www.bea.gov, which is the Web site of the Bureau of Economic Analysis.)

6. Consider an economy that produces and con- sumes bread and automobiles. In the following table are data for two different years.

2000 2010

Good Quantity Price Quantity Price

Automobiles 100 $50,000 120 $60,000

Bread 500,000 $10 400,000 $20

a. Using 2000 as the base year, compute the following statistics for each year: nominal GDP, real GDP, the implicit price defl ator for GDP, and a fi xed-weight price index such as the CPI.

b. How much did prices rise between 2000 and 2010? Compare the answers given by the Laspeyres and Paasche price indexes. Explain the difference.

c. Suppose you are a senator writing a bill to index Social Security and federal pensions. That is, your bill will adjust these benefi ts to offset changes in the cost of living. Will you use the GDP defl ator or the CPI? Why?

7. Abby consumes only apples. In year 1, red apples cost $1 each, green apples cost $2 each, and Abby buys 10 red apples. In year 2, red apples

cost $2, green apples cost $1, and Abby buys 10 green apples.

a. Compute a consumer price index for apples for each year. Assume that year 1 is the base year in which the consumer basket is fi xed. How does your index change from year 1 to year 2?

b. Compute Abby’s nominal spending on apples in each year. How does it change from year 1 to year 2?

c. Using year 1 as the base year, compute Abby’s real spending on apples in each year. How does it change from year 1 to year 2?

d. Defi ning the implicit price defl ator as nominal spending divided by real spending, compute the defl ator for each year. How does the defl ator change from year 1 to year 2?

e. Suppose that Abby is equally happy eat- ing red or green apples. How much has the true cost of living increased for Abby? Compare this answer to your answers to parts (a) and (d). What does this example tell you about Laspeyres and Paasche price indexes?

8. Consider whether each of the following events is likely to increase or decrease real GDP. In each case, do you think economic well-being most likely changes in the same direction as real GDP? Why or why not?

a. A hurricane in Florida forces Disney World to shut down for a month.

b. The discovery of a new, easy-to-grow strain of wheat increases farm harvests.

c. Increased hostility between unions and management sparks a rash of strikes.

d. Firms throughout the economy experi- ence falling demand, causing them to lay off workers.

e. Congress passes new environmental laws that prohibit fi rms from using production methods that emit large quantities of pollution.

f. More high school students drop out of school to take jobs mowing lawns.

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44 | P A R T I Introduction

g. Fathers around the country reduce their workweeks to spend more time with their children.

9. In a speech that Senator Robert Kennedy gave when he was running for president in 1968, he said the following about GDP:

[It] does not allow for the health of our children, the quality of their education, or the joy of their play. It does not include the beauty of our poetry or the

strength of our marriages, the intelligence of our public debate or the integrity of our public offi cials. It measures neither our courage, nor our wisdom, nor our devotion to our country. It measures every- thing, in short, except that which makes life worth- while, and it can tell us everything about America except why we are proud that we are Americans.

Was Robert Kennedy right? If so, why do we care about GDP?

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P A R T I I

Classical Theory: The Economy

in the Long Run

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47

National Income: Where It Comes From and Where It Goes

3C H A P T E R

A large income is the best recipe for happiness I ever heard of.

—Jane Austen

The most important macroeconomic variable is gross domestic product (GDP). As we have seen, GDP measures both a nation’s total output of goods and services and its total income. To appreciate the signifi cance of GDP, one need only take a quick look at international data: compared with their poorer counterparts, nations with a high level of GDP per person have every- thing from better childhood nutrition to more computers per household. A large GDP does not ensure that all of a nation’s citizens are happy, but it may be the best recipe for happiness that macroeconomists have to offer.

This chapter addresses four groups of questions about the sources and uses of a nation’s GDP:

■ How much do the fi rms in the economy produce? What determines a nation’s total income?

■ Who gets the income from production? How much goes to compensate workers, and how much goes to compensate owners of capital?

■ Who buys the output of the economy? How much do households pur- chase for consumption, how much do households and fi rms purchase for investment, and how much does the government buy for public purposes?

■ What equilibrates the demand for and supply of goods and services? What ensures that desired spending on consumption, investment, and government purchases equals the level of production?

To answer these questions, we must examine how the various parts of the economy interact.

A good place to start is the circular fl ow diagram. In Chapter 2 we traced the circular fl ow of dollars in a hypothetical economy that used one input (labor ser- vices) to produce one output (bread). Figure 3-1 more accurately refl ects how real economies function. It shows the linkages among the economic actors—households,

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48 | P A R T I I Classical Theory: The Economy in the Long Run

fi rms, and the government—and how dollars fl ow among them through the various markets in the economy.

Let’s look at the fl ow of dollars from the viewpoints of these economic actors. Households receive income and use it to pay taxes to the government, to consume goods and services, and to save through the fi nancial markets. Firms receive revenue from the sale of the goods and services they produce and use it to pay for the factors of production. Households and fi rms borrow in fi nancial markets to buy investment goods, such as houses and factories. The government receives revenue from taxes and uses it to pay for govern- ment purchases. Any excess of tax revenue over government spending is called public saving, which can be either positive (a budget surplus) or negative (a budget defi cit).

In this chapter we develop a basic classical model to explain the economic interactions depicted in Figure 3-1. We begin with fi rms and look at what

3-1FIGURE

The Circular Flow of Dollars Through the Economy This figure is a more realistic version of the circular flow diagram found in Chapter 2. Each yellow box represents an economic actor—households, firms, and the government. Each blue box represents a type of market—the markets for goods and services, the markets for the factors of production, and financial markets. The green arrows show the flow of dollars among the economic actors through the three types of markets.

Income

Private saving

Taxes

Consumption Firm revenue

Investment

Public saving

Government purchases

Factor paymentsMarkets for Factors of Production

Markets for Goods and Services

Financial Markets

Government FirmsHouseholds

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 49

determines their level of production (and thus the level of national income). Then we examine how the markets for the factors of production distribute this income to households. Next, we consider how much of this income households consume and how much they save. In addition to discussing the demand for goods and services arising from the consumption of households, we discuss the demand arising from investment and government purchases. Finally, we come full circle and examine how the demand for goods and services (the sum of consumption, investment, and government purchases) and the supply of goods and services (the level of production) are brought into balance.

3- What Determines the Total Production of Goods and Services?

An economy’s output of goods and services—its GDP—depends on (1) its quan- tity of inputs, called the factors of production, and (2) its ability to turn inputs into output, as represented by the production function. We discuss each of these in turn.

The Factors of Production

Factors of production are the inputs used to produce goods and services. The two most important factors of production are capital and labor. Capital is the set of tools that workers use: the construction worker’s crane, the accountant’s calculator, and this author’s personal computer. Labor is the time people spend working. We use the symbol K to denote the amount of capital and the symbol L to denote the amount of labor.

In this chapter we take the economy’s factors of production as given. In other words, we assume that the economy has a fi xed amount of capital and a fi xed amount of labor. We write

_ K = K. _ L = L.

The overbar means that each variable is fi xed at some level. In Chapter 8 we examine what happens when the factors of production change over time, as they do in the real world. For now, to keep our analysis simple, we assume fi xed amounts of capital and labor.

We also assume here that the factors of production are fully utilized. That is, no resources are wasted. Again, in the real world, part of the labor force is unemployed, and some capital lies idle. In Chapter 7 we examine the reasons for unemployment, but for now we assume that capital and labor are fully employed.

3-1

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50 | P A R T I I Classical Theory: The Economy in the Long Run

The Production Function

The available production technology determines how much output is produced from given amounts of capital and labor. Economists express this relationship using a production function. Letting Y denote the amount of output, we write the production function as

Y = F(K, L).

This equation states that output is a function of the amount of capital and the amount of labor.

The production function refl ects the available technology for turning capital and labor into output. If someone invents a better way to produce a good, the result is more output from the same amounts of capital and labor. Thus, techno- logical change alters the production function.

Many production functions have a property called constant returns to scale. A production function has constant returns to scale if an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. If the production function has constant returns to scale, then we get 10 percent more output when we increase both capital and labor by 10 percent. Mathematically, a production function has constant returns to scale if

zY = F(zK, zL)

for any positive number z. This equation says that if we multiply both the amount of capital and the amount of labor by some number z, output is also multiplied by z. In the next section we see that the assumption of constant returns to scale has an important implication for how the income from produc- tion is distributed.

As an example of a production function, consider production at a bakery. The kitchen and its equipment are the bakery’s capital, the workers hired to make the bread are its labor, and the loaves of bread are its output. The bakery’s production function shows that the number of loaves produced depends on the amount of equipment and the number of workers. If the production function has constant returns to scale, then doubling the amount of equipment and the number of workers doubles the amount of bread produced.

The Supply of Goods and Services

We can now see that the factors of production and the production function together determine the quantity of goods and services supplied, which in turn equals the economy’s output. To express this mathematically, we write

_ _ Y = F(K, L)

_ = Y.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 51

In this chapter, because we assume that the supplies of capital and labor and the technology are fi xed, output is also fi xed (at a level denoted here as Y– ). When we discuss economic growth in Chapters 8 and 9, we will examine how increases in capital and labor and advances in technology lead to growth in the economy’s output.

3-1 How Is National Income Distributed to the Factors of Production?

As we discussed in Chapter 2, the total output of an economy equals its total income. Because the factors of production and the production function together determine the total output of goods and services, they also determine national income. The circular fl ow diagram in Figure 3-1 shows that this national income fl ows from fi rms to households through the markets for the factors of production.

In this section we continue to develop our model of the economy by discuss- ing how these factor markets work. Economists have long studied factor markets to understand the distribution of income. For example, Karl Marx, the noted nineteenth-century economist, spent much time trying to explain the incomes of capital and labor. The political philosophy of communism was in part based on Marx’s now-discredited theory.

Here we examine the modern theory of how national income is divided among the factors of production. It is based on the classical (eighteenth- century) idea that prices adjust to balance supply and demand, applied here to the markets for the factors of production, together with the more recent (nineteenth-century) idea that the demand for each factor of production depends on the marginal productivity of that factor. This theory, called the neoclassical theory of distribution, is accepted by most economists today as the best place to start in understanding how the economy’s income is distributed from fi rms to households.

Factor Prices

The distribution of national income is determined by factor prices. Factor prices are the amounts paid to the factors of production. In an economy where the two factors of production are capital and labor, the two factor prices are the wage workers earn and the rent the owners of capital collect.

As Figure 3-2 illustrates, the price each factor of production receives for its services is in turn determined by the supply and demand for that factor. Because we have assumed that the economy’s factors of production are fi xed, the factor supply curve in Figure 3-2 is vertical. Regardless of the factor price, the quantity of the factor supplied to the market is the same. The intersection of the downward- sloping factor demand curve and the vertical supply curve determines the equi- librium factor price.

3-2

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52 | P A R T I I Classical Theory: The Economy in the Long Run

To understand factor prices and the distribution of income, we must examine the demand for the factors of production. Because factor demand arises from the thousands of fi rms that use capital and labor, we start by examining the decisions a typical fi rm makes about how much of these factors to employ.

The Decisions Facing a Competitive Firm

The simplest assumption to make about a typical fi rm is that it is competitive. A competitive fi rm is small relative to the markets in which it trades, so it has little infl uence on market prices. For example, our fi rm produces a good and sells it at the market price. Because many fi rms produce this good, our fi rm can sell as much as it wants without causing the price of the good to fall or it can stop selling altogether without causing the price of the good to rise. Similarly, our fi rm cannot infl uence the wages of the workers it employs because many other local fi rms also employ workers. The fi rm has no reason to pay more than the market wage, and if it tried to pay less, its workers would take jobs elsewhere. Therefore, the competitive fi rm takes the prices of its output and its inputs as given by market conditions.

To make its product, the fi rm needs two factors of production, capital and labor. As we did for the aggregate economy, we represent the fi rm’s production technology with the production function

Y = F(K, L),

where Y is the number of units produced (the fi rm’s output), K the number of machines used (the amount of capital), and L the number of hours worked by the fi rm’s employees (the amount of labor). Holding constant the technology as expressed in the production function, the fi rm produces more output only if it uses more machines or if its employees work more hours.

3-2FIGURE

How a Factor of Production Is Compensated The price paid to any factor of produc- tion depends on the supply and demand for that factor’s services. Because we have assumed that supply is fi xed, the supply curve is vertical. The demand curve is downward sloping. The intersection of supply and demand determines the equilibrium factor price.Equilibrium

factor price

Factor supply

Factor demand

Quantity of factor

Factor price

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 53

The fi rm sells its output at a price P, hires workers at a wage W, and rents capital at a rate R. Notice that when we speak of fi rms renting capital, we are assuming that households own the economy’s stock of capital. In this analysis, households rent out their capital, just as they sell their labor. The fi rm obtains both factors of production from the households that own them.1

The goal of the fi rm is to maximize profi t. Profi t equals revenue minus costs; it is what the owners of the fi rm keep after paying for the costs of pro- duction. Revenue equals P × Y, the selling price of the good P multiplied by the amount of the good the fi rm produces Y. Costs include labor and capital costs. Labor costs equal W × L, the wage W times the amount of labor L. Capital costs equal R × K, the rental price of capital R times the amount of capital K. We can write

Profi t = Revenue − Labor Costs − Capital Costs

= PY − WL − RK.

To see how profi t depends on the factors of production, we use the production function Y = F(K, L) to substitute for Y to obtain

Profi t = PF(K, L) − WL − RK.

This equation shows that profi t depends on the product price P, the factor prices W and R, and the factor quantities L and K. The competitive fi rm takes the product price and the factor prices as given and chooses the amounts of labor and capital that maximize profi t.

The Firm’s Demand for Factors

We now know that our fi rm will hire labor and rent capital in the quanti- ties that maximize profi t. But what are those profi t-maximizing quantities? To answer this question, we fi rst consider the quantity of labor and then the quantity of capital.

The Marginal Product of Labor The more labor the fi rm employs, the more output it produces. The marginal product of labor (MPL) is the extra amount of output the fi rm gets from one extra unit of labor, holding the amount of capital fi xed. We can express this using the production function:

MPL = F(K, L + 1) − F(K, L).

The fi rst term on the right-hand side is the amount of output produced with K units of capital and L + 1 units of labor; the second term is the amount of output produced with K units of capital and L units of labor. This equation states that

1This is a simplifi cation. In the real world, the ownership of capital is indirect because fi rms own capital and households own the fi rms. That is, real fi rms have two functions: owning capital and producing output. To help us understand how the factors of production are compensated, however, we assume that fi rms only produce output and that households own capital directly.

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54 | P A R T I I Classical Theory: The Economy in the Long Run

the marginal product of labor is the difference between the amount of output produced with L + 1 units of labor and the amount produced with only L units of labor.

Most production functions have the property of diminishing marginal product: holding the amount of capital fi xed, the marginal product of labor decreases as the amount of labor increases. To see why, consider again the pro- duction of bread at a bakery. As a bakery hires more labor, it produces more bread. The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fi xed amount of capital, however, the MPL falls. Fewer additional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fi xed, each additional worker adds fewer loaves of bread to the bakery’s output.

Figure 3-3 graphs the production function. It illustrates what happens to the amount of output when we hold the amount of capital constant and vary the amount of labor. This fi gure shows that the marginal product of labor is the slope of the production function. As the amount of labor increases, the production function becomes fl atter, indicating diminishing marginal product.

From the Marginal Product of Labor to Labor Demand When the competitive, profi t-maximizing fi rm is deciding whether to hire an additional unit of labor, it considers how that decision would affect profi ts. It therefore

3-3FIGURE

The Production Function This curve shows how output depends on labor input, holding the amount of capital con- stant. The marginal product of labor MPL is the change in output when the labor input is increased by 1 unit. As the amount of labor increases, the production function becomes fl atter, indicating diminishing marginal product.

Output, Y

Labor, L

MPL

1

1. The slope of the production function equals the marginal product of labor.

MPL

1

F(K, L) MPL 1

2. As more labor is added, the marginal product of labor declines.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 55

compares the extra revenue from increased production with the extra cost from hiring the additional labor. The increase in revenue from an additional unit of labor depends on two variables: the marginal product of labor and the price of the output. Because an extra unit of labor produces MPL units of output and each unit of output sells for P dollars, the extra revenue is P × MPL. The extra cost of hiring one more unit of labor is the wage W. Thus, the change in profi t from hiring an additional unit of labor is

�Profi t = �Revenue − �Cost

= (P × MPL) − W.

The symbol � (called delta) denotes the change in a variable. We can now answer the question we asked at the beginning of this section:

how much labor does the fi rm hire? The fi rm’s manager knows that if the extra revenue P × MPL exceeds the wage W, an extra unit of labor increases profi t. Therefore, the manager continues to hire labor until the next unit would no lon- ger be profi table—that is, until the MPL falls to the point where the extra rev- enue equals the wage. The competitive fi rm’s demand for labor is determined by

P × MPL = W.

We can also write this as

MPL = W/P.

W/P is the real wage—the payment to labor measured in units of output rather than in dollars. To maximize profi t, the fi rm hires up to the point at which the marginal product of labor equals the real wage.

For example, again consider a bakery. Suppose the price of bread P is $2 per loaf, and a worker earns a wage W of $20 per hour. The real wage W/P is 10 loaves per hour. In this example, the fi rm keeps hiring workers as long as the additional worker would produce at least 10 loaves per hour. When the MPL falls to 10 loaves per hour or less, hiring additional workers is no longer profi table.

Figure 3-4 shows how the marginal product of labor depends on the amount of labor employed (holding the fi rm’s capital stock constant). That is, this fi gure graphs the MPL schedule. Because the MPL diminishes as the amount of labor increases, this curve slopes downward. For any given real wage, the fi rm hires up to the point at which the MPL equals the real wage. Hence, the MPL schedule is also the fi rm’s labor demand curve.

The Marginal Product of Capital and Capital Demand The fi rm decides how much capital to rent in the same way it decides how much labor to hire. The marginal product of capital (MPK) is the amount of extra output the fi rm gets from an extra unit of capital, holding the amount of labor constant:

MPK = F(K + 1, L) − F(K, L).

Thus, the marginal product of capital is the difference between the amount of output produced with K + 1 units of capital and that produced with only K units of capital.

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56 | P A R T I I Classical Theory: The Economy in the Long Run

Like labor, capital is subject to diminishing marginal product. Once again con- sider the production of bread at a bakery. The fi rst several ovens installed in the kitchen will be very productive. However, if the bakery installs more and more ovens, while holding its labor force constant, it will eventually contain more ovens than its employees can effectively operate. Hence, the marginal product of the last few ovens is lower than that of the fi rst few.

The increase in profi t from renting an additional machine is the extra revenue from selling the output of that machine minus the machine’s rental price:

�Profi t = �Revenue − �Cost

= (P × MPK ) − R.

To maximize profi t, the fi rm continues to rent more capital until the MPK falls to equal the real rental price:

MPK = R/P.

The real rental price of capital is the rental price measured in units of goods rather than in dollars.

To sum up, the competitive, profi t-maximizing fi rm follows a simple rule about how much labor to hire and how much capital to rent. The fi rm demands each factor of production until that factor’s marginal product falls to equal its real factor price.

The Division of National Income

Having analyzed how a fi rm decides how much of each factor to employ, we can now explain how the markets for the factors of production distribute the economy’s total income. If all fi rms in the economy are competitive and profi t

3-4FIGURE

The Marginal Product of Labor Schedule The mar- ginal product of labor MPL depends on the amount of labor. The MPL curve slopes downward because the MPL declines as L increases. The fi rm hires labor up to the point where the real wage W/P equals the MPL. Hence, this schedule is also the fi rm’s labor demand curve.

Units of labor, L

MPL, Labor demand

Units of output

Quantity of labor demanded

Real wage

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 57

maximizing, then each factor of production is paid its marginal contribution to the production process. The real wage paid to each worker equals the MPL, and the real rental price paid to each owner of capital equals the MPK. The total real wages paid to labor are therefore MPL × L, and the total real return paid to capital owners is MPK × K.

The income that remains after the fi rms have paid the factors of production is the economic profi t of the owners of the fi rms. Real economic profi t is

Economic Profi t = Y − (MPL × L) − (MPK × K ).

Because we want to examine the distribution of national income, we rearrange the terms as follows:

Y = (MPL × L) + (MPK × K ) + Economic Profi t.

Total income is divided among the return to labor, the return to capital, and economic profi t.

How large is economic profi t? The answer is surprising: if the production function has the property of constant returns to scale, as is often thought to be the case, then economic profi t must be zero. That is, nothing is left after the factors of production are paid. This conclusion follows from a famous math- ematical result called Euler’s theorem,2 which states that if the production function has constant returns to scale, then

F(K, L) = (MPK × K ) + (MPL × L).

If each factor of production is paid its marginal product, then the sum of these factor payments equals total output. In other words, constant returns to scale, profi t maximization, and competition together imply that economic profi t is zero.

If economic profi t is zero, how can we explain the existence of “profi t” in the economy? The answer is that the term “profi t” as normally used is differ- ent from economic profi t. We have been assuming that there are three types of agents: workers, owners of capital, and owners of fi rms. Total income is divided among wages, return to capital, and economic profi t. In the real world, however, most fi rms own rather than rent the capital they use. Because fi rm owners and capital owners are the same people, economic profi t and the return to capital are often lumped together. If we call this alternative defi nition accounting profi t, we can say that

Accounting Profi t = Economic Profi t + (MPK × K ).

2Mathematical note: To prove Euler’s theorem, we need to use some multivariate calculus. Begin with the defi nition of constant returns to scale: zY � F(zK, zL). Now differentiate with respect to z to obtain:

Y � F1(zK, zL)K � F2(zK, zL)L,

where F1 and F2 denote partial derivatives with respect to the fi rst and second arguments of the function. Evaluating this expression at z � 1, and noting that the partial derivatives equal the marginal products, yields Euler’s theorem.

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58 | P A R T I I Classical Theory: The Economy in the Long Run

Under our assumptions—constant returns to scale, profi t maximization, and competition—economic profi t is zero. If these assumptions approximately describe the world, then the “profi t” in the national income accounts must be mostly the return to capital.

We can now answer the question posed at the beginning of this chapter about how the income of the economy is distributed from fi rms to households. Each factor of production is paid its marginal product, and these factor payments exhaust total output. Total output is divided between the payments to capital and the payments to labor, depending on their marginal productivities.

The Black Death and Factor Prices

According to the neoclassical theory of distribution, factor prices equal the marginal products of the factors of production. Because the marginal products depend on the quantities of the factors, a change in the quantity of any one factor alters the marginal products of all the factors. Therefore, a change in the supply of a factor alters equilibrium factor prices and the distribution of income.

Fourteenth-century Europe provides a grisly natural experiment to study how factor quantities affect factor prices. The outbreak of the bubonic plague—the Black Death—in 1348 reduced the population of Europe by about one-third within a few years. Because the marginal product of labor increases as the amount of labor falls, this massive reduction in the labor force should have raised the marginal product of labor and equilibrium real wages. (That is, the economy should have moved to the left along the curves in Figures 3-3 and 3-4.) The evi- dence confi rms the theory: real wages approximately doubled during the plague years. The peasants who were fortunate enough to survive the plague enjoyed economic prosperity.

The reduction in the labor force caused by the plague should also have affected the return to land, the other major factor of production in medieval Europe. With fewer workers available to farm the land, an additional unit of land would have produced less additional output, and so land rents should have fallen. Once again, the theory is confi rmed: real rents fell 50 percent or more during this period. While the peasant classes prospered, the landed classes suffered reduced incomes.3 ■

The Cobb—Douglas Production Function

What production function describes how actual economies turn capital and labor into GDP? One answer to this question came from a historic collaboration between a U.S. senator and a mathematician.

CASE STUDY

3Carlo M. Cipolla, Before the Industrial Revolution: European Society and Economy, 1000�1700, 2nd ed. (New York: Norton, 1980), 200�202.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 59

Paul Douglas was a U.S. senator from Illinois from 1949 to 1966. In 1927, however, when he was still a professor of economics, he noticed a surprising fact: the division of national income between capital and labor had been roughly con- stant over a long period. In other words, as the economy grew more prosperous over time, the total income of workers and the total income of capital owners grew at almost exactly the same rate. This observation caused Douglas to wonder what conditions might lead to constant factor shares.

Douglas asked Charles Cobb, a mathematician, what production function, if any, would produce constant factor shares if factors always earned their marginal products. The production function would need to have the property that

Capital Income = MPK × K = �Y

and

Labor Income = MPL × L = (1 − �)Y,

where � is a constant between zero and one that measures capital’s share of income. That is, � determines what share of income goes to capital and what share goes to labor. Cobb showed that the function with this property is

F(K, L) = A K�L1−�,

where A is a parameter greater than zero that measures the productivity of the available technology. This function became known as the Cobb−Douglas production function.

Let’s take a closer look at some of the properties of this production function. First, the Cobb−Douglas production function has constant returns to scale. That is, if capital and labor are increased by the same proportion, then output increases by that proportion as well.4

4Mathematical note: To prove that the Cobb–Douglas production function has constant returns to scale, examine what happens when we multiply capital and labor by a constant z:

F(zK, zL) � A(zK)�(zL)1��.

Expanding terms on the right,

F(zK, zL) � Az� K�z1��L1��.

Rearranging to bring like terms together, we get

F(zK, zL) � Az� z1�� K�L1��.

Since z� z1�� � z, our function becomes

F(zK, zL) � z A K�L1��

But A K�L1�� � F(K, L). Thus,

F(zK, zL) � zF(K, L) � zY.

Hence, the amount of output Y increases by the same factor z, which implies that this production function has constant returns to scale.

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60 | P A R T I I Classical Theory: The Economy in the Long Run

Next, consider the marginal products for the Cobb−Douglas production func- tion. The marginal product of labor is5

MPL = (1 − �) A K�L−�,

and the marginal product of capital is

MPK = � A K �−1L1−�.

From these equations, recalling that � is between zero and one, we can see what causes the marginal products of the two factors to change. An increase in the amount of capital raises the MPL and reduces the MPK. Similarly, an increase in the amount of labor reduces the MPL and raises the MPK. A technologi- cal advance that increases the parameter A raises the marginal product of both factors proportionately.

The marginal products for the Cobb−Douglas production function can also be written as6

MPL = (1 − �)Y/L.

MPK = �Y/K.

The MPL is proportional to output per worker, and the MPK is propor- tional to output per unit of capital. Y/L is called average labor productivity, and Y/K is called average capital productivity. If the production function is Cobb−Douglas, then the marginal productivity of a factor is proportional to its average productivity.

We can now verify that if factors earn their marginal products, then the parameter � indeed tells us how much income goes to labor and how much goes to capital. The total amount paid to labor, which we have seen is MPL × L, equals (1 − �)Y. Therefore, (1 − �) is labor’s share of output. Similarly, the total amount paid to capital, MPK × K, equals �Y, and � is capital’s share of output. The ratio of labor income to capital income is a con- stant, (1 − �)/�, just as Douglas observed. The factor shares depend only on the

5Mathematical note: Obtaining the formulas for the marginal products from the production function requires a bit of calculus. To fi nd the MPL, differentiate the production function with respect to L. This is done by multiplying by the exponent (1 � �) and then subtracting 1 from the old exponent to obtain the new exponent, ��. Similarly, to obtain the MPK, differentiate the production function with respect to K. 6Mathematical note: To check these expressions for the marginal products, substitute in the production function for Y to show that these expressions are equivalent to the earlier formulas for the marginal products.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 61

parameter �, not on the amounts of capital or labor or on the state of technology as measured by the parameter A.

More recent U.S. data are also consistent with the Cobb−Douglas produc- tion function. Figure 3-5 shows the ratio of labor income to total income in the United States from 1960 to 2010. Despite the many changes in the economy over the past fi ve decades, this ratio has remained about 0.7. This division of income is easily explained by a Cobb−Douglas production function in which the parameter � is about 0.3. According to this parameter, capital receives 30 percent of income, and labor receives 70 percent.

The Cobb−Douglas production function is not the last word in explaining the economy’s production of goods and services or the distribution of national income between capital and labor. It is, however, a good place to start.

3-5FIGURE

The Ratio of Labor Income to Total Income Labor income has remained about 0.7 of total income over a long period of time. This approximate constancy of factor shares is consistent with the Cobb�Douglas production function.

Source: U.S. Department of Commerce. This fi gure is produced from U.S. national income accounts data. Labor income is compensation of employees. Total income is the sum of labor income, corporate profi ts, net interest, rental income, and depreciation. Proprietors’ income is excluded from these calculations, because it is a combination of labor income and capital income.

1.0

0.8

0.6

0.4

0.2

0

Labor’s share of total income

1960 1965 Year

1970 1975 1980 1985 1990 1995 2000 2005 2010

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62 | P A R T I I Classical Theory: The Economy in the Long Run

Labor Productivity as the Key Determinant of Real Wages

The neoclassical theory of distribution tells us that the real wage W/P equals the marginal product of labor. The Cobb−Douglas production function tells us that the marginal product of labor is proportional to average labor productivity Y/L. If this theory is right, then workers should enjoy rapidly rising living standards when labor productivity is growing robustly. Is this true?

CASE STUDY

The approximate constancy of the labor and capi- tal shares in U.S. data has a simple meaning: the distribution of income between workers and own- ers of capital has not radically changed over the course of history. There is, however, another way to look at the data on the income distribution that shows more substantial changes. If we look within labor income, we fi nd that the gap between the earnings of high-wage workers and the earnings of low-wage workers has grown substantially since the 1970s. As a result, income inequality today is much greater than it was four decades ago.

What has caused this growing income disparity between rich and poor? Economists do not have a defi nitive answer, but one diagnosis comes from economists Claudia Goldin and Lawrence Katz in their book The Race Between Education and Technology.7 Their bottom line is that “the sharp rise in inequal- ity was largely due to an educational slowdown.”

According to Goldin and Katz, for the past century technological progress has been a steady force, not only increasing average living stan- dards but also increasing the demand for skilled workers relative to unskilled workers. Skilled workers are needed to apply and manage new technologies, while less skilled workers are more likely to become obsolete.

For much of the twentieth century, however, skill-biased technological change was outpaced by advances in educational attainment. In other words, while technological progress increased

The Growing Gap Between Rich and Poor the demand for skilled workers, our educational system increased the supply of them even faster. As a result, skilled workers did not benefi t dispro- portionately from economic growth.

But recently things have changed. Over the last several decades, technological advance has kept up its pace, but educational advancement has slowed down. The cohort of workers born in 1950 aver- aged 4.67 more years of schooling than the cohort born in 1900, representing an increase of 0.93 years of schooling in each decade. By contrast, the cohort born in 1975 had only 0.74 more years of schooling than that born in 1950, an increase of only 0.30 years per decade. That is, the pace of educational advance has fallen by 68 percent.

Because growth in the supply of skilled workers has slowed, their wages have grown relative to those of the unskilled. This is evident in Goldin and Katz’s estimates of the fi nancial return to education. In 1980, each year of college raised a person’s wage by 7.6 percent. In 2005, each year of college yielded an additional 12.9 percent. Over this time period, the rate of return from each year of graduate school rose even more—from 7.3 to 14.2 percent.

The implication of this analysis for public policy is that reversing the rise in income inequal- ity will likely require putting more of society’s resources into education (which economists call human capital). The implication for personal deci- sionmaking is that college and graduate school are investments well worth making.

F Y I

7Claudia Goldin and Lawrence F. Katz, The Race Between Education and Technology (Cambridge, Mass.: Belknap Press, 2011).

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 63

Table 3-1 presents some data on growth in productivity and real wages for the U.S. economy. From 1960 to 2010, productivity as measured by output per hour of work grew about 2.2 percent per year. Real wages grew at 1.9 percent—almost the same rate. With a growth rate of 2 percent per year, productivity and real wages double about every 35 years.

Productivity growth varies over time. The table shows the data for three shorter periods that economists have identifi ed as having different productivity experiences. (A case study in Chapter 9 examines the reasons for these changes in productivity growth.) Around 1973, the U.S. economy experienced a signifi - cant slowdown in productivity growth that lasted until 1995. The cause of the productivity slowdown is not well understood, but the link between productivity and real wages was exactly as standard theory predicts. The slowdown in produc- tivity growth from 2.9 to 1.4 percent per year coincided with a slowdown in real wage growth from 2.8 to 1.2 percent per year.

Productivity growth picked up again around 1995, and many observers hailed the arrival of the “new economy.” This productivity acceleration is often attrib- uted to the spread of computers and information technology. As theory predicts, growth in real wages picked up as well. From 1995 to 2010, productivity grew by 2.7 percent per year and real wages by 2.2 percent per year.

Theory and history both confi rm the close link between labor productivity and real wages. This lesson is the key to understanding why workers today are better off than workers in previous generations. ■

3-1 What Determines the Demand for Goods and Services?

We have seen what determines the level of production and how the income from production is distributed to workers and owners of capital. We now continue our tour of the circular fl ow diagram, Figure 3-1, and examine how the output from production is used.

3-3

Growth Rate of Labor Growth Rate of Real Time Period Productivity (Percent) Wages (Percent)

1960�2010 2.2 1.9

1960�1973 2.9 2.8 1973�1995 1.4 1.2 1995�2010 2.7 2.2

Source: Economic Report of the President 2011, Table B-49, and updates from the U.S. Department of Commerce Web site. Growth in labor productivity is measured here as the annualized rate of change in output per hour in the nonfarm business sector. Growth in real wages is measured as the annualized change in compensation per hour in the nonfarm business sector divided by the implicit price defl ator for that sector.

Growth in Labor Productivity and Real Wages: The U.S. Experience

TABLE 3-1

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64 | P A R T I I Classical Theory: The Economy in the Long Run

In Chapter 2 we identifi ed the four components of GDP:

■ Consumption (C )

■ Investment (I )

■ Government purchases (G )

■ Net exports (NX ).

The circular fl ow diagram contains only the fi rst three components. For now, to simplify the analysis, we assume our economy is a closed economy—a country that does not trade with other countries. Thus, net exports are always zero. (We examine the macroeconomics of open economies in Chapter 6.)

A closed economy has three uses for the goods and services it produces. These three components of GDP are expressed in the national income accounts identity:

Y = C + I + G.

Households consume some of the economy’s output, fi rms and households use some of the output for investment, and the government buys some of the output for public purposes. We want to see how GDP is allocated among these three uses.

Consumption

When we eat food, wear clothing, or go to a movie, we are consuming some of the output of the economy. All forms of consumption together make up about two-thirds of GDP. Because consumption is so large, macroeconomists have devoted much energy to studying how households make their consumption decisions. Chapter 16 examines this topic in detail. Here we consider the simplest story of consumer behavior.

Households receive income from their labor and their ownership of capi- tal, pay taxes to the government, and then decide how much of their after-tax income to consume and how much to save. As we discussed in Section 3-2, the income that households receive equals the output of the economy Y. The government then taxes households an amount T. (Although the govern- ment imposes many kinds of taxes, such as personal and corporate income taxes and sales taxes, for our purposes we can lump all these taxes together.) We defi ne income after the payment of all taxes, Y − T, to be disposable income. Households divide their disposable income between consumption and saving.

We assume that the level of consumption depends directly on the level of disposable income. A higher level of disposable income leads to greater con- sumption. Thus,

C = C(Y − T ).

This equation states that consumption is a function of disposable income. The rela- tionship between consumption and disposable income is called the consumption function.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 65

The marginal propensity to consume (MPC) is the amount by which consumption changes when disposable income increases by one dollar. The MPC is between zero and one: an extra dollar of income increases consumption, but by less than one dollar. Thus, if households obtain an extra dollar of income, they save a portion of it. For example, if the MPC is 0.7, then households spend 70 cents of each additional dollar of disposable income on consumer goods and services and save 30 cents.

Figure 3-6 illustrates the consumption function. The slope of the consumption function tells us how much consumption increases when disposable income increases by one dollar. That is, the slope of the consumption function is the MPC.

Investment

Both fi rms and households purchase investment goods. Firms buy investment goods to add to their stock of capital and to replace existing capital as it wears out. Households buy new houses, which are also part of investment. Total invest- ment in the United States averages about 15 percent of GDP.

The quantity of investment goods demanded depends on the interest rate, which measures the cost of the funds used to fi nance investment. For an invest- ment project to be profi table, its return (the revenue from increased future pro- duction of goods and services) must exceed its cost (the payments for borrowed funds). If the interest rate rises, fewer investment projects are profi table, and the quantity of investment goods demanded falls.

For example, suppose a fi rm is considering whether it should build a $1 mil- lion factory that would yield a return of $100,000 per year, or 10 percent. The fi rm compares this return to the cost of borrowing the $1 million. If the interest rate is below 10 percent, the fi rm borrows the money in fi nancial markets and

3-6FIGURE

The Consumption Function The consumption function relates consump- tion C to disposable income Y � T. The marginal pro- pensity to consume MPC is the amount by which con- sumption increases when disposable income increases by one dollar.

Consumption, C

MPC 1

Consumption function

Disposable income, Y � T

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66 | P A R T I I Classical Theory: The Economy in the Long Run

makes the investment. If the interest rate is above 10 percent, the fi rm forgoes the investment opportunity and does not build the factory.

The fi rm makes the same investment decision even if it does not have to bor- row the $1 million but rather uses its own funds. The fi rm can always deposit this money in a bank or a money market fund and earn interest on it. Building the factory is more profi table than depositing the money if and only if the interest rate is less than the 10 percent return on the factory.

A person wanting to buy a new house faces a similar decision. The higher the interest rate, the greater the cost of carrying a mortgage. A $100,000 mortgage costs $6,000 per year if the interest rate is 6 percent and $8,000 per year if the interest rate is 8 percent. As the interest rate rises, the cost of owning a home rises, and the demand for new homes falls.

When studying the role of interest rates in the economy, economists distin- guish between the nominal interest rate and the real interest rate. This distinction is relevant when the overall level of prices is changing. The nominal interest rate is the interest rate as usually reported: it is the rate of interest that investors pay to borrow money. The real interest rate is the nominal interest rate cor- rected for the effects of infl ation. If the nominal interest rate is 8 percent and the infl ation rate is 3 percent, then the real interest rate is 5 percent. In Chapter 5 we discuss the relation between nominal and real interest rates in detail. Here it is suffi cient to note that the real interest rate measures the true cost of borrowing and, thus, determines the quantity of investment.

We can summarize this discussion with an equation relating investment I to the real interest rate r:

I = I(r).

Figure 3-7 shows this investment function. It slopes downward, because as the interest rate rises, the quantity of investment demanded falls.

3-7FIGURE

The Investment Function The invest- ment function relates the quantity of investment I to the real interest rate r. Investment depends on the real interest rate because the interest rate is the cost of borrowing. The investment function slopes downward: when the interest rate rises, fewer investment projects are profi table.

Real interest rate, r

Quantity of investment, I

Investment function, I(r)

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 67

Government Purchases

Government purchases are the third component of the demand for goods and services. The federal government buys guns, missiles, and the services of gov- ernment employees. Local governments buy library books, build schools, and hire teachers. Governments at all levels build roads and other public works. All these transactions make up government purchases of goods and services, which account for about 20 percent of GDP in the United States.

These purchases are only one type of government spending. The other type is transfer payments to households, such as welfare for the poor and Social Security payments for the elderly. Unlike government purchases, transfer payments are not made in exchange for some of the economy’s output of goods and services. Therefore, they are not included in the variable G.

If you look in the business section of a newspa- per, you will fi nd many different interest rates reported. By contrast, throughout this book, we will talk about “the” interest rate, as if there was only one interest rate in the economy. The only distinction we will make is between the nominal interest rate (which is not corrected for infl ation) and the real interest rate (which is corrected for infl ation). Almost all of the interest rates reported in the newspaper are nominal.

Why does the newspaper report so many interest rates? The various interest rates differ in three ways:

■ Term. Some loans in the economy are for short periods of time, even as short as over- night. Other loans are for thirty years or even longer. The interest rate on a loan depends on its term. Long-term interest rates are usu- ally, but not always, higher than short-term interest rates.

■ Credit risk. In deciding whether to make a loan, a lender must take into account the probability that the borrower will repay. The law allows borrowers to default on their loans by declaring bankruptcy. The higher the perceived probability of default,

The Many Different Interest Rates the higher the interest rate. Because the government has the lowest credit risk, government bonds tend to pay a low inter- est rate. At the other extreme, fi nancially shaky corporations can raise funds only by issuing junk bonds, which pay a high inter- est rate to compensate for the high risk of default.

■ Tax treatment. The interest on different types of bonds is taxed differently. Most impor- tant, when state and local governments issue bonds, called municipal bonds, the holders of the bonds do not pay federal income tax on the interest income. Because of this tax advantage, municipal bonds pay a lower interest rate.

When you see two different interest rates in the newspaper, you can almost always explain the difference by considering the term, the credit risk, and the tax treatment of the loan.

Although there are many different interest rates in the economy, macroeconomists can usually ignore these distinctions. The vari- ous interest rates tend to move up and down together. For many purposes, we will not go far wrong by assuming there is only one inter- est rate.

F Y I

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68 | P A R T I I Classical Theory: The Economy in the Long Run

Transfer payments do affect the demand for goods and services indirectly. Transfer payments are the opposite of taxes: they increase households’ dispos- able income, just as taxes reduce disposable income. Thus, an increase in transfer payments fi nanced by an increase in taxes leaves disposable income unchanged. We can now revise our defi nition of T to equal taxes minus transfer payments. Disposable income, Y − T, includes both the negative impact of taxes and the positive impact of transfer payments.

If government purchases equal taxes minus transfers, then G = T and the government has a balanced budget. If G exceeds T, the government runs a budget defi cit, which it funds by issuing government debt—that is, by borrowing in the fi nancial markets. If G is less than T, the government runs a budget surplus, which it can use to repay some of its outstanding debt.

Here we do not try to explain the political process that leads to a particular fi scal policy—that is, to the level of government purchases and taxes. Instead, we take government purchases and taxes as exogenous variables. To denote that these variables are fi xed outside of our model of national income, we write

_ G = G.

_ T = T.

We do, however, want to examine the impact of fi scal policy on the endogenous variables, which are determined within the model. The endogenous variables here are consumption, investment, and the interest rate.

To see how the exogenous variables affect the endogenous variables, we must complete the model. This is the subject of the next section.

3-4 What Brings the Supply and Demand for Goods and Services Into Equilibrium?

We have now come full circle in the circular fl ow diagram, Figure 3-1. We began by examining the supply of goods and services, and we have just discussed the demand for them. How can we be certain that all these fl ows balance? In other words, what ensures that the sum of consumption, investment, and government purchases equals the amount of output produced? In this classical model, the interest rate is the price that has the crucial role of equilibrating supply and demand.

There are two ways to think about the role of the interest rate in the economy. We can consider how the interest rate affects the supply and demand for goods or services. Or we can consider how the interest rate affects the supply and demand for loanable funds. As we will see, these two approaches are two sides of the same coin.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 69

Equilibrium in the Market for Goods and Services: The Supply and Demand for the Economy’s Output

The following equations summarize the discussion of the demand for goods and services in Section 3-3:

Y = C + I + G.

C = C(Y − T ).

I = I(r). _ G = G. _ T = T.

The demand for the economy’s output comes from consumption, investment, and government purchases. Consumption depends on disposable income, invest- ment depends on the real interest rate, and government purchases and taxes are the exogenous variables set by fi scal policymakers.

To this analysis, let’s add what we learned about the supply of goods and services in Section 3-1. There we saw that the factors of production and the production function determine the quantity of output supplied to the economy:

_ _ Y = F(K, L)

_ = Y.

Now let’s combine these equations describing the supply and demand for output. If we substitute the consumption function and the investment function into the national income accounts identity, we obtain

Y = C(Y − T ) + I(r) + G.

Because the variables G and T are fi xed by policy, and the level of output Y is fi xed by the factors of production and the production function, we can write

_ _ _ _ Y = C(Y − T ) + I(r) + G.

This equation states that the supply of output equals its demand, which is the sum of consumption, investment, and government purchases.

Notice that the interest rate r is the only variable not already determined in the last equation. This is because the interest rate still has a key role to play: it must adjust to ensure that the demand for goods equals the supply. The greater the interest rate, the lower the level of investment, and thus the lower the demand for goods and services, C + I + G. If the interest rate is too high, then investment is too low and the demand for output falls short of the supply. If the interest rate is too low, then investment is too high and the demand exceeds the supply. At the equilibrium interest rate, the demand for goods and services equals the supply.

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70 | P A R T I I Classical Theory: The Economy in the Long Run

This conclusion may seem somewhat mysterious: how does the interest rate get to the level that balances the supply and demand for goods and services? The best way to answer this question is to consider how fi nancial markets fi t into the story.

Equilibrium in the Financial Markets: The Supply and Demand for Loanable Funds

Because the interest rate is the cost of borrowing and the return to lending in fi nancial markets, we can better understand the role of the interest rate in the economy by thinking about the fi nancial markets. To do this, rewrite the national income accounts identity as

Y − C − G = I.

The term Y − C − G is the output that remains after the demands of consumers and the government have been satisfi ed; it is called national saving or simply saving (S ). In this form, the national income accounts identity shows that saving equals investment.

To understand this identity more fully, we can split national saving into two parts—one part representing the saving of the private sector and the other rep- resenting the saving of the government:

S = (Y − T − C ) + (T − G) = I.

The term (Y − T − C ) is disposable income minus consumption, which is private saving. The term (T − G ) is government revenue minus government spending, which is public saving. (If government spending exceeds government revenue, then the government runs a budget defi cit and public saving is nega- tive.) National saving is the sum of private and public saving. The circular fl ow diagram in Figure 3-1 reveals an interpretation of this equation: this equation states that the fl ows into the fi nancial markets (private and public saving) must balance the fl ows out of the fi nancial markets (investment).

To see how the interest rate brings fi nancial markets into equilibrium, sub- stitute the consumption function and the investment function into the national income accounts identity:

Y − C(Y − T ) − G = I(r).

Next, note that G and T are fi xed by policy and Y is fi xed by the factors of production and the production function:

_ _ _ _ Y − C(Y − T ) − G = I(r)

_ S = I(r).

The left-hand side of this equation shows that national saving depends on income Y and the fi scal-policy variables G and T. For fi xed values of Y, G, and

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 71

T, national saving S is also fi xed. The right-hand side of the equation shows that investment depends on the interest rate.

Figure 3-8 graphs saving and investment as a function of the interest rate. The saving function is a vertical line because in this model saving does not depend on the interest rate (we relax this assumption later). The investment function slopes downward: as the interest rate decreases, more investment projects become profi table.

From a quick glance at Figure 3-8, one might think it was a supply-and- demand diagram for a particular good. In fact, saving and investment can be interpreted in terms of supply and demand. In this case, the “good” is loanable funds, and its “price” is the interest rate. Saving is the supply of loanable funds— households lend their saving to investors or deposit their saving in a bank that then loans the funds out. Investment is the demand for loanable funds—investors borrow from the public directly by selling bonds or indirectly by borrowing from banks. Because investment depends on the interest rate, the quantity of loanable funds demanded also depends on the interest rate.

The interest rate adjusts until the amount that fi rms want to invest equals the amount that households want to save. If the interest rate is too low, investors want more of the economy’s output than households want to save. Equivalently, the quantity of loanable funds demanded exceeds the quantity supplied. When this happens, the interest rate rises. Conversely, if the inter- est rate is too high, households want to save more than fi rms want to invest; because the quantity of loanable funds supplied is greater than the quantity demanded, the interest rate falls. The equilibrium interest rate is found where the two curves cross. At the equilibrium interest rate, households’ desire to save bal- ances fi rms’ desire to invest, and the quantity of loanable funds supplied equals the quantity demanded.

3-8FIGURE

Saving, Investment, and the Interest Rate The interest rate adjusts to bring saving and invest- ment into balance. The vertical line represents saving—the supply of loanable funds. The downward-sloping line represents investment— the demand for loanable funds. The intersection of these two curves deter- mines the equilibrium interest rate.

Real interest rate, r

S

Saving , S

Investment, Saving, I, S

Desired investment, I(r)

Equilibrium interest rate

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72 | P A R T I I Classical Theory: The Economy in the Long Run

Changes in Saving: The Effects of Fiscal Policy

We can use our model to show how fi scal policy affects the economy. When the government changes its spending or the level of taxes, it affects the demand for the economy’s output of goods and services and alters national saving, invest- ment, and the equilibrium interest rate.

An Increase in Government Purchases Consider fi rst the effects of an increase in government purchases by an amount �G. The immediate impact is to increase the demand for goods and services by �G. But because total output is fi xed by the factors of production, the increase in government purchases must be met by a decrease in some other category of demand. Disposable income Y − T is unchanged, so consumption C is unchanged as well. Therefore, the increase in government purchases must be met by an equal decrease in investment.

To induce investment to fall, the interest rate must rise. Hence, the increase in government purchases causes the interest rate to increase and investment to decrease. Government purchases are said to crowd out investment.

To grasp the effects of an increase in government purchases, consider the impact on the market for loanable funds. Because the increase in government purchases is not accompanied by an increase in taxes, the government fi nances the additional spending by borrowing—that is, by reducing public saving. With private saving unchanged, this government borrowing reduces national saving. As Figure 3-9 shows, a reduction in national saving is represented by a leftward shift in the supply of loanable funds available for investment. At the initial interest rate, the demand for loanable funds exceeds the supply. The equilibrium inter- est rate rises to the point where the investment schedule crosses the new saving schedule. Thus, an increase in government purchases causes the interest rate to rise from r1 to r2.

3-9FIGURE

A Reduction in Saving A reduction in saving, pos- sibly the result of a change in fi scal policy, shifts the saving schedule to the left. The new equilibrium is the point at which the new saving schedule crosses the investment schedule. A reduction in saving lowers the amount of investment and raises the interest rate. Fiscal-policy actions that reduce saving are said to crowd out investment.

Real interest rate, r

I(r)

Investment, Saving, I, S

r2

r1

S2 S1

1. A fall in saving ...

2. ... raises the interest rate.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 73

Wars and Interest Rates in the United Kingdom, 1730�1920

Wars are traumatic—both for those who fi ght them and for a nation’s economy. Because the economic changes accompanying them are often large, wars provide a natural experiment with which economists can test their theories. We can learn about the economy by seeing how in wartime the endogenous variables respond to the major changes in the exogenous variables.

One exogenous variable that changes substantially in wartime is the level of government purchases. Figure 3-10 shows military spending as a percentage of GDP for the United Kingdom from 1730 to 1919. This graph shows, as one would expect, that government purchases rose suddenly and dramatically during the eight wars of this period.

CASE STUDY

3-10FIGURE

Military Spending and the Interest Rate in the United Kingdom This fi gure shows military spending as a percentage of GDP in the United Kingdom from 1730 to 1919. Not surprisingly, military spending rose substantially during each of the eight wars of this period. This fi gure also shows that the interest rate tended to rise when military spending rose.

Source: Series constructed from various sources described in Robert J. Barro, “Government Spending, Interest Rates, Prices, and Budget Defi cits in the United Kingdom, 1701�1918,” Journal of Monetary Economics 20 (September 1987): 221�248.

50

45

40

35

30

25

20

15

10

5

0

6

5

4

3

2

1

0

Crimean War

Wars with France

War of American Independence

War of Austrian

Succession Seven Years War Boer War

World War I

Percentage of GDP

Interest rate (percent)

1730 1750 1770 1790 1810 1830 Year

1850 1870 1890 1910

Interest rates (right scale)

Military spending (left scale)

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74 | P A R T I I Classical Theory: The Economy in the Long Run

A Decrease in Taxes Now consider a reduction in taxes of �T. The immedi- ate impact of the tax cut is to raise disposable income and thus to raise consump- tion. Disposable income rises by �T, and consumption rises by an amount equal to �T times the marginal propensity to consume MPC. The higher the MPC, the greater the impact of the tax cut on consumption.

Because the economy’s output is fi xed by the factors of production and the level of government purchases is fi xed by the government, the increase in con- sumption must be met by a decrease in investment. For investment to fall, the interest rate must rise. Hence, a reduction in taxes, like an increase in government purchases, crowds out investment and raises the interest rate.

We can also analyze the effect of a tax cut by looking at saving and invest- ment. Because the tax cut raises disposable income by �T, consumption goes up by MPC × �T. National saving S, which equals Y − C − G, falls by the same amount as consumption rises. As in Figure 3-9, the reduction in saving shifts the supply of loanable funds to the left, which increases the equilibrium interest rate and crowds out investment.

Changes in Investment Demand

So far, we have discussed how fi scal policy can change national saving. We can also use our model to examine the other side of the market—the demand for investment. In this section we look at the causes and effects of changes in investment demand.

Our model predicts that this wartime increase in government purchases—and the increase in government borrowing to fi nance the wars—should have raised the demand for goods and services, reduced the supply of loanable funds, and raised the interest rate. To test this prediction, Figure 3-10 also shows the interest rate on long-term government bonds, called consols in the United Kingdom. A positive association between military purchases and interest rates is apparent in this fi gure. These data support the model’s prediction: interest rates do tend to rise when government purchases increase.8

One problem with using wars to test theories is that many economic changes may be occurring at the same time. For example, in World War II, while govern- ment purchases increased dramatically, rationing also restricted consumption of many goods. In addition, the risk of defeat in the war and default by the government on its debt presumably increases the interest rate the government must pay. Economic models predict what happens when one exogenous variable changes and all the other exogenous variables remain constant. In the real world, however, many exogenous variables may change at once. Unlike controlled laboratory experiments, the natural experiments on which economists must rely are not always easy to interpret. ■

8Daniel K. Benjamin and Levis A. Kochin, “War, Prices, and Interest Rates: A Martial Solution to Gibson’s Paradox,” in M. D. Bordo and A. J. Schwartz, eds., A Retrospective on the Classical Gold Standard, 1821�1931 (Chicago: University of Chicago Press, 1984), 587�612; Robert J. Barro, “Government Spending, Interest Rates, Prices, and Budget Defi cits in the United Kingdom, 1701�1918,” Journal of Monetary Economics 20 (September 1987): 221�248.

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 75

One reason investment demand might increase is technological innovation. Suppose, for example, that someone invents a new technology, such as the rail- road or the computer. Before a fi rm or household can take advantage of the innovation, it must buy investment goods. The invention of the railroad had no value until railroad cars were produced and tracks were laid. The idea of the computer was not productive until computers were manufactured. Thus, tech- nological innovation leads to an increase in investment demand.

Investment demand may also change because the government encourages or discourages investment through the tax laws. For example, suppose that the government increases personal income taxes and uses the extra revenue to pro- vide tax cuts for those who invest in new capital. Such a change in the tax laws makes more investment projects profi table and, like a technological innovation, increases the demand for investment goods.

Figure 3-11 shows the effects of an increase in investment demand. At any given interest rate, the demand for investment goods (and also for loanable funds) is higher. This increase in demand is represented by a shift in the investment schedule to the right. The economy moves from the old equilibrium, point A, to the new equilibrium, point B.

The surprising implication of Figure 3-11 is that the equilibrium amount of invest- ment is unchanged. Under our assumptions, the fi xed level of saving determines the amount of investment; in other words, there is a fi xed supply of loanable funds. An increase in investment demand merely raises the equilibrium interest rate.

We would reach a different conclusion, however, if we modifi ed our simple con- sumption function and allowed consumption (and its fl ip side, saving) to depend on the interest rate. Because the interest rate is the return to saving (as well as the cost of borrowing), a higher interest rate might reduce consumption and increase saving. If so, the saving schedule would be upward sloping rather than vertical.

3-11FIGURE

An Increase in the Demand for Investment An increase in the demand for investment goods shifts the investment schedule to the right. At any given interest rate, the amount of investment is greater. The equilibrium moves from point A to point B. Because the amount of saving is fi xed, the increase in investment demand raises the inter- est rate while leaving the equilibrium amount of investment unchanged.

Real interest rate, r

Investment, Saving, I, S

I2

I1

S

A

B

1. An increase in desired investment ...

2. ... raises the interest rate.

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76 | P A R T I I Classical Theory: The Economy in the Long Run

With an upward-sloping saving schedule, an increase in investment demand would raise both the equilibrium interest rate and the equilibrium quantity of investment. Figure 3-12 shows such a change. The increase in the interest rate causes households to consume less and save more. The decrease in consumption frees resources for investment.

3-5 Conclusion

In this chapter we have developed a model that explains the production, distribu- tion, and allocation of the economy’s output of goods and services. The model relies on the classical assumption that prices adjust to equilibrate supply and demand. In this model, factor prices equilibrate factor markets, and the interest rate equilibrates the supply and demand for goods and services (or, equivalently, the supply and demand for loanable funds). Because the model incorporates all the interactions illustrated in the circular fl ow diagram in Figure 3-1, it is some- times called a general equilibrium model.

Throughout the chapter, we have discussed various applications of the model. The model can explain how income is divided among the factors of production and how factor prices depend on factor supplies. We have also used the model to discuss how fi scal policy alters the allocation of output among its alternative uses—consumption, investment, and government purchases—and how it affects the equilibrium interest rate.

At this point it is useful to review some of the simplifying assumptions we have made in this chapter. In the following chapters we relax some of these assumptions to address a greater range of questions.

■ We have ignored the role of money, the asset with which goods and services are bought and sold. In Chapters 4 and 5 we discuss how money affects the economy and the infl uence of monetary policy.

3-12FIGURE

An Increase in Investment Demand When Saving Depends on the Interest Rate When saving is positively related to the interest rate, a rightward shift in the investment schedule increases the interest rate and the amount of invest- ment. The higher interest rate induces people to increase saving, which in turn allows investment to increase.

Real interest rate, r

2. ... raises the interest rate ...

Investment, Saving, I, S

S(r)

A

B

1. An increase in desired investment ...

3. ... and raises equilibrium investment and saving.

I2

I1

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 77

■ We have assumed that there is no trade with other countries. In Chapter 6 we consider how international interactions affect our conclusions.

■ We have assumed that the labor force is fully employed. In Chapter 7 we examine the reasons for unemployment and see how public policy infl u- ences the level of unemployment.

■ We have assumed that the capital stock, the labor force, and the produc- tion technology are fi xed. In Chapters 8 and 9 we see how changes over time in each of these lead to growth in the economy’s output of goods and services.

■ We have ignored the role of short-run sticky prices. In Chapters 10 through 14, we develop a model of short-run fl uctuations that includes sticky prices. We then discuss how the model of short-run fl uctuations relates to the model of national income developed in this chapter.

Before going on to these chapters, go back to the beginning of this one and make sure you can answer the four groups of questions about national income that begin the chapter.

Summary

1. The factors of production and the production technology determine the economy’s output of goods and services. An increase in one of the factors of production or a technological advance raises output.

2. Competitive, profi t-maximizing fi rms hire labor until the marginal product of labor equals the real wage. Similarly, these fi rms rent capital until the marginal product of capital equals the real rental price. Therefore, each factor of production is paid its marginal product. If the production function has constant returns to scale, then according to Euler’s theorem, all output is used to compensate the inputs.

3. The economy’s output is used for consumption, investment, and govern- ment purchases. Consumption depends positively on disposable income. Investment depends negatively on the real interest rate. Government purchases and taxes are the exogenous variables of fi scal policy.

4. The real interest rate adjusts to equilibrate the supply and demand for the economy’s output—or, equivalently, the supply of loanable funds (saving) and the demand for loanable funds (investment). A decrease in national saving, perhaps because of an increase in government purchases or a decrease in taxes, decreases the supply of loanable funds, reduces the equi- librium amount of investment, and raises the interest rate. An increase in investment demand, perhaps because of a technological innovation or a tax incentive for investment, increases the demand for loanable funds and also raises the interest rate. An increase in investment demand increases the quantity of investment only if a higher interest rate stimulates additional saving.

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78 | P A R T I I Classical Theory: The Economy in the Long Run

K E Y C O N C E P T S

Factors of production

Production function

Constant returns to scale

Factor prices

Competition

Profi t

Marginal product of labor (MPL)

Diminishing marginal product

Real wage

Marginal product of capital (MPK )

Real rental price of capital

Economic profi t versus accounting profi t

Cobb−Douglas production function

Disposable income

Consumption function

Marginal propensity to consume (MPC )

Interest rate

Nominal interest rate

Real interest rate

National saving (saving)

Private saving

Public saving

Loanable funds

Crowding out

1. What determines the amount of output an economy produces?

2. Explain how a competitive, profi t-maximizing fi rm decides how much of each factor of pro- duction to demand.

3. What is the role of constant returns to scale in the distribution of income?

4. Write a Cobb−Douglas production function for which capital earns one-fourth of total income.

Q U E S T I O N S F O R R E V I E W

5. What determines consumption and investment?

6. Explain the difference between government pur- chases and transfer payments. Give two examples of each.

7. What makes the demand for the economy’s out- put of goods and services equal the supply?

8. Explain what happens to consumption, invest- ment, and the interest rate when the govern- ment increases taxes.

1. Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the following events:

a. A wave of immigration increases the labor force.

b. An earthquake destroys some of the capital stock.

c. A technological advance improves the pro- duction function.

d. High infl ation doubles the prices of all factors and outputs in the economy.

2. Suppose the production function in medieval Europe is Y = K0.5L0.5, where K is the amount of land and L is the amount of labor. The

P R O B L E M S A N D A P P L I C A T I O N S

economy begins with 100 units of land and 100 units of labor. Use a calculator and equations in the chapter to fi nd a numerical answer to each of the following questions.

a. How much output does the economy produce?

b. What are the wage and the rental price of land?

c. What share of output does labor receive?

d. If a plague kills half the population, what is the new level of output?

e. What is the new wage and rental price of land?

f. What share of output does labor receive now?

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C H A P T E R 3 National Income: Where It Comes From and Where It Goes | 79

3. If a 10 percent increase in both capital and labor causes output to increase by less than 10 per- cent, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more than 10 percent, the produc- tion function is said to exhibit increasing returns to scale. Why might a production function exhibit decreasing or increasing returns to scale?

4. Suppose that an economy’s production function is Cobb−Douglas with parameter � = 0.3. a. What fractions of income do capital and labor

receive?

b. Suppose that immigration increases the labor force by 10 percent. What happens to total output (in percent)? The rental price of capi- tal? The real wage?

c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?

5. Figure 3-5 shows that in U.S. data, labor’s share of total income is approximately a constant over time. Table 3-1 shows that the trend in the real wage closely tracks the trend in labor productiv- ity. How are these facts related? Could the fi rst fact be true without the second also being true? Use the mathematical expression for labor’s share to justify your answer.

6. According to the neoclassical theory of distribu- tion, the real wage earned by any worker equals that worker’s marginal productivity. Let’s use this insight to examine the incomes of two groups of workers: farmers and barbers.

a. Over the past century, the productivity of farmers has risen substantially because of technological progress. According to the neo- classical theory, what should have happened to their real wage?

b. In what units is the real wage discussed in part (a) measured?

c. Over the same period, the productivity of barbers has remained constant. What should have happened to their real wage?

d. In what units is the real wage in part (c) measured?

e. Suppose workers can move freely between being farmers and being barbers. What does this mobility imply for the wages of farmers and barbers?

f. What do your previous answers imply for the price of haircuts relative to the price of food?

g. Who benefi ts from technological progress in farming—farmers or barbers?

7. (This problem requires the use of calculus.) Consider a Cobb–Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is

Y = K1/3L1/3H1/3.

a. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?

b. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the mar- ginal product of human capital?

c. What is the income share paid to labor? What is the income share paid to human capi- tal? In the national income accounts of this economy, what share of total income do you think workers would appear to receive? (Hint: Consider where the return to human capital shows up.)

d. An unskilled worker earns the marginal prod- uct of labor, whereas a skilled worker earns the marginal product of labor plus the mar- ginal product of human capital. Using your answers to parts (a) and (b), fi nd the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain.

e. Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preced- ing questions shed light on this debate?

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80 | P A R T I I Classical Theory: The Economy in the Long Run

8. The government raises taxes by $100 billion. If the marginal propensity to consume is 0.6, what happens to the following? Do they rise or fall? By what amounts?

a. Public saving

b. Private saving

c. National saving

d. Investment

9. Suppose that an increase in consumer confi - dence raises consumers’ expectations about their future income and thus increases the amount they want to consume today. This might be interpreted as an upward shift in the consump- tion function. How does this shift affect invest- ment and the interest rate?

10. Consider an economy described by the follow- ing equations:

Y = C + I + G

Y = 5,000

G = 1,000

T = 1,000

C = 250 + 0.75(Y − T )

I = 1,000 − 50r

a. In this economy, compute private saving, pub- lic saving, and national saving.

b. Find the equilibrium interest rate.

c. Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.

d. Find the new equilibrium interest rate.

11. Suppose that the government increases taxes and government purchases by equal amounts. What happens to the interest rate and investment in response to this balanced-budget change? Explain how your answer depends on the mar- ginal propensity to consume.

12. When the government subsidizes investment, such as with an investment tax credit, the sub- sidy often applies to only some types of invest- ment. This question asks you to consider the effect of such a change. Suppose there are two types of investment in the economy: business investment and residential investment. The inter- est rate adjusts to equilibrate national saving and

total investment, which is the sum of business investment and residential investment. Now sup- pose that the government institutes an invest- ment tax credit only for business investment.

a. How does this policy affect the demand curve for business investment? The demand curve for residential investment?

b. Draw the economy’s supply and demand for loanable funds. How does this policy affect the supply and demand for loanable funds? What happens to the equilibrium interest rate?

c. Compare the old and the new equilibria. How does this policy affect the total quan- tity of investment? The quantity of business investment? The quantity of residential investment?

13. Suppose that consumption depends on the inter- est rate. How, if at all, does this alter the conclu- sions reached in the chapter about the impact of an increase in government purchases on invest- ment, consumption, national saving, and the interest rate?

14. Macroeconomic data do not show a strong correlation between investment and interest rates. Let’s examine why this might be so. Use our model in which the interest rate adjusts to equilibrate the supply of loanable funds (which is upward sloping) and the demand for loanable funds (which is downward sloping).

a. Suppose the demand for loanable funds is stable but the supply fl uctuates from year to year. What might cause these fl uctuations in supply? In this case, what correlation between investment and interest rates would you fi nd?

b. Suppose the supply of loanable funds is stable but the demand fl uctuates from year to year. What might cause these fl uctuations in demand? In this case, what correlation between investment and interest rates would you fi nd now?

c. Suppose that both supply and demand in this market fl uctuate over time. If you were to construct a scatterplot of investment and the interest rate, what would you fi nd?

d. Which of the above three cases seems most empirically realistic to you?

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81

The Monetary System: What It Is and How It Works

4C H A P T E R

There have been three great inventions since the beginning of time: fi re,

the wheel, and central banking.

—Will Rogers

The two arms of macroeconomic policy are monetary and fi scal policy. Fiscal policy encompasses the government’s decisions about spending and taxation, as we saw in the previous chapter. Monetary policy refers to decisions about the nation’s system of coin, currency, and banking. Fiscal policy is usually made by elected representatives, such as the U.S. Congress, British Parliament, or Japanese Diet. Monetary policy is made by central banks, which are typically set up by elected representatives but allowed to operate indepen- dently. Examples include the U.S. Federal Reserve, the Bank of England, and the Bank of Japan. Will Rogers was exaggerating when he said that central banking was one of the three greatest inventions of all time, but he was right in imply- ing that these policymaking institutions have a great infl uence over the lives and livelihoods of citizens of all nations around the world.

Much of this book is aimed at explaining the effects and proper role of monetary and fi scal policy. This chapter begins our analysis of monetary policy. We address three related questions. First, what is money? Second, what is the role of a nation’s banking system in determining the amount of money in the economy? Third, how does a nation’s central bank infl uence the banking system and the money supply?

This chapter’s introduction to the monetary system provides the foundation for understanding monetary policy. In the next chapter, consistent with the long- run focus of this part of book, we examine the long-run effects of monetary policy. The short-run effects of monetary policy are more complex. We start discussing that topic in Chapter 10, but it will take several chapters to develop a complete explanation. This chapter gets us ready. Both the long-run and short- run analysis of monetary policy must be grounded in a fi rm understanding of what money is, how banks affect it, and how central banks control it.

4-1 What Is Money?

When we say that a person has a lot of money, we usually mean that he or she is wealthy. By contrast, economists use the term “money” in a more specialized way. To an economist, money does not refer to all wealth but only to one type

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of it: money is the stock of assets that can be readily used to make transactions. Roughly speaking, the dollars (or, in other countries, for example, pounds or yen) in the hands of the public make up the nation’s stock of money.

The Functions of Money

Money has three purposes: it is a store of value, a unit of account, and a medium of exchange.

As a store of value, money is a way to transfer purchasing power from the present to the future. If I work today and earn $100, I can hold the money and spend it tomorrow, next week, or next month. Money is not a perfect store of value: if prices are rising, the amount you can buy with any given quantity of money is falling. Even so, people hold money because they can trade it for goods and services at some time in the future.

As a unit of account, money provides the terms in which prices are quoted and debts are recorded. Microeconomics teaches us that resources are allocated according to relative prices—the prices of goods relative to other goods—yet stores post their prices in dollars and cents. A car dealer tells you that a car costs $20,000, not 400 shirts (even though it may amount to the same thing). Similarly, most debts require the debtor to deliver a specifi ed number of dollars in the future, not a specifi ed amount of some commodity. Money is the yardstick with which we measure economic transactions.

As a medium of exchange, money is what we use to buy goods and ser- vices. “This note is legal tender for all debts, public and private” is printed on the U.S. dollar. When we walk into stores, we are confi dent that the shopkeep- ers will accept our money in exchange for the items they are selling. The ease with which an asset can be converted into the medium of exchange and used to buy other things—goods and services—is sometimes called the asset’s liquidity. Because money is the medium of exchange, it is the economy’s most liquid asset.

To better understand the functions of money, try to imagine an economy without it: a barter economy. In such a world, trade requires the double coincidence of wants—the unlikely happenstance of two people each having a good that the other wants at the right time and place to make an exchange. A barter economy permits only simple transactions.

Money makes more indirect transactions possible. A professor uses her salary to buy books; the book publisher uses its revenue from the sale of books to buy paper; the paper company uses its revenue from the sale of paper to buy wood that it grinds into paper pulp; the lumber company uses revenue from the sale of wood to pay the lumberjack; the lumberjack uses his income to send his child to college; and the college uses its tuition receipts to pay the salary of the professor. In a complex, modern economy, trade is usually indirect and requires the use of money.

The Types of Money

Money takes many forms. In the U.S. economy we make transactions with an item whose sole function is to act as money: dollar bills. These pieces of green

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paper with small portraits of famous Americans would have little value if they were not widely accepted as money. Money that has no intrinsic value is called fi at money because it is estab- lished as money by government decree, or fi at.

Fiat money is the norm in most economies today, but most societies in the past have used a commodity with some intrinsic value for money. This type of money is called commod- ity money. The most widespread example is gold. When people use gold as money (or use paper money that is redeemable for gold), the economy is said to be on a gold standard. Gold is a form of commodity money because it can be used for various purposes—jewelry, dental fi llings, and so on—as well as for transactions. The gold standard was com- mon throughout the world during the late nineteenth century.

Money in a POW Camp

An unusual form of commodity money developed in some Nazi prisoner of war (POW) camps during World War II. The Red Cross supplied the prisoners with various goods—food, clothing, cigarettes, and so on. Yet these rations were allocated without close attention to personal preferences, so the allocations were often ineffi cient. One prisoner might have preferred chocolate, while another might have preferred cheese, and a third might have wanted a new shirt. The differing tastes and endowments of the prisoners led them to trade with one another.

Barter proved to be an inconvenient way to allocate these resources, however, because it required the double coincidence of wants. In other words, a barter system was not the easiest way to ensure that each prisoner received the goods he valued most. Even the limited economy of the POW camp needed some form of money to facilitate transactions.

Eventually, cigarettes became the established “currency’’ in which prices were quoted and with which trades were made. A shirt, for example, cost about 80 cigarettes. Services were also quoted in cigarettes: some prisoners offered to do other prisoners’ laundry for 2 cigarettes per garment. Even nonsmokers were happy to accept cigarettes in exchange, knowing they could trade the cigarettes in the future for some good they did enjoy. Within the POW camp the cigarette became the store of value, the unit of account, and the medium of exchange.1 ■

CASE STUDY

1R. A. Radford, “The Economic Organisation of a P.O.W. Camp,’’ Economica (November 1945): 189–201. The use of cigarettes as money is not limited to this example. In the Soviet Union in the late 1980s, packs of Marlboros were preferred to the ruble in the large underground economy.

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84 | P A R T I I Classical Theory: The Economy in the Long Run

The Development of Fiat Money

It is not surprising that in any society, no matter how primitive, some form of commodity money arises to facilitate exchange: people are willing to accept a commodity currency such as gold because it has intrinsic value. The develop- ment of fi at money, however, is more perplexing. What would make people begin to value something that is intrinsically useless?

To understand how the evolution from commodity money to fi at money takes place, imagine an economy in which people carry around bags of gold. When a purchase is made, the buyer measures out the appropriate amount of gold. If the seller is convinced that the weight and purity of the gold are right, the buyer and seller make the exchange.

The government might fi rst get involved in the monetary system to help people reduce transaction costs. Using raw gold as money is costly because it takes time to verify the purity of the gold and to measure the correct quantity. To reduce these costs, the government can mint gold coins of known purity and weight. The coins are easier to use than gold bullion because their values are widely recognized.

The next step is for the government to accept gold from the public in exchange for gold certifi cates—pieces of paper that can be redeemed for a cer- tain quantity of gold. If people believe the government’s promise to redeem the paper bills for gold, the bills are just as valuable as the gold itself. In addition, because the bills are lighter than gold (and gold coins), they are easier to use in transactions. Eventually, no one carries gold around at all, and these gold-backed government bills become the monetary standard.

Finally, the gold backing becomes irrelevant. If no one ever bothers to redeem the bills for gold, no one cares if the option is abandoned. As long as everyone continues to accept the paper bills in exchange, they will have value and serve as money. Thus, the system of commodity money evolves into a system of fi at money. Notice that in the end the use of money in exchange is a social conven- tion: everyone values fi at money because they expect everyone else to value it.

Money and Social Conventions on the Island of Yap

The economy of Yap, a small island in the Pacifi c, once had a type of money that was something between commodity and fi at money. The traditional medium of exchange in Yap was fei, stone wheels up to 12 feet in diameter. These stones had holes in the center so that they could be carried on poles and used for exchange.

Large stone wheels are not a convenient form of money. The stones were heavy, so it took substantial effort for a new owner to take his fei home after completing a transaction. Although the monetary system facilitated exchange, it did so at great cost.

Eventually, it became common practice for the new owner of the fei not to bother to take physical possession of the stone. Instead, the new owner accepted a claim to the fei without moving it. In future bargains, he traded this claim for goods that he wanted. Having physical possession of the stone became less important than having legal claim to it.

CASE STUDY

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How the Quantity of Money Is Controlled

The quantity of money available in an economy is called the money supply. In a system of commodity money, the money supply is simply the quantity of that commodity. In an economy that uses fi at money, such as most economies today, the government controls the supply of money: legal restrictions give the government a monopoly on the printing of money. Just as the level of taxation and the level of government purchases are policy instruments of the government, so is the quantity of money. The government’s control over the money supply is called monetary policy.

In the United States and many other countries, monetary policy is delegated to a partially independent institution called the central bank. The central bank of the United States is the Federal Reserve—often called the Fed. If you look at a U.S. dollar bill, you will see that it is called a Federal Reserve Note. Decisions about monetary policy are made by the Fed’s Federal Open Market Committee. This committee is made up of members of the Federal Reserve Board, who are appointed by the President and confi rmed by Congress, together with the presi- dents of the regional Federal Reserve Banks. The Federal Open Market Com- mittee meets about every six weeks to discuss and set monetary policy.

The primary way in which the Fed controls the supply of money is through open-market operations—the purchase and sale of government bonds. When the Fed wants to increase the money supply, it uses some of the dollars it has to buy government bonds from the public. Because these dollars leave the Fed and enter into the hands of the public, the purchase increases the quantity of money in circulation. Conversely, when the Fed wants to decrease the money supply, it sells some government bonds from its own portfolio. This open-market sale of bonds takes some dollars out of the hands of the public and, thus, decreases the quantity of money in circulation. (Later in the chapter, we explore in more detail how the Fed controls the supply of money.)

How the Quantity of Money Is Measured

One of our goals is to determine how the money supply affects the economy; we turn to that topic in the next chapter. As a background for that analysis, let’s fi rst discuss how economists measure the quantity of money.

Because money is the stock of assets used for transactions, the quantity of money is the quantity of those assets. In simple economies, this quantity is easy to measure. In the POW camp, the quantity of money was the number of

This practice was put to a test when a valuable stone was lost at sea during a storm. Because the owner lost his money by accident rather than through negli- gence, everyone agreed that his claim to the fei remained valid. Even generations later, when no one alive had ever seen this stone, the claim to this fei was still valued in exchange.2 ■

2Norman Angell, The Story of Money (New York: Frederick A. Stokes Company, 1929), 88–89.

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cigarettes in the camp. On the island of Yap, the quantity of money was the num- ber of fei on the island. But how can we measure the quantity of money in more complex economies? The answer is not obvious, because no single asset is used for all transactions. People can use various assets, such as cash in their wallets or deposits in their checking accounts, to make transactions, although some assets are more convenient to use than others.

The most obvious asset to include in the quantity of money is currency, the sum of outstanding paper money and coins. Most day-to-day transactions use currency as the medium of exchange.

A second type of asset used for transactions is demand deposits, the funds people hold in their checking accounts. If most sellers accept personal checks or debit cards that access checking accounts balances, then assets in a checking account are almost as convenient as currency. That is, the assets are in a form that can easily facilitate a transaction. Demand deposits are therefore added to currency when measuring the quantity of money.

Once we admit the logic of including demand deposits in the measured money stock, many other assets become candidates for inclusion. Funds in sav- ings accounts, for example, can be easily transferred into checking accounts or accessed by debit cards; these assets are almost as convenient for transac- tions. Money market mutual funds allow investors to write checks against their accounts, although restrictions sometimes apply with regard to the size of the check or the number of checks written. Because these assets can be easily used for transactions, they should arguably be included in the quantity of money.

Because it is hard to judge which assets should be included in the money stock, more than one measure is available. Table 4-1 presents the three measures of the money stock that the Federal Reserve calculates for the U.S. economy, together with a list of which assets are included in each measure. From the smallest to the largest, they are designated C, M1, and M2. The most common measures for studying the effects of money on the economy are M1 and M2.

Amount in July 2011 Symbol Assets Included (billions of dollars)

C Currency 972

M1 Currency plus demand deposits, 2,006 traveler’s checks, and other checkable deposits

M2 M1 plus retail money market mutual 9,314 fund balances, saving deposits (including

money market deposit accounts), and small time deposits

Source: Federal Reserve.

The Measures of Money

TABLE 4-1

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4-2 The Role of Banks in the Monetary System

Earlier, we introduced the concept of “money supply’’ in a highly simplifi ed manner. We defi ned the quantity of money as the number of dollars held by the public, and we assumed that the Federal Reserve controls the supply of money by increasing or decreasing the number of dollars in circulation through open- market operations. This explanation was a good starting point for understanding what determines the supply of money, but it is incomplete because it omits the role of the banking system in this process.

In this section we see that the money supply is determined not only by Fed policy but also by the behavior of households (which hold money) and banks (in which money is held). We begin by recalling that the money supply includes both currency in the hands of the public and deposits (such as checking account balances) at banks that households can use on demand for transactions. If M denotes the money supply, C currency, and D demand deposits, we can write

Money Supply = Currency + Demand Deposits

M = C + D.

Many people use credit or debit cards to make purchases. Because money is the medium of exchange, one might naturally wonder how these cards fi t into the measurement and analysis of money.

Let’s start with credit cards. One might guess that credit cards are part of the economy’s stock of money, but in fact measures of the quantity of money do not take credit cards into account. This is because credit cards are not really a method of payment but a method of deferring payment. When you buy an item with a credit card, the bank that issued the card pays the store what it is due. Later, you repay the bank. When the time comes to pay your credit card bill, you will likely do so by writing a check against your checking account. The balance in this checking account is part of the economy’s stock of money.

The story is different with debit cards, which automatically withdraw funds from a bank

How Do Credit Cards and Debit Cards Fit Into the Monetary System?

account to pay for items bought. Rather than allowing users to postpone payment for their purchases, a debit card allows users immedi- ate access to deposits in their bank accounts. Using a debit card is similar to writing a check. The account balances that lie behind debit cards are included in measures of the quantity of money.

Even though credit cards are not a form of money, they are still important for analyzing the monetary system. Because people with credit cards can pay many of their bills all at once at the end of the month, rather than sporadically as they make purchases, they may hold less money on average than people without credit cards. Thus, the increased popularity of credit cards may reduce the amount of money that people choose to hold. In other words, credit cards are not part of the supply of money, but they may affect the demand for money.

F Y I

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To understand the money supply, we must understand the interaction between currency and demand deposits and how the banking system, together with Fed policy, infl uences these two components of the money supply.

100-Percent-Reserve Banking

We begin by imagining a world without banks. In such a world, all money takes the form of currency, and the quantity of money is simply the amount of cur- rency that the public holds. For this discussion, suppose that there is $1,000 of currency in the economy.

Now introduce banks. At fi rst, suppose that banks accept deposits but do not make loans. The only purpose of the banks is to provide a safe place for deposi- tors to keep their money.

The deposits that banks have received but have not lent out are called reserves. Some reserves are held in the vaults of local banks throughout the country, but most are held at a central bank, such as the Federal Reserve. In our hypothetical economy, all deposits are held as reserves: banks simply accept deposits, place the money in reserve, and leave the money there until the depositor makes a with- drawal or writes a check against the balance. This system is called 100-percent- reserve banking.

Suppose that households deposit the economy’s entire $1,000 in Firstbank. Firstbank’s balance sheet—its accounting statement of assets and liabilities— looks like this:

Firstbank’s Balance Sheet

Assets Liabilities

Reserves $1,000 Deposits $1,000

The bank’s assets are the $1,000 it holds as reserves; the bank’s liabilities are the $1,000 it owes to depositors. Unlike banks in our economy, this bank is not mak- ing loans, so it will not earn profi t from its assets. The bank presumably charges depositors a small fee to cover its costs.

What is the money supply in this economy? Before the creation of Firstbank, the money supply was the $1,000 of currency. After the creation of Firstbank, the money supply is the $1,000 of demand deposits. A dollar deposited in a bank reduces currency by one dollar and raises deposits by one dollar, so the money supply remains the same. If banks hold 100 percent of deposits in reserve, the banking system does not affect the supply of money.

Fractional-Reserve Banking

Now imagine that banks start to use some of their deposits to make loans—for example, to families who are buying houses or to fi rms that are investing in new plants and equipment. The advantage to banks is that they can charge interest on the loans. The banks must keep some reserves on hand so that reserves are

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available whenever depositors want to make withdrawals. But as long as the amount of new deposits approximately equals the amount of withdrawals, a bank need not keep all its deposits in reserve. Thus, bankers have an incentive to make loans. When they do so, we have fractional-reserve banking, a system under which banks keep only a fraction of their deposits in reserve.

Here is Firstbank’s balance sheet after it makes a loan:

Firstbank’s Balance Sheet

Assets Liabilities

Reserves $200 Deposits $1,000

Loans $800

This balance sheet assumes that the reserve–deposit ratio—the fraction of deposits kept in reserve—is 20 percent. Firstbank keeps $200 of the $1,000 in deposits in reserve and lends out the remaining $800.

Notice that Firstbank increases the supply of money by $800 when it makes this loan. Before the loan is made, the money supply is $1,000, equaling the deposits in Firstbank. After the loan is made, the money supply is $1,800: the depositor still has a demand deposit of $1,000, but now the borrower holds $800 in currency. Thus, in a system of fractional-reserve banking, banks create money.

The creation of money does not stop with Firstbank. If the borrower deposits the $800 in another bank (or if the borrower uses the $800 to pay someone who then deposits it), the process of money creation continues. Here is the balance sheet of Secondbank:

Secondbank’s Balance Sheet

Assets Liabilities

Reserves $160 Deposits $800

Loans $640

Secondbank receives the $800 in deposits, keeps 20 percent, or $160, in reserve, and then loans out $640. Thus, Secondbank creates $640 of money. If this $640 is eventually deposited in Thirdbank, this bank keeps 20 percent, or $128, in reserve and loans out $512, resulting in this balance sheet:

Thirdbank’s Balance Sheet

Assets Liabilities

Reserves $128 Deposits $640

Loans $512

The process goes on and on. With each deposit and subsequent loan, more money is created.

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This process of money creation can continue forever, but it does not create an infi nite amount of money. Letting rr denote the reserve–deposit ratio, the amount of money that the original $1,000 creates is

Original Deposit = $1,000 Firstbank Lending = (1 − rr) × $1,000 Secondbank Lending = (1 − rr)2 × $1,000 Thirdbank Lending = (1 − rr)3 × $1,000

Total Money Supply = [1 + (1 − rr) + (1 − rr)2

+ (1 − rr)3 + … ] × $1,000 = (1/rr) × $1,000.

Each $1 of reserves generates $(1/rr) of money. In our example, rr = 0.2, so the original $1,000 generates $5,000 of money.3

The banking system’s ability to create money is the primary differ- ence between banks and other fi nancial institutions. As we fi rst discussed in Chapter 3, fi nancial markets have the important function of transferring the economy’s resources from those households that wish to save some of their income for the future to those households and fi rms that wish to borrow to buy investment goods to be used in future production. The process of transfer- ring funds from savers to borrowers is called fi nancial intermediation. Many institutions in the economy act as fi nancial intermediaries: the most prominent examples are the stock market, the bond market, and the banking system. Yet, of these fi nancial institutions, only banks have the legal authority to create assets (such as checking accounts) that are part of the money supply. Therefore, banks are the only fi nancial institutions that directly infl uence the money supply.

Note that although the system of fractional-reserve banking creates money, it does not create wealth. When a bank loans out some of its reserves, it gives borrowers the ability to make transactions and therefore increases the supply of money. The borrowers are also undertaking a debt obligation to the bank, how- ever, so the loan does not make them wealthier. In other words, the creation of money by the banking system increases the economy’s liquidity, not its wealth.

Bank Capital, Leverage, and Capital Requirements

The model of the banking system presented so far is simplifi ed. That is not necessarily a problem; after all, all models are simplifi ed. But it is worth drawing attention to one particular simplifying assumption.

3Mathematical note: The last step in the derivation of the total money supply uses the algebraic result for the sum of an infi nite geometric series. According to this result, if x is a number between −1 and 1, then

1 + x + x2 + x3 + … = 1/(1 − x). In this application, x = (1 − rr).

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In the bank balance sheets we just examined, a bank takes in deposits and either uses them to make loans or holds them as reserves. Based on this discussion, you might think that it does not take any resources to open up a bank. That is, how- ever, not true. Opening a bank requires some capital. That is, the bank owners must start with some fi nancial resources to get the business going. Those resources are called bank capital or, equivalently, the equity of the bank’s owners.

Here is what a more realistic balance sheet for a bank would look like:

Realbank’s Balance Sheet

Assets Liabilities and Owners’ Equity

Reserves $200 Deposits $750

Loans $500 Debt $200

Securities $300 Capital (owners’ equity) $50

The bank obtains resources from its owners, who provide capital, and also by taking in deposits and issuing debt. It uses these resources in three ways. Some funds are held as reserves; some are used to make bank loans; and some are used to buy fi nancial securities, such as government or corporate bonds. The bank allocates its resources among these asset classes, taking into account the risk and return that each offers and any regulations that restrict its choices. The reserves, loans, and securities on the left side of the balance sheet must equal, in total, the deposits, debt, and capital on the right side of the balance sheet.

This business strategy relies on a phenomenon called leverage, which is the use of borrowed money to supplement existing funds for purposes of investment. The leverage ratio is the ratio of the bank’s total assets (the left side of the balance sheet) to bank capital (the one item on the right side of the balance sheet that represents the owners’ equity). In this example, the leverage ratio is $1000/$50, or 20. This means that for every dollar of capital that the bank owners have con- tributed, the bank has $20 of assets and, thus, $19 of deposits and debts.

One implication of leverage is that, in bad times, a bank can lose much of its capital very quickly. To see how, let’s continue with this numerical example. If the bank’s assets fall in value by a mere 5 percent, then the $1,000 of assets is now worth only $950. Because the depositors and debt holders have the legal right to be paid fi rst, the value of the owners’ equity falls to zero. That is, when the leverage ratio is 20, a 5 percent fall in the value of the bank assets leads to a 100 percent fall in bank capital. The fear that bank capital may be running out, and thus that depositors may not be fully repaid, is typically what generates bank runs when there is no deposit insurance.

One of the restrictions that bank regulators put on banks is that the banks must hold suffi cient capital. The goal of such a capital requirement is to ensure that banks will be able to pay off their depositors. The amount of capital required depends on the kind of assets a bank holds. If the bank holds safe assets such as government bonds, regulators require less capital than if the bank holds risky assets such as loans to borrowers whose credit is of dubious quality.

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4-3 How Central Banks Influence the Money Supply

Now that we have seen what money is and how the banking system affects the amount of money in the economy, we are ready to examine how the central bank infl uences the banking system and the money supply. This infl uence is the essence of monetary policy.

A Model of the Money Supply

We begin by presenting a model of the money supply under fractional-reserve banking. The model has three exogenous variables:

■ The monetary base B is the total number of dollars held by the public as currency C and by the banks as reserves R. It is directly controlled by the Federal Reserve.

■ The reserve–deposit ratio rr is the fraction of deposits that banks hold in reserve. It is determined by the business policies of banks and the laws regulating banks.

■ The currency–deposit ratio cr is the amount of currency C people hold as a fraction of their holdings of demand deposits D. It refl ects the preferences of households about the form of money they wish to hold.

Our model shows how the money supply depends on the monetary base, the reserve–deposit ratio, and the currency–deposit ratio. It allows us to examine how Fed policy and the choices of banks and households infl uence the money supply.

We begin with the defi nitions of the money supply and the monetary base:

M = C + D,

B = C + R.

The fi rst equation states that the money supply is the sum of currency and demand deposits. The second equation states that the monetary base is the sum of currency and bank reserves. To solve for the money supply as a function of the three exogenous variables (B, rr, and cr), we divide the fi rst equation by the second to obtain

M C + D = . B C + R

We then divide both the top and bottom of the expression on the right by D.

M C/D + 1 = . B C/D + R/D

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Note that C/D is the currency–deposit ratio cr and that R/D is the reserve– deposit ratio rr. Making these substitutions, and bringing the B from the left to the right side of the equation, we obtain

cr + 1 M = × B. cr + rr

This equation shows how the money supply depends on the three exogenous variables.

We can now see that the money supply is proportional to the monetary base. The factor of proportionality, (cr + 1)/(cr + rr), is denoted m and is called the money multiplier. We can write

M = m × B.

Each dollar of the monetary base produces m dollars of money. Because the monetary base has a multiplied effect on the money supply, the monetary base is sometimes called high-powered money.

Here’s a numerical example. Suppose that the monetary base B is $800 billion, the reserve–deposit ratio rr is 0.1, and the currency–deposit ratio cr is 0.8. In this case, the money multiplier is

0.8 + 1 m = = 2.0, 0.8 + 0.1

and the money supply is

M = 2.0 × $800 billion = $1,600 billion.

Each dollar of the monetary base generates two dollars of money, so the total money supply is $1,600 billion.

We can now see how changes in the three exogenous variables—B, rr, and cr—cause the money supply to change.

1. The money supply is proportional to the monetary base. Thus, an increase in the monetary base increases the money supply by the same percentage.

2. The lower the reserve–deposit ratio, the more loans banks make, and the more money banks create from every dollar of reserves. Thus, a decrease in the reserve–deposit ratio raises the money multiplier and the money supply.

3. The lower the currency–deposit ratio, the fewer dollars of the monetary base the public holds as currency, the more base dollars banks hold as reserves, and the more money banks can create. Thus, a decrease in the currency–deposit ratio raises the money multiplier and the money supply.

With this model in mind, we can discuss the ways in which the Fed infl uences the money supply.

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The Instruments of Monetary Policy

Although it is often convenient to make the simplifying assumption that the Federal Reserve controls the money supply directly, in fact the Fed controls the money supply indirectly using a variety of instruments. These instruments can be classifi ed into two broad groups: those that infl uence the monetary base and those that infl uence the reserve–deposit ratio and thereby the money multiplier.

How the Fed Changes the Monetary Base As we discussed earlier in the chapter, open-market operations are the purchases and sales of government bonds by the Fed. When the Fed buys bonds from the public, the dollars it pays for the bonds increase the monetary base and thereby increase the money supply. When the Fed sells bonds to the public, the dollars it receives reduce the monetary base and thus decrease the money supply. Open-market operations are the policy instrument that the Fed uses most often. In fact, the Fed conducts open-market operations in New York bond markets almost every weekday.

The Fed can also alter the monetary base and the money supply by lending reserves to banks. Banks borrow from the Fed when they think they do not have enough reserves on hand, either to satisfy bank regulators, meet depositor withdrawals, make new loans, or satisfy some other business requirement. When the Fed lends to a bank that is having trouble obtaining funds from elsewhere, it is said to act as the lender of last resort.

There are various ways in which banks can borrow from the Fed. Traditionally, banks have borrowed at the Fed’s so-called discount window; the discount rate is the interest rate that the Fed charges on these loans. The lower the discount rate, the cheaper are borrowed reserves, and the more banks borrow at the Fed’s discount window. Hence, a reduction in the discount rate raises the monetary base and the money supply.

In recent years, the Federal Reserve has set up new mechanisms for banks to borrow from it. For example, under the Term Auction Facility, the Fed sets a quantity of funds it wants to lend to banks, and eligible banks then bid to borrow those funds. The loans go to the highest eligible bidders—that is, to the banks that have acceptable collateral and are offering to pay the highest interest rate. Unlike at the discount window, where the Fed sets the price of a loan and the banks determine the quantity of borrowing, at the Term Auction Facility the Fed sets the quantity of borrowing and a competitive bidding process among banks determines the price. The more funds the Fed makes available through this and similar facilities, the greater the monetary base and the money supply.

How the Fed Changes the Reserve–Deposit Ratio As our model of the money supply shows, the money multiplier is the link between the monetary base and the money supply. The money multiplier depends on the reserve– deposit ratio, which in turn is infl uenced by various Fed policy instruments.

Reserve requirements are Fed regulations that impose a minimum reserve– deposit ratio on banks. An increase in reserve requirements tends to raise the reserve–deposit ratio and thus lower the money multiplier and the money supply. Changes in reserve requirements are the least frequently used of the Fed’s

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policy instruments. Moreover, in recent years, this particular tool has become less effective because many banks hold more reserves than are required. Reserves above the minimum required are called excess reserves.

In October 2008, the Fed started paying interest on reserves. That is, when a bank holds reserves on deposit at the Fed, the Fed now pays the bank interest on those deposits. This change gives the Fed another tool with which to infl u- ence the economy. The higher the interest rate on reserves, the more reserves banks will choose to hold. Thus, an increase in the interest rate on reserves will tend to increase the reserve–deposit ratio, lower the money multiplier, and lower the money supply. Because the Fed has paid interest on reserves for a relatively short time, it is not yet clear how important this new instrument will be in the conduct of monetary policy.

Quantitative Easing and the Exploding Monetary Base

Figure 4-1 shows the monetary base from 1960 to 2011. You can see that some- thing extraordinary happened in the last few years of this period. From 1960 to 2007, the monetary base grew gradually over time. But then from 2007 to 2011 it spiked up substantially, approximately tripling over just a few years.

This huge increase in the monetary base is attributable to actions the Federal Reserve took during the fi nancial crisis and economic downturn of this period.

CASE STUDY

The Monetary Base The monetary base has historically grown relatively smoothly over time, but from 2007 to 2011 it increased approximately threefold. The huge expansion in the monetary base, however, was not accompanied by similar increases in M1 and M2.

FIGURE 4-1 Monetary base

(billions of dollars)

1960 1965 1970 1975 Year

1980 1985 1990 1995 2005 20102000

1,000

1,500

2,000

2,500

3,000

500

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With the fi nancial markets in turmoil, the Fed pursued its job as a lender of last resort with historic vigor. It began by buying large quantities of mortgage-backed securities. Its goal was to restore order to the mortgage market so that would-be homeowners could borrow. Later, the Fed pursued a policy of buying long-term government bonds to keep their prices up and long-term interest rates down. This policy, called quantitative easing, is a kind of open-market operation. But rather than buying short-term Treasury bills, as the Fed normally does in an open-market operation, it bought longer-term and somewhat riskier securities. These open- market purchases led to the substantial increase in the monetary base.

The huge expansion in the monetary base, however, did not lead to a similar increase in broader measures of the money supply. While the monetary base increased about 200 percent from 2007 to 2011, M1 increased by only 40 percent and M2 by only 25 percent. These fi gures show that the tremendous expansion in the monetary base was accompanied by a large decline in the money multiplier. Why did this decline occur?

The model of the money supply presented earlier in this chapter shows that a key determinant of the money multiplier is the reserve ratio rr. From 2007 to 2011, the reserve ratio increased substantially because banks chose to hold sub- stantial quantities of excess reserves. That is, rather than making loans, the banks kept much of their available funds in reserve. This decision prevented the normal process of money creation that occurs in a system of fractional-reserve banking.

Why did banks choose to hold so much in excess reserves? Part of the reason is that banks had made many bad loans leading up to the fi nancial crisis; when this fact became apparent, bankers tried to tighten their credit standards and make loans only to those they were confi dent could repay. In addition, interest rates had fallen to such low levels that making loans was not as profi table as it normally is. Banks did not lose much by leaving their fi nancial resources idle as excess reserves.

Although the explosion in the monetary base did not lead to a similar explosion in the money supply, some observers feared that it still might. As the economy recovered from the economic downturn and interest rates rose to normal levels, they argued, banks could reduce their holdings of excess reserves by making loans. The money supply would start growing, perhaps too quickly.

Policymakers at the Federal Reserve, however, thought they could handle this problem if and when it arose. One possibility would be to drain the banking system of reserves by engaging in the opposite open-market operation that had created them in the fi rst place—that is, by selling the Treasury bonds and other securities in the Fed’s portfolio. Another policy option for the Fed would be to increase the interest rate it pays on reserves. A higher interest on reserves would make holding reserves more profi table for banks, thereby discouraging bank lend- ing and keeping the money multiplier low. Which of these “exit strategies” the Fed would use was still to be determined as this book was going to press. ■

Problems in Monetary Control

The various instruments give the Fed substantial power to infl uence the money supply. Nonetheless, the Fed cannot control the money supply perfectly. Bank discretion in conducting business can cause the money supply to change in

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ways the Fed did not anticipate. For example, banks may choose to hold more excess reserves, a decision that increases the reserve–deposit ratio and lowers the money supply. As another example, the Fed cannot precisely control the amount banks borrow from the discount window. The less banks borrow, the smaller the monetary base, and the smaller the money supply. Hence, the money supply sometimes moves in ways the Fed does not intend.

Bank Failures and the Money Supply in the 1930s

Between August 1929 and March 1933, the money supply fell 28 percent. As we will discuss in Chapter 12, some economists believe that this large decline in the money supply was the primary cause of the Great Depression of the 1930s, when unemployment reached unprecendented levels, prices fell precipitously, and eco- nomic hardship was widepread. In light of this hypothesis, one is naturally drawn to ask why the money supply fell so dramatically.

The three variables that determine the money supply—the monetary base, the reserve–deposit ratio, and the currency–deposit ratio—are shown in Table 4-2 for 1929 and 1933. You can see that the fall in the money supply cannot be attributed to a fall in the monetary base: in fact, the monetary base rose 18 per- cent over this period. Instead, the money supply fell because the money multi- plier fell 38 percent. The money multiplier fell because the currency–deposit and reserve–deposit ratios both rose substantially.

Most economists attribute the fall in the money multiplier to the large number of bank failures in the early 1930s. From 1930 to 1933, more than 9,000 banks suspended operations, often defaulting on their depositors. The bank failures caused the money supply to fall by altering the behavior of both depositors and bankers.

CASE STUDY

August 1929 March 1933

Money Supply 26.5 19.0 Currency 3.9 5.5 Demand deposits 22.6 13.5

Monetary Base 7.1 8.4 Currency 3.9 5.5 Reserves 3.2 2.9

Money Multiplier 3.7 2.3 Reserve–deposit ratio 0.14 0.21 Currency–deposit ratio 0.17 0.41

Source: Adapted from Milton Friedman and Anna Schwartz, A Monetary History of the United States, 1867–1960 (Princeton, N.J.: Princeton University Press, 1963), Appendix A.

The Money Supply and Its Determinants: 1929 and 1933

TABLE 4-2

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Bank failures raised the currency–deposit ratio by reducing public confi dence in the banking system. People feared that bank failures would continue, and they began to view currency as a more desirable form of money than demand depos- its. When they withdrew their deposits, they drained the banks of reserves. The process of money creation reversed itself, as banks responded to lower reserves by reducing their outstanding balance of loans.

In addition, the bank failures raised the reserve–deposit ratio by making bankers more cautious. Having just observed many bank runs, bankers became apprehensive about operating with a small amount of reserves. They therefore increased their holdings of reserves to well above the legal minimum. Just as households responded to the banking crisis by holding more currency relative to deposits, bankers responded by holding more reserves relative to loans. Together these changes caused a large fall in the money multiplier.

Although it is easy to explain why the money supply fell, it is more diffi cult to decide whether to blame the Federal Reserve. One might argue that the monetary base did not fall, so the Fed should not be blamed. Critics of Fed policy during this period make two counterarguments. First, they claim that the Fed should have taken a more vigorous role in preventing bank failures by acting as a lender of last resort when banks needed cash during bank runs. This would have helped main- tain confi dence in the banking system and prevented the large fall in the money multiplier. Second, they point out that the Fed could have responded to the fall in the money multiplier by increasing the monetary base even more than it did. Either of these actions would likely have prevented such a large fall in the money supply, which in turn might have reduced the severity of the Great Depression.

Since the 1930s, many policies have been put into place that make such a large and sudden fall in the money multiplier less likely today. Most important, the sys- tem of federal deposit insurance protects depositors when a bank fails. This policy is designed to maintain public confi dence in the banking system and thus prevents large swings in the currency–deposit ratio. Deposit insurance has a cost: in the late 1980s and early 1990s, for example, the federal government incurred the large expense of bailing out many insolvent savings-and-loan institutions. Yet deposit insurance helps stabilize the banking system and the money supply. That is why, during the fi nancial crisis of 2008–2009, the Federal Deposit Insurance Corpora- tion raised the amount guaranteed from $100,000 to $250,000 per depositor. ■

4-4 Conclusion

You should now understand what money is and how central banks affect its supply. Yet this accomplishment, valuable as it is, is only the fi rst step toward understanding monetary policy. The next and more interesting step is to see how changes in the money supply infl uence the economy. We begin our study of that question in the next chapter. As we examine the effects of monetary policy, we move toward an appreciation of what central bankers can do to improve the functioning of the economy and, just as important, an appreciation of what they cannot do. But be forewarned: you will have to wait until the end of the book to see all the pieces of the puzzle fall into place.

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Summary

1. Money is the stock of assets used for transactions. It serves as a store of value, a unit of account, and a medium of exchange. Different sorts of assets are used as money: commodity money systems use an asset with intrinsic value, whereas fi at money systems use an asset whose sole function is to serve as money. In modern economies, a central bank such as the Federal Reserve is responsible for controlling the supply of money.

2. The system of fractional-reserve banking creates money because each dollar of reserves generates many dollars of demand deposits.

3. To start a bank, the owners must contribute some of their own fi nancial resources, which become the bank’s capital. Because banks are highly leveraged, however, a small decline in the value of their assets can poten- tially have a major impact on the value of bank capital. Bank regulators require that banks hold suffi cient capital to ensure that depositors can be repaid.

4. The supply of money depends on the monetary base, the reserve–deposit ratio, and the currency–deposit ratio. An increase in the monetary base leads to a proportionate increase in the money supply. A decrease in the reserve– deposit ratio or in the currency–deposit ratio increases the money multi- plier and thus the money supply.

5. The Federal Reserve infl uences the money supply either by changing the monetary base or by changing the reserve ratio and thereby the money multiplier. It can change the monetary base through open-market opera- tions or by making loans to banks. It can infl uence the reserve ratio by altering reserve requirements or by changing the interest rate it pays banks for reserves they hold.

K E Y C O N C E P T S

Money

Store of value

Unit of account

Medium of exchange

Fiat money

Commodity money

Gold standard

Money supply

Monetary policy

Central bank

Federal Reserve

Open-market operations

Currency

Demand deposits

Reserves

100-percent-reserve banking

Balance sheet

Fractional-reserve banking

Financial intermediation

Bank capital

Leverage

Capital requirement

Monetary base

Reserve–deposit ratio

Currency–deposit ratio

Money multiplier

High-powered money

Discount rate

Reserve requirements

Excess reserves

Interest on reserves

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100 | P A R T I I Classical Theory: The Economy in the Long Run

1. Describe the functions of money.

2. What is fi at money? What is commodity money?

3. What are open-market operations, and how do they infl uence the money supply?

Q U E S T I O N S F O R R E V I E W

4. Explain how banks create money.

5. What are the various ways in which the Federal Reserve can infl uence the money supply?

6. Why might a banking crisis lead to a fall in the money supply?

1. What are the three functions of money? Which of the functions do the following items satisfy? Which do they not satisfy?

a. A credit card

b. A painting by Rembrandt

c. A subway token

2. Explain how each of the following events affects the monetary base, the money multiplier, and the money supply.

a. The Federal Reserve buys bonds in an open- market operation.

b. The Fed increases the interest rate it pays banks for holding reserves.

c. The Fed reduces its lending to banks through its Term Auction Facility.

d. Rumors about a computer virus attack on ATMs increase the amount of money people hold as currency rather than demand deposits.

e. The Fed fl ies a helicopter over 5th Avenue in New York City and drops newly printed $100 bills.

3. An economy has a monetary base of 1,000 $1 bills. Calculate the money supply in scenarios (a)–(d) and then answer part (e).

a. All money is held as currency.

b. All money is held as demand deposits. Banks hold 100 percent of deposits as reserves.

c. All money is held as demand deposits. Banks hold 20 percent of deposits as reserves.

d. People hold equal amounts of currency and demand deposits. Banks hold 20 percent of deposits as reserves.

e. The central bank decides to increase the money supply by 10 percent. In each of the

P R O B L E M S A N D A P P L I C A T I O N S

above four scenarios, how much should it increase the monetary base?

4. As a Case Study in the chapter discusses, the money supply fell from 1929 to 1933 because both the currency–deposit ratio and the reserve–deposit ratio increased. Use the model of the money sup- ply and the data in Table 4-2 to answer the follow- ing hypothetical questions about this episode.

a. What would have happened to the money sup- ply if the currency–deposit ratio had risen but the reserve–deposit ratio had remained the same?

b. What would have happened to the money sup- ply if the reserve–deposit ratio had risen but the currency–deposit ratio had remained the same?

c. Which of the two changes was more respon- sible for the fall in the money supply?

5. To increase tax revenue, the U.S. government in 1932 imposed a 2-cent tax on checks written on bank account deposits. (In today’s dollars, this tax would amount to about 34 cents per check.)

a. How do you think the check tax affected the currency–deposit ratio? Explain.

b. Use the model of the money supply under fractional-reserve banking to discuss how this tax affected the money supply.

c. Many economists believe that a falling money supply was in part responsible for the severity of the Great Depression of the 1930s. From this perspective, was the check tax a good policy to implement in the middle of the Great Depression?

6. Give an example of a bank balance sheet with a leverage ratio of 10. If the value of the bank’s assets rises by 5 percent, what happens to the value of the owners’ equity in this bank? How large a decline in the value of bank assets would it take to reduce this bank’s capital to zero?

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101

Infl ation: Its Causes, Effects, and Social Costs

5C H A P T E R

Lenin is said to have declared that the best way to destroy the Capitalist

System was to debauch the currency. . . . Lenin was certainly right. There is

no subtler, no surer means of overturning the existing basis of society than to

debauch the currency. The process engages all the hidden forces of economic law

on the side of destruction, and does it in a manne r which not one man in a

million is able to diagnose.

—John Maynard Keynes

In 1970 the New York Times cost 15 cents, the median price of a single-family home was $23,400, and the average wage in manufacturing was $3.36 per hour. In 2011 the Times cost $2, the median price of a home was $209,100, and the average wage was $23.09 per hour. This overall increase in prices is called infl ation, which is the subject of this chapter.

The rate of infl ation—the percentage change in the overall level of prices— varies greatly over time and across countries. In the United States, according to the consumer price index, prices rose at an average annual rate of 2.4 percent in the 1960s, 7.1 percent in the 1970s, 5.5 percent in the 1980s, 3.0 percent in the 1990s, and 2.3 percent in the 2000s. Even when the U.S. infl ation problem became severe during the 1970s, however, it was nothing compared to the epi- sodes of extraordinarily high infl ation, called hyperinfl ation, that other countries have experienced from time to time. A classic example is Germany in 1923, when prices increased an average of 500 percent per month. In 2008, a similar hyperinfl ation gripped the nation of Zimbabwe.

In this chapter we examine the classical theory of the causes, effects, and social costs of infl ation. The theory is “classical” in the sense that it assumes that prices are fl exible. As we fi rst discussed in Chapter 1, most economists believe this assumption describes the behavior of the economy in the long run. By contrast, many prices are thought to be sticky in the short run, and beginning in Chap- ter 10 we incorporate this fact into our analysis. For now, we ignore short-run price stickiness. As we will see, the classical theory of infl ation not only provides a good description of the long run, it also provides a useful foundation for the short-run analysis we develop later.

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The “hidden forces of economic law” that lead to infl ation are not as mys- terious as Keynes claims in the quotation that opens this chapter. Infl ation is simply an increase in the average level of prices, and a price is the rate at which money is exchanged for a good or a service. To understand infl ation, therefore, we must understand money—what it is, what affects its supply and demand, and what infl uence it has on the economy. In the previous chapter, we introduced the economist’s concept of “money” and discussed how, in most modern econo- mies, a central bank set up by the government controls the quantity of money in the hands of the public. This chapter begins in Section 5-1 by showing that the quantity of money determines the price level and that the rate of growth in the quantity of money determines the rate of infl ation.

Infl ation in turn has numerous effects of its own on the economy. Section 5-2 discusses the revenue that governments can raise by printing money, sometimes called the infl ation tax. Section 5-3 examines how infl ation affects the nominal interest rate. Section 5-4 discusses how the nominal interest rate in turn affects the quantity of money people wish to hold and, thereby, the price level.

After completing our analysis of the causes and effects of infl ation, in Sec- tion 5-5 we address what is perhaps the most important question about infl ation: Is it a major social problem? Does infl ation amount to “overturning the existing basis of society,’’ as the chapter’s opening quotation suggests?

Finally, in Section 5-6, we discuss the dramatic case of hyperinfl ation. Hyper- infl ations are interesting to examine because they show clearly the causes, effects, and costs of infl ation. Just as seismologists learn much by studying earthquakes, economists learn much by studying how hyperinfl ations begin and end.

5-1 The Quantity Theory of Money

In Chapter 4 we defi ned what money is and learned that the quantity of money available in the economy is called the money supply. We also saw how the money supply is determined by the banking system together with the policy decisions of the central bank. With that foundation, we can now start to examine the broad macroeconomic effects of monetary policy. To do this, we need a theory that tells us how the quantity of money is related to other economic variables, such as prices and incomes. The theory we develop in this section, called the quantity theory of money, has its roots in the work of the early monetary theorists, including the philosopher and economist David Hume (1711–1776). It remains the leading explanation for how money affects the economy in the long run.

Transactions and the Quantity Equation

If you hear an economist use the word “supply,” you can be sure that the word “demand” is not far behind. Indeed, having fully explored the supply of money, we now focus on the demand for it.

The starting point of the quantity theory of money is the insight that people hold money to buy goods and services. The more money they need for such

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transactions, the more money they hold. Thus, the quantity of money in the economy is related to the number of dollars exchanged in transactions.

The link between transactions and money is expressed in the following equa- tion, called the quantity equation:

Money × Velocity = Price × Transactions

M × V = P × T.

Let’s examine each of the four variables in this equation. The right-hand side of the quantity equation tells us about transactions.

T represents the total number of transactions during some period of time, say, a year. In other words, T is the number of times in a year that goods or services are exchanged for money. P is the price of a typical transaction—the number of dollars exchanged. The product of the price of a transaction and the number of transactions, PT, equals the number of dollars exchanged in a year.

The left-hand side of the quantity equation tells us about the money used to make the transactions. M is the quantity of money. V, called the transactions velocity of money, measures the rate at which money circulates in the econ- omy. In other words, velocity tells us the number of times a dollar bill changes hands in a given period of time.

For example, suppose that 60 loaves of bread are sold in a given year at $0.50 per loaf. Then T equals 60 loaves per year, and P equals $0.50 per loaf. The total number of dollars exchanged is

PT = $0.50/loaf × 60 loaves/year = $30/year.

The right-hand side of the quantity equation equals $30 per year, the dollar value of all transactions.

Suppose further that the quantity of money in the economy is $10. By re arranging the quantity equation, we can compute velocity as

V = PT/M

= ($30/year)/($10)

= 3 times per year.

That is, for $30 of transactions per year to take place with $10 of money, each dollar must change hands 3 times per year.

The quantity equation is an identity: the defi nitions of the four variables make it true. This type of equation is useful because it shows that if one of the variables changes, one or more of the others must also change to maintain the equality. For example, if the quantity of money increases and the velocity of money remains unchanged, then either the price or the number of transactions must rise.

From Transactions to Income

When studying the role of money in the economy, economists usually use a slightly different version of the quantity equation than the one just introduced.

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The problem with the fi rst equation is that the number of transactions is diffi cult to measure. To solve this problem, the number of transactions T is replaced by the total output of the economy Y.

Transactions and output are related because the more the economy produces, the more goods are bought and sold. They are not the same, however. When one person sells a used car to another person, for example, they make a transaction using money, even though the used car is not part of current output. Nonetheless, the dollar value of transactions is roughly proportional to the dollar value of output.

If Y denotes the amount of output and P denotes the price of one unit of output, then the dollar value of output is PY. We encountered measures for these variables when we discussed the national income accounts in Chapter 2: Y is real GDP; P, the GDP defl ator; and PY, nominal GDP. The quantity equation becomes

Money × Velocity = Price × Output

M × V = P × Y.

Because Y is also total income, V in this version of the quantity equation is called the income velocity of money. The income velocity of money tells us the number of times a dollar bill enters someone’s income in a given period of time. This version of the quantity equation is the most common, and it is the one we use from now on.

The Money Demand Function and the Quantity Equation

When we analyze how money affects the economy, it is often useful to express the quantity of money in terms of the quantity of goods and services it can buy. This amount, M/P, is called real money balances.

Real money balances measure the purchasing power of the stock of money. For example, consider an economy that produces only bread. If the quantity of money is $10, and the price of a loaf is $0.50, then real money balances are 20 loaves of bread. That is, at current prices, the stock of money in the economy is able to buy 20 loaves.

A money demand function is an equation that shows the determinants of the quantity of real money balances people wish to hold. A simple money demand function is

(M/P )d = kY,

where k is a constant that tells us how much money people want to hold for every dollar of income. This equation states that the quantity of real money bal- ances demanded is proportional to real income.

The money demand function is like the demand function for a particular good. Here the “good” is the convenience of holding real money balances. Just as owning an automobile makes it easier for a person to travel, holding money

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makes it easier to make transactions. Therefore, just as higher income leads to a greater demand for automobiles, higher income also leads to a greater demand for real money balances.

This money demand function offers another way to view the quantity equa- tion. To see this, add to the money demand function the condition that the demand for real money balances (M/P)d must equal the supply M/P. Therefore,

M/P = kY.

A simple rearrangement of terms changes this equation into

M(1/k) = PY,

which can be written as

MV = PY,

where V = 1/k. These few steps of simple mathematics show the link between the demand for money and the velocity of money. When people want to hold a lot of money for each dollar of income (k is large), money changes hands infre- quently (V is small). Conversely, when people want to hold only a little money (k is small), money changes hands frequently (V is large). In other words, the money demand parameter k and the velocity of money V are opposite sides of the same coin.

The Assumption of Constant Velocity

The quantity equation can be viewed as a defi nition: it defi nes velocity V as the ratio of nominal GDP, PY, to the quantity of money M. Yet if we make the additional assumption that the velocity of money is constant, then the quantity equation becomes a useful theory about the effects of money, called the quantity theory of money.

As with many of the assumptions in economics, the assumption of constant velocity is only a simplifi cation of reality. Velocity does change if the money demand function changes. For example, when automatic teller machines were introduced, people could reduce their average money holdings, which meant a fall in the money demand parameter k and an increase in velocity V. Nonethe- less, experience shows that the assumption of constant velocity is a useful one in many situations. Let’s therefore assume that velocity is constant and see what this assumption implies about the effects of the money supply on the economy.

With this assumption included, the quantity equation can be seen as a theory of what determines nominal GDP. The quantity equation says

M V– = P Y,

where the bar over V means that velocity is fi xed. Therefore, a change in the quantity of money (M ) must cause a proportionate change in nominal GDP (PY ). That is, if velocity is fi xed, the quantity of money determines the dollar value of the economy’s output.

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106 | P A R T I I Classical Theory: The Economy in the Long Run

Money, Prices, and Inflation

We now have a theory to explain what determines the economy’s overall level of prices. The theory has three building blocks:

1. The factors of production and the production function determine the level of output Y. We borrow this conclusion from Chapter 3.

2. The money supply M set by the central bank determines the nominal value of output PY. This conclusion follows from the quantity equation and the assumption that the velocity of money is fi xed.

3. The price level P is then the ratio of the nominal value of output PY to the level of output Y.

In other words, the productive capability of the economy determines real GDP, the quantity of money determines nominal GDP, and the GDP defl ator is the ratio of nominal GDP to real GDP.

This theory explains what happens when the central bank changes the supply of money. Because velocity V is fi xed, any change in the money supply M must lead to a proportionate change in the nominal value of output PY. Because the factors of production and the production function have already determined output Y, the nominal value of output PY can adjust only if the price level P changes. Hence, the quantity theory implies that the price level is proportional to the money supply.

Because the infl ation rate is the percentage change in the price level, this theory of the price level is also a theory of the infl ation rate. The quantity equa- tion, written in percentage-change form, is

% Change in M + % Change in V = % Change in P + % Change in Y.

Consider each of these four terms. First, the percentage change in the quantity of money M is under the control of the central bank. Second, the percentage change in velocity V refl ects shifts in money demand; we have assumed that velocity is constant, so the percentage change in velocity is zero. Third, the per- centage change in the price level P is the rate of infl ation; this is the variable in the equation that we would like to explain. Fourth, the percentage change in output Y depends on growth in the factors of production and on technological progress, which for our present purposes we are taking as given. This analysis tells us that (except for a constant that depends on exogenous growth in output) the growth in the money supply determines the rate of infl ation.

Thus, the quantity theory of money states that the central bank, which controls the money supply, has ultimate control over the rate of infl ation. If the central bank keeps the money supply stable, the price level will be stable. If the central bank increases the money supply rapidly, the price level will rise rapidly.

Inflation and Money Growth

“Infl ation is always and everywhere a monetary phenomenon.” So wrote Milton Friedman, the great economist who won the Nobel Prize in economics in 1976.

CASE STUDY

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C H A P T E R 5 Inflation: Its Causes, Effects, and Social Costs | 107

FIGURE 5-1

Historical Data on U.S. Infl ation and Money Growth In this scatterplot of money growth and infl ation, each point represents a decade. The horizontal axis shows the average growth in the money supply (as measured by M2) over the decade, and the vertical axis shows the average rate of infl ation (as measured by the GDP defl a- tor). The positive correlation between money growth and infl ation is evidence for the quantity theory’s prediction that high money growth leads to high infl ation.

Source: For the data through the 1960s: Milton Friedman and Anna J. Schwartz, Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates 1867–1975 (Chicago: University of Chicago Press, 1982). For recent data: U.S. Department of Commerce and Federal Reserve Board.

Growth in money supply (percent)

1970s

1910s 1940s

1980s

1960s 1950s

1990s

2000s

1930s

1920s

1870s

1890s

1880s

1900s

Inflation rate (percent)

0 2 4 6 8 10 12

8

6

4

2

0

–2

–4

1Milton Friedman and Anna J. Schwartz, A Monetary History of the United States, 1867–1960 (Princeton, N.J.: Princeton University Press, 1963); Milton Friedman and Anna J. Schwartz, Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates, 1867–1975 (Chicago: University of Chicago Press, 1982).

The quantity theory of money leads us to agree that the growth in the quantity of money is the primary determinant of the infl ation rate. Yet Friedman’s claim is empirical, not theoretical. To evaluate his claim, and to judge the usefulness of our theory, we need to look at data on money and prices.

Friedman, together with fellow economist Anna Schwartz, wrote two treatises on monetary history that documented the sources and effects of changes in the quantity of money over the past century.1 Figure 5-1 uses some of their data and plots the average rate of money growth and the average rate of infl ation in the United States over each decade since the 1870s. The data verify the link between infl ation and growth in the quantity of money. Decades with high money growth

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108 | P A R T I I Classical Theory: The Economy in the Long Run

FIGURE 5-2

International Data on Infl ation and Money Growth In this scatterplot, each point represents a country. The horizontal axis shows the average growth in the money supply (as measured by currency plus demand deposits) during the period 2000 to 2010, and the vertical axis shows the average rate of infl ation (as measured by the CPI). Once again, the positive correlation is evidence for the quantity theory’s prediction that high money growth leads to high infl ation.

Source: International Monetary Fund.

Inflation rate (percent)

40.0

Money supply growth (percent) 0 10 20 30 40 50

Argentina

Belarus

China

Iraq

Malta

SingaporeSwitzerland

Turkey

United States

–5.0

5.0

0

10.0

15.0

20.0

25.0

30.0

35.0

–10

(such as the 1970s) tend to have high infl ation, and decades with low money growth (such as the 1930s) tend to have low infl ation.

As you may have learned in a statistics class, one way to quantity a relationship between two variables is with a measure called correlation. A correlation is �1 if the two variables move exactly in tandem, 0 if they are unrelated, and –1 if they move exactly opposite each other. In Figure 5-1, the correlation is 0.79.

Figure 5-2 examines the same question using international data. It shows the average rate of infl ation and the average rate of money growth in over 100 coun- tries during the period from 2000 to 2010. Again, the link between money growth and infl ation is clear. Countries with high money growth (such as Turkey and Belarus) tend to have high infl ation, and countries with low money growth (such as Singapore and Switzerland) tend to have low infl ation. The correlation here is 0.61.

If we looked at monthly data on money growth and infl ation, rather than data for decade-long periods, we would not see as close a connection between these two variables. This theory of infl ation works best in the long run, not in the short run. We examine the short-run impact of changes in the quantity of money when we turn to economic fl uctuations in Part Four of this book. ■

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5-2 Seigniorage: The Revenue From Printing Money

So far, we have seen how growth in the money supply causes infl ation. With infl ation as a consequence, what would ever induce a central bank to increase the money supply substantially? Here we examine one answer to this question.

Let’s start with an indisputable fact: all governments spend money. Some of this spending is to buy goods and services (such as roads and police), and some is to provide transfer payments (for the poor and elderly, for example). A government can fi nance its spending in three ways. First, it can raise revenue through taxes, such as personal and corporate income taxes. Second, it can borrow from the public by selling government bonds. Third, it can print money.

The revenue raised by the printing of money is called seigniorage. The term comes from seigneur, the French word for “feudal lord.” In the Middle Ages, the lord had the exclusive right on his manor to coin money. Today this right belongs to the central government, and it is one source of revenue.

When the government prints money to fi nance expenditure, it increases the money supply. The increase in the money supply, in turn, causes infl ation. Print- ing money to raise revenue is like imposing an infl ation tax.

At fi rst it may not be obvious that infl ation can be viewed as a tax. After all, no one receives a bill for this tax—the government merely prints the money it needs. Who, then, pays the infl ation tax? The answer is the holders of money. As prices rise, the real value of the money in your wallet falls. Therefore, when the government prints new money for its use, it makes the old money in the hands of the public less valuable. Infl ation is like a tax on holding money.

The amount of revenue raised by printing money varies from country to country. In the United States, the amount has been small: seigniorage has usually accounted for less than 3 percent of government revenue. In Italy and Greece, seigniorage has often been more than 10 percent of government revenue.2 In countries experiencing hyperinfl ation, seigniorage is often the government’s chief source of revenue—indeed, the need to print money to fi nance expenditure is a primary cause of hyperinfl ation.

Paying for the American Revolution

Although seigniorage has not been a major source of revenue for the U.S. gov- ernment in recent history, the situation was very different two centuries ago. Beginning in 1775, the Continental Congress needed to fi nd a way to fi nance the Revolution, but it had limited ability to raise revenue through taxation. It therefore relied on the printing of fi at money to help pay for the war.

The Continental Congress’s reliance on seigniorage increased over time. In 1775 new issues of continental currency were about $6 million. This amount increased to $19 million in 1776, $13 million in 1777, $63 million in 1778, and $125 million in 1779.

CASE STUDY

2Stanley Fischer, “Seigniorage and the Case for a National Money,’’ Journal of Political Economy 90 (April 1982): 295–313.

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110 | P A R T I I Classical Theory: The Economy in the Long Run

5-3 Inflation and Interest Rates

As we fi rst discussed in Chapter 3, interest rates are among the most important macroeconomic variables. In essence, they are the prices that link the present and the future. Here we discuss the relationship between infl ation and interest rates.

Two Interest Rates: Real and Nominal

Suppose you deposit your savings in a bank account that pays 8 percent interest annually. Next year, you withdraw your savings and the accumulated interest. Are you 8 percent richer than you were when you made the deposit a year earlier?

The answer depends on what “richer’’ means. Certainly, you have 8 percent more dollars than you had before. But if prices have risen, each dollar buys less, and your purchasing power has not risen by 8 percent. If the infl ation rate was 5 percent over the year, then the amount of goods you can buy has increased by only 3 percent. And if the infl ation rate was 10 percent, then your purchasing power has fallen by 2 percent.

The interest rate that the bank pays is called the nominal interest rate, and the increase in your purchasing power is called the real interest rate. If i denotes the nominal interest rate, r the real interest rate, and � the rate of infl a- tion, then the relationship among these three variables can be written as

r = i – �. The real interest rate is the difference between the nominal interest rate and the rate of infl ation.3

The Fisher Effect

Rearranging terms in our equation for the real interest rate, we can show that the nominal interest rate is the sum of the real interest rate and the infl ation rate:

i = r + �. The equation written in this way is called the Fisher equation, after economist Irving Fisher (1867–1947). It shows that the nominal interest rate can change

Not surprisingly, this rapid growth in the money supply led to massive infl a- tion. At the end of the war, the price of gold measured in continental dollars was more than 100 times its level of only a few years earlier. The large quantity of the continental currency made the continental dollar nearly worthless. This experi- ence also gave birth to a once-popular expression: people used to say something was “not worth a continental’’ to mean that the item had little real value.

When the new nation won its independence, there was a natural skepti- cism about fi at money. Upon the recommendation of the fi rst Secretary of the Treasury, Alexander Hamilton, Congress passed the Mint Act of 1792, which established gold and silver as the basis for a new system of commodity money. ■

3Mathematical note: This equation relating the real interest rate, nominal interest rate, and infl ation rate is only an approximation. The exact formula is (1 � r) � (1 � i)/(1 � �). The approximation in the text is reasonably accurate as long as r, i, and � are relatively small (say, less than 20 percent per year).

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for two reasons: because the real interest rate changes or because the infl ation rate changes.

Once we separate the nominal interest rate into these two parts, we can use this equation to develop a theory that explains the nominal interest rate. Chapter 3 showed that the real interest rate adjusts to equilibrate saving and investment. The quantity theory of money shows that the rate of money growth determines the rate of infl ation. The Fisher equation then tells us to add the real interest rate and the infl ation rate together to determine the nominal interest rate.

The quantity theory and the Fisher equation together tell us how money growth affects the nominal interest rate. According to the quantity theory, an increase in the rate of money growth of 1 percent causes a 1 percent increase in the rate of infl ation. According to the Fisher equation, a 1 percent increase in the rate of infl ation in turn causes a 1 percent increase in the nominal interest rate. The one-for-one relation between the infl ation rate and the nominal interest rate is called the Fisher effect.

FIGURE 5-3

Percent 16

14

12

10

8

6

4

4

2

0

1955 1960 1965 1970 Year

1975 1980 1985 1990 2000 2005 20101995 –2

Nominal interest rate

Inflation rate

Infl ation and Nominal Interest Rates Over Time This fi gure plots the nominal interest rate (on three-month Treasury bills) and the infl ation rate (as measured by the CPI) in the United States since 1954. It shows the Fisher effect: higher infl ation leads to a higher nominal interest rate.

Source: Federal Reserve and U.S. Department of Labor.

Inflation and Nominal Interest Rates

How useful is the Fisher effect in explaining interest rates? To answer this ques- tion, we look at two types of data on infl ation and nominal interest rates.

Figure 5-3 shows the variation over time in the nominal interest rate and the infl ation rate in the United States. You can see that the Fisher effect has done a

CASE STUDY

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112 | P A R T I I Classical Theory: The Economy in the Long Run

Two Real Interest Rates: Ex Ante and Ex Post

When a borrower and lender agree on a nominal interest rate, they do not know what the infl ation rate over the term of the loan will be. Therefore, we must distinguish between two concepts of the real interest rate: the real inter- est rate that the borrower and lender expect when the loan is made, called the

FIGURE 5-4

Nominal interest rate (percent)

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

–5 0 5 10 15 20 25 Inflation rate (percent)

Brazil

Germany Israel

Jamaica

Japan

Malawi

Romania

Switzerland

Serbia

Turkey

United States

good job explaining fl uctuations in the nominal interest rate over the past half century. When infl ation is high, nominal interest rates are typically high, and when infl ation is low, nominal interest rates are typically low as well. Their cor- relation is 0.77.

Similar support for the Fisher effect comes from examining the variation across countries. As Figure 5-4 shows, a nation’s infl ation rate and its nominal interest rate are related. Countries with high infl ation tend to have high nominal interest rates as well, and countries with low infl ation tend to have low nominal interest rates. The correlation between these two variables is 0.76.

The link between infl ation and interest rates is well known to Wall Street investment fi rms. Because bond prices move inversely with interest rates, one can get rich by correctly predicting the direction in which interest rates will move. Many Wall Street fi rms hire Fed watchers to monitor monetary policy and news about infl ation to anticipate changes in interest rates. ■

Infl ation and Nominal Interest Rates Across Countries This scatterplot shows the average nominal interest rate on short-term Treasury bills and the average infl ation rate in almost 100 countries during the period 2000 to 2010. The positive correlation between the infl ation rate and the nominal interest rate is evidence for the Fisher effect.

Source: International Monetary Fund.

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ex ante real interest rate, and the real interest rate that is actually realized, called the ex post real interest rate.

Although borrowers and lenders cannot predict future infl ation with certainty, they do have some expectation about what the infl ation rate will be. Let � denote actual future infl ation and E� the expectation of future infl ation. The ex ante real interest rate is i – E�, and the ex post real interest rate is i – �. The two real inter- est rates differ when actual infl ation � differs from expected infl ation E�.

How does this distinction between actual and expected infl ation modify the Fisher effect? Clearly, the nominal interest rate cannot adjust to actual infl ation, because actual infl ation is not known when the nominal interest rate is set. The nominal interest rate can adjust only to expected infl ation. The Fisher effect is more precisely written as

i = r + E�.

The ex ante real interest rate r is determined by equilibrium in the market for goods and services, as described by the model in Chapter 3. The nominal interest rate i moves one-for-one with changes in expected infl ation E�.

Nominal Interest Rates in the Nineteenth Century

Although recent data show a positive relationship between nominal interest rates and infl ation rates, this fi nding is not universal. In data from the late nineteenth and early twentieth centuries, high nominal interest rates did not accompany high infl ation. The apparent absence of any Fisher effect during this time puz- zled Irving Fisher. He suggested that infl ation “caught merchants napping.’’

How should we interpret the absence of an apparent Fisher effect in nine- teenth-century data? Does this period of history provide evidence against the adjustment of nominal interest rates to infl ation? Recent research suggests that this period has little to tell us about the validity of the Fisher effect. The reason is that the Fisher effect relates the nominal interest rate to expected infl ation and, according to this research, infl ation at this time was largely unexpected.

Although expectations are not easily observable, we can draw inferences about them by examining the persistence of infl ation. In recent experience, infl ation has been very persistent: when it is high one year, it tends to be high the next year as well. Therefore, when people have observed high infl ation, it has been rational for them to expect high infl ation in the future. By contrast, during the nineteenth century, when the gold standard was in effect, infl ation had little per- sistence. High infl ation in one year was just as likely to be followed the next year by low infl ation as by high infl ation. Therefore, high infl ation did not imply high expected infl ation and did not lead to high nominal interest rates. So, in a sense, Fisher was right to say that infl ation “caught merchants napping.’’4 ■

CASE STUDY

4Robert B. Barsky, “The Fisher Effect and the Forecastability and Persistence of Infl ation,’’ Journal of Monetary Economics 19 (January 1987): 3–24.

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114 | P A R T I I Classical Theory: The Economy in the Long Run

5-4 The Nominal Interest Rate and the Demand for Money

The quantity theory is based on a simple money demand function: it assumes that the demand for real money balances is proportional to income. The quantity theory is a good place to start when analyzing the effects of money on the economy, but it is not the whole story. Here we add another determinant of the quantity of money demanded—the nominal interest rate.

The Cost of Holding Money

The money you hold in your wallet does not earn interest. If, instead of holding that money, you used it to buy government bonds or deposited it in a savings account, you would earn the nominal interest rate. Therefore, the nominal interest rate is the opportunity cost of holding money: it is what you give up by holding money rather than bonds.

Another way to see that the cost of holding money equals the nominal interest rate is by comparing the real returns on alternative assets. Assets other than money, such as government bonds, earn the real return r. Money earns an expected real return of –E�, because its real value declines at the rate of infl ation. When you hold money, you give up the difference between these two returns. Thus, the cost of holding money is r – (–E�), which the Fisher equation tells us is the nominal interest rate i.

Just as the quantity of bread demanded depends on the price of bread, the quantity of money demanded depends on the price of holding money. Hence, the demand for real money balances depends both on the level of income and on the nominal interest rate. We write the general money demand function as

(M/P )d = L(i, Y ).

The letter L is used to denote money demand because money is the economy’s most liquid asset (the asset most easily used to make transactions). This equation states that the demand for the liquidity of real money balances is a function of income and the nominal interest rate. The higher the level of income Y, the greater the demand for real money balances. The higher the nominal interest rate i, the lower the demand for real money balances.

Future Money and Current Prices

Money, prices, and interest rates are now related in several ways. Figure 5-5 illus- trates the linkages we have discussed. As the quantity theory of money explains, money supply and money demand together determine the equilibrium price level. Changes in the price level are, by defi nition, the rate of infl ation. Infl a- tion, in turn, affects the nominal interest rate through the Fisher effect. But now, because the nominal interest rate is the cost of holding money, the nominal inter- est rate feeds back to affect the demand for money.

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Consider how the introduction of this last link affects our theory of the price level. First, equate the supply of real money balances M/P to the demand L(i, Y):

M/P = L(i, Y ). Next, use the Fisher equation to write the nominal interest rate as the sum of the real interest rate and expected infl ation:

M/P = L(r + E�, Y ). This equation states that the level of real money balances depends on the expected rate of infl ation.

The last equation tells a more sophisticated story about the determination of the price level than does the quantity theory. The quantity theory of money says that today’s money supply determines today’s price level. This conclusion remains partly true: if the nominal interest rate and the level of output are held constant, the price level moves proportionately with the money supply. Yet the nominal interest rate is not constant; it depends on expected infl ation, which in turn depends on growth in the money supply. The presence of the nominal interest rate in the money demand function yields an additional channel through which money supply affects the price level.

This general money demand equation implies that the price level depends not only on today’s money supply but also on the money supply expected in the future. To see why, suppose the Fed announces that it will increase the money supply in the future, but it does not change the money supply today. This announcement causes people to expect higher money growth and higher infl ation. Through the Fisher effect, this increase in expected infl ation raises the nominal interest rate. The higher nominal interest rate increases the cost of hold- ing money and therefore reduces the demand for real money balances. Because

FIGURE 5-5

The Linkages Among Money, Prices, and Interest Rates This fi gure illustrates the relationships among money, prices, and interest rates. Money supply and money demand determine the price level. Changes in the price level determine the infl ation rate. The infl ation rate infl uences the nominal interest rate. Because the nominal interest rate is the cost of holding money, it may affect money demand. This last link (shown as a blue line) is omitted from the basic quantity theory of money.

Inflation Rate

Price Level

Money Supply

Money Demand

Nominal Interest Rate

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116 | P A R T I I Classical Theory: The Economy in the Long Run

the Fed has not changed the quantity of money available today, the reduced demand for real money balances leads to a higher price level. Hence, expectations of higher money growth in the future lead to a higher price level today.

The effect of money on prices is complex. The appendix to this chapter pres- ents the Cagan model, which shows how the price level is related to current and expected future monetary policy. In particular, the analysis concludes that the price level depends on a weighted average of the current money supply and the money supply expected to prevail in the future.

5-5 The Social Costs of Inflation

Our discussion of the causes and effects of infl ation does not tell us much about the social problems that result from infl ation. We turn to those problems now.

The Layman’s View and the Classical Response

If you ask the average person why infl ation is a social problem, he will probably answer that infl ation makes him poorer. “Each year my boss gives me a raise, but prices go up and that takes some of my raise away from me.’’ The implicit assumption in this statement is that if there were no infl ation, he would get the same raise and be able to buy more goods.

This complaint about infl ation is a common fallacy. As we know from Chapter 3, the purchasing power of labor—the real wage—depends on the marginal pro- ductivity of labor, not on how much money the government chooses to print. If the central bank reduces infl ation by slowing the rate of money growth, workers will not see their real wage increasing more rapidly. Instead, when infl ation slows, fi rms will increase the prices of their products less each year and, as a result, will give their workers smaller raises.

According to the classical theory of money, a change in the overall price level is like a change in the units of measurement. It is as if we switched from measur- ing distances in feet to measuring them in inches: numbers get larger, but noth- ing really changes. Imagine that tomorrow morning you wake up and fi nd that, for some reason, all dollar fi gures in the economy have been multiplied by ten. The price of everything you buy has increased tenfold, but so have your wage and the value of your savings. What difference would such a price increase make to your life? All numbers would have an extra zero at the end, but nothing else would change. Your economic well-being depends on relative prices, not the overall price level.

Why, then, is a persistent increase in the price level a social problem? It turns out that the costs of infl ation are subtle. Indeed, economists disagree about the size of the social costs. To the surprise of many laymen, some economists argue that the costs of infl ation are small—at least for the moderate rates of infl ation that most countries have experienced in recent years.5

5See, for example, Chapter 2 of Alan Blinder, Hard Heads, Soft Hearts: Tough-Minded Economics for a Just Society (Reading, Mass.: Addison Wesley, 1987).

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The Costs of Expected Inflation

Consider fi rst the case of expected infl ation. Suppose that every month the price level rose by 1 percent. What would be the social costs of such a steady and pre- dictable 12 percent annual infl ation?

One cost is the distorting effect of the infl ation tax on the amount of money people hold. As we have already discussed, a higher infl ation rate leads to a higher nominal interest rate, which in turn leads to lower real money balances. If people hold lower money balances on average, they must make more frequent trips to the bank to withdraw money—for example, they might withdraw $50 twice

What Economists and the Public Say About Inflation

As we have been discussing, laymen and economists hold very different views about the costs of infl ation. In 1996, economist Robert Shiller documented this difference of opinion in a survey of the two groups. The survey results are strik- ing, for they show how the study of economics changes a person’s attitudes.

In one question, Shiller asked people whether their “biggest gripe about infl ation” was that “infl ation hurts my real buying power, it makes me poorer.” Of the general public, 77 percent agreed with this statement, compared to only 12 percent of economists. Shiller also asked people whether they agreed with the following statement: “When I see projections about how many times more a college education will cost, or how many times more the cost of living will be in coming decades, I feel a sense of uneasiness; these infl ation projections really make me worry that my own income will not rise as much as such costs will.” Among the general public, 66 percent said they fully agreed with this statement, whereas only 5 percent of economists agreed with it.

Survey respondents were asked to judge the seriousness of infl ation as a policy problem: “Do you agree that preventing high infl ation is an important national priority, as important as preventing drug abuse or preventing deterioration in the quality of our schools?” Shiller found that 52 percent of laymen, but only 18 percent of economists, fully agreed with this view. Apparently, infl ation worries the public much more than it does the economics profession.

The public’s distaste for infl ation may be psychological. Shiller asked those surveyed if they agreed with the following statement: “I think that if my pay went up I would feel more satisfaction in my job, more sense of fulfi llment, even if prices went up just as much.” Of the public, 49 percent fully or partly agreed with this statement, compared to 8 percent of economists.

Do these survey results mean that laymen are wrong and economists are right about the costs of infl ation? Not necessarily. But economists do have the advan- tage of having given the issue more thought. So let’s now consider what some of the costs of infl ation might be.6 ■

CASE STUDY

6Robert J. Shiller, “Why Do People Dislike Infl ation?” in Christina D. Romer and David H. Romer, eds., Reducing Infl ation: Motivation and Strategy (Chicago: University of Chicago Press, 1997): 13–65.

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a week rather than $100 once a week. The inconvenience of reducing money holding is metaphorically called the shoeleather cost of infl ation, because walking to the bank more often causes one’s shoes to wear out more quickly.

A second cost of infl ation arises because high infl ation induces fi rms to change their posted prices more often. Changing prices is sometimes costly; for example, it may require printing and distributing a new catalog. These costs are called menu costs, because the higher the rate of infl ation, the more often res- taurants have to print new menus.

A third cost of infl ation arises because fi rms facing menu costs change prices infrequently; therefore, the higher the rate of infl ation, the greater the variability in relative prices. For example, suppose a fi rm issues a new catalog every January. If there is no infl ation, then the fi rm’s prices relative to the overall price level are constant over the year. Yet if infl ation is 1 percent per month, then from the beginning to the end of the year the fi rm’s relative prices fall by 12 percent. Sales from this catalog will tend to be low early in the year (when its prices are rela- tively high) and high later in the year (when its prices are relatively low). Hence, when infl ation induces variability in relative prices, it leads to microeconomic ineffi ciencies in the allocation of resources.

A fourth cost of infl ation results from the tax laws. Many provisions of the tax code do not take into account the effects of infl ation. Infl ation can alter individu- als’ tax liability, often in ways that lawmakers did not intend.

One example of the failure of the tax code to deal with infl ation is the tax treat- ment of capital gains. Suppose you buy some stock today and sell it a year from now at the same real price. It would seem reasonable for the government not to levy a tax, because you have earned no real income from this investment. Indeed, if there is no infl ation, a zero tax liability would be the outcome. But suppose the rate of infl ation is 12 percent and you initially paid $100 per share for the stock; for the real price to be the same a year later, you must sell the stock for $112 per share. In this case the tax code, which ignores the effects of infl ation, says that you have earned $12 per share in income, and the government taxes you on this capital gain. The problem is that the tax code measures income as the nominal rather than the real capital gain. In this example, and in many others, infl ation distorts how taxes are levied.

A fi fth cost of infl ation is the inconvenience of living in a world with a changing price level. Money is the yardstick with which we measure economic transactions. When there is infl ation, that yardstick is changing in length. To continue the anal- ogy, suppose that Congress passed a law specifying that a yard would equal 36 inches in 2013, 35 inches in 2014, 34 inches in 2015, and so on. Although the law would result in no ambiguity, it would be highly inconvenient. When someone measured a distance in yards, it would be necessary to specify whether the measurement was in 2013 yards or 2014 yards; to compare distances measured in different years, one would need to make an “infl ation’’ correction. Similarly, the dollar is a less useful measure when its value is always changing. The changing value of the dollar requires that we correct for infl ation when comparing dollar fi gures from different times.

For example, a changing price level complicates personal fi nancial planning. One important decision that all households face is how much of their income to consume today and how much to save for retirement. A dollar saved today and invested at a fi xed nominal interest rate will yield a fi xed dollar amount in the future. Yet the real

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value of that dollar amount—which will determine the retiree’s living standard— depends on the future price level. Deciding how much to save would be much sim- pler if people could count on the price level in 30 years being similar to its level today.

The Costs of Unexpected Inflation

Unexpected infl ation has an effect that is more pernicious than any of the costs of steady, anticipated infl ation: it arbitrarily redistributes wealth among indi- viduals. You can see how this works by examining long-term loans. Most loan agreements specify a nominal interest rate, which is based on the rate of infl ation expected at the time of the agreement. If infl ation turns out differently from what was expected, the ex post real return that the debtor pays to the creditor differs from what both parties anticipated. On the one hand, if infl ation turns out to be higher than expected, the debtor wins and the creditor loses because the debtor repays the loan with less valuable dollars. On the other hand, if infl a- tion turns out to be lower than expected, the creditor wins and the debtor loses because the repayment is worth more than the two parties anticipated.

Consider, for example, a person taking out a mortgage in 1960. At the time, a 30-year mortgage had an interest rate of about 6 percent per year. This rate was based on a low rate of expected infl ation—infl ation over the previous decade had averaged only 2.5 percent. The creditor probably expected to receive a real return of about 3.5 percent, and the debtor expected to pay this real return. In fact, over the life of the mortgage, the infl ation rate averaged 5 percent, so the ex post real return was only 1 percent. This unanticipated infl ation benefi ted the debtor at the expense of the creditor.

Unanticipated infl ation also hurts individuals on fi xed pensions. Workers and fi rms often agree on a fi xed nominal pension when the worker retires (or even earlier). Because the pension is deferred earnings, the worker is essentially providing the fi rm a loan: the worker provides labor services to the fi rm while young but does not get fully paid until old age. Like any creditor, the worker is hurt when infl ation is higher than anticipated. Like any debtor, the fi rm is hurt when infl ation is lower than anticipated.

These situations provide a clear argument against variable infl ation. The more variable the rate of infl ation, the greater the uncertainty that both debtors and creditors face. Because most people are risk averse—they dislike uncertainty—the unpredictability caused by highly variable infl ation hurts almost everyone.

Given these effects of uncertain infl ation, it is puzzling that nominal contracts are so prevalent. One might expect debtors and creditors to protect themselves from this uncertainty by writing contracts in real terms—that is, by indexing to some measure of the price level. In economies with high and variable infl ation, indexation is often widespread; sometimes this indexation takes the form of writing contracts using a more stable foreign currency. In economies with mod- erate infl ation, such as the United States, indexation is less common. Yet even in the United States, some long-term obligations are indexed. For example, Social Security benefi ts for the elderly are adjusted annually in response to changes in the consumer price index. And in 1997, the U.S. federal government issued infl ation-indexed bonds for the fi rst time.

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Finally, in thinking about the costs of infl ation, it is important to note a widely documented but little understood fact: high infl ation is variable infl ation. That is, countries with high average infl ation also tend to have infl ation rates that change greatly from year to year. The implication is that if a country decides to pursue a high-infl ation monetary policy, it will likely have to accept highly vari- able infl ation as well. As we have just discussed, highly variable infl ation increases uncertainty for both creditors and debtors by subjecting them to arbitrary and potentially large redistributions of wealth.

The Free Silver Movement, the Election of 1896, and The Wizard of Oz The redistributions of wealth caused by unexpected changes in the price level are often a source of political turmoil, as evidenced by the Free Silver movement in the late nineteenth century. From 1880 to 1896 the price level in the United States fell 23 percent. This defl ation was good for creditors, primarily the bankers of the North- east, but it was bad for debtors, primarily the farmers of the South and West. One proposed solution to this problem was to replace the gold standard with a bimetallic standard, under which both gold and silver could be minted into coin. The move to a bimetallic standard would increase the money supply and stop the defl ation.

The silver issue dominated the presidential election of 1896. William McKinley, the Republican nominee, campaigned on a platform of preserving the gold standard. William Jennings Bryan, the Democratic nominee, supported the bimetallic standard. In a famous speech, Bryan proclaimed, “You shall not press down upon the brow of labor this crown of thorns, you shall not crucify mankind upon a cross of gold.’’ Not surprisingly, McKinley was the candidate of the conservative eastern establishment, whereas Bryan was the candidate of the southern and western populists.

This debate over silver found its most memorable expression in a children’s book, The Wizard of Oz. Written by a midwestern journalist, L. Frank Baum, just after the 1896 election, it tells the story of Dorothy, a girl lost in a strange land far from her home in Kansas. Dorothy (representing traditional American values) makes three friends: a scarecrow (the farmer), a tin woodman (the indus- trial worker), and a lion whose roar exceeds his might (William Jennings Bryan). Together, the four of them make their way along a perilous yellow brick road (the gold standard), hoping to fi nd the Wizard who will help Dorothy return home. Eventually they arrive in Oz (Washington), where everyone sees the world through green glasses (money). The Wizard (William McKinley) tries to be all things to all people but turns out to be a fraud. Dorothy’s problem is solved only when she learns about the magical power of her silver slippers.7

CASE STUDY

7The movie made forty years later hid much of the allegory by changing Dorothy’s slippers from silver to ruby. For more on this topic, see Henry M. Littlefi eld, “The Wizard of Oz: Parable on Populism,’’ American Quarterly 16 (Spring 1964): 47–58; and Hugh Rockoff, “The Wizard of Oz as a Monetary Allegory,’’ Journal of Political Economy 98 (August 1990): 739–760. It should be noted that there is no direct evidence that Baum intended his work as a monetary allegory, so some people believe that the parallels are the work of economic historians’ overactive imaginations.

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One Benefit of Inflation

So far, we have discussed the many costs of infl ation. These costs lead many economists to conclude that monetary policymakers should aim for zero infl a- tion. Yet there is another side to the story. Some economists believe that a little bit of infl ation—say, 2 or 3 percent per year—can be a good thing.

The argument for moderate infl ation starts with the observation that cuts in nominal wages are rare: fi rms are reluctant to cut their workers’ nominal wages, and workers are reluctant to accept such cuts. A 2 percent wage cut in a zero- infl ation world is, in real terms, the same as a 3 percent raise with 5 percent infl ation, but workers do not always see it that way. The 2 percent wage cut may seem like an insult, whereas the 3 percent raise is, after all, still a raise. Empirical studies confi rm that nominal wages rarely fall.

This fi nding suggests that some infl ation may make labor markets work better. The supply and demand for different kinds of labor are always changing. Sometimes an increase in supply or decrease in demand leads to a fall in the equilibrium real wage for a group of workers. If nominal wages can’t be cut, then the only way to cut real wages is to allow infl ation to do the job. Without infl ation, the real wage will be stuck above the equilibrium level, resulting in higher unemployment.

For this reason, some economists argue that infl ation “greases the wheels” of labor markets. Only a little infl ation is needed: an infl ation rate of 2 percent lets real wages fall by 2 percent per year, or 20 percent per decade, without cuts in nominal wages. Such automatic reductions in real wages are impossible with zero infl ation.8

5-6 Hyperinflation

Hyperinfl ation is often defi ned as infl ation that exceeds 50 percent per month, which is just over 1 percent per day. Compounded over many months, this rate of infl ation leads to very large increases in the price level. An infl ation rate of 50 percent per month implies a more than 100-fold increase in the price level over a year and a more than 2-million-fold increase over three years. Here we consider the costs and causes of such extreme infl ation.

The Republicans won the election of 1896, and the United States stayed on a gold standard, but the Free Silver advocates got the infl ation that they wanted. Around the time of the election, gold was discovered in Alaska, Australia, and South Africa. In addition, gold refi ners devised the cyanide process, which facilitated the extraction of gold from ore. These developments led to increases in the money supply and in prices. From 1896 to 1910 the price level rose 35 percent. ■

8For an examination of this benefi t of infl ation, see George A. Akerlof, William T. Dickens, and George L. Perry, “The Macroeconomics of Low Infl ation,” Brookings Papers on Economic Activity, 1996:1, pp. 1–76. Another argument for positive infl ation is that it allows for the possibility of negative real interest rates. This issue is discussed in Chapter 12 in an FYI box on The Liquidity Trap.

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The Costs of Hyperinflation

Although economists debate whether the costs of moderate infl ation are large or small, no one doubts that hyperinfl ation extracts a high toll on society. The costs are qualitatively the same as those we discussed earlier. When infl ation reaches extreme levels, however, these costs are more apparent because they are so severe.

The shoeleather costs associated with reduced money holding, for instance, are serious under hyperinfl ation. Business executives devote much time and energy to cash management when cash loses its value quickly. By diverting this time and energy from more socially valuable activities, such as production and investment decisions, hyperinfl ation makes the economy run less effi ciently.

Menu costs also become larger under hyperinfl ation. Firms have to change prices so often that normal business practices, such as printing and distribut- ing catalogs with fi xed prices, become impossible. In one restaurant during the German hyperinfl ation of the 1920s, a waiter would stand up on a table every 30 minutes to call out the new prices.

Similarly, relative prices do not do a good job of refl ecting true scarcity during hyperinfl ations. When prices change frequently by large amounts, it is hard for cus- tomers to shop around for the best price. Highly volatile and rapidly rising prices can alter behavior in many ways. According to one report, when patrons entered a pub during the German hyperinfl ation, they would often buy two pitchers of beer. Although the second pitcher would lose value by getting warm over time, it would lose value less rapidly than the money left sitting in the patron’s wallet.

Tax systems are also distorted by hyperinfl ation—but in ways that are different from the distortions of moderate infl ation. In most tax systems there is a delay between the time a tax is levied and the time it is actually paid to the govern- ment. In the United States, for example, taxpayers are required to make estimated income tax payments every three months. This short delay does not matter much under low infl ation. By contrast, during hyperinfl ation, even a short delay greatly reduces real tax revenue. By the time the government gets the money it is due, the money has fallen in value. As a result, once hyperinfl ations start, the real tax revenue of the government often falls substantially.

Finally, no one should underestimate the sheer inconvenience of living with hyper- infl ation. When carrying money to the grocery store is as burdensome as carrying the groceries back home, the monetary system is not doing its best to facilitate exchange. The government tries to overcome this problem by adding more and more zeros to the paper currency, but often it cannot keep up with the exploding price level.

Eventually, these costs of hyperinfl ation become intolerable. Over time, money loses its role as a store of value, unit of account, and medium of exchange. Barter becomes more common. And more stable unoffi cial monies—cigarettes or the U.S. dollar—start to replace the offi cial money.

The Causes of Hyperinflation

Why do hyperinfl ations start, and how do they end? This question can be answered at different levels.

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The most obvious answer is that hyper- infl ations are due to excessive growth in the supply of money. When the central bank prints money, the price level rises. When it prints money rapidly enough, the result is hyperinfl ation. To stop the hyper- infl ation, the central bank must reduce the rate of money growth.

This answer is incomplete, however, for it leaves open the question of why central banks in hyperinfl ating econo- mies choose to print so much money. To address this deeper question, we must turn our attention from monetary to fi scal policy. Most hyperinfl ations begin when the government has inadequate tax revenue to pay for its spending. Although the government might prefer to fi nance this budget defi cit by issu- ing debt, it may fi nd itself unable to borrow, perhaps because lenders view the government as a bad credit risk. To cover the defi cit, the government turns to the only mechanism at its disposal—the printing press. The result is rapid money growth and hyperinfl ation.

Once the hyperinfl ation is under way, the fi scal problems become even more severe. Because of the delay in collecting tax payments, real tax revenue falls as infl ation rises. Thus, the government’s need to rely on seigniorage is self-reinforc- ing. Rapid money creation leads to hyperinfl ation, which leads to a larger budget defi cit, which leads to even more rapid money creation.

The ends of hyperinfl ations almost always coincide with fi scal reforms. Once the magnitude of the problem becomes apparent, the government musters the political will to reduce government spending and increase taxes. These fi scal reforms reduce the need for seigniorage, which allows a reduction in money growth. Hence, even if infl ation is always and everywhere a monetary phenom- enon, the end of hyperinfl ation is often a fi scal phenomenon as well.9

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9For more on these issues, see Thomas J. Sargent, “The End of Four Big Infl ations,’’ in Robert Hall, ed., Infl ation (Chicago: University of Chicago Press, 1983), 41–98; and Rudiger Dornbusch and Stanley Fischer, “Stopping Hyperinfl ations: Past and Present,’’ Weltwirtschaftliches Archiv 122 (April 1986): 1–47.

Hyperinflation in Interwar Germany

After World War I, Germany experienced one of history’s most spectacular examples of hyperinfl ation. At the war’s end, the Allies demanded that Germany pay substan- tial reparations. These payments led to fi scal defi cits in Germany, which the German government eventually fi nanced by printing large quantities of money.

Panel (a) of Figure 5-6 shows the quantity of money and the general price level in Germany from January 1922 to December 1924. During this period

CASE STUDY

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124 | P A R T I I Classical Theory: The Economy in the Long Run

FIGURE 5-6

Money and Prices in Interwar Germany Panel (a) shows the money supply and the price level in Germany from January 1922 to December 1924. The immense increases in the money supply and the price level provide a dramatic illustration of the effects of print- ing large amounts of money. Panel (b) shows infl ation and real money balances. As infl ation rose, real money balances fell. When the infl ation ended at the end of 1923, real money balances rose.

Source: Adapted from Thomas J. Sargent, “The End of Four Big Infl ations,” in Robert Hall, ed., Infl ation (Chicago: University of Chicago Press, 1983), 41–98.

Money supply (paper marks)

Price level (index 1913 = 100)

1922 1923 Year

1924 1925

120

100

80

60

40

20

0

100,000

10,000

1,000

100

10

0

Index of real balances (January 1922 = 100)

Monthly inflation rate (logarithmic scale)

1922 1923 Year

Real balances (left scale)

Monthly inflation rate (right scale)

1924 1925

(a) Money and Prices

(b) Inflation and Real Money Balances

1022

1020

1018

1016

1014

1012

1010

108

1016

1014

1012

1010

108

106

104

102

Money supply (left scale)

Price level (right scale)

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Hyperinflation in Zimbabwe

In 1980, after years of colonial rule, the old British colony of Rhodesia became the new African nation of Zimbabwe. A new currency, the Zimbabwe dollar, was introduced to replace the Rhodesian dollar. For the fi rst decade, infl ation in the new nation was modest—about 10 to 20 percent per year. That, however, would soon change.

The hero of the Zimbabwe independence movement was Robert Mugabe. In general elections in 1980, he became the nation’s fi rst prime minister and later, after a government reorganization, its president. Over the years, he continued to get reelected. In his 2008 reelection, however, there were widespread claims of electoral fraud and threats against voters who supported rival candidates. At the age of 84, Mugabe was no longer as popular as he once was, but he gave no sign of any willingness to relinquish power.

Throughout his tenure, Mugabe’s economic philosophy was Marxist, and one of his goals was to redistribute wealth. In the 1990s his government instituted a series of land reforms with the ostensible purpose of redistributing land from

CASE STUDY

10The data on newspaper prices are from Michael Mussa, “Sticky Individual Prices and the Dynamics of the General Price Level,’’ Carnegie-Rochester Conference on Public Policy 15 (Autumn 1981): 261–296.

both money and prices rose at an amazing rate. For example, the price of a daily newspaper rose from 0.30 mark in January 1921 to 1 mark in May 1922, to 8 marks in October 1922, to 100 marks in February 1923, and to 1,000 marks in September 1923. Then, in the fall of 1923, prices took off: the newspaper sold for 2,000 marks on October 1, 20,000 marks on October 15, 1 million marks on October 29, 15 million marks on November 9, and 70 million marks on November 17. In December 1923 the money supply and prices abruptly stabilized.10

Just as fi scal problems caused the German hyperinfl ation, a fi scal reform ended it. At the end of 1923, the number of government employees was cut by one- third, and the reparations payments were temporarily suspended and eventually reduced. At the same time, a new central bank, the Rentenbank, replaced the old central bank, the Reichsbank. The Rentenbank was committed to not fi nancing the government by printing money.

According to our theoretical analysis of money demand, an end to a hyperin- fl ation should lead to an increase in real money balances as the cost of holding money falls. Panel (b) of Figure 5-6 shows that real money balances in Germany did fall as infl ation increased and then increased again as infl ation fell. Yet the increase in real money balances was not immediate. Perhaps the adjustment of real money balances to the cost of holding money is a gradual process. Or per- haps it took time for people in Germany to believe that the infl ation had ended, so that expected infl ation fell more gradually than actual infl ation. ■

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5-7 Conclusion: The Classical Dichotomy

Over the course of this and the previous chapter, we have studied the meaning of money and the impact of the money supply on infl ation and various other variables. This analysis builds on our model of national income in Chapter 3. Let’s now step back and examine a key assumption that has been implicit in our discussion.

In Chapter 3, we explained many macroeconomic variables. Some of these variables were quantities, such as real GDP and the capital stock; others were rela- tive prices, such as the real wage and the real interest rate. But all of these variables had one thing in common—they measured a physical (rather than a monetary) quantity. Real GDP is the quantity of goods and services produced in a given year, and the capital stock is the quantity of machines and structures available at a given time. The real wage is the quantity of output a worker earns for each hour of work, and the real interest rate is the quantity of output a person earns in the future by lending one unit of output today. All variables measured in physical units, such as quantities and relative prices, are called real variables.

the white minority who ruled Zimbabwe during the colonial era toward the historically disenfranchised black population. One result of these reforms was widespread corruption. Many abandoned and expropriated white farms ended up in the hands of cabinet ministers and senior government offi cials. Another result was a substantial decline in farm output. Productivity fell as many of the experienced white farmers fl ed the country.

The decline in the economy’s output led to a fall in the government’s tax rev- enue. The government responded to this revenue shortfall by printing money to pay the salaries of government employees. As textbook economic theory predicts, the monetary expansion led to higher infl ation.

Mugabe tried to deal with infl ation by imposing price controls. Once again, the result was predictable: a shortage of many goods and the growth of an underground economy where price controls and tax collection were evaded. The government’s tax revenue declined further, inducing even more monetary expansion and yet higher infl ation. In July 2008, the offi cially reported infl a- tion rate was 231 million percent. Other observers put the infl ation rate even higher.

The repercussions of the hyperinfl ation were widespread. In an article in the Washington Post, one Zimbabwean citizen describes the situation as follows: “If you don’t get a bill collected in 48 hours, it isn’t worth collecting, because it is worthless. Whenever we get money, we must immediately spend it, just go and buy what we can. Our pension was destroyed ages ago. None of us have any savings left.”

The Zimbabwe hyperinfl ation fi nally ended in March 2009, when the gov- ernment abandoned its own money. The U.S. dollar became the nation’s offi cial currency. Infl ation quickly stabilized. Zimbabwe still had its problems, but at least hyperinfl ation was not among them. ■

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In this chapter we examined nominal variables—variables expressed in terms of money. The economy has many nominal variables, such as the price level, the infl ation rate, and the dollar wage a person earns.

At fi rst it may seem surprising that we were able to explain real variables without introducing nominal variables or the existence of money. In Chapter 3 we studied the level and allocation of the economy’s output without mentioning the price level or the rate of infl ation. Our theory of the labor market explained the real wage without explaining the nominal wage.

Economists call this theoretical separation of real and nominal variables the classical dichotomy. It is the hallmark of classical macroeconomic theory. The classical dichotomy is an important insight because it simplifi es economic theory. In particular, it allows us to examine real variables, as we have done, while ignoring nominal variables. The classical dichotomy arises because, in classical economic theory, changes in the money supply do not infl uence real variables. This irrelevance of money for real variables is called monetary neutrality. For many purposes—in particular for studying long-run issues—monetary neutrality is approximately correct.

Yet monetary neutrality does not fully describe the world in which we live. Beginning in Chapter 10, we discuss departures from the classical model and monetary neutrality. These departures are crucial for understanding many mac- roeconomic phenomena, such as short-run economic fl uctuations.

Summary

1. The quantity theory of money assumes that the velocity of money is stable and concludes that nominal GDP is proportional to the stock of money. Because the factors of production and the production function determine real GDP, the quantity theory implies that the price level is proportional to the quantity of money. Therefore, the rate of growth in the quantity of money determines the infl ation rate.

2. Seigniorage is the revenue that the government raises by printing money. It is a tax on money holding. Although seigniorage is quantitatively small in most economies, it is often a major source of government revenue in economies experiencing hyperinfl ation.

3. The real interest rate is the nominal interest rate (the interest rate as usually reported) corrected for the effects of infl ation. The ex post real interest rate is based on actual infl ation, whereas the ex ante real interest rate is based on expected infl ation. The Fisher effect says that the nominal interest rate moves one-for-one with expected infl ation.

4. The nominal interest rate is the opportunity cost of holding money. Thus, one might expect the demand for money to depend on the nominal inter- est rate. If it does, then the price level depends on both the current quantity of money and the quantities of money expected in the future.

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K E Y C O N C E P T S

Infl ation

Hyperinfl ation

Quantity equation

Transactions velocity of money

Income velocity of money

Real money balances

Money demand function

Quantity theory of money

Seigniorage

Nominal and real interest rates

Fisher equation and Fisher effect

Ex ante and ex post real interest rates

Shoeleather costs

Menu costs

Real and nominal variables

Classical dichotomy

Monetary neutrality

5. The costs of expected infl ation include shoeleather costs, menu costs, the cost of relative price variability, tax distortions, and the inconvenience of making infl ation corrections. In addition, unexpected infl ation causes arbitrary redis- tributions of wealth between debtors and creditors. One possible benefi t of infl ation is that it improves the functioning of labor markets by allowing real wages to reach equilibrium levels without cuts in nominal wages.

6. During hyperinfl ations, most of the costs of infl ation become severe. Hyperinfl a- tions typically begin when governments fi nance large budget defi cits by printing money. They end when fi scal reforms eliminate the need for seigniorage.

7. According to classical economic theory, money is neutral: the money supply does not affect real variables. Therefore, classical theory allows us to study how real variables are determined without any reference to the money sup- ply. The equilibrium in the money market then determines the price level and, as a result, all other nominal variables. This theoretical separation of real and nominal variables is called the classical dichotomy.

1. Write the quantity equation and explain it.

2. What does the assumption of constant velocity imply?

3. Who pays the infl ation tax?

4. If infl ation rises from 6 to 8 percent, what hap- pens to real and nominal interest rates according to the Fisher effect?

Q U E S T I O N S F O R R E V I E W

5. List all the costs of infl ation you can think of, and rank them according to how important you think they are.

6. Explain the roles of monetary and fi scal policy in causing and ending hyperinfl ations.

7. Defi ne the terms “real variable” and “nominal variable,” and give an example of each.

P R O B L E M S A N D A P P L I C A T I O N S

1. In the country of Wiknam, the velocity of money is constant. Real GDP grows by 5 percent per year, the money stock grows by

14 percent per year, and the nominal interest rate is 11 percent. What is the real interest rate?

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C H A P T E R 5 Inflation: Its Causes, Effects, and Social Costs | 129

2. A newspaper article once reported that the U.S. economy was experiencing a low rate of infl a- tion. It said that “low infl ation has a downside: 45 million recipients of Social Security and other benefi ts will see their checks go up by just 2.8 percent next year.”

a. Why does infl ation affect the increase in Social Security and other benefi ts?

b. Is this effect a cost of infl ation, as the article suggests? Why or why not?

3. Suppose a country has a money demand func- tion (M/P)d = kY, where k is a constant param- eter. The money supply grows by 12 percent per year, and real income grows by 4 percent per year.

a. What is the average infl ation rate?

b. How would infl ation be different if real income growth were higher? Explain.

c. How do you interpret the parameter k? What is its relationship to the velocity of money?

d. Suppose, instead of a constant money demand function, the velocity of money in this econ- omy was growing steadily because of fi nancial innovation. How would that affect the infl a- tion rate? Explain.

4. During World War II, both Germany and England had plans for a paper weapon: they each printed the other’s currency, with the intention of dropping large quantities by airplane. Why might this have been an effective weapon?

5. Suppose that the money demand function takes the form

(M/P )d = L(i, Y ) = Y/(5i )

a. If output grows at rate g, at what rate will the demand for real balances grow (assuming constant nominal interest rates)?

b. What is the velocity of money in this economy?

c. If infl ation and nominal interest rates are con- stant, at what rate, if any, will velocity grow?

d. How will a permanent (once-and-for-all) increase in the level of interest rates affect the level of velocity? How will it affect the subse- quent growth rate of velocity?

6. In each of the following scenarios, explain and categorize the cost of infl ation.

a. Because infl ation has risen, the L.L. Bean Company decides to issue a new catalog quarterly rather than annually.

b. Grandma buys an annuity for $100,000 from an insurance company, which promises to pay her $10,000 a year for the rest of her life. After buying it, she is surprised that high infl ation triples the price level over the next few years.

c. Maria lives in an economy with hyperinfl a- tion. Each day after being paid, she runs to the store as quickly as possible so she can spend her money before it loses value.

d. Warren lives in an economy with an infl a- tion rate of 10 percent. Over the past year, he earned a return of $50,000 on his million- dollar portfolio of stocks and bonds. Because his tax rate is 20 percent, he paid $10,000 to the government.

e. Your father tells you that when he was your age, he worked for only $3 an hour. He sug- gests that you are lucky to have a job that pays $7 an hour.

7. When Calvin Coolidge was vice president and giving a speech about government fi nances, he said that “infl ation is repudiation.’’ What might he have meant by this? Do you agree? Why or why not? Does it matter whether the infl ation is expected or unexpected?

8. Some economic historians have noted that during the period of the gold standard, gold discoveries were most likely to occur after a long defl ation. (The discoveries of 1896 are an example.) Why might this be true?

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130 |

In this chapter we showed that if the quantity of real money balances demanded depends on the cost of holding money, the price level depends on both the current money supply and the future money supply. This appendix develops the Cagan model to show more explicitly how this relationship works.11

To keep the math as simple as possible, we posit a money demand function that is linear in the natural logarithms of all the variables. The money demand function is

mt – pt = –�(pt + 1 – pt), (A1)

where mt is the log of the quantity of money at time t, pt is the log of the price level at time t, and � is a parameter that governs the sensitivity of money demand to the rate of infl ation. By the property of logarithms, mt – pt is the log of real money balances, and pt + 1 – pt is the infl ation rate between period t and period t + 1. This equation states that if infl ation goes up by 1 percentage point, real money balances fall by � percent.

We have made a number of assumptions in writing the money demand func- tion in this way. First, by excluding the level of output as a determinant of money demand, we are implicitly assuming that it is constant. Second, by including the rate of infl ation rather than the nominal interest rate, we are assuming that the real interest rate is constant. Third, by including actual infl ation rather than expected infl ation, we are assuming perfect foresight. All of these assumptions are made to keep the analysis as simple as possible.

We want to solve Equation A1 to express the price level as a function of cur- rent and future money. To do this, note that Equation A1 can be rewritten as

pt = a 11 + gbmt + a g

1 + g bpt + 1. (A2)

This equation states that the current price level pt is a weighted average of the current money supply mt and the next period’s price level pt + 1. The next period’s price level will be determined the same way as this period’s price level:

pt + 1 = a 11 + gbmt + 1 + a g

1 + g bpt + 2. (A3)

The Cagan Model: How Current and Future Money Affect the Price Level

A P P E N D I X

11This model is derived from Phillip Cagan, “The Monetary Dynamics of Hyperinfl ation,” in Milton Friedman, ed., Studies in the Quantity Theory of Money (Chicago: University of Chicago Press, 1956): 25–117.

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C H A P T E R 5 Inflation: Its Causes, Effects, and Social Costs | 131

Now substitute Equation A3 for pt + 1 in Equation A2 to obtain

pt = 1

1 + g mt +

g

11 + g 2 2 mt + 1 + g2

11 + g 2 2 pt + 2. (A4) Equation A4 states that the current price level is a weighted average of the cur- rent money supply, the next period’s money supply, and the following period’s price level. Once again, the price level in period t + 2 is determined as in Equa- tion A2:

pt + 2 = a 11 + gb mt + 2 + a g

1 + g b pt + 3. (A5)

Now substitute Equation A5 into Equation A4 to obtain

pt = 1

1 + g mt +

g

11 + g 2 2 mt + 1 + g2

11 + g 2 3 mt + 2 + g3

11 + g 2 3 pt + 3. (A6) By now you see the pattern. We can continue to use Equation A2 to substitute for the future price level. If we do this an infi nite number of times, we fi nd

pt = a 11 + g b cmt + a g

1 + g b mt + 1 + a g1 + gb

2

mt + 2 + a g1 + gb 3

mt + 3 + cd , (A7)

where “. . .’’ indicates an infi nite number of analogous terms. According to Equa- tion A7, the current price level is a weighted average of the current money sup- ply and all future money supplies.

Note the importance of �, the parameter governing the sensitivity of real money balances to infl ation. The weights on the future money supplies decline geometrically at rate �/(1 + �). If � is small, then �/(1 + �) is small, and the weights decline quickly. In this case, the current money supply is the primary determinant of the price level. (Indeed, if � equals zero, we obtain the quantity theory of money: the price level is proportional to the current money supply, and the future money supplies do not matter at all.) If � is large, then �/(1 + �) is close to 1, and the weights decline slowly. In this case, the future money supplies play a key role in determining today’s price level.

Finally, let’s relax the assumption of perfect foresight. If the future is not known with certainty, then we should write the money demand function as

mt − pt = −�(Ept + 1 − pt), (A8) where Ept+1 is the expected price level. Equation A8 states that real money bal- ances depend on expected infl ation. By following steps similar to those above, we can show that

pt = a 11 + g b cmt + a g

1 + g b Emt + 1 + a g1 + gb

2

Emt + 2 + a g1 + gb 3

Emt + 3 + cd . (A9)

Equation A9 states that the price level depends on the current money supply and expected future money supplies.

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132 | P A R T I I Classical Theory: The Economy in the Long Run

Some economists use this model to argue that credibility is important for ending hyperinfl ation. Because the price level depends on both current and expected future money, infl ation depends on both current and expected future money growth. Therefore, to end high infl ation, both money growth and expected money growth must fall. Expectations, in turn, depend on credibility—the per- ception that the central bank is committed to a new, more stable policy.

How can a central bank achieve credibility in the midst of hyperinfl ation? Credibility is often achieved by removing the underlying cause of the hyperinfl a- tion—the need for seigniorage. Thus, a credible fi scal reform is often necessary for a credible change in monetary policy. This fi scal reform might take the form of reducing government spending and making the central bank more indepen- dent from the government. Reduced spending decreases the need for seignior- age, while increased independence allows the central bank to resist government demands for seigniorage.

1. In the Cagan model, if the money supply is expected to grow at some constant rate m (so that Emt+s = mt + sm), then Equation A9 can be shown to imply that pt = mt + �m. a. Interpret this result.

b. What happens to the price level pt when the money supply mt changes, holding the money growth rate m constant?

c. What happens to the price level pt when the money growth rate m changes, holding the current money supply mt constant?

M O R E P R O B L E M S A N D A P P L I C A T I O N S

d. If a central bank is about to reduce the rate of money growth m but wants to hold the price level pt constant, what should it do with mt? Can you see any practical problems that might arise in following such a policy?

e. How do your previous answers change in the special case where money demand does not depend on the expected rate of infl ation (so that � = 0)?

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133

The Open Economy

6C H A P T E R

No nation was ever ruined by trade.

—Benjamin Franklin

Even if you never leave your hometown, you are an active participant in the global economy. When you go to the grocery store, for instance, you might choose between apples grown locally and grapes grown in Chile. When you make a deposit into your local bank, the bank might lend those funds to your next-door neighbor or to a Japanese company building a factory outside Tokyo. Because our economy is integrated with many others around the world, consumers have more goods and services from which to choose, and savers have more opportunities to invest their wealth.

In previous chapters we simplifi ed our analysis by assuming a closed economy. In actuality, however, most economies are open: they export goods and services abroad, they import goods and services from abroad, and they borrow and lend in world fi nancial markets. Figure 6-1 gives some sense of the importance of these international interactions by showing imports and exports as a percentage of GDP for 10 major countries. As the fi gure shows, exports from the United States are about 9 percent of GDP, and imports are about 14 percent. Trade is even more important for many other countries—imports and exports are about a quarter of GDP in Canada and China and about a third in Germany. In these countries, international trade is central to analyzing economic developments and formulating economic policies.

This chapter begins our study of open-economy macroeconomics. We begin in Section 6-1 with questions of measurement. To understand how an open economy works, we must understand the key macroeconomic variables that measure the interactions among countries. Accounting identities reveal a key insight: the fl ow of goods and services across national borders is always matched by an equivalent fl ow of funds to fi nance capital accumulation.

In Section 6-2 we examine the determinants of these international fl ows. We develop a model of the small open economy that corresponds to our model of the closed economy in Chapter 3. The model shows the factors that determine whether a country is a borrower or a lender in world markets and how policies at home and abroad affect the fl ows of capital and goods.

In Section 6-3 we extend the model to discuss the prices at which a country makes exchanges in world markets. We examine what determines the price of

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134 | P A R T I I Classical Theory: The Economy in the Long Run

domestic goods relative to foreign goods. We also examine what determines the rate at which the domestic currency trades for foreign currencies. Our model shows how protectionist trade policies—policies designed to protect domestic industries from foreign competition—infl uence the amount of international trade and the exchange rate.

6-1 The International Flows of Capital and Goods

The key macroeconomic difference between open and closed economies is that, in an open economy, a country’s spending in any given year need not equal its output of goods and services. A country can spend more than it produces by bor- rowing from abroad, or it can spend less than it produces and lend the difference to foreigners. To understand this more fully, let’s take another look at national income accounting, which we fi rst discussed in Chapter 2.

The Role of Net Exports

Consider the expenditure on an economy’s output of goods and services. In a closed economy, all output is sold domestically, and expenditure is divided into

FIGURE 6-1

Imports and Exports as a Percentage of Output: 2010 While international trade is important for the United States, it is even more vital for other countries.

Source: International Monetary Fund.

Canada France Germany Italy Japan United Kingdom

United StatesImports Exports

Percentage of GDP

Brazil China India 0

5

10

15

20

25

30

35

40

45

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C H A P T E R 6 The Open Economy | 135

three components: consumption, investment, and government purchases. In an open economy, some output is sold domestically and some is exported to be sold abroad. We can divide expenditure on an open economy’s output Y into four components:

■ Cd, consumption of domestic goods and services,

■ Id, investment in domestic goods and services,

■ Gd, government purchases of domestic goods and services,

■ X, exports of domestic goods and services.

The division of expenditure into these components is expressed in the identity

Y = Cd + Id + Gd + X.

The sum of the fi rst three terms, Cd + Id + Gd, is domestic spending on domestic goods and services. The fourth term, X, is foreign spending on domestic goods and services.

A bit of manipulation can make this identity more useful. Note that domestic spending on all goods and services equals domestic spending on domestic goods and services plus domestic spending on foreign goods and services. Hence, total consumption C equals consumption of domestic goods and services Cd plus consumption of foreign goods and services Cf; total investment I equals invest- ment in domestic goods and services Id plus investment in foreign goods and services I f; and total government purchases G equals government purchases of domestic goods and services Gd plus government purchases of foreign goods and services Gf. Thus,

C = Cd + Cf,

I = Id + I f,

G = Gd + Gf.

We substitute these three equations into the identity above:

Y = (C − Cf) + (I − I f) + (G − Gf) + X.

We can rearrange to obtain

Y = C + I + G + X − (Cf + I f + Gf).

The sum of domestic spending on foreign goods and services (Cf + I f + Gf) is expenditure on imports (IM). We can thus write the national income accounts identity as

Y = C + I + G + X − IM.

Because spending on imports is included in domestic spending (C + I + G ), and because goods and services imported from abroad are not part of a country’s output, this equation subtracts spending on imports. Defi ning net exports to be exports minus imports (NX = X − IM), the identity becomes

Y = C + I + G + NX.

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136 | P A R T I I Classical Theory: The Economy in the Long Run

This equation states that expenditure on domestic output is the sum of con- sumption, investment, government purchases, and net exports. This is the most common form of the national income accounts identity; it should be familiar from Chapter 2.

The national income accounts identity shows how domestic output, domestic spending, and net exports are related. In particular,

NX = Y − (C + I + G )

Net Exports = Output − Domestic Spending.

This equation shows that in an open economy, domestic spending need not equal the output of goods and services. If output exceeds domestic spending, we export the difference: net exports are positive. If output falls short of domestic spending, we import the difference: net exports are negative.

International Capital Flows and the Trade Balance

In an open economy, as in the closed economy we discussed in Chapter 3, fi nancial markets and goods markets are closely related. To see the relationship, we must rewrite the national income accounts identity in terms of saving and investment. Begin with the identity

Y = C + I + G + NX.

Subtract C and G from both sides to obtain

Y − C − G = I + NX.

Recall from Chapter 3 that Y − C − G is national saving S, which equals the sum of private saving, Y − T − C, and public saving, T − G, where T stands for taxes. Therefore,

S = I + NX.

Subtracting I from both sides of the equation, we can write the national income accounts identity as

S − I = NX.

This form of the national income accounts identity shows that an economy’s net exports must always equal the difference between its saving and its investment.

Let’s look more closely at each part of this identity. The easy part is the right-hand side, NX, the net export of goods and services. Another name for net exports is the trade balance, because it tells us how our trade in goods and services departs from the benchmark of equal imports and exports.

The left-hand side of the identity is the difference between domestic sav- ing and domestic investment, S − I, which we’ll call net capital outfl ow. (It’s sometimes called net foreign investment.) Net capital outfl ow equals the amount that domestic residents are lending abroad minus the amount that foreigners are lending to us. If net capital outfl ow is positive, the economy’s saving exceeds its

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C H A P T E R 6 The Open Economy | 137

investment, and it is lending the excess to foreigners. If the net capital outfl ow is negative, the economy is experiencing a capital infl ow: investment exceeds saving, and the economy is fi nancing this extra investment by borrowing from abroad. Thus, net capital outfl ow refl ects the international fl ow of funds to fi nance capital accumulation.

The national income accounts identity shows that net capital outfl ow always equals the trade balance. That is,

Net Capital Outfl ow = Trade Balance

S − I = NX.

If S − I and NX are positive, we have a trade surplus. In this case, we are net lenders in world fi nancial markets, and we are exporting more goods than we are importing. If S − I and NX are negative, we have a trade defi cit. In this case, we are net borrowers in world fi nancial markets, and we are importing more goods than we are exporting. If S − I and NX are exactly zero, we are said to have balanced trade because the value of imports equals the value of exports.

The national income accounts identity shows that the international fl ow of funds to fi nance capital accumulation and the international fl ow of goods and services are two sides of the same coin. If domestic saving exceeds domestic investment, the surplus sav- ing is used to make loans to foreigners. Foreigners require these loans because we are providing them with more goods and services than they are providing us. That is, we are running a trade surplus. If investment exceeds saving, the extra investment must be fi nanced by borrowing from abroad. These foreign loans enable us to import more goods and services than we export. That is, we are running a trade defi cit. Table 6-1 summarizes these lessons.

Note that the international fl ow of capital can take many forms. It is easiest to assume—as we have done so far—that when we run a trade defi cit, foreign- ers make loans to us. This happens, for example, when the Chinese buy the debt issued by U.S. corporations or by the U.S. government. But the fl ow of capital can also take the form of foreigners buying domestic assets, such as when a citi- zen of Germany buys stock from an American on the New York Stock Exchange. Whether foreigners buy domestically issued debt or domestically owned assets,

This table shows the three outcomes that an open economy can experience.

Trade Surplus Balanced Trade Trade Defi cit

Exports > Imports Exports � Imports Exports < Imports Net Exports > 0 Net Exports � 0 Net Exports < 0 Y > C � I � G Y � C � I � G Y < C � I � G Saving > Investment Saving � Investment Saving < Investment Net Capital Outfl ow > 0 Net Capital Outfl ow � 0 Net Capital Outfl ow < 0

International Flows of Goods and Capital: Summary

TABLE 6-1

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138 | P A R T I I Classical Theory: The Economy in the Long Run

they obtain a claim to the future returns to domestic capital. In both cases, for- eigners end up owning some of the domestic capital stock.

International Flows of Goods and Capital: An Example

The equality of net exports and net capital outfl ow is an identity: it must hold because of how the variables are defi ned and the numbers are added up. But it is easy to miss the intuition behind this important relationship. The best way to understand it is to consider an example.

Imagine that Bill Gates sells a copy of the Windows operating system to a Japanese consumer for 5,000 yen. Because Mr. Gates is a U.S. resident, the sale represents an export of the United States. Other things equal, U.S. net exports rise. What else happens to make the identity hold? It depends on what Mr. Gates does with the 5,000 yen.

Suppose Mr. Gates decides to stuff the 5,000 yen in his mattress. In this case, Mr. Gates has allocated some of his saving to an investment in the Japanese economy (in the form of the Japanese currency) rather than to an investment in the U.S. economy. Thus, U.S. saving exceeds U.S. investment. The rise in U.S. net exports is matched by a rise in the U.S. net capital outfl ow.

If Mr. Gates wants to invest in Japan, however, he is unlikely to make currency his asset of choice. He might use the 5,000 yen to buy some stock in, say, the Sony Corporation, or he might buy a bond issued by the Japanese government. In either case, some of U.S. saving fl ows abroad. Once again, the U.S. net capital outfl ow exactly balances U.S. net exports.

The opposite situation occurs in Japan. When the Japanese consumer buys a copy of the Windows operating system, Japan’s purchases of goods and ser- vices (C + I + G ) rise, but there is no change in what Japan has produced (Y ). Japan’s imports increase, and its net exports decrease. In addition, the transac- tion reduces Japan’s saving (S = Y − C − G ) for a given level of investment (I ). While the United States experiences a net capital outfl ow, Japan experiences a net capital infl ow.

Now let’s change the example. Suppose that instead of investing his 5,000 yen in a Japanese asset, Mr. Gates uses it to buy something made in Japan, such as a Walkman video MP3 player produced by the Japanese fi rm Sony. In this case, imports into the United State rise. Together, the Windows export and the Walkman import represent balanced trade between Japan and the United States. Because exports and imports rise equally, net exports and net capital outfl ow are both unchanged.

A fi nal possibility is that Mr. Gates exchanges his 5,000 yen for U.S. dollars at a local bank. But this doesn’t change the situation: the bank now has to do something with the 5,000 yen. It can buy Japanese assets (a U.S. net capital outfl ow); it can buy a Japanese good (a U.S. import); or it can sell the yen to another American who wants to make such a transaction. If you follow the money, you can see that, in the end, U.S. net exports must equal U.S. net capital outfl ow.

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C H A P T E R 6 The Open Economy | 139

6-2 Saving and Investment in a Small Open Economy

So far in our discussion of the international fl ows of goods and capital, we have rearranged accounting identities. That is, we have defi ned some of the variables that measure transactions in an open economy, and we have shown the links among these variables that follow from their defi nitions. Our next step is to develop a model that explains the behavior of these variables. We can then use the model to answer questions such as how the trade balance responds to changes in policy.

Capital Mobility and the World Interest Rate

In a moment we present a model of the international fl ows of capital and goods. Because the trade balance equals the net capital outfl ow, which in turn equals saving minus investment, our model focuses on saving and investment. To

The trade balance we have been discussing mea- sures the difference between a nation’s exports and its imports with the rest of the world. Sometimes you might hear a media report on a nation’s trade balance with a specifi c other nation. This is called a bilateral trade balance. For example, the U.S. bilateral trade balance with China equals exports that the United States sells to China minus imports that the United States buys from China.

The overall trade balance is, as we have seen, inextricably linked to a nation’s saving and investment. That is not true of a bilateral trade balance. Indeed, a nation can have large trade defi cits and surpluses with specifi c trading part- ners while having balanced trade overall.

For example, suppose the world has three countries: the United States, China, and Austra- lia. The United States sells $100 billion in machine tools to Australia, Australia sells $100 billion in wheat to China, and China sells $100 billion in toys to the United States. In this case, the Unit- ed States has a bilateral trade defi cit with China, China has a bilateral trade defi cit with Australia, and Australia has a bilateral trade defi cit with the United States. But each of the three nations has

The Irrelevance of Bilateral Trade Balances balanced trade overall because it has exported and imported $100 billion in goods.

Bilateral trade defi cits receive more attention in the political arena than they deserve. This is in part because international relations are conducted country to country, so politicians and diplo- mats are naturally drawn to statistics measur- ing country-to-country economic transactions. Most economists, however, believe that bilateral trade balances are not very meaningful. From a macroeconomic standpoint, it is a nation’s trade balance with all foreign nations put together that matters.

The same lesson applies to individuals as it does to nations. Your own personal trade bal- ance is the difference between your income and your spending, and you may be concerned if these two variables are out of line. But you should not be concerned with the difference between your income and spending with a particular person or fi rm. Economist Robert Solow once explained the irrelevance of bilateral trade balances as fol- lows: “I have a chronic defi cit with my barber, who doesn’t buy a darned thing from me.” But that doesn’t stop Mr. Solow from living within his means—or getting a haircut when he needs it.

F Y I

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140 | P A R T I I Classical Theory: The Economy in the Long Run

develop this model, we use some elements that should be familiar from Chap- ter 3, but in contrast to the Chapter 3 model, we do not assume that the real interest rate equilibrates saving and investment. Instead, we allow the economy to run a trade defi cit and borrow from other countries or to run a trade surplus and lend to other countries.

If the real interest rate does not adjust to equilibrate saving and investment in this model, what does determine the real interest rate? We answer this question here by considering the simple case of a small open economy with perfect capital mobility. By “small’’ we mean that this economy is a small part of the world market and thus, by itself, can have only a negligible effect on the world interest rate. By “perfect capital mobility’’ we mean that residents of the country have full access to world fi nancial markets. In particular, the government does not impede international borrowing or lending.

Because of this assumption of perfect capital mobility, the interest rate in our small open economy, r, must equal the world interest rate r∗, the real interest rate prevailing in world fi nancial markets:

r = r∗.

Residents of the small open economy need never borrow at any interest rate above r∗, because they can always get a loan at r∗ from abroad. Similarly, residents of this economy need never lend at any interest rate below r∗ because they can always earn r∗ by lending abroad. Thus, the world interest rate determines the interest rate in our small open economy.

Let’s briefl y discuss what determines the world real interest rate. In a closed economy, the equilibrium of domestic saving and domestic investment determines the interest rate. Barring interplanetary trade, the world economy is a closed economy. Therefore, the equilibrium of world saving and world investment determines the world interest rate. Our small open economy has a negligible effect on the world real interest rate because, being a small part of the world, it has a negligible effect on world saving and world investment. Hence, our small open economy takes the world interest rate as exogenously given.

Why Assume a Small Open Economy?

The analysis in the body of this chapter assumes that the nation being studied is a small open economy. (The same approach is taken in Chapter 13, which examines short-run fl uctuations in an open economy.) This assumption raises some questions.

Q: Is the United States well described by the assumption of a small open economy?

A: No, it is not, at least not completely. The United States does borrow and lend in world fi nancial markets, and these markets exert a strong infl uence over the U.S. real interest rate, but it would be an exaggeration to say that the U.S. real interest rate is determined solely by world fi nancial markets.

Q: So why are we assuming a small open economy?

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C H A P T E R 6 The Open Economy | 141

A: Some nations, such as Canada and the Netherlands, are better described by the assumption of a small open economy. Yet the main reason for making this assumption is to develop understanding and intuition for the macroeconomics of open economies. Remember from Chapter 1 that economic models are built with simplifying assumptions. An assumption need not be realistic to be useful. Assuming a small open economy simplifi es the analysis greatly and, therefore, helps clarify our thinking.

Q: Can we relax this assumption and make the model more realistic? A: Yes, we can, and we will. The appendix to this chapter (and the appendix

to Chapter 13) considers the more realistic and more complicated case of a large open economy. Some instructors skip directly to this material when teaching these topics because the approach is more realistic for economies such as that of the United States. Others think that students should walk before they run and, there- fore, begin with the simplifying assumption of a small open economy.

The Model

To build the model of the small open economy, we take three assumptions from Chapter 3:

■ The economy’s output Y is fi xed by the factors of production and the production function. We write this as

_ _ _ Y = Y = F(K, L).

■ Consumption C is positively related to disposable income Y − T. We write the consumption function as

C = C(Y − T ).

■ Investment I is negatively related to the real interest rate r. We write the investment function as

I = I(r ).

These are the three key parts of our model. If you do not understand these relationships, review Chapter 3 before continuing.

We can now return to the accounting identity and write it as

NX = (Y − C − G ) − I

NX = S − I.

Substituting the Chapter 3 assumptions recapped above and the assumption that the interest rate equals the world interest rate, we obtain _ _

NX = [Y − C(Y − T ) − G] − I(r∗) _ = S − I(r∗).

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142 | P A R T I I Classical Theory: The Economy in the Long Run

This equation shows that the trade balance NX depends on those variables that determine saving S and investment I. Because saving depends on fi scal policy (lower government purchases G or higher taxes T raise national saving) and investment depends on the world real interest rate r∗ (a higher interest rate makes some investment projects unprofi table), the trade balance depends on these vari- ables as well.

In Chapter 3 we graphed saving and investment as in Figure 6-2. In the closed economy studied in that chapter, the real interest rate adjusts to equilibrate sav- ing and investment—that is, the real interest rate is found where the saving and investment curves cross. In the small open economy, however, the real interest rate equals the world real interest rate. The trade balance is determined by the differ- ence between saving and investment at the world interest rate.

At this point, you might wonder about the mechanism that causes the trade balance to equal the net capital outfl ow. The determinants of the capital fl ows are easy to understand. When saving falls short of investment, investors borrow from abroad; when saving exceeds investment, the excess is lent to other countries. But what causes those who import and export to behave so as to ensure that the international fl ow of goods exactly balances this international fl ow of capital? For now we leave this question unanswered, but we return to it in Section 6-3 when we discuss the determination of exchange rates.

How Policies Influence the Trade Balance

Suppose that the economy begins in a position of balanced trade. That is, at the world interest rate, investment I equals saving S, and net exports NX equal zero. Let’s use our model to predict the effects of government policies at home and abroad.

FIGURE 6-2

Saving and Investment in a Small Open Economy In a closed economy, the real interest rate adjusts to equilibrate sav- ing and investment. In a small open economy, the interest rate is determined in world fi nancial markets. The difference between saving and investment determines the trade balance. Here there is a trade surplus, because at the world interest rate, saving exceeds investment.

Real interest rate, r

r*

NX

S

Investment, Saving, I, S

I(r)

World interest rate

Trade surplus

Interest rate if the economy were closed

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C H A P T E R 6 The Open Economy | 143

Fiscal Policy at Home Consider fi rst what happens to the small open economy if the government expands domestic spending by increasing government pur- chases. The increase in G reduces national saving, because S = Y − C − G. With an unchanged world real interest rate, investment remains the same. Therefore, saving falls below investment, and some investment must now be fi nanced by borrowing from abroad. Because NX = S − I, the fall in S implies a fall in NX. The economy now runs a trade defi cit.

The same logic applies to a decrease in taxes. A tax cut lowers T, raises dispos- able income Y − T, stimulates consumption, and reduces national saving. (Even though some of the tax cut fi nds its way into private saving, public saving falls by the full amount of the tax cut; in total, saving falls.) Because NX = S − I, the reduction in national saving in turn lowers NX.

Figure 6-3 illustrates these effects. A fi scal policy change that increases private consumption C or public consumption G reduces national saving (Y − C − G) and, therefore, shifts the vertical line that represents saving from S1 to S2. Because NX is the distance between the saving schedule and the investment schedule at the world interest rate, this shift reduces NX. Hence, starting from balanced trade, a change in fi scal policy that reduces national saving leads to a trade defi cit.

Fiscal Policy Abroad Consider now what happens to a small open economy when foreign governments increase their government purchases. If these foreign countries are a small part of the world economy, then their fi scal change has a negligible impact on other countries. But if these foreign countries are a large part of the world economy, their increase in government purchases reduces world saving. The decrease in world saving causes the world interest rate to rise, just as we saw in our closed-economy model (remember, Earth is a closed economy).

The increase in the world interest rate raises the cost of borrowing and, thus, reduces investment in our small open economy. Because there has been no change in domestic saving, saving S now exceeds investment I, and some of our

FIGURE 6-3

A Fiscal Expansion at Home in a Small Open Economy An increase in government purchases or a reduction in taxes reduces national saving and thus shifts the saving schedule to the left, from S1 to S2. The result is a trade defi cit.

Real interest rate, r

r*

NX < 0

S1

Investment, Saving, I, S

I(r)

S2 2. ... but when a fiscal expansion reduces saving, ...

1. This economy begins with balanced trade, ...

3. ... a trade deficit results.

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144 | P A R T I I Classical Theory: The Economy in the Long Run

saving begins to fl ow abroad. Because NX = S − I, the reduction in I must also increase NX. Hence, reduced saving abroad leads to a trade surplus at home.

Figure 6-4 illustrates how a small open economy starting from balanced trade responds to a foreign fi scal expansion. Because the policy change occurs abroad, the domestic saving and investment schedules remain the same. The only change is an increase in the world interest rate from r1* to r2*. The trade balance is the difference between the saving and investment schedules; because saving exceeds investment at r2*, there is a trade surplus. Hence, starting from balanced trade, an increase in the world interest rate due to a fi scal expansion abroad leads to a trade surplus.

Shifts in Investment Demand Consider what happens to our small open economy if its investment schedule shifts outward—that is, if the demand for investment goods at every interest rate increases. This shift would occur if, for example, the government changed the tax laws to encourage investment by providing an investment tax credit. Figure 6-5 illustrates the impact of a shift in the investment schedule. At a given world interest rate, investment is now higher. Because saving is unchanged, some investment must now be fi nanced by borrowing from abroad. Because capital fl ows into the economy to fi nance the increased investment, the net capital outfl ow is negative. Put differently, because NX = S − I, the increase in I implies a decrease in NX. Hence, starting from balanced trade, an outward shift in the investment schedule causes a trade defi cit.

Evaluating Economic Policy

Our model of the open economy shows that the fl ow of goods and services mea- sured by the trade balance is inextricably connected to the international fl ow of funds for capital accumulation. The net capital outfl ow is the difference between domestic saving and domestic investment. Thus, the impact of economic policies

FIGURE 6-4

A Fiscal Expansion Abroad in a Small Open Economy A fi scal expansion in a foreign economy large enough to infl uence world saving and investment raises the world interest rate from r1* to r2*. The higher world interest rate reduces investment in this small open economy, causing a trade surplus.

Real interest rate, r

NX > 0

S

Investment, Saving, I, S

I(r)

1. An increase in the world interest rate ...

2. ... reduces investment and leads to a trade surplus.

r*

r*

2

1

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C H A P T E R 6 The Open Economy | 145

on the trade balance can always be found by examining their impact on domestic saving and domestic investment. Policies that increase investment or decrease sav- ing tend to cause a trade defi cit, and policies that decrease investment or increase saving tend to cause a trade surplus.

Our analysis of the open economy has been positive, not normative. That is, our analysis of how economic policies infl uence the international fl ows of capital and goods has not told us whether these policies are desirable. Evaluating economic policies and their impact on the open economy is a frequent topic of debate among economists and policymakers.

When a country runs a trade defi cit, policymakers must confront the ques- tion of whether it represents a national problem. Most economists view a trade defi cit not as a problem in itself, but perhaps as a symptom of a problem. A trade defi cit could be a refl ection of low saving. In a closed economy, low saving leads to low investment and a smaller future capital stock. In an open economy, low saving leads to a trade defi cit and a growing foreign debt, which eventually must be repaid. In both cases, high current consumption leads to lower future consumption, implying that future generations bear the burden of low national saving.

Yet trade defi cits are not always a refl ection of an economic malady. When poor rural economies develop into modern industrial economies, they some- times fi nance their high levels of investment with foreign borrowing. In these cases, trade defi cits are a sign of economic development. For example, South Korea ran large trade defi cits throughout the 1970s, and it became one of the success stories of economic growth. The lesson is that one cannot judge eco- nomic performance from the trade balance alone. Instead, one must look at the underlying causes of the international fl ows.

FIGURE 6-5

A Shift in the Investment Schedule in a Small Open Economy An outward shift in the investment schedule from I(r)1 to I(r)2 increases the amount of investment at the world inter- est rate r*. As a result, invest- ment now exceeds saving, which means the economy is borrowing from abroad and running a trade defi cit.

Real interest rate, r

r* NX < 0

S

Investment, Saving, I, S

I(r) 2

I(r) 1

1. An increase in investment demand ...

2. ... leads to a trade deficit.

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146 | P A R T I I Classical Theory: The Economy in the Long Run

The U.S. Trade Deficit

During the 1980s, 1990s, and 2000s, the United States ran large trade defi cits. Panel (a) of Figure 6-6 documents this experience by showing net exports as a percentage of GDP. The exact size of the trade defi cit fl uctuated over time, but it was large throughout these three decades. In 2010, the trade defi cit was $517 billion, or 3.6 percent of GDP. As accounting identities require, this trade defi cit had to be fi nanced by borrowing from abroad (or, equivalently, by selling U.S. assets abroad). During this period, the United States went from being the world’s largest creditor to the world’s largest debtor.

What caused the U.S. trade defi cit? There is no single explanation. But to understand some of the forces at work, it helps to look at national saving and domestic investment, as shown in panel (b) of the fi gure. Keep in mind that the trade defi cit is the difference between saving and investment.

The start of the trade defi cit coincided with a fall in national saving. This development can be explained by the expansionary fi scal policy in the 1980s. With the support of President Reagan, the U.S. Congress passed legislation in 1981 that substantially cut personal income taxes over the next three years. Because these tax cuts were not met with equal cuts in government spending, the federal budget went into defi cit. These budget defi cits were among the largest ever experienced in a period of peace and prosperity, and they continued long after Reagan left offi ce. According to our model, such a policy should reduce national saving, thereby causing a trade defi cit. And, in fact, that is exactly what happened. Because the government budget and trade balance went into defi cit at roughly the same time, these shortfalls were called the twin defi cits.

Things started to change in the 1990s, when the U.S. federal government got its fi scal house in order. The fi rst President Bush and President Clinton both signed tax increases, while Congress kept a lid on spending. In addition to these policy changes, rapid productivity growth in the late 1990s raised incomes and, thus, further increased tax revenue. These developments moved the U.S. federal budget from defi cit to surplus, which in turn caused national saving to rise.

In contrast to what our model predicts, the increase in national saving did not coincide with a shrinking trade defi cit, because domestic investment rose at the same time. The likely explanation is that the boom in information technology caused an expansionary shift in the U.S. investment function. Even though fi scal policy was pushing the trade defi cit toward surplus, the investment boom was an even stronger force pushing the trade balance toward defi cit.

In the early 2000s, fi scal policy once again put downward pressure on national saving. With the second President Bush in the White House, tax cuts were signed into law in 2001 and 2003, while the war on terror led to substan- tial increases in government spending. The federal government was again run- ning budget defi cits. National saving fell to historic lows, and the trade defi cit reached historic highs.

A few years later, the trade defi cit started to shrink somewhat, as the economy experienced a substantial decline in housing prices (a phenomenon examined in

CASE STUDY

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C H A P T E R 6 The Open Economy | 147

FIGURE 6-6

The Trade Balance, Saving, and Investment: The U.S. Experience Panel (a) shows the trade balance as a percentage of GDP. Positive numbers represent a surplus, and negative numbers represent a defi cit. Panel (b) shows national saving and investment as a percentage of GDP from 1960 to 2010. The trade balance equals saving minus investment.

Source: U.S. Department of Commerce.

2

1

0

–1

–2

–3

–4

–5

–6

–7 1960

Year

Percentage of GDP

Year

10

12

14

16

18

20

22

24

(b) U.S. Saving and Investment

(a) The U.S. Trade Balance

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Investment

Saving

Percentage of GDP

Surplus

Deficit

Trade balance

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148 | P A R T I I Classical Theory: The Economy in the Long Run

Case Studies in Chapters 12 and 17). Lower housing prices led to a substantial decline in residential investment. The trade defi cit fell from 5.8 percent of GDP at its peak in 2006 to 3.6 percent in 2010.

The history of the U.S. trade defi cit shows that this statistic, by itself, does not tell us much about what is happening in the economy. We have to look deeper at saving, investment, and the policies and events that cause them (and thus the trade balance) to change over time.1 ■

1For more on this topic, see Catherine L. Mann, Is the U.S. Trade Defi cit Sustainable? Institute for International Economics, 1999.

Why Doesn’t Capital Flow to Poor Countries?

The U.S. trade defi cit discussed in the previous Case Study represents a fl ow of capi- tal into the United States from the rest of the world. What countries were the source of these capital fl ows? Because the world is a closed economy, the capital must have been coming from those countries that were running trade surpluses. In 2010, this group included many nations that were far poorer than the United States, such as Russia, Malaysia, Venezuela, and China. In these nations, saving exceeded investment in domestic capital. These countries were sending funds abroad to countries like the United States, where investment in domestic capital exceeded saving.

From one perspective, the direction of international capital fl ows is a paradox. Recall our discussion of production functions in Chapter 3. There, we established that an empirically realistic production function is the Cobb–Douglas form:

F(K, L) � A K�L1��,

where K is capital, L is labor, A is a variable representing the state of technol- ogy, and � is a parameter that determines capital’s share of total income. For this production function, the marginal product of capital is

MPK � � A (K/L)�–1.

The marginal product of capital tells us how much extra output an extra unit of capital would produce. Because � is capital’s share, it must be less than 1, so � � 1 < 0. This means that an increase in K/L decreases MPK. In other words, holding other variables constant, the more capital a nation has, the less valuable an extra unit of capital is. This phenomenon of diminishing marginal product says that capital should be more valuable where capital is scarce.

This prediction, however, seems at odds with the international fl ow of capital rep- resented by trade imbalances. Capital does not seem to fl ow to those nations where it should be most valuable. Instead of capital-rich countries like the United States lending to capital-poor countries, we often observe the opposite. Why is that?

One reason is that there are important differences among nations other than their accumulation of capital. Poor nations have not only lower levels of capital accumulation per worker (represented by K/L) but also inferior pro- duction capabilities (represented by the variable A). For example, compared to

CASE STUDY

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C H A P T E R 6 The Open Economy | 149

6-3 Exchange Rates

Having examined the international fl ows of capital and of goods and services, we now extend the analysis by considering the prices that apply to these transactions. The exchange rate between two countries is the price at which residents of those countries trade with each other. In this section we fi rst examine precisely what the exchange rate measures and then discuss how exchange rates are determined.

Nominal and Real Exchange Rates

Economists distinguish between two exchange rates: the nominal exchange rate and the real exchange rate. Let’s discuss each in turn and see how they are related.

The Nominal Exchange Rate The nominal exchange rate is the rela- tive price of the currencies of two countries. For example, if the exchange rate between the U.S. dollar and the Japanese yen is 80 yen per dollar, then you can exchange one dollar for 80 yen in world markets for foreign currency. A Japanese who wants to obtain dollars would pay 80 yen for each dollar he bought. An American who wants to obtain yen would get 80 yen for each dollar he paid. When people refer to “the exchange rate’’ between two countries, they usually mean the nominal exchange rate.

rich nations, poor nations may have less access to advanced technologies, lower levels of education (or human capital), or less effi cient economic policies. Such differences could mean less output for given inputs of capital and labor; in the Cobb–Douglas production function, this is translated into a lower value of the parameter A. If so, then capital need not be more valuable in poor nations, even though capital is scarce.

A second reason capital might not fl ow to poor nations is that property rights are often not enforced. Corruption is much more prevalent; revolutions, coups, and expropriation of wealth are more common; and governments often default on their debts. So even if capital is more valuable in poor nations, foreigners may avoid investing their wealth there simply because they are afraid of losing it. Moreover, local investors face similar incentives. Imagine that you live in a poor nation and are lucky enough to have some wealth to invest; you might well decide that putting it in a safe country like the United States is your best option, even if capital is less valuable there than in your home country.

Whichever of these two reasons is correct, the challenge for poor nations is to fi nd ways to reverse the situation. If these nations offered the same production effi ciency and legal protections as the U.S. economy, the direction of interna- tional capital fl ows would likely reverse. The U.S. trade defi cit would become a trade surplus, and capital would fl ow to these emerging nations. Such a change would help the poor of the world escape poverty.2 ■

2For more on this topic, see Robert E. Lucas, “Why Doesn’t Capital Flow From Rich to Poor Countries?” American Economic Review 80 (May 1990): 92–96.

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150 | P A R T I I Classical Theory: The Economy in the Long Run

Notice that an exchange rate can be reported in two ways. If one dollar buys 80 yen, then one yen buys 0.0125 dollar. We can say the exchange rate is 80 yen per dollar, or we can say the exchange rate is 0.0125 dollar per yen. Because 0.0125 equals 1/80, these two ways of expressing the exchange rate are equivalent.

This book always expresses the exchange rate in units of foreign currency per dollar. With this convention, a rise in the exchange rate—say, from 80 to 100 yen per dollar—is called an appreciation of the dollar; a fall in the exchange rate is called a depreciation. When the domestic currency appreciates, it buys more of the foreign currency; when it depreciates, it buys less. An appreciation is sometimes called a strengthening of the currency, and a depreciation is sometimes called a weakening of the currency.

The Real Exchange Rate The real exchange rate is the relative price of the goods of two countries. That is, the real exchange rate tells us the rate at which we can trade the goods of one country for the goods of another. The real exchange rate is sometimes called the terms of trade.

To see the relation between the real and nominal exchange rates, consider a single good produced in many countries: cars. Suppose an American car costs $25,000 and a similar Japanese car costs 4,000,000 yen. To compare the prices of the two cars, we must convert them into a common currency. If a dollar is worth 80 yen, then the American car costs 80 × 25,000, or 2,000,000 yen. Comparing the price of the American car (2,000,000 yen) and the price of the Japanese car (4,000,000 yen), we conclude that the American car costs one-half of what the Japanese car costs. In other words, at current prices, we can exchange 2 American cars for 1 Japanese car.

We can summarize our calculation as follows:

(80 Yen/Dollar) × (25,000 Dollars/American Car) Real Exchange Rate = (4,000,000 Yen/Japanese Car)

Japanese Car = 0.5 . American Car

At these prices and this exchange rate, we obtain one-half of a Japanese car per American car. More generally, we can write this calculation as

Nominal Exchange Rate × Price of Domestic Good Real Exchange Rate = . Price of Foreign Good

The rate at which we exchange foreign and domestic goods depends on the prices of the goods in the local currencies and on the rate at which the curren- cies are exchanged.

This calculation of the real exchange rate for a single good suggests how we should defi ne the real exchange rate for a broader basket of goods. Let e be the nominal exchange rate (the number of yen per dollar), P be the price level in

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C H A P T E R 6 The Open Economy | 151

the United States (measured in dollars), and P∗ be the price level in Japan (mea- sured in yen). Then the real exchange rate � is

Real Nominal Ratio of Exchange = Exchange × Price Rate Rate Levels

� = e × (P/P∗).

The real exchange rate between two countries is computed from the nominal exchange rate and the price levels in the two countries. If the real exchange rate is high, foreign goods are relatively cheap, and domestic goods are relatively expensive. If the real exchange rate is low, foreign goods are relatively expensive, and domestic goods are relatively cheap.

The Real Exchange Rate and the Trade Balance

What macroeconomic infl uence does the real exchange rate exert? To answer this question, remember that the real exchange rate is nothing more than a relative price. Just as the relative price of hamburgers and pizza determines which you choose for lunch, the relative price of domestic and foreign goods affects the demand for these goods.

Suppose fi rst that the real exchange rate is low. In this case, because domestic goods are relatively cheap, domestic residents will want to purchase fewer import- ed goods: they will buy Fords rather than Toyotas, drink Coors rather than Heineken, and vacation in Florida rather than Italy. For the same reason, foreign- ers will want to buy many of our goods. As a result of both of these actions, the quantity of our net exports demanded will be high.

The opposite occurs if the real exchange rate is high. Because domestic goods are expensive relative to foreign goods, domestic resi- dents will want to buy many imported goods, and foreigners will want to buy few of our goods. Therefore, the quantity of our net exports demanded will be low.

We write this relationship between the real exchange rate and net exports as

NX = NX(�).

This equation states that net exports are a function of the real exchange rate. Figure 6-7 illustrates the negative relationship between the trade balance and the real exchange rate.

The Determinants of the Real Exchange Rate

We now have all the pieces needed to construct a model that explains what fac- tors determine the real exchange rate. In particular, we combine the relationship between net exports and the real exchange rate we just discussed with the model

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152 | P A R T I I Classical Theory: The Economy in the Long Run

of the trade balance we developed earlier in the chapter. We can summarize the analysis as follows:

■ The real exchange rate is related to net exports. When the real exchange rate is lower, domestic goods are less expensive relative to foreign goods, and net exports are greater.

■ The trade balance (net exports) must equal the net capital outfl ow, which in turn equals saving minus investment. Saving is fi xed by the consumption function and fi scal policy; investment is fi xed by the investment function and the world interest rate.

Figure 6-8 illustrates these two conditions. The line showing the relationship between net exports and the real exchange rate slopes downward because a low real exchange rate makes domestic goods relatively inexpensive. The line

FIGURE 6-7

Net Exports and the Real Exchange Rate The fi gure shows the relationship between the real exchange rate and net exports: the lower the real exchange rate, the less expen- sive are domestic goods relative to foreign goods, and thus the greater are our net exports. Note that a portion of the hori- zontal axis measures negative values of NX: because imports can exceed exports, net exports can be less than zero.

Real exchange rate, �

Net exports, NX0

NX(�)

FIGURE 6-8

How the Real Exchange Rate Is Determined The real exchange rate is determined by the intersection of the vertical line representing saving minus investment and the downward- sloping net-exports schedule. At this intersection, the quantity of dollars supplied for the fl ow of capital abroad equals the quantity of dollars demanded for the net export of goods and services.

Real exchange rate, �

Net exports, NX

Equilibrium real exchange rate

S � I

NX(�)

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C H A P T E R 6 The Open Economy | 153

representing the excess of saving over investment, S − I, is vertical because neither saving nor investment depends on the real exchange rate. The crossing of these two lines determines the equilibrium real exchange rate.

Figure 6-8 looks like an ordinary supply-and-demand diagram. In fact, you can think of this diagram as representing the supply and demand for foreign- currency exchange. The vertical line, S − I, represents the net capital outfl ow and thus the supply of dollars to be exchanged into foreign currency and invested abroad. The downward-sloping line, NX(�), represents the net demand for dollars coming from foreigners who want dollars to buy our goods. At the equilibrium real exchange rate, the supply of dollars available from the net capital outfl ow balances the demand for dollars by foreigners buying our net exports.

How Policies Influence the Real Exchange Rate

We can use this model to show how the changes in economic policy we dis- cussed earlier affect the real exchange rate.

Fiscal Policy at Home What happens to the real exchange rate if the gov- ernment reduces national saving by increasing government purchases or cutting taxes? As we discussed earlier, this reduction in saving lowers S − I and thus NX. That is, the reduction in saving causes a trade defi cit.

Figure 6-9 shows how the equilibrium real exchange rate adjusts to ensure that NX falls. The change in policy shifts the vertical S − I line to the left, lowering the supply of dollars to be invested abroad. The lower supply causes the equilibrium real exchange rate to rise from �1 to �2—that is, the dollar becomes more valu- able. Because of the rise in the value of the dollar, domestic goods become more expensive relative to foreign goods, which causes exports to fall and imports to rise. The change in exports and the change in imports both act to reduce net exports.

FIGURE 6-9

The Impact of Expansionary Fiscal Policy at Home on the Real Exchange Rate Expansionary fi scal policy at home, such as an increase in government purchases or a cut in taxes, reduces national sav- ing. The fall in saving reduces the supply of dollars to be exchanged into foreign currency, from S1 − I to S2 − I. This shift raises the equilibrium real exchange rate from �1 to �2.

Real exchange rate, �

Net exports, NX

1. A reduction in saving reduces the supply of dollars, ...

2. ... which raises the real exchange rate ...

�2

�1

NX2 NX1

NX(�)

S2 � I S1 � I

3. ... and causes net exports to fall.

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154 | P A R T I I Classical Theory: The Economy in the Long Run

Fiscal Policy Abroad What happens to the real exchange rate if foreign governments increase government purchases or cut taxes? Either change in fi scal policy reduces world saving and raises the world interest rate. The increase in the world interest rate reduces domestic investment I, which raises S − I and thus NX. That is, the increase in the world interest rate causes a trade surplus.

Figure 6-10 shows that this change in policy shifts the vertical S − I line to the right, raising the supply of dollars to be invested abroad. The equilibrium real exchange rate falls. That is, the dollar becomes less valuable, and domestic goods become less expensive relative to foreign goods.

Shifts in Investment Demand What happens to the real exchange rate if invest- ment demand at home increases, perhaps because Congress passes an investment tax credit? At the given world interest rate, the increase in investment demand leads to higher investment. A higher value of I means lower values of S − I and NX. That is, the increase in investment demand causes a trade defi cit.

Figure 6-11 shows that the increase in investment demand shifts the vertical S − I line to the left, reducing the supply of dollars to be invested abroad. The equilibrium real exchange rate rises. Hence, when the investment tax credit makes investing in the United States more attractive, it also increases the value of the U.S. dollars necessary to make these investments. When the dollar appreciates, domestic goods become more expensive relative to foreign goods, and net exports fall.

The Effects of Trade Policies

Now that we have a model that explains the trade balance and the real exchange rate, we have the tools to examine the macroeconomic effects of trade policies. Trade policies, broadly defi ned, are policies designed to directly infl uence the

FIGURE 6-10

The Impact of Expansionary Fiscal Policy Abroad on the Real Exchange Rate Expansionary fi scal policy abroad reduces world saving and raises the world interest rate from r1* to r2*. The increase in the world interest rate reduces investment at home, which in turn raises the sup- ply of dollars to be exchanged into foreign currencies. As a result, the equilibrium real exchange rate falls from �1 to �2.

Real exchange rate, �

Net exports, NX

* *

�1

�2

NX1 NX2

NX(�)

S � I(r1) S � I(r2)

3. ... and raises net exports.

2. ... causes the real exchange rate to fall, ...

1. An increase in world interest rates reduces investment, which increases the supply of dollars, ...

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C H A P T E R 6 The Open Economy | 155

amount of goods and services exported or imported. Most often, trade policies take the form of protecting domestic industries from foreign competition— either by placing a tax on foreign imports (a tariff) or restricting the amount of goods and services that can be imported (a quota).

As an example of a protectionist trade policy, consider what would happen if the government prohibited the import of foreign cars. For any given real exchange rate, imports would now be lower, implying that net exports (exports minus imports) would be higher. Thus, the net-exports schedule would shift outward, as in Figure 6-12. To see the effects of the policy, we compare the old equilibrium and the new equilibrium. In the new equilibrium, the real exchange rate is higher, and net exports are unchanged. Despite the shift in the net-exports schedule, the equilibrium level of net exports remains the same, because the pro- tectionist policy does not alter either saving or investment.

This analysis shows that protectionist trade policies do not affect the trade bal- ance. This surprising conclusion is often overlooked in the popular debate over trade policies. Because a trade defi cit refl ects an excess of imports over exports, one might guess that reducing imports—such as by prohibiting the import of foreign cars—would reduce a trade defi cit. Yet our model shows that protection- ist policies lead only to an appreciation of the real exchange rate. The increase in the price of domestic goods relative to foreign goods tends to lower net exports by stimulating imports and depressing exports. Thus, the appreciation offsets the increase in net exports that is directly attributable to the trade restriction.

Although protectionist trade policies do not alter the trade balance, they do affect the amount of trade. As we have seen, because the real exchange rate appre- ciates, the goods and services we produce become more expensive relative to for- eign goods and services. We therefore export less in the new equilibrium. Because

FIGURE 6-11

The Impact of an Increase in Investment Demand on the Real Exchange Rate An increase in investment demand raises the quantity of domestic investment from I1 to I2. As a result, the supply of dollars to be exchanged into foreign currencies falls from S – I1 to S – I2. This fall in supply raises the equilibrium real exchange rate from �1 to �2.

Real exchange rate, �

Net exports, NX

�2

�1

NX2 NX1

NX(�)

S � I2 S � I1 1. An increase in investment reduces the supply of dollars, ...

2. ... which raises the exchange rate ...

3. ... and reduces net exports.

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156 | P A R T I I Classical Theory: The Economy in the Long Run

net exports are unchanged, we must import less as well. (The appreciation of the exchange rate does stimulate imports to some extent, but this only partly offsets the decrease in imports due to the trade restriction.) Thus, protectionist policies reduce both the quantity of imports and the quantity of exports.

This fall in the total amount of trade is the reason economists almost always oppose protectionist policies. International trade benefi ts all countries by allowing each country to specialize in what it produces best and by providing each country with a greater variety of goods and services. Protectionist policies diminish these gains from trade. Although these policies benefi t certain groups within society— for example, a ban on imported cars helps domestic car producers—society on average is worse off when policies reduce the amount of international trade.

The Determinants of the Nominal Exchange Rate

Having seen what determines the real exchange rate, we now turn our attention to the nominal exchange rate—the rate at which the currencies of two countries trade. Recall the relationship between the real and the nominal exchange rate:

Real Nominal Ratio of Exchange = Exchange × Price Rate Rate Levels

� = e × (P/P∗).

We can write the nominal exchange rate as

e = � × (P∗/P).

FIGURE 6-12

The Impact of Protectionist Trade Policies on the Real Exchange Rate A protectionist trade policy, such as a ban on imported cars, shifts the net- exports schedule from NX(�)1 to NX(�)2, which raises the real exchange rate from �1 to �2. Notice that, despite the shift in the net-exports schedule, the equilibrium level of net exports is unchanged.

Real exchange rate, �

Net exports, NX

�1

�2

S � I

NX(�)2

NX(�)1

NX1 � NX2

3. ... but leave net exports unchanged.

2. ... and raise the exchange rate ...

1. Protectionist policies raise the demand for net exports ...

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C H A P T E R 6 The Open Economy | 157

This equation shows that the nominal exchange rate depends on the real exchange rate and the price levels in the two countries. Given the value of the real exchange rate, if the domestic price level P rises, then the nominal exchange rate e will fall: because a dollar is worth less, a dollar will buy fewer yen. However, if the Japanese price level P∗ rises, then the nominal exchange rate will increase: because the yen is worth less, a dollar will buy more yen.

It is instructive to consider changes in exchange rates over time. The exchange rate equation can be written

% Change in e = % Change in � + % Change in P∗ − % Change in P.

The percentage change in � is the change in the real exchange rate. The percent- age change in P is the domestic infl ation rate �, and the percentage change in P∗ is the foreign country’s infl ation rate �∗. Thus, the percentage change in the nominal exchange rate is

% Change in e = % Change in � + (�∗ − �)

Percentage Change in Percentage Change in + Difference in

Nominal Exchange Rate =

Real Exchange Rate Infl ation Rates.

This equation states that the percentage change in the nominal exchange rate between the currencies of two countries equals the percentage change in the real exchange rate plus the difference in their infl ation rates. If a country has a high rate of infl ation relative to the United States, a dollar will buy an increasing amount of the foreign currency over time. If a country has a low rate of infl ation relative to the United States, a dollar will buy a decreasing amount of the foreign currency over time.

This analysis shows how monetary policy affects the nominal exchange rate. We know from Chapter 5 that high growth in the money supply leads to high infl a- tion. Here, we have just seen that one consequence of high infl ation is a depreciating currency: high � implies falling e. In other words, just as growth in the amount of money raises the price of goods measured in terms of money, it also tends to raise the price of foreign currencies measured in terms of the domestic currency.

Inflation and Nominal Exchange Rates

If we look at data on exchange rates and price levels of different countries, we quickly see the importance of infl ation for explaining changes in the nominal exchange rate. The most dramatic examples come from periods of very high infl ation. For example, the price level in Mexico rose by 2,300 percent from 1983 to 1988. Because of this infl ation, the number of pesos a person could buy with a U.S. dollar rose from 144 in 1983 to 2,281 in 1988.

The same relationship holds true for countries with more moderate infl ation. Figure 6-13 is a scatterplot showing the relationship between infl ation and the exchange rate for 15 countries. On the horizontal axis is the difference between each

CASE STUDY

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158 | P A R T I I Classical Theory: The Economy in the Long Run

FIGURE 6-13

Infl ation Differentials and the Exchange Rate This scatterplot shows the relationship between infl ation and the nominal exchange rate. The horizontal axis shows the country’s average infl ation rate minus the U.S. average infl ation rate over the period 2001–2010. The vertical axis is the average percentage change in the country’s exchange rate (per U.S. dollar) over that period. This fi gure shows that countries with relatively high infl a- tion tend to have depreciating currencies and that countries with relatively low infl ation tend to have appreciating currencies.

Source: International Monetary Fund.

Percentage change in nominal exchange rate

Inflation differential

Depreciation relative to United States dollar

Appreciation relative to United States dollar

Canada Australia

Japan

Denmark

Iceland

Norway

Sweden

Switzerland

U.K.

Pakistan

Singapore

New Zealand

South Africa South Korea

Mexico

–6

–4

–2

0

2

4

6

8

–4 –2 0 2 4 6 8

country’s average infl ation rate and the average infl ation rate of the United States (�∗ − �). On the vertical axis is the average percentage change in the exchange rate between each country’s currency and the U.S. dollar (percentage change in e). The positive relationship between these two variables is clear in this fi gure. The correla- tion between these variables—a statistic that runs from −1 to +1 and measures how closely the variables are related—is 0.81. Countries with relatively high infl ation tend to have depreciating currencies (you can buy more of them with your dollars over time), and countries with relatively low infl ation tend to have appreciating cur- rencies (you can buy less of them with your dollars over time).

As an example, consider the exchange rate between Swiss francs and U.S. dollars. Both Switzerland and the United States have experienced infl ation over this decade, so both the franc and the dollar buy fewer goods than they once did. But, as Figure 6-13 shows, infl ation in Switzerland has been lower than infl ation in the United States. This means that the value of the franc has fallen less than the value of the dollar. Therefore, the number of Swiss francs you can buy with a U.S. dollar has been falling over time. ■

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The Special Case of Purchasing-Power Parity

A famous hypothesis in economics, called the law of one price, states that the same good cannot sell for different prices in different locations at the same time. If a bushel of wheat sold for less in New York than in Chicago, it would be profi table to buy wheat in New York and then sell it in Chicago. This profi t opportunity would become quickly apparent to astute arbitrageurs—people who specialize in “buying low” in one market and “selling high” in another. As the arbitrageurs took advantage of this opportunity, they would increase the demand for wheat in New York and increase the supply of wheat in Chicago. Their actions would drive the price up in New York and down in Chicago, thereby ensuring that prices are equalized in the two markets.

The law of one price applied to the international marketplace is called purchasing- power parity. It states that if international arbitrage is possible, then a dollar (or any other currency) must have the same purchasing power in every coun- try. The argument goes as follows. If a dollar could buy more wheat domestically than abroad, there would be opportunities to profi t by buying wheat domestically and selling it abroad. Profi t-seeking arbitrageurs would drive up the domestic price of wheat relative to the foreign price. Similarly, if a dollar could buy more wheat abroad than domestically, the arbitrageurs would buy wheat abroad and sell it domestically, driving down the domestic price relative to the foreign price. Thus, profi t-seeking by international arbitrageurs causes wheat prices to be the same in all countries.

We can interpret the doctrine of purchasing-power parity using our model of the real exchange rate. The quick action of these international arbitrageurs implies that net exports are highly sensitive to small movements in the real exchange rate. A small decrease in the price of domestic goods relative to for- eign goods—that is, a small decrease in the real exchange rate—causes arbitra- geurs to buy goods domestically and sell them abroad. Similarly, a small increase in the relative price of domestic goods causes arbitrageurs to import goods from abroad. Therefore, as in Figure 6-14, the net-exports schedule is very fl at at the

FIGURE 6-14

Purchasing-Power Parity The law of one price applied to the international marketplace sug- gests that net exports are highly sensitive to small movements in the real exchange rate. This high sensitivity is refl ected here with a very fl at net-exports schedule.

Real exchange rate, �

Net exports, NX

NX(�)

S � I

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160 | P A R T I I Classical Theory: The Economy in the Long Run

real exchange rate that equalizes purchasing power among countries: any small movement in the real exchange rate leads to a large change in net exports. This extreme sensitivity of net exports guarantees that the equilibrium real exchange rate is always close to the level that ensures purchasing-power parity.

Purchasing-power parity has two important implications. First, because the net-exports schedule is fl at, changes in saving or investment do not infl uence the real or nominal exchange rate. Second, because the real exchange rate is fi xed, all changes in the nominal exchange rate result from changes in price levels.

Is this doctrine of purchasing-power parity realistic? Most economists believe that, despite its appealing logic, purchasing-power parity does not pro- vide a completely accurate description of the world. First, many goods are not easily traded. A haircut can be more expensive in Tokyo than in New York, yet there is no room for international arbitrage because it is impossible to transport haircuts. Second, even tradable goods are not always perfect substitutes. Some consumers prefer Toyotas, and others prefer Fords. Thus, the relative price of Toyotas and Fords can vary to some extent without leaving any profi t oppor- tunities. For these reasons, real exchange rates do in fact vary over time.

Although the doctrine of purchasing-power parity does not describe the world perfectly, it does provide a reason why movement in the real exchange rate will be limited. There is much validity to its underlying logic: the farther the real exchange rate drifts from the level predicted by purchasing-power parity, the greater the incentive for individuals to engage in international arbitrage in goods. We cannot rely on purchasing-power parity to eliminate all changes in the real exchange rate, but this doctrine does provide a reason to expect that fl uctua- tions in the real exchange rate will typically be small or temporary.3

The Big Mac Around the World

The doctrine of purchasing-power parity says that after we adjust for exchange rates, we should fi nd that goods sell for the same price everywhere. Conversely, it says that the exchange rate between two currencies should depend on the price levels in the two countries.

To see how well this doctrine works, The Economist, an international news- magazine, regularly collects data on the price of a good sold in many countries: the McDonald’s Big Mac hamburger. According to purchasing-power parity, the price of a Big Mac should be closely related to the country’s nominal exchange rate. The higher the price of a Big Mac in the local currency, the higher the exchange rate (measured in units of local currency per U.S. dollar) should be.

Table 6-2 presents the international prices in 2011, when a Big Mac sold for $4.07 in the United States (this was the average price in New York, San Francisco,

CASE STUDY

3To learn more about purchasing-power parity, see Kenneth A. Froot and Kenneth Rogoff, “Perspectives on PPP and Long-Run Real Exchange Rates,” in Gene M. Grossman and Kenneth Rogoff, eds., Handbook of International Economics, vol. 3 (Amsterdam: North-Holland, 1995).

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Exchange rate (per U.S. dollar) Price of a Country Currency Big Mac Predicted Actual

Indonesia Rupiah 22534.00 5537 8523.0 Colombia Peso 8400.00 2064 1771.0 South Korea Won 3700.00 909 1056.0 Chile Peso 1850.00 455 463.0 Hungary Forint 760.00 187 188.0 Japan Yen 320.00 78.6 78.4 Pakistan Rupee 205.00 50.4 86.3 Philippines Peso 118.00 29.0 42.0 India Rupee 84.00 20.6 44.4 Russia Rouble 75.00 18.4 27.8 Taiwan NT Dollar 75.00 18.4 28.8 Thailand Baht 70.00 17.2 29.8 Czech Republic Koruna 69.30 17.0 17.0 Sweden Krona 48.40 11.9 6.3 Norway Kroner 45.00 11.1 5.4 Mexico Peso 32.00 7.86 11.70 Denmark D. Krone 28.50 7.00 5.20 Argentina Peso 20.00 4.91 4.13 South Africa Rand 19.45 4.78 6.77 Israel Shekel 15.90 3.91 3.40 Hong Kong HK Dollar 15.10 3.71 7.79 China Yuan 14.70 3.61 6.45 Egypt Pound 14.10 3.46 5.96 Peru Sol 10.00 2.46 2.74 Saudi Arabia Riyal 10.00 2.46 3.75 Brazil Real 9.50 2.33 1.54 Poland Zloty 8.63 2.12 2.80 Malaysia Ringgit 7.20 1.77 2.97 Switzerland S. Franc 6.50 1.60 0.81 Turkey Lira 6.50 1.60 1.72 New Zealand NZ Dollar 5.10 1.25 1.16 Canada C. Dollar 4.73 1.16 0.95 Australia A. Dollar 4.56 1.12 0.92 Singapore S. Dollar 4.41 1.08 1.21 United States Dollar 4.07 1.00 1.00 Euro area Euro 3.44 0.85 0.70 Britain Pound 2.39 0.59 0.61

Note: The predicted exchange rate is the exchange rate that would make the price of a Big Mac in that country equal to its price in the United States. Source: The Economist, July 28, 2011.

Big Mac Prices and the Exchange Rate: An Application of Purchasing-Power Parity

TABLE 6-2

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162 | P A R T I I Classical Theory: The Economy in the Long Run

6-4 Conclusion: The United States as a Large Open Economy

In this chapter we have seen how a small open economy works. We have exam- ined the determinants of the international fl ow of funds for capital accumulation and the international fl ow of goods and services. We have also examined the determinants of a country’s real and nominal exchange rates. Our analysis shows how various policies—monetary policies, fi scal policies, and trade policies—affect the trade balance and the exchange rate.

The economy we have studied is “small’’ in the sense that its interest rate is fi xed by world fi nancial markets. That is, we have assumed that this economy does not affect the world interest rate and that the economy can borrow and lend at the world interest rate in unlimited amounts. This assumption contrasts with the assumption we made when we studied the closed economy in Chapter 3. In the closed economy, the domestic interest rate equilibrates domestic saving and domestic investment, implying that policies that infl uence saving or investment alter the equilibrium interest rate.

Which of these analyses should we apply to an economy such as that of the United States? The answer is a little of both. The United States is neither so large nor so isolated that it is immune to developments occurring abroad. The large trade defi cits of the 1980s, 1990s, and 2000s show the importance of international fi nancial markets for funding U.S. investment. Hence, the closed-economy analysis of Chapter 3 cannot by itself fully explain the impact of policies on the U.S. economy.

Yet the U.S. economy is not so small and so open that the analysis of this chapter applies perfectly either. First, the United States is large enough that it can infl uence world fi nancial markets. Second, capital may not be perfectly mobile across countries. If individuals prefer holding their wealth in domestic rather

Chicago, and Atlanta). With these data we can use the doctrine of purchasing- power parity to predict nominal exchange rates. For example, because a Big Mac cost 320 yen in Japan, we would predict that the exchange rate between the dollar and the yen was 320/4.07, or 78.6, yen per dollar. At this exchange rate, a Big Mac would have cost the same in Japan and the United States.

Table 6-2 shows the predicted and actual exchange rates for 36 countries, plus the euro area, ranked by the predicted exchange rate. You can see that the evidence on purchasing-power parity is mixed. As the last two columns show, the actual and predicted exchange rates are usually in the same ballpark. Our theory predicts, for instance, that a U.S. dollar should buy the greatest number of Indonesian rupiahs and fewest British pounds, and this turns out to be true. In the case of Japan, the predicted exchange rate of 78.6 yen per dollar is very close to the actual exchange rate of 78.4. Yet the theory’s predictions are far from exact and, in many cases, are off by 30 percent or more. Hence, although the theory of purchasing-power parity provides a rough guide to the level of exchange rates, it does not explain exchange rates completely. ■

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C H A P T E R 6 The Open Economy | 163

than foreign assets, funds for capital accumulation will not fl ow freely to equate interest rates in all countries. For these two reasons, we cannot directly apply our model of the small open economy to the United States.

When analyzing policy for a country such as the United States, we need to combine the closed-economy logic of Chapter 3 and the small-open-economy logic of this chapter. The appendix to this chapter builds a model of an economy between these two extremes. In this intermediate case, there is international bor- rowing and lending, but the interest rate is not fi xed by world fi nancial markets. Instead, the more the economy borrows from abroad, the higher the interest rate it must offer foreign investors. The results, not surprisingly, are a mixture of the two polar cases we have already examined.

Consider, for example, a reduction in national saving due to a fi scal expansion. As in the closed economy, this policy raises the real interest rate and crowds out domes- tic investment. As in the small open economy, it also reduces the net capital outfl ow, leading to a trade defi cit and an appreciation of the exchange rate. Hence, although the model of the small open economy examined here does not precisely describe an economy such as that of the United States, it does provide approximately the right answer to how policies affect the trade balance and the exchange rate.

Summary

1. Net exports are the difference between exports and imports. They are equal to the difference between what we produce and what we demand for con- sumption, investment, and government purchases.

2. The net capital outfl ow is the excess of domestic saving over domestic investment. The trade balance is the amount received for our net exports of goods and services. The national income accounts identity shows that the net capital outfl ow always equals the trade balance.

3. The impact of any policy on the trade balance can be determined by examining its impact on saving and investment. Policies that raise saving or lower investment lead to a trade surplus, and policies that lower saving or raise investment lead to a trade defi cit.

4. The nominal exchange rate is the rate at which people trade the currency of one country for the currency of another country. The real exchange rate is the rate at which people trade the goods produced by the two countries. The real exchange rate equals the nominal exchange rate multiplied by the ratio of the price levels in the two countries.

5. Because the real exchange rate is the price of domestic goods relative to foreign goods, an appreciation of the real exchange rate tends to reduce net exports. The equilibrium real exchange rate is the rate at which the quan- tity of net exports demanded equals the net capital outfl ow.

6. The nominal exchange rate is determined by the real exchange rate and the price levels in the two countries. Other things equal, a high rate of infl ation leads to a depreciating currency.

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164 | P A R T I I Classical Theory: The Economy in the Long Run

K E Y C O N C E P T S

Net exports

Trade balance

Net capital outfl ow

Trade surplus and trade defi cit

Balanced trade

Small open economy

World interest rate

Nominal exchange rate

Real exchange rate

Purchasing-power parity

1. What are the net capital outfl ow and the trade balance? Explain how they are related.

2. Defi ne the nominal exchange rate and the real exchange rate.

3. If a small open economy cuts defense spending, what happens to saving, investment, the trade balance, the interest rate, and the exchange rate?

Q U E S T I O N S F O R R E V I E W

4. If a small open economy bans the import of Japanese DVD players, what happens to saving, investment, the trade balance, the interest rate, and the exchange rate?

5. According to the theory of purchasing-power par- ity, if Japan has low infl ation and Mexico has high infl ation, what will happen to the exchange rate between the Japanese yen and the Mexican peso?

1. Use the model of the small open economy to predict what would happen to the trade balance, the real exchange rate, and the nominal exchange rate in response to each of the following events.

a. A fall in consumer confi dence about the future induces consumers to spend less and save more.

b. A tax reform increases the incentive for busi- nesses to build new factories.

c. The introduction of a stylish line of Toyotas makes some consumers prefer foreign cars over domestic cars.

d. The central bank doubles the money supply.

e. New regulations restricting the use of credit cards increase the demand for money.

2. Consider an economy described by the follow- ing equations:

Y = C + I + G + NX, Y = 5,000, G = 1,000, T = 1,000, C = 250 + 0.75(Y − T ), I = 1,000 − 50r, NX = 500 − 500�, r = r∗ = 5.

P R O B L E M S A N D A P P L I C A T I O N S

a. In this economy, solve for national saving, investment, the trade balance, and the equilib- rium exchange rate.

b. Suppose now that G rises to 1,250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you fi nd.

c. Now suppose that the world interest rate rises from 5 to 10 percent. (G is again 1,000.) Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you fi nd.

3. The country of Leverett is a small open economy. Suddenly, a change in world fashions makes the exports of Leverett unpopular.

a. What happens in Leverett to saving, invest- ment, net exports, the interest rate, and the exchange rate?

b. The citizens of Leverett like to travel abroad. How will this change in the exchange rate affect them?

c. The fi scal policymakers of Leverett want to adjust taxes to maintain the exchange rate at its previous level. What should they do? If they do this, what are the overall effects on saving, investment, net exports, and the interest rate?

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C H A P T E R 6 The Open Economy | 165

4. In 2005, Federal Reserve Governor Ben Ber- nanke said in a speech: “Over the past decade a combination of diverse forces has created a sig- nifi cant increase in the global supply of saving—a global saving glut—which helps to explain both the increase in the U.S. current account defi cit [a broad measure of the trade defi cit] and the relatively low level of long-term real interest rates in the world today.” Is this statement consistent with the models you have learned? Explain.

5. What will happen to the trade balance and the real exchange rate of a small open economy when government purchases increase, such as during a war? Does your answer depend on whether this is a local war or a world war?

6. A Case Study in this chapter concludes that if poor nations offered better production effi ciency and legal protections, the trade balance in rich nations such as the United States would move toward surplus. Let’s consider why this might be the case.

a. If the world’s poor nations offer better pro- duction effi ciency and legal protection, what would happen to the investment demand function in those countries?

b. How would the change you describe in part (a) affect the demand for loanable funds in world fi nancial markets?

c. How would the change you describe in part (b) affect the world interest rate?

d. How would the change you describe in part (c) affect the trade balance in rich nations?

7. The president is considering placing a tariff on the import of Japanese luxury cars. Using the model presented in this chapter, discuss the economics and politics of such a policy. In particular, how would the policy affect the U.S. trade defi cit? How would it affect the exchange rate? Who would be hurt by such a policy? Who would benefi t?

8. Suppose China exports TVs and uses the yuan as its currency, whereas Russia exports vodka and uses the ruble. China has a stable money supply and slow, steady technological progress in TV production, while Russia has very rapid growth in the money supply and no technologi- cal progress in vodka production. Based on this

information, what would you predict for the real exchange rate (measured as bottles of vodka per TV) and the nominal exchange rate (measured as rubles per yuan)? Explain your reasoning. (Hint: For the real exchange rate, think about the link between scarcity and relative prices.)

9. Oceania is a small open economy. Suppose that a large number of foreign countries begin to subsidize investment by instituting an investment tax credit (while adjusting other taxes to hold their tax revenue constant), but Oceania does not institute such an investment subsidy.

a. What happens to world investment demand as a function of the world interest rate?

b. What happens to the world interest rate?

c. What happens to investment in Oceania?

d. What happens to Oceania’s trade balance?

e. What happens to Oceania’s real exchange rate?

10. “Traveling in Mexico is much cheaper now than it was ten years ago,’’ says a friend. “Ten years ago, a dollar bought 10 pesos; this year, a dollar buys 15 pesos.’’ Is your friend right or wrong? Given that total infl ation over this period was 25 percent in the United States and 100 percent in Mexico, has it become more or less expensive to travel in Mexico? Write your answer using a concrete example—such as an American hot dog versus a Mexican taco—that will convince your friend.

11. You read in a newspaper that the nominal inter- est rate is 12 percent per year in Canada and 8 percent per year in the United States. Sup- pose that international capital fl ows equalize the real interest rates in the two countries and that purchasing-power parity holds.

a. Using the Fisher equation (discussed in Chapter 5), what can you infer about expected infl ation in Canada and in the United States?

b. What can you infer about the expected change in the exchange rate between the Canadian dollar and the U.S. dollar?

c. A friend proposes a get-rich-quick scheme: borrow from a U.S. bank at 8 percent, deposit the money in a Canadian bank at 12 percent, and make a 4 percent profi t. What’s wrong with this scheme?

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166 |

When analyzing policy for a country such as the United States, we need to com- bine the closed-economy logic of Chapter 3 and the small-open-economy logic of this chapter. This appendix presents a model of an economy between these two extremes, called the large open economy.

Net Capital Outflow

The key difference between the small and large open economies is the behavior of the net capital outfl ow. In the model of the small open economy, capital fl ows freely into or out of the economy at a fi xed world interest rate r∗. The model of the large open economy makes a different assumption about international capital fl ows. To understand this assumption, keep in mind that the net capital outfl ow is the amount that domestic investors lend abroad minus the amount that foreign investors lend here.

Imagine that you are a domestic investor—such as the portfolio manager of a university endowment—deciding where to invest your funds. You could invest domestically (for example, by making loans to U.S. companies), or you could invest abroad (by making loans to foreign companies). Many factors may affect your decision, but surely one of them is the interest rate you can earn. The higher the interest rate you can earn domestically, the less attractive you would fi nd foreign investment.

Investors abroad face a similar decision. They have a choice between investing in their home country and lending to someone in the United States. The higher the interest rate in the United States, the more willing foreigners are to lend to U.S. companies and to buy U.S. assets.

Thus, because of the behavior of both domestic and foreign investors, the net fl ow of capital to other countries, which we’ll denote as CF, is negatively related to the domestic real interest rate r. As the interest rate rises, less of our saving fl ows abroad, and more funds for capital accumulation fl ow in from other countries. We write this as

CF = CF(r).

This equation states that the net capital outfl ow is a function of the domestic interest rate. Figure 6-15 illustrates this relationship. Notice that CF can be either positive or negative, depending on whether the economy is a lender or borrower in world fi nancial markets.

To see how this CF function relates to our previous models, consider Fig- ure 6-16 This fi gure shows two special cases: a vertical CF function and a hori- zontal CF function.

The Large Open Economy

A P P E N D I X

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C H A P T E R 6 The Open Economy | 167

The closed economy is the special case shown in panel (a) of Figure 6-16. In the closed economy, there is no international borrowing or lending, and the interest rate adjusts to equilibrate domestic saving and investment. This means that CF = 0 at all interest rates. This situation would arise if investors here and abroad were unwilling to hold foreign assets, regardless of the return. It might also arise if the government prohibited its citizens from transacting in foreign fi nancial markets, as some governments do.

The small open economy with perfect capital mobility is the special case shown in panel (b) of Figure 6-16. In this case, capital fl ows freely into and out of the country at the fi xed world interest rate r∗. This situation would arise if inves- tors here and abroad bought whatever asset yielded the highest return and if this economy were too small to affect the world interest rate. The economy’s interest rate would be fi xed at the interest rate prevailing in world fi nancial markets.

FIGURE 6-15

How the Net Capital Outfl ow Depends on the Interest Rate A higher domestic interest rate dis- courages domestic investors from lending abroad and encourages foreign investors to lend here. Therefore, net capital outfl ow CF is negatively related to the interest rate.

Real interest rate, r

Net capital outflow, CFLend to abroad

(CF > 0) Borrow from abroad (CF < 0)

0

FIGURE 6-16

Two Special Cases In the closed economy, shown in panel (a), the net capital outfl ow is zero for all interest rates. In the small open economy with perfect capital mobility, shown in panel (b), the net capital outfl ow is perfectly elastic at the world interest rate r*.

Real interest rate, r

Real interest rate, r

Net capital outflow, CF

Net capital outflow, CF

(a) The Closed Economy (b) The Small Open Economy With

Perfect Capital Mobility

0

r*

0

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168 | P A R T I I Classical Theory: The Economy in the Long Run

Why isn’t the interest rate of a large open economy such as the United States fi xed by the world interest rate? There are two reasons. The fi rst is that the United States is large enough to infl uence world fi nancial markets. The more the United States lends abroad, the greater is the supply of loans in the world economy, and the lower interest rates become around the world. The more the United States borrows from abroad (that is, the more negative CF becomes), the higher are world interest rates. We use the label “large open economy” because this model applies to an economy large enough to affect world interest rates.

There is, however, a second reason the interest rate in an economy may not be fi xed by the world interest rate: capital may not be perfectly mobile. That is, investors here and abroad may prefer to hold their wealth in domestic rather than foreign assets. Such a preference for domestic assets could arise because of imperfect information about foreign assets or because of government impedi- ments to international borrowing and lending. In either case, funds for capital accumulation will not fl ow freely to equalize interest rates in all countries. Instead, the net capital outfl ow will depend on domestic interest rates relative to foreign interest rates. U.S. investors will lend abroad only if U.S. interest rates are comparatively low, and foreign investors will lend in the United States only if U.S. interest rates are comparatively high. The large-open-economy model, therefore, may apply even to a small economy if capital does not fl ow freely into and out of the economy.

Hence, either because the large open economy affects world interest rates, or because capital is imperfectly mobile, or perhaps for both reasons, the CF function slopes downward. Except for this new downward-sloping CF function, the model of the large open economy resembles the model of the small open economy. We put all the pieces together in the next section.

The Model

To understand how the large open economy works, we need to consider two key markets: the market for loanable funds (where the interest rate is determined) and the market for foreign exchange (where the exchange rate is determined). The interest rate and the exchange rate are two prices that guide the allocation of resources.

The Market for Loanable Funds An open economy’s saving S is used in two ways: to fi nance domestic investment I and to fi nance the net capital outfl ow CF. We can write

S = I + CF.

Consider how these three variables are determined. National saving is fi xed by the level of output, fi scal policy, and the consumption function. Investment and net capital outfl ow both depend on the domestic real interest rate. We can write

–S = I(r) + CF(r).

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C H A P T E R 6 The Open Economy | 169

FIGURE 6-17

The Market for Loanable Funds in the Large Open Economy At the equilibrium interest rate, the supply of loanable funds from saving S balances the demand for loanable funds from domestic investment I and capital investments abroad CF.

Real interest rate, r

Loanable funds, S, I � CF

S

I(r) � CF(r)

Equilibrium real interest rate

FIGURE 6-18

The Market for Foreign-Currency Exchange in the Large Open Economy At the equilibri- um exchange rate, the supply of dollars from the net capital outfl ow, CF, balances the demand for dollars from our net exports of goods and services, NX.

Real exchange rate, �

Net exports, NX

Equilibrium real exchange rate

CF

NX(�)

Figure 6-17 shows the market for loanable funds. The supply of loanable funds is national saving. The demand for loanable funds is the sum of the demand for domestic investment and the demand for foreign investment (net capital out- fl ow). The interest rate adjusts to equilibrate supply and demand.

The Market for Foreign Exchange Next, consider the relationship between the net capital outfl ow and the trade balance. The national income accounts iden- tity tells us

NX = S − I.

Because NX is a function of the real exchange rate, and because CF = S − I, we can write

NX(�) = CF.

Figure 6-18 shows the equilibrium in the market for foreign exchange. Once again, the real exchange rate is the price that equilibrates the trade balance and the net capital outfl ow.

The last variable we should consider is the nominal exchange rate. As before, the nominal exchange rate is the real exchange rate times the ratio of the price levels:

e = � × (P∗/P).

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170 | P A R T I I Classical Theory: The Economy in the Long Run

The real exchange rate is determined as in Figure 6-18, and the price levels are determined by monetary policies here and abroad, as we discussed in Chapter 5. Forces that move the real exchange rate or the price levels also move the nominal exchange rate.

Policies in the Large Open Economy

We can now consider how economic policies infl uence the large open economy. Figure 6-19 shows the three diagrams we need for the analysis. Panel (a) shows the equilibrium in the market for loanable funds; panel (b) shows the relationship between the equilibrium interest rate and the net capital outfl ow; and panel (c) shows the equilibrium in the market for foreign exchange.

Fiscal Policy at Home Consider the effects of expansionary fi scal policy—an increase in government purchases or a decrease in taxes. Figure 6-20 shows what happens. The policy reduces national saving S, thereby reducing the supply of loanable funds and raising the equilibrium interest rate r. The higher interest rate reduces both domestic investment I and the net capital outfl ow CF. The fall in the net capital outfl ow reduces the supply of dollars to be exchanged into foreign currency. The exchange rate appreciates, and net exports fall.

FIGURE 6-19

Real interest rate, r

Loanable funds, S, I � CF Net capital outflow, CF

Real exchange rate, �

Net exports, NX

(a) The Market for Loanable Funds (b) Net Capital Outflow

(c) The Market for Foreign Exchange

NX(�)

CF

r

CF(r)

S

I � CF

The Equilibrium in the Large Open Economy Panel (a) shows that the market for loanable funds determines the equilibrium interest rate. Panel (b) shows that the interest rate determines the net capital outfl ow, which in turn determines the supply of dollars to be exchanged into foreign currency. Panel (c) shows that the real exchange rate adjusts to balance this supply of dollars with the demand coming from net exports.

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C H A P T E R 6 The Open Economy | 171

Note that the impact of fi scal policy in this model combines its impact in the closed economy and its impact in the small open economy. As in the closed economy, a fi scal expansion in a large open economy raises the interest rate and crowds out investment. As in the small open economy, a fi scal expansion causes a trade defi cit and an appreciation in the exchange rate.

One way to see how the three types of economy are related is to consider the identity

S = I + NX.

In all three cases, expansionary fi scal policy reduces national saving S. In the closed economy, the fall in S coincides with an equal fall in I, and NX stays con- stant at zero. In the small open economy, the fall in S coincides with an equal fall in NX, and I remains constant at the level fi xed by the world interest rate. The large open economy is the intermediate case: both I and NX fall, each by less than the fall in S.

FIGURE 6-20

Real interest rate, r

r2

r1

Loanable funds, S, I � CF Net capital outflow, CF

Real exchange rate, �

Net exports, NX

r2

r1

(a) The Market for Loanable Funds (b) Net Capital Outflow

(c) The Market for Foreign Exchange

S

I � CF

r

CF(r)

CF2 CF1

NX2

�2

�1

NX1

NX(�)

CF

2. ... raises the interest rate, ...

1. A fall in saving ...

3. ... which lowers net capital outflow, ...

4. ... raises the exchange rate, ...

5. ... and reduces net exports.

A Reduction in National Saving in the Large Open Economy Panel (a) shows that a reduction in national sav- ing lowers the supply of loanable funds. The equilibrium interest rate rises. Panel (b) shows that the higher inter- est rate lowers the net capital outfl ow. Panel (c) shows that the reduced capital outfl ow means a reduced supply of dol- lars in the market for foreign-currency exchange. The reduced supply of dollars causes the real exchange rate to appreci- ate and net exports to fall.

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172 | P A R T I I Classical Theory: The Economy in the Long Run

Shifts in Investment Demand Suppose that the investment demand schedule shifts outward, perhaps because Congress passes an investment tax credit. Figure 6-21 shows the effect. The demand for loanable funds rises, rais- ing the equilibrium interest rate. The higher interest rate reduces the net capital outfl ow: Americans make fewer loans abroad, and foreigners make more loans to Americans. The fall in the net capital outfl ow reduces the supply of dollars in the market for foreign exchange. The exchange rate appreciates, and net exports fall.

Trade Policies Figure 6-22 shows the effect of a trade restriction, such as an import quota. The reduced demand for imports shifts the net exports schedule outward in panel (c). Because nothing has changed in the market for loanable funds, the interest rate remains the same, which in turn implies that the net capital outfl ow remains the same. The shift in the net-exports schedule causes the exchange rate to appreciate. The rise in the exchange rate makes U.S. goods expensive relative to foreign goods, which depresses exports and stimulates imports. In the end, the trade restriction does not affect the trade balance.

FIGURE 6-21

Real interest rate, r

r2

r1

Real exchange rate, �

Net exports, NX

CF2 CF1

NX2

�2

�1

NX1

2. ... raises the interest rate, ...

NX(�)

CF

r

CF(r)

S

I � CF

r2

r1

4. ... raises the exchange rate, ...

3. ... which reduces net capital outflow, ...

5. ... and reduces net exports.

(a) The Market for Loanable Funds (b) Net Capital Outflow

(c) The Market for Foreign Exchange

Loanable funds, S, I � CF Net capital outflow, CF

1. An increase in investment demand ...

An Increase in Investment Demand in the Large Open Economy Panel (a) shows that an increase in investment demand raises the interest rate. Panel (b) shows that the higher interest rate lowers the net capital outfl ow. Panel (c) shows that a lower capital outfl ow causes the real exchange rate to appreciate and net exports to fall.

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C H A P T E R 6 The Open Economy | 173

Shifts in Net Capital Outflow There are various reasons that the CF schedule might shift. One reason is fi scal policy abroad. For example, suppose that Germany pursues a fi scal policy that raises German saving. This policy reduces the German interest rate. The lower German interest rate discourages American investors from lending in Germany and encourages German inves- tors to lend in the United States. For any given U.S. interest rate, the U.S. net capital outfl ow falls.

Another reason the CF schedule might shift is political instability abroad. Sup- pose that a war or revolution breaks out in another country. Investors around the world will try to withdraw their assets from that country and seek a “safe haven” in a stable country such as the United States. The result is a reduction in the U.S. net capital outfl ow.

Figure 6-23 shows the impact of a leftward shift in the CF schedule. The reduced demand for loanable funds lowers the equilibrium interest rate. The

FIGURE 6-22

Real interest rate, r

Net exports, NX NX2 NX1

Loanable funds, S, I � CF Net capital outflow, CF

S

I � CF

r

CF(r)

NX(�)

CF �2

�1

Real exchange rate, �

(a) The Market for Loanable Funds (b) Net Capital Outflow

(c) The Market for Foreign Exchange

1. Protectionist policies raise the demand for net exports, ...

3. ... leaving net exports unchanged.

2. ... which increases the exchange rate, . . .

An Import Restriction in the Large Open Economy An import restric- tion raises the demand for net exports, as shown in panel (c). The real exchange rate appreciates, while the equilibrium trade balance remains the same. Nothing happens in the market for loanable funds in panel (a) or to the net capital outfl ow in panel (b).

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174 | P A R T I I Classical Theory: The Economy in the Long Run

lower interest rate tends to raise net capital outfl ow, but because this only partly mitigates the shift in the CF schedule, CF still falls. The reduced level of net capital outfl ow reduces the supply of dollars in the market for foreign exchange. The exchange rate appreciates, and net exports fall.

Conclusion

How different are large and small open economies? Certainly, policies affect the interest rate in a large open economy, unlike in a small open economy. But, in other ways, the two models yield similar conclusions. In both large and small open economies, policies that raise saving or lower investment lead to trade surpluses. Similarly, policies that lower saving or raise investment lead to trade defi cits. In both economies, protectionist trade policies cause the exchange rate to appreciate and do not infl uence the trade balance. Because the results are so similar, for most questions one can use the simpler model of the small open economy, even if the economy being examined is not really small.

FIGURE 6-23

Real interest rate, r

Real exchange rate, �

Net exports, NX

CF2 CF1

NX2

�2

�1

NX1

2. ... causes the interest rate to fall, ...

3. ... the exchange rate to rise, ...

S

I � CF

r

CF(r)

NX(�)

CF

Net capital outflow, CF

Loanable funds, S, I � CF

r1

r2

4. ... and net exports to fall.

�2

�1

(a) The Market for Loanable Funds (b) Net Capital Outflow

(c) The Market for Foreign Exchange

1. A fall in net capital outflow ...

A Fall in the Net Capital Outfl ow in the Large Open Economy Panel (a) shows that a downward shift in the CF schedule reduces the demand for loans and thereby reduces the equilibrium interest rate. Panel (b) shows that the level of the net capital outfl ow falls. Panel (c) shows that the real exchange rate appreciates and net exports fall.

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C H A P T E R 6 The Open Economy | 175

1. If a war broke out abroad, it would affect the U.S. economy in many ways. Use the model of the large open economy to examine each of the following effects of such a war. What happens in the United States to saving, investment, the trade balance, the interest rate, and the exchange rate? (To keep things simple, consider each of the fol- lowing effects separately.)

a. The U.S. government, fearing it may need to enter the war, increases its purchases of mili- tary equipment.

b. Other countries raise their demand for high- tech weapons, a major export of the United States.

c. The war makes U.S. fi rms uncertain about the future, and the fi rms delay some invest- ment projects.

d. The war makes U.S. consumers uncertain about the future, and the consumers save more in response.

M O R E P R O B L E M S A N D A P P L I C A T I O N S

e. Americans become apprehensive about travel- ing abroad, so more of them spend their vaca- tions in the United States.

f. Foreign investors seek a safe haven for their portfolios in the United States.

2. On September 21, 1995, “House Speaker Newt Gingrich threatened to send the United States into default on its debt for the fi rst time in the nation’s history, to force the Clinton Adminis- tration to balance the budget on Republican terms” (New York Times, September 22, 1995, p. A1). That same day, the interest rate on 30-year U.S. government bonds rose from 6.46 to 6.55 percent, and the dollar fell in value from 102.7 to 99.0 yen. Use the model of the large open economy to explain this event.

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177

Unemployment

7C H A P T E R

A man willing to work, and unable to fi nd work, is perhaps the saddest sight

that fortune’s inequality exhibits under the sun.

—Thomas Carlyle

Unemployment is the macroeconomic problem that affects people most directly and severely. For most people, the loss of a job means a reduced liv-ing standard and psychological distress. It is no surprise that unemployment is a frequent topic of political debate and that politicians often claim that their pro- posed policies would help create jobs. While the issue is perennial, it rose to particular prominence in the aftermath of the fi nancial crisis and recession of 2008�2009, when the unemployment rate lingered around 9 percent for several years.

Economists study unemployment to identify its causes and to help improve the public policies that affect the unemployed. Some of these policies, such as job-training programs, help people fi nd employment. Others, such as unemploy- ment insurance, alleviate some of the hardships that the unemployed face. Still other policies affect the prevalence of unemployment inadvertently. Laws man- dating a high minimum wage, for instance, are widely thought to raise unem- ployment among the least skilled and experienced members of the labor force.

Our discussions of the labor market so far have ignored unemployment. In particular, the model of national income in Chapter 3 was built with the assump- tion that the economy is always at full employment. In reality, not everyone in the labor force has a job all the time: in all free-market economies, at any moment, some people are unemployed.

Figure 7-1 shows the rate of unemployment—the percentage of the labor force unemployed—in the United States from 1950 to 2010. Although the rate of unemployment fl uctuates from year to year, it never gets even close to zero. The average is between 5 and 6 percent, meaning that about 1 out of every 18 people wanting a job does not have one.

In this chapter we begin our study of unemployment by discussing why there is always some unemployment and what determines its level. We do not study what determines the year-to-year fl uctuations in the rate of unemployment until Part Four of this book, which examines short-run economic fl uctuations. Here we examine the determinants of the natural rate of unemployment—the average rate of unemployment around which the economy fl uctuates. The natural rate is the rate of unemployment toward which the economy gravitates in the long run, given all the labor-market imperfections that impede workers from instantly fi nding jobs.

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178 | P A R T I I Classical Theory: The Economy in the Long Run

7-1 Job Loss, Job Finding, and the Natural Rate of Unemployment

Every day some workers lose or quit their jobs, and some unemployed workers are hired. This perpetual ebb and fl ow determines the fraction of the labor force that is unemployed. In this section we develop a model of labor-force dynamics that shows what determines the natural rate of unemployment.1

We start with some notation. Let L denote the labor force, E the number of employed workers, and U the number of unemployed workers. Because every worker is either employed or unemployed, the labor force is the sum of the employed and the unemployed:

L � E � U.

In this notation, the rate of unemployment is U/L. To see what factors determine the unemployment rate, we assume that the

labor force L is fi xed and focus on the transition of individuals in the labor force

1Robert E. Hall, “A Theory of the Natural Rate of Unemployment and the Duration of Unemployment,” Journal of Monetary Economics 5 (April 1979): 153–169.

FIGURE 7-1

The Unemployment Rate and the Natural Rate of Unemployment in the United States There is always some unemployment. The natural rate of unemployment is the aver- age level around which the unemployment rate fl uctuates. (The natural rate of unemploy- ment for any particular month is estimated here by averaging all the unemployment rates from ten years earlier to ten years later. Future unemployment rates are set at 5.5 percent.)

Source: Bureau of Labor Statistics.

Natural rate of unemployment

Unemployment rate

Percent unemployed

10

12

8

6

4

2

0

Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

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C H A P T E R 7 Unemployment | 179

between employment E and unemployment U. This is illustrated in Figure 7-2. Let s denote the rate of job separation, the fraction of employed individuals who lose or leave their job each month. Let f denote the rate of job fi nding, the fraction of unemployed individuals who fi nd a job each month. Together, the rate of job separation s and the rate of job fi nding f determine the rate of unemployment.

If the unemployment rate is neither rising nor falling—that is, if the labor market is in a steady state—then the number of people fi nding jobs f U must equal the number of people losing jobs sE. We can write the steady-state condition as

f U � sE.

We can use this equation to fi nd the steady-state unemployment rate. From our defi nition of the labor force, we know that E � L � U; that is, the number of employed equals the labor force minus the number of unemployed. If we substi- tute (L � U ) for E in the steady-state condition, we fi nd

f U � s(L � U ).

Next, we divide both sides of this equation by L to obtain

f U L

= sa1 2 U L b.

Now we can solve for the unemployment rate U/L to fi nd

U L

= s

s + f .

This can also be written as

U L

= 1

1 + f /s .

FIGURE 7-2

The Transitions Between Employment and Unemployment In every period, a frac- tion s of the employed lose their jobs, and a fraction f of the unemployed fi nd jobs. The rates of job separation and job fi nding determine the rate of unemployment.

Job Separation (s)

Job Finding (f)

Employed Unemployed

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180 | P A R T I I Classical Theory: The Economy in the Long Run

This equation shows that the steady-state rate of unemployment U/L depends on the rates of job separation s and job fi nding f. The higher the rate of job separa- tion, the higher the unemployment rate. The higher the rate of job fi nding, the lower the unemployment rate.

Here’s a numerical example. Suppose that 1 percent of the employed lose their jobs each month (s � 0.01). This means that the average spell of employ- ment lasts 1/0.01, or 100 months, about 8 years. Suppose further that 20 percent of the unemployed fi nd a job each month ( f � 0.20), so that the average spell of unemployment last 5 months. Then the steady-state rate of unemployment is

U L

= 0.01

0.01 + 0.20

� 0.0476.

The rate of unemployment in this example is about 5 percent. This simple model of the natural rate of unemployment has an important

implication for public policy. Any policy aimed at lowering the natural rate of unem- ployment must either reduce the rate of job separation or increase the rate of job fi nding. Similarly, any policy that affects the rate of job separation or job fi nding also changes the natural rate of unemployment.

Although this model is useful in relating the unemployment rate to job sepa- ration and job fi nding, it fails to answer a central question: why is there unem- ployment in the fi rst place? If a person could always fi nd a job quickly, then the rate of job fi nding would be very high and the rate of unemployment would be near zero. This model of the unemployment rate assumes that job fi nding is not instantaneous, but it fails to explain why. In the next two sections, we examine two underlying reasons for unemployment: job search and wage rigidity.

7-2 Job Search and Frictional Unemployment

One reason for unemployment is that it takes time to match workers and jobs. The equilibrium model of the aggregate labor market discussed in Chapter 3 assumes that all workers and all jobs are identical and, therefore, that all workers are equally well suited for all jobs. If this were true and the labor market were in equilibrium, then a job loss would not cause unemployment: a laid-off worker would immediately fi nd a new job at the market wage.

In fact, workers have different preferences and abilities, and jobs have different attributes. Furthermore, the fl ow of information about job candidates and job vacancies is imperfect, and the geographic mobility of workers is not instanta- neous. For all these reasons, searching for an appropriate job takes time and effort, and this tends to reduce the rate of job fi nding. Indeed, because different jobs require different skills and pay different wages, unemployed workers may not accept the fi rst job offer they receive. The unemployment caused by the time it takes workers to search for a job is called frictional unemployment.

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C H A P T E R 7 Unemployment | 181

Causes of Frictional Unemployment

Some frictional unemployment is inevitable in a changing economy. For many reasons, the types of goods that fi rms and households demand vary over time. As the demand for goods shifts, so does the demand for the labor that produces those goods. The invention of the personal computer, for example, reduced the demand for typewriters and the demand for labor by typewriter manufacturers. At the same time, it increased the demand for labor in the electronics industry. Similarly, because different regions produce different goods, the demand for labor may be rising in one part of the country and falling in another. An increase in the price of oil may cause the demand for labor to rise in oil-producing states such as Texas, but because expensive oil means expensive gasoline, it makes driving less attractive and may decrease the demand for labor in auto-producing states such as Michigan. Econo- mists call a change in the composition of demand among industries or regions a sectoral shift. Because sectoral shifts are always occurring, and because it takes time for workers to change sectors, there is always frictional unemployment.

Sectoral shifts are not the only cause of job separation and frictional unem- ployment. In addition, workers fi nd themselves unexpectedly out of work when their fi rms fail, when their job performance is deemed unacceptable, or when their particular skills are no longer needed. Workers also may quit their jobs to change careers or to move to different parts of the country. Regardless of the cause of the job separation, it will take time and effort for the worker to fi nd a new job. As long as the supply and demand for labor among fi rms is changing, frictional unemployment is unavoidable.

Public Policy and Frictional Unemployment

Many public policies seek to decrease the natural rate of unemployment by reducing frictional unemployment. Government employment agencies dissemi- nate information about job vacancies to match jobs and workers more effi ciently. Publicly funded retraining programs are designed to ease the transition of work- ers from declining to growing industries. If these programs succeed at increasing the rate of job fi nding, they decrease the natural rate of unemployment.

Other government programs inadvertently increase the amount of frictional unemployment. One of these is unemployment insurance. Under this pro- gram, unemployed workers can collect a fraction of their wages for a certain period after losing their jobs. Although the precise terms of the program differ from year to year and from state to state, a typical worker covered by unemploy- ment insurance in the United States receives 50 percent of his or her former wages for 26 weeks. In many European countries, unemployment-insurance programs are signifi cantly more generous.

By softening the economic hardship of unemployment, unemployment insur- ance increases the amount of frictional unemployment and raises the natural rate. The unemployed who receive unemployment-insurance benefi ts are less pressed to search for new employment and are more likely to turn down unattractive job offers. Both of these changes in behavior reduce the rate of job fi nding. In addition, because workers know that their incomes are partially protected by

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182 | P A R T I I Classical Theory: The Economy in the Long Run

unemployment insurance, they are less likely to seek jobs with stable employ- ment prospects and are less likely to bargain for guarantees of job security. These behavioral changes raise the rate of job separation.

That unemployment insurance raises the natural rate of unemployment does not necessarily imply that the policy is ill advised. The program has the benefi t of reducing workers’ uncertainty about their incomes. Moreover, inducing workers to reject unattractive job offers may lead to a better matching between workers and jobs. Evaluating the costs and benefi ts of different systems of unemployment insurance is a diffi cult task that continues to be a topic of much research.

Economists often propose reforms to the unemployment-insurance system that would reduce the amount of unemployment. One common proposal is to require a fi rm that lays off a worker to bear the full cost of that worker’s unem- ployment benefi ts. Such a system is called 100 percent experience rated, because the rate that each fi rm pays into the unemployment-insurance system fully refl ects the unemployment experience of its own workers. Most current programs are partially experience rated. Under this system, when a fi rm lays off a worker, it is charged for only part of the worker’s unemployment benefi ts; the remainder comes from the program’s general revenue. Because a fi rm pays only a fraction of the cost of the unemployment it causes, it has an incentive to lay off workers when its demand for labor is temporarily low. By reducing that incentive, the proposed reform may reduce the prevalence of temporary layoffs.

Unemployment Insurance and the Rate of Job Finding

Many studies have examined the effect of unemployment insurance on job search. The most persuasive studies use data on the experiences of unemployed individuals rather than economy-wide rates of unemployment. Individual data often yield sharp results that are open to few alternative explanations.

One study followed the experience of individual workers as they used up their eligibility for unemployment-insurance benefi ts. It found that when unemployed workers become ineligible for benefi ts, they are more likely to fi nd jobs. In particular, the probability of a person fi nding a job more than doubles when his or her benefi ts run out. One possible explanation is that an absence of benefi ts increases the search effort of unemployed workers. Another possibility is that workers without benefi ts are more likely to accept job offers that would other- wise be declined because of low wages or poor working conditions.2

Additional evidence on how economic incentives affect job search comes from an experiment that the state of Illinois ran in 1985. Randomly selected new claim- ants for unemployment insurance were each offered a $500 bonus if they found employment within 11 weeks. The subsequent experience of this group was com- pared to that of a control group not offered the incentive. The average duration of unemployment for the group offered the $500 bonus was 17.0 weeks, compared to

CASE STUDY

2Lawrence F. Katz and Bruce D. Meyer, “Unemployment Insurance, Recall Expectations, and Unemployment Outcomes,” Quarterly Journal of Economics 105 (November 1990): 973�1002.

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7-3 Real-Wage Rigidity and Structural Unemployment

A second reason for unemployment is wage rigidity—the failure of wages to adjust to a level at which labor supply equals labor demand. In the equilibrium model of the labor market, as outlined in Chapter 3, the real wage adjusts to equilibrate labor supply and labor demand. Yet wages are not always fl exible. Sometimes the real wage is stuck above the market-clearing level.

Figure 7-3 shows why wage rigidity leads to unemployment. When the real wage is above the level that equilibrates supply and demand, the quantity of labor supplied exceeds the quantity demanded. Firms must in some way ration the scarce jobs among workers. Real-wage rigidity reduces the rate of job fi nding and raises the level of unemployment.

The unemployment resulting from wage rigidity and job rationing is some- times called structural unemployment. Workers are unemployed not because they are actively searching for the jobs that best suit their individual skills but because there is a fundamental mismatch between the number of people who

FIGURE 7-3

Real-Wage Rigidity Leads to Job Rationing If the real wage is stuck above the equilibrium level, then the supply of labor exceeds the demand. The result is unemployment.Amount ofunemployment

Amount of labor hired

Amount of labor willing to work

Rigid real wage

Real wage

Labor

Supply

Demand

18.3 weeks for the control group. Thus, the prospect of earning the bonus reduced the average spell of unemployment by 7 percent, suggesting that more effort was devoted to job search. This experiment shows clearly that the incentives provided by the unemployment-insurance system affect the rate of job fi nding.3 ■

3Stephen A. Woodbury and Robert G. Spiegelman, “Bonuses to Workers and Employers to Reduce Unemployment: Randomized Trials in Illinois,” American Economic Review 77 (September 1987): 513�530.

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want to work and the number of jobs that are available. At the going wage, the quantity of labor supplied exceeds the quantity of labor demanded; many workers are simply waiting for jobs to open up.

To understand wage rigidity and structural unemployment, we must examine why the labor market does not clear. When the real wage exceeds the equilibrium level and the supply of workers exceeds the demand, we might expect fi rms to lower the wages they pay. Structural unemployment arises because fi rms fail to reduce wages despite an excess supply of labor. We now turn to three causes of this wage rigidity: minimum-wage laws, the monopoly power of unions, and effi ciency wages.

Minimum-Wage Laws

The government causes wage rigidity when it prevents wages from falling to equilibrium levels. Minimum-wage laws set a legal minimum on the wages that fi rms pay their employees. Since the passage of the Fair Labor Standards Act of 1938, the U.S. federal government has enforced a minimum wage that has usually been between 30 and 50 percent of the average wage in manufacturing. For most workers, then, this minimum wage is not binding, because they earn well above the minimum. Yet for some workers, especially the unskilled and inexperienced, the minimum wage raises their wage above its equilibrium level and, therefore, reduces the quantity of their labor that fi rms demand.

Economists believe that the minimum wage has its greatest impact on teen- age unemployment. The equilibrium wages of teenagers tend to be low for two reasons. First, because teenagers are among the least skilled and least experienced members of the labor force, they tend to have low marginal productivity. Second, teenagers often take some of their “compensation’’ in the form of on-the-job training rather than direct pay. An apprenticeship is a classic example of training offered in place of wages. For both these reasons, the wage at which the supply of teenage workers equals the demand is low. The minimum wage is therefore more often binding for teenagers than for others in the labor force.

Many economists have studied the impact of the minimum wage on teenage employment. These researchers compare the variation in the minimum wage over time with the variation in the number of teenagers with jobs. These studies fi nd that a 10 percent increase in the minimum wage reduces teenage employ- ment by 1 to 3 percent.4

The minimum wage is a perennial source of political debate. Advocates of a higher minimum wage view it as a way to raise the income of the working poor.

4Charles Brown, “Minimum Wage Laws: Are They Overrated?” Journal of Economic Perspectives 2 (Summer 1988): 133�146. Brown presents the mainstream view of the effects of minimum wages, but it should be noted that the magnitude of employment effects is controversial. For research suggesting negligible employment effects, see David Card and Alan Krueger, Myth and Measurement: The New Economics of the Minimum Wage (Princeton, N.J.: Princeton University Press, 1995); and Lawrence Katz and Alan Krueger, “The Effects of the Minimum Wage on the Fast-Food Industry,” Industrial and Labor Relations Review 46 (October 1992): 6�21. For research suggesting the opposite conclusion, see David Neumark and William Wascher, “Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws,” Industrial and Labor Relations Review 46 (October 1992): 55�81.

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Certainly, the minimum wage provides only a meager standard of living: in the United States, two adults working full time at minimum-wage jobs would just exceed the offi cial poverty level for a family of four. Although minimum-wage advocates often admit that the policy causes unemployment for some workers, they argue that this cost is worth bearing to raise others out of poverty.

Opponents of a higher minimum wage claim that it is not the best way to help the working poor. They contend not only that the increased labor costs raise unem- ployment but also that the minimum wage is poorly targeted. Many minimum-wage earners are teenagers from middle-class homes working for discretionary spending money, rather than heads of households working to support their families.

Many economists and policymakers believe that tax credits are a better way to increase the incomes of the working poor. The earned income tax credit is an amount that poor working families are allowed to subtract from the taxes they owe. For a family with very low income, the credit exceeds its taxes, and the family receives a payment from the government. Unlike the minimum wage, the earned income tax credit does not raise labor costs to fi rms and, therefore, does not reduce the quantity of labor that fi rms demand. It has the disadvantage, how- ever, of reducing the government’s tax revenue.

The Characteristics of Minimum-Wage Workers

Who earns the minimum wage? The question can be answered using the Current Population Survey, the labor-market survey used to calculate the unemployment rate and many other statistics. In 2011, the Bureau of Labor Statistics released a report describing the workers who earned at or below the minimum wage in 2010, when the prevaling minimum wage was $7.25 per hour. Here is a summary:

■ About 73 million American workers are paid hourly, representing 59 percent of all wage and salary workers. Of these workers, 1.8 million reported earn- ing exactly the prevailing minimum wage, and another 2.5 million reported earning less. A reported wage below the minimum is possible because some workers are exempt from the statute (newspaper delivery workers, for exam- ple), because enforcement is imperfect, and because some workers round down when reporting their wages on surveys.

■ Minimum-wage workers are more likely to be women than men. About 5 percent of men and 7 percent of women reported wages at or below the prevailing federal minimum.

■ Minimum-wage workers tend to be young. About half of all hourly-paid workers earning the minimum wage or less were under age 25. Among teenagers, about 25 percent earned the minimum wage or less, compared with about 4 percent of workers age 25 and over.

■ Minimum-wage workers tend to be less educated. Among hourly-paid workers age 16 and over, about 5 percent of those who had only a high school diploma earned the minimum wage or less, compared with about 3 percent of those who had a college degree. Of those without a high school diploma, the proportion was 13 percent.

CASE STUDY

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186 | P A R T I I Classical Theory: The Economy in the Long Run

Unions and Collective Bargaining

A second cause of wage rigidity is the monopoly power of unions. Table 7-1 shows the importance of unions in several major countries. In the United States,

South Korea 12% United States 13 Japan 16 Turkey 24 Canada 32 Poland 35 United Kingdom 35 Switzerland 48 Israel 56 Australia 60 Russian Federation 62 Germany 63 Italy 80 Spain 80 Netherlands 82 Greece 85 Sweden 92 France 95 Belgium 96

Source: Danielle Venn, “Legislation, Collective Bargaining and Enforcement: Updating the OECD Employment Protection Indicators.” OECD Social, Employment and Migration Working Papers, 2009.

Percent of Workers Covered by Collective Bargaining

TABLE 7-1

■ Minimum-wage workers are more likely to be working part time. Among part-time workers (those who usually work less than 35 hours per week), 14 percent were paid the minimum wage or less, compared to 3 percent of full-time workers.

■ The industry with the highest proportion of workers with reported hourly wages at or below the minimum wage was leisure and hospitality (about 23 percent). About one-half of all workers paid at or below the minimum wage were employed in this industry, primarily in food services and drinking places. For many of these workers, tips supplement the hourly wages received.

These facts by themselves do not tell us whether the minimum wage is a good or bad policy, or whether it is too high or too low. But when evaluating any public policy, it is useful to keep in mind those individuals who are affected by it.5 ■

5The fi gures reported here are from the Web site of the Bureau of Labor Statistics. The link is http://www.bls.gov/cps/minwage2010.htm

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C H A P T E R 7 Unemployment | 187

only 13 percent of workers have their wages set through collective bargaining. In most European countries, unions play a much larger role.

The wages of unionized workers are determined not by the equilibrium of supply and demand but by bargaining between union leaders and fi rm manage- ment. Often, the fi nal agreement raises the wage above the equilibrium level and allows the fi rm to decide how many workers to employ. The result is a reduction in the number of workers hired, a lower rate of job fi nding, and an increase in structural unemployment.

Unions can also infl uence the wages paid by fi rms whose workforces are not unionized because the threat of unionization can keep wages above the equi- librium level. Most fi rms dislike unions. Unions not only raise wages but also increase the bargaining power of labor on many other issues, such as hours of employment and working conditions. A fi rm may choose to pay its workers high wages to keep them happy and discourage them from forming a union.

The unemployment caused by unions and by the threat of unionization is an instance of confl ict between different groups of workers—insiders and outsiders. Those workers already employed by a fi rm, the insiders, typically try to keep their fi rm’s wages high. The unemployed, the outsiders, bear part of the cost of higher wages because at a lower wage they might be hired. These two groups inevitably have confl icting interests. The effect of any bargaining process on wages and employment depends crucially on the relative infl uence of each group.

The confl ict between insiders and outsiders is resolved differently in different countries. In some countries, such as the United States, wage bargaining takes place at the level of the fi rm or plant. In other countries, such as Sweden, wage bargaining takes place at the national level—with the government often playing a key role. Despite a highly unionized labor force, Sweden has not experienced extraordinarily high unemployment throughout its history. One possible expla- nation is that the centralization of wage bargaining and the role of the govern- ment in the bargaining process give more infl uence to the outsiders, which keeps wages closer to the equilibrium level.

Efficiency Wages

Effi ciency-wage theories propose a third cause of wage rigidity in addition to minimum-wage laws and unionization. These theories hold that high wages make workers more productive. The infl uence of wages on worker effi ciency may explain the failure of fi rms to cut wages despite an excess supply of labor. Even though a wage reduction would lower a fi rm’s wage bill, it would also—if these theories are correct—lower worker productivity and the fi rm’s profi ts.

Economists have proposed various theories to explain how wages affect worker productivity. One effi ciency-wage theory, which is applied mostly to poorer countries, holds that wages infl uence nutrition. Better-paid workers can afford a more nutritious diet, and healthier workers are more productive. A fi rm may decide to pay a wage above the equilibrium level to maintain a healthy work- force. Obviously, this consideration is not important for employers in wealthier countries, such as the United States and most of Europe, because the equilibrium wage is well above the level necessary to maintain good health.

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A second effi ciency-wage theory, which is more relevant for developed coun- tries, holds that high wages reduce labor turnover. Workers quit jobs for many reasons—to accept better positions at other fi rms, to change careers, or to move to other parts of the country. The more a fi rm pays its workers, the greater is their incentive to stay with the fi rm. By paying a high wage, a fi rm reduces the frequency at which its workers quit, thereby decreasing the time and money spent hiring and training new workers.

A third effi ciency-wage theory holds that the average quality of a fi rm’s work- force depends on the wage it pays its employees. If a fi rm reduces its wage, the best employees may take jobs elsewhere, leaving the fi rm with inferior employees who have fewer alternative opportunities. Economists recognize this unfavorable sorting as an example of adverse selection—the tendency of people with more information (in this case, the workers, who know their own outside opportuni- ties) to self-select in a way that disadvantages people with less information (the fi rm). By paying a wage above the equilibrium level, the fi rm may reduce adverse selection, improve the average quality of its workforce, and thereby increase productivity.

A fourth effi ciency-wage theory holds that a high wage improves worker effort. This theory posits that fi rms cannot perfectly monitor their employees’ work effort and that employees must themselves decide how hard to work. Workers can choose to work hard, or they can choose to shirk and risk getting caught and fi red. Economists recognize this possibility as an example of moral hazard—the tendency of people to behave inappropriately when their behavior is imperfectly monitored. The fi rm can reduce the problem of moral hazard by paying a high wage. The higher the wage, the greater the cost to the worker of getting fi red. By paying a higher wage, a fi rm induces more of its employees not to shirk and thus increases their productivity.

Although these four effi ciency-wage theories differ in detail, they share a common theme: because a fi rm operates more effi ciently if it pays its workers a high wage, the fi rm may fi nd it profi table to keep wages above the level that balances supply and demand. The result of this higher-than-equilibrium wage is a lower rate of job fi nding and greater unemployment.6

Henry Ford’s $5 Workday

In 1914 the Ford Motor Company started paying its workers $5 per day. The prevailing wage at the time was between $2 and $3 per day, so Ford’s wage was well above the equilibrium level. Not surprisingly, long lines of job seekers waited outside the Ford plant gates hoping for a chance to earn this high wage.

CASE STUDY

6For more extended discussions of effi ciency wages, see Janet Yellen, “Effi ciency Wage Models of Unemployment,” American Economic Review Papers and Proceedings (May 1984): 200�205; and Lawrence Katz, “Effi ciency Wages: A Partial Evaluation,” NBER Macroeconomics Annual (1986): 235�276.

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7-4 Labor-Market Experience: The United States

So far we have developed the theory behind the natural rate of unemployment. We began by showing that the economy’s steady-state unemployment rate depends on the rates of job separation and job fi nding. Then we discussed two reasons why job fi nding is not instantaneous: the process of job search (which leads to frictional unemployment) and wage rigidity (which leads to structural unemployment). Wage rigidity, in turn, arises from minimum-wage laws, union- ization, and effi ciency wages.

With these theories as background, we now examine some additional facts about unemployment, focusing at fi rst on the case of American labor markets. These facts will help us to evaluate our theories and assess public policies aimed at reducing unemployment.

The Duration of Unemployment

When a person becomes unemployed, is the spell of unemployment likely to be short or long? The answer to this question is important because it indicates

What was Ford’s motive? Henry Ford later wrote, “We wanted to pay these wages so that the business would be on a lasting foundation. We were building for the future. A low wage business is always insecure. . . . The payment of fi ve dollars a day for an eight hour day was one of the fi nest cost cutting moves we ever made.’’

From the standpoint of traditional economic theory, Ford’s explanation seems peculiar. He was suggesting that high wages imply low costs. But perhaps Ford had discovered effi ciency-wage theory. Perhaps he was using the high wage to increase worker productivity.

Evidence suggests that paying such a high wage did benefi t the company. According to an engineering report written at the time, “The Ford high wage does away with all the inertia and living force resistance. . . . The workingmen are absolutely docile, and it is safe to say that since the last day of 1913, every single day has seen major reductions in Ford shops’ labor costs.’’ Absenteeism fell by 75 percent, suggesting a large increase in worker effort. Alan Nevins, a histo- rian who studied the early Ford Motor Company, wrote, “Ford and his associates freely declared on many occasions that the high wage policy had turned out to be good business. By this they meant that it had improved the discipline of the workers, given them a more loyal interest in the institution, and raised their personal effi ciency.’’7 ■

7Jeremy I. Bulow and Lawrence H. Summers, “A Theory of Dual Labor Markets With Application to Industrial Policy, Discrimination, and Keynesian Unemployment,” Journal of Labor Economics 4 (July 1986): 376�414; Daniel M. G. Raff and Lawrence H. Summers, “Did Henry Ford Pay Effi ciency Wages?” Journal of Labor Economics 5 (October 1987, Part 2): S57�S86.

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190 | P A R T I I Classical Theory: The Economy in the Long Run

the reasons for the unemployment and what policy response is appropriate. On the one hand, if most unemployment is short term, one might argue that it is frictional and perhaps unavoidable. Unemployed workers may need some time to search for the job that is best suited to their skills and tastes. On the other hand, long-term unemployment cannot easily be attributed to the time it takes to match jobs and workers: we would not expect this matching process to take many months. Long-term unemployment is more likely to be structural unem- ployment, representing a mismatch between the number of jobs available and the number of people who want to work. Thus, data on the duration of unemploy- ment can affect our view about the reasons for unemployment.

The answer to our question turns out to be subtle. The data show that many spells of unemployment are short but that most weeks of unemployment are attributable to the long-term unemployed. For example, during the period from 1990 to 2006, 38 percent of unemployed people were unemployed for less than 4 weeks, while only 31 percent were unemployed for more than 15 weeks. However, 71 percent of the total amount of time spent unemployed was expe- rienced by those who were unemployed for more than 15 weeks, while only 7 percent of the time spent unemployed was experienced by people who were unemployed for less than 4 weeks.

To see how these facts can all be true, consider an extreme but simple example. Suppose that 10 people are unemployed for part of a given year. Of these 10 people, 8 are unemployed for 1 month and 2 are unemployed for 12 months, totaling 32 months of unemployment. In this example, most spells of unemployment are short: 8 of the 10 unemployment spells, or 80 percent, end in 1 month. Yet most months of unemployment are attributable to the long-term unemployed: 24 of the 32 months of unemployment, or 75 percent, are experi- enced by the 2 workers who are each unemployed for 12 months. Depending on whether we look at spells of unemployment or months of unemployment, most unemployment can appear to be either short-term or long-term.

This evidence on the duration of unemployment has an important implica- tion for public policy. If the goal is to substantially lower the natural rate of unemployment, policies must aim at the long-term unemployed, because these individuals account for a large amount of unemployment. Yet policies must be carefully targeted, because the long-term unemployed constitute a small minor- ity of those who become unemployed. Most people who become unemployed fi nd work within a short time.

The Increase in U.S. Long-Term Unemployment and the Debate Over Unemployment Insurance

In 2008 and 2009, as the U.S. economy experienced a deep recession, the labor market demonstrated a new and striking phenomenon: a large upward spike in the duration of unemployment. Figure 7-4 shows the median duration of unemployment for jobless workers from 1969 to 2011. Recessions are indicated

CASE STUDY

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C H A P T E R 7 Unemployment | 191

FIGURE 7-4

The Median Duration of Unemployment The median duration of unemployment typically rises during recessions, shown as the shaded areas here, but its spike upward during the recession of 2008–2009 was unprecedented.

Recession

Median unemployment

duration

Duration of unemployment (weeks)

197519701969 1980 1985 1990 Year

1995 2000 2005 2010

5

0

10

15

20

25

30

by shaded areas. The fi gure shows that the duration of unemployment typically rises during recessions. The huge increase during the recession of 2008-2009, however, is without precedent in modern history.

What explains this phenomenon? Economists fall into two camps. Some economists believe that the increase in long-term unemployment is a

result of government policies. In particular, in February 2009, Congress extend- ed the eligibility for unemployment insurance from the normal 26 weeks to 99 weeks. Extending unemployment-insurance benefi ts is typical during reces- sions, because jobs are harder to fi nd, but the extension to nearly two years was extraordinary.

Harvard economist Robert Barro wrote an article in the August 30, 2010, issue of the Wall Street Journal titled “The Folly of Subsidizing Unemployment.” According to Barro, “the dramatic expansion of unemployment insurance eligi- bility to 99 weeks is almost surely the culprit” responsible for the rise in long- term unemployment. He writes:

Generous unemployment insurance programs have been found to raise unem- ployment in many Western European countries in which unemployment rates have been far higher than the current U.S. rate. In Europe, the infl uence has worked particularly through increases in long-term unemployment.

Barro concludes that the “reckless expansion of unemployment-insurance cover- age to 99 weeks was unwise economically and politically.”

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192 | P A R T I I Classical Theory: The Economy in the Long Run

Variation in the Unemployment Rate Across Demographic Groups

The rate of unemployment varies substantially across different groups within the population. Table 7-2 presents the U.S. unemployment rates for different demo- graphic groups in 2010, when the overall unemployment rate was 9.6 percent.

This table shows that younger workers have much higher unemployment rates than older ones. To explain this difference, recall our model of the natural rate of unemployment. The model isolates two possible causes for a high rate of unemployment: a low rate of job fi nding and a high rate of job separation. When

Age White Men White Women Black Men Black Women

16–19 26.3 20.0 45.4 40.7 20 and over 8.9 7.2 17.3 12.8

Source: Bureau of Labor Statistics.

Unemployment Rate by Demographic Group

TABLE 7-2

Other economists, however, are skeptical that these government policies are to blame. In their opinion, the extraordinary increase in eligibility for unemploy- ment insurance was a reasonable and compassionate response to a historically deep economic downturn and weak labor market.

Here is Princeton economist Paul Krugman, writing in his July 4, 2010, New York Times column titled “Punishing the Jobless”:

Do unemployment benefi ts reduce the incentive to seek work? Yes: workers receiving unemployment benefi ts aren’t quite as desperate as workers without benefi ts, and are likely to be slightly more choosy about accepting new jobs. The operative word here is “slightly”: recent economic research suggests that the effect of unemployment benefi ts on worker behavior is much weaker than was previously believed. Still, it’s a real effect when the economy is doing well.

But it’s an effect that is completely irrelevant to our current situation. When the economy is booming, and lack of suffi cient willing workers is limiting growth, generous unemployment benefi ts may keep employment lower than it would have been otherwise. But as you may have noticed, right now the econ- omy isn’t booming—there are fi ve unemployed workers for every job opening. Cutting off benefi ts to the unemployed will make them even more desperate for work—but they can’t take jobs that aren’t there.

Wait: there’s more. One main reason there aren’t enough jobs right now is weak consumer demand. Helping the unemployed, by putting money in the pockets of people who badly need it, helps support consumer spending.

Barro and Krugman are both prominent economists, but they have diametrically opposed views about this fundamental policy debate. The cause of the spike in U.S. long-term unemployment remains an unsettled debate. ■

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C H A P T E R 7 Unemployment | 193

economists study data on the transition of individuals between employment and unemployment, they fi nd that those groups with high unemployment tend to have high rates of job separation. They fi nd less variation across groups in the rate of job fi nding. For example, an employed white male is four times more likely to become unemployed if he is a teenager than if he is middle-aged; once unemployed, his rate of job fi nding is not closely related to his age.

These fi ndings help explain the higher unemployment rates for younger workers. Younger workers have only recently entered the labor market, and they are often uncertain about their career plans. It may be best for them to try differ- ent types of jobs before making a long-term commitment to a specifi c occupa- tion. If they do so, we should expect a higher rate of job separation and a higher rate of frictional unemployment for this group.

Another fact that stands out from Table 7-2 is that unemployment rates are much higher for blacks than for whites. This phenomenon is not well under- stood. Data on transitions between employment and unemployment show that the higher unemployment rates for blacks, especially for black teenagers, arise because of both higher rates of job separation and lower rates of job fi nding. Possible reasons for the lower rates of job fi nding include less access to informal job-fi nding networks and discrimination by employers.

Transitions Into and Out of the Labor Force

So far we have ignored an important aspect of labor-market dynamics: the move- ment of individuals into and out of the labor force. Our model of the natural rate of unemployment assumes that the labor force is fi xed. In this case, the sole reason for unemployment is job separation, and the sole reason for leaving unem- ployment is job fi nding.

In fact, movements into and out of the labor force are important. About one-third of the unemployed have only recently entered the labor force. Some of these entrants are young workers still looking for their fi rst jobs; others have worked before but had temporarily left the labor force. In addition, not all unem- ployment ends with job fi nding: almost half of all spells of unemployment end in the unemployed person’s withdrawal from the labor market.

Individuals entering and leaving the labor force make unemployment statistics more diffi cult to interpret. On the one hand, some individuals calling themselves unemployed may not be seriously looking for jobs and perhaps should best be viewed as out of the labor force. Their “unemployment’’ may not represent a social problem. On the other hand, some individuals may want jobs but, after unsuccessful searches, have given up looking. These discouraged workers are counted as being out of the labor force and do not show up in unemployment statistics. Even though their joblessness is unmeasured, it may nonetheless be a social problem.

Because of these and many other issues that complicate the interpretation of the unemployment data, the Bureau of Labor Statistics calculates several measures of labor underutilization. Table 7-3 gives the defi nitions and their values as of August 2011. The measures range from 5.4 to 16.2 percent, depending on the characteristics one uses to classify a worker as not fully employed.

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194 | P A R T I I Classical Theory: The Economy in the Long Run

7-5 Labor-Market Experience: Europe

Although our discussion has focused largely on the United States, many fascinating and sometimes puzzling phenomena become apparent when economists compare the experiences of Americans in the labor market with those of Europeans.

The Rise in European Unemployment

Figure 7-5 shows the rate of unemployment from 1960 to 2010 in the four larg- est European countries—France, Germany, Italy, and the United Kingdom. As you can see, the rate of unemployment in these countries has risen substantially. For France and Germany, the change is particularly pronounced: unemployment averaged about 2 percent in the 1960s and about 9 percent in recent years.

What is the cause of rising European unemployment? No one knows for sure, but there is a leading theory. Many economists believe that the problem can

Variable Description Rate

U-1 Persons unemployed 15 weeks or longer, 5.4% as a percent of the civilian labor force (includes only very long-term unemployed) U-2 Job losers and persons who have completed 5.3 temporary jobs, as a percent of the civilian labor force (excludes job leavers) U-3 Total unemployed, as a percent of the civilian 9.1 labor force (offi cial unemployment rate) U-4 Total unemployed, plus discouraged workers, 9.7 as a percent of the civilian labor force plus discouraged workers U-5 Total unemployed plus all marginally attached workers, 10.6 as a percent of the civilian labor force plus all marginally attached workers U-6 Total unemployed, plus all marginally attached 16.2 workers, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all marginally attached workers

Note: Marginally attached workers are persons who currently are neither working nor looking for work but indicate that they want and are available for a job and have looked for work sometime in the recent past. Discouraged workers, a subset of the marginally attached, have given a job-market–related reason for not currently looking for a job. Persons employed part time for economic reasons are those who want and are available for full-time work but have had to settle for a part-time schedule. Source: U.S. Department of Labor. Data are for August 2011.

Alternative Measures of Labor Underutilization

TABLE 7-3

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C H A P T E R 7 Unemployment | 195

be traced to the interaction between a long-standing policy and a more recent shock. The long-standing policy is generous benefi ts for unemployed workers. The recent shock is a technologically driven fall in the demand for unskilled workers relative to skilled workers.

There is no question that most European countries have generous programs for those without jobs. These programs go by various names: social insurance, the welfare state, or simply “the dole.” Many countries allow the unemployed to collect benefi ts for years, rather than for only a short period of time as in the United States. In some sense, those living on the dole are really out of the labor force: given the employment opportunities available, taking a job is less attractive than remaining without work. Yet these people are often counted as unemployed in government statistics.

There is also no question that the demand for unskilled workers has fallen relative to the demand for skilled workers. This change in demand is probably due to changes in technology: computers, for example, increase the demand for workers who can use them and reduce the demand for those who cannot. In the United States, this change in demand has been refl ected in wages rather than unemployment: over the past three decades, the wages of unskilled workers have fallen substantially relative to the wages of skilled workers. In Europe, however, the welfare state provides unskilled workers with an alternative to working for low wages. As the wages of unskilled workers fall, more workers view the dole as their best available option. The result is higher unemployment.

FIGURE 7-5

Unemployment in Europe This fi gure shows the unemployment rate in the four largest nations in Europe. The fi gure shows that the European unemployment rate has risen substantially over time, especially in France and Germany.

Source: Bureau of Labor Statistics.

France

Italy

Germany

United Kingdom

14

12

10

8

6

4

2

0

Percent unemployed

1960 1964 1968 1972 1976 1980

Year

1984 1988 1992 1996 2000 2004 2008

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196 | P A R T I I Classical Theory: The Economy in the Long Run

This diagnosis of high European unemployment does not suggest an easy remedy. Reducing the magnitude of government benefi ts for the unemployed would encourage workers to get off the dole and accept low-wage jobs. But it would also exacerbate economic inequality—the very problem that welfare-state policies were designed to address.8

Unemployment Variation Within Europe

Europe is not a single labor market but is, instead, a collection of national labor mar- kets, separated not only by national borders but also by differences in culture and language. Because these countries differ in their labor-market policies and institutions, variation within Europe provides a useful perspective on the causes of unemployment. Many empirical studies have, therefore, focused on these international differences.

The fi rst noteworthy fact is that the unemployment rate varies substantially from country to country. For example, in August 2011, when the unemploy- ment rate was 9 percent in the United States, it was 3 percent in Switzerland and 21 percent in Spain. Although in recent years average unemployment has been higher in Europe than in the United States, about one-third of Europeans have been living in nations with unemployment rates lower than the U.S. rate.

A second notable fact is that much of the variation in unemployment rates is attributable to the long-term unemployed. The unemployment rate can be sepa- rated into two pieces—the percentage of the labor force that has been unemployed for less than a year and the percentage of the labor force that has been unemployed for more than a year. The long-term unemployment rate exhibits more variability from country to country than does the short-term unemployment rate.

National unemployment rates are correlated with a variety of labor-market policies. Unemployment rates are higher in nations with more generous unem- ployment insurance, as measured by the replacement rate—the percentage of previous wages that is replaced when a worker loses a job. In addition, nations tend to have higher unemployment, especially higher long-term unemployment, if benefi ts can be collected for longer periods of time.

Although government spending on unemployment insurance seems to raise unemployment, spending on “active” labor-market policies appears to decrease it. These active labor-market policies include job training, assistance with job search, and subsidized employment. Spain, for instance, has historically had a high rate of unemployment, a fact that can be explained by the combination of generous pay- ments to the unemployed with minimal assistance at helping them fi nd new jobs.

The role of unions also varies from country to country, as we saw in Table 7-1. This fact also helps explain differences in labor-market outcomes. National unemployment rates are positively correlated with the percentage of the labor force whose wages are set by collective bargaining with unions. The adverse impact of unions on unemployment is smaller, however, in nations where there is substantial coordination among employers in bargaining with unions, perhaps because coordination may moderate the upward pressure on wages.

8For more discussion of these issues, see Paul Krugman, “Past and Prospective Causes of High Unemployment,” in Reducing Unemployment: Current Issues and Policy Options, Federal Reserve Bank of Kansas City, August 1994.

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C H A P T E R 7 Unemployment | 197

A word of warning: Correlation does not imply causation, so empirical results such as these should be interpreted with caution. But they do suggest that a nation’s unemployment rate, rather than being immutable, is instead a function of the choices a nation makes.9

The Secrets to Happiness

Why are some people more satisfi ed with their lives than others? This is a deep and diffi cult question, most often left to philosophers, psychologists, and self-help gurus. But part of the answer is macroeconomic. Recent research has shown that people are happier when they are living in a country with low infl ation and low unemployment.

From 1975 to 1991, a survey called the Euro-Barometer Survey Series asked 264,710 people living in 12 European countries about their happiness and over- all satisfaction with life. One question asked, “On the whole, are you very satis- fi ed, fairly satisfi ed, not very satisfi ed, or not at all satisfi ed with the life you lead?” To see what determines happiness, the answers to this question were correlated with individual and macroeconomic variables. Other things equal, people are more satisfi ed with their lives if they are rich, educated, married, in school, self- employed, retired, female, or either young or old (as opposed to middle-aged). They are less satisfi ed if they are unemployed, divorced, or living with adolescent children. (Some of these correlations may refl ect the effects, rather than causes, of happiness; for example, a happy person may fi nd it easier than an unhappy one to keep a job and a spouse.)

Beyond these individual characteristics, the economy’s overall rates of unem- ployment and infl ation also play a signifi cant role in explaining reported hap- piness. An increase in the unemployment rate of 4 percentage points is large enough to move 11 percent of the population down from one life-satisfaction category to another. The overall unemployment rate reduces satisfaction even after controlling for an individual’s employment status. That is, the employed in a high-unemployment nation are less happy than their counterparts in a low- unemployment nation, perhaps because they are more worried about job loss or perhaps out of sympathy with their fellow citizens.

High infl ation is also associated with lower life satisfaction, although the effect is not as large. A 1.7-percentage-point increase in infl ation reduces happiness by about as much as a 1-percentage-point increase in unemployment. The commonly cited “misery index,” which is the sum of the infl ation and unemployment rates, apparently gives too much weight to infl ation relative to unemployment.10 ■

CASE STUDY

9Stephen Nickell, “Unemployment and Labor Market Rigidities: Europe Versus North America,” Journal of Economic Perspectives 11 (September 1997): 55�74. 10Rafael Di Tella, Robert J. MacCulloch, and Andrew J. Oswald, “Preferences Over Infl ation and Unemployment: Evidence From Surveys of Happiness,” American Economic Review 91 (March 2001): 335�341.

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198 | P A R T I I Classical Theory: The Economy in the Long Run

The Rise of European Leisure

Higher unemployment rates in Europe are part of the larger phenomenon that Europeans typically work fewer hours than do their American counterparts. Figure 7-6 presents some data on how many hours a typical person works in the United States, France, and Germany. In the 1960s, the number of hours worked was about the same in each of these countries. But since then, the number of hours has stayed level in the United States, while it has declined substantially in Europe. Today, the typical American works many more hours than the typical resident of these two western European countries.

The difference in hours worked refl ects two facts. First, the average employed person in the United States works more hours per year than the average employed person in Europe. Europeans typically enjoy shorter workweeks and more frequent holidays. Second, more potential workers are employed in the United States. That is, the employment-to-population ratio is higher in the United States than it is in Europe. Higher unemployment is one reason for the lower employment-to-population ratio in Europe. Another reason is earlier retirement in Europe and thus lower labor-force participation among older workers.

What is the underlying cause of these differences in work patterns? Econo- mists have proposed several hypotheses.

FIGURE 7-6

Annual Hours Worked per Person Over time, many Europeans have substantially reduced the number of hours they work, while typical Americans have not.

Sources: OECD Employment Database and Bureau of Labor Statistics. Calculated as the average annual hours actually worked per employed person multiplied by the employment rate.

United States

France

Germany

1400

1000

1200

800

600

400

200

0

Hours per year

1960 1965 1970 1975 1980 1985

Year

1990 1995 2000 2005 2010

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C H A P T E R 7 Unemployment | 199

Edward Prescott, the 2004 winner of the Nobel Prize in economics, has con- cluded that “virtually all of the large differences between U.S. labor supply and those of Germany and France are due to differences in tax systems.” This hypoth- esis is consistent with two facts: (1) Europeans face higher tax rates than Americans, and (2) European tax rates have risen signifi cantly over the past several decades. Some economists take these facts as powerful evidence for the impact of taxes on work effort. Yet others are skeptical, arguing that to explain the difference in hours worked by tax rates alone requires an implausibly large elasticity of labor supply.

A related hypothesis is that the difference in observed work effort may be attributable to the underground economy. When tax rates are high, people have a greater incentive to work “off the books” to evade taxes. For obvious reasons, data on the underground economy are hard to come by. But economists who study the subject believe the underground economy is larger in Europe than it is in the United States. This fact suggests that the difference in actual hours worked, including work in the underground economy, may be smaller than the difference in measured hours worked.

Another hypothesis stresses the role of unions. As we have seen, collective bargaining is more important in European than in U.S. labor markets. Unions often push for shorter workweeks in contract negotiations, and they lobby the government for a variety of labor-market regulations, such as offi cial holidays. Economists Alberto Alesina, Edward Glaeser, and Bruce Sacerdote conclude that “mandated holidays can explain 80 percent of the difference in weeks worked between the U.S. and Europe and 30 percent of the difference in total labor supply between the two regions.” They suggest that Prescott may overstate the role of taxes because, looking across countries, tax rates and unionization rates are positively correlated; as a result, the effects of high taxes and the effects of widespread unionization are hard to disentangle.

A fi nal hypothesis emphasizes the possibility of different preferences. As tech- nological advance and economic growth have made all advanced countries richer, people around the world must decide whether to take the greater prosperity in the form of increased consumption of goods and services or increased lei- sure. According to economist Olivier Blanchard, “the main difference [between the continents] is that Europe has used some of the increase in productivity to increase leisure rather than income, while the U.S. has done the opposite.” Blanchard believes that Europeans simply have more taste for leisure than do Americans. (As a French economist working in the United States, he may have special insight into this phenomenon.) If Blanchard is right, this raises the even harder question of why tastes vary by geography.

Economists continue to debate the merits of these alternative hypotheses. In the end, there may be some truth to all of them.11

11To read more about this topic, see Edward C. Prescott “Why Do Americans Work So Much More Than Europeans?” Federal Reserve Bank of Minneapolis Quarterly Review 28, number 1 (July 2004): 2�13; Alberto Alesina, Edward Glaeser, and Bruce Sacerdote, “Work and Leisure in the U.S. and Europe: Why So Different?” NBER Macroeconomics Annual 2005; and Olivier Blanchard, “The Economic Future of Europe,” Journal of Economic Perspectives 18, number 4 (Fall 2004): 3–26.

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200 | P A R T I I Classical Theory: The Economy in the Long Run

7-6 Conclusion

Unemployment represents wasted resources. Unemployed workers have the potential to contribute to national income but are not doing so. Those searching for jobs to suit their skills are happy when the search is over, and those waiting for jobs in fi rms that pay above-equilibrium wages are happy when positions open up.

Unfortunately, neither frictional unemployment nor structural unemployment can be easily reduced. The government cannot make job search instantaneous, and it cannot easily bring wages closer to equilibrium levels. Zero unemploy- ment is not a plausible goal for free-market economies.

Yet public policy is not powerless in the fi ght to reduce unemployment. Job-training programs, the unemployment-insurance system, the minimum wage, and the laws governing collective bargaining are often topics of political debate. The policies we choose are likely to have important effects on the economy’s natural rate of unemployment.

Summary

1. The natural rate of unemployment is the steady-state rate of unemploy- ment. It depends on the rate of job separation and the rate of job fi nding.

2. Because it takes time for workers to search for the job that best suits their individual skills and tastes, some frictional unemployment is inevitable. Vari- ous government policies, such as unemployment insurance, alter the amount of frictional unemployment.

3. Structural unemployment results when the real wage remains above the level that equilibrates labor supply and labor demand. Minimum-wage leg- islation is one cause of wage rigidity. Unions and the threat of unionization are another. Finally, effi ciency-wage theories suggest that, for various rea- sons, fi rms may fi nd it profi table to keep wages high despite an excess supply of labor.

4. Whether we conclude that most unemployment is short-term or long-term depends on how we look at the data. Most spells of unemployment are short. Yet most weeks of unemployment are attributable to the small number of long-term unemployed.

5. The unemployment rates among demographic groups differ substantially. In particular, the unemployment rates for younger workers are much higher than for older workers. This results from a difference in the rate of job separation rather than from a difference in the rate of job fi nding.

6. Individuals who have recently entered the labor force, including both new entrants and reentrants, make up about one-third of the unemployed. Tran- sitions into and out of the labor force make unemployment statistics more diffi cult to interpret.

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C H A P T E R 7 Unemployment | 201

7. American and European labor markets exhibit some signifi cant differences. In recent years, Europe has experienced signifi cantly more unemploy- ment than the United States. In addition, because of higher unemployment, shorter workweeks, more holidays, and earlier retirement, Europeans work fewer hours than Americans.

1. Answer the following questions about your own experience in the labor force.

a. When you or one of your friends is looking for a part-time job, how many weeks does it typically take? After you fi nd a job, how many weeks does it typically last?

b. From your estimates, calculate (in a rate per week) your rate of job fi nding f and your rate of job separation s. (Hint: If f is the rate of job fi nding, then the average spell of unemploy- ment is 1/f.)

c. What is the natural rate of unemployment for the population you represent?

2. In this chapter we saw that the steady-state rate of unemployment is U/L � s/(s � f ). Suppose that the unemployment rate does not begin at this level. Show that unemployment will evolve over time and reach this steady state. (Hint: Express the change in the number of unem- ployed as a function of s, f, and U. Then show

P R O B L E M S A N D A P P L I C A T I O N S

K E Y C O N C E P T S

Natural rate of unemployment

Frictional unemployment

Sectoral shift

Unemployment insurance

Wage rigidity

Structural unemployment

Insiders versus outsiders

Effi ciency wages

Discouraged workers

1. What determines the natural rate of unemployment?

2. Describe the difference between frictional unemployment and structural unemployment.

3. Give three explanations why the real wage may remain above the level that equilibrates labor supply and labor demand.

Q U E S T I O N S F O R R E V I E W

4. Is most unemployment long-term or short-term? Explain your answer.

5. Do Europeans work more or fewer hours than Americans? List three hypotheses that have been suggested to explain the difference.

that if unemployment is above the natural rate, unemployment falls, and if unemployment is below the natural rate, unemployment rises.)

3. The residents of a certain dormitory have col- lected the following data: People who live in the dorm can be classifi ed as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 5 percent enter into a relationship every month. What is the steady-state fraction of resi- dents who are uninvolved?

4. Suppose that Congress passes legislation mak- ing it more diffi cult for fi rms to fi re workers. (An example is a law requiring severance pay for fi red workers.) If this legislation reduces the rate of job separation without affecting the rate of job fi nding, how would the natural rate of unemployment change? Do you think it is plau- sible that the legislation would not affect the rate of job fi nding? Why or why not?

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202 | P A R T I I Classical Theory: The Economy in the Long Run

5. Consider an economy with the following Cobb–Douglas production function:

Y � K1/3L2/3.

The economy has 1,000 units of capital and a labor force of 1,000 workers.

a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.)

b. If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employ- ment, output, and the total amount earned by workers?

c. Now suppose that Congress, concerned about the welfare of the working class, passes a law requiring fi rms to pay workers a real wage of one unit of output. How does this wage compare to the equilibrium wage?

d. Congress cannot dictate how many workers fi rms hire at the mandated wage. Given this fact, what are the effects of this law? Specifi cally, what happens to employment, output, and the total amount earned by workers?

e. Will Congress succeed in its goal of helping the working class? Explain.

f. Do you think that this analysis provides a good way of thinking about a minimum- wage law? Why or why not?

6. Suppose that a country experiences a reduction in productivity—that is, an adverse shock to the production function.

a. What happens to the labor demand curve?

b. How would this change in productivity affect the labor market—that is, employment, unemployment, and real wages—if the labor market is always in equilibrium?

c. How would this change in productivity affect the labor market if unions prevent real wages from falling?

7. When workers’ wages rise, their decision about how much time to spend working is affected in two confl icting ways—as you may have learned in courses in microeconomics. The income effect is the impulse to work less, because greater incomes mean workers can afford to consume more leisure. The substitution effect is the impulse to work more, because the reward for working an additional hour has risen (equivalently, the opportunity cost of leisure has gone up). Apply these concepts to Blanchard’s hypothesis about American and European tastes for leisure. On which side of the Atlantic do income effects appear larger than substitution effects? On which side do the two effects approximately cancel? Do you think it is a reasonable hypothesis that tastes for leisure vary by geography? Why or why not?

8. In any city at any time, some of the stock of usable offi ce space is vacant. This vacant offi ce space is unemployed capital. How would you explain this phenomenon? Is it a social problem?

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P A R T I I I

Growth Theory: The Economy in

the Very Long Run

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205

Economic Growth I: Capital Accumulation and Population Growth

8C H A P T E R

The question of growth is nothing new but a new disguise for an age-old

issue, one which has always intrigued and preoccupied economics: the present

versus the future.

—James Tobin

If you have ever spoken with your grandparents about what their lives were like when they were young, most likely you learned an important lesson about economic growth: material standards of living have improved substan- tially over time for most families in most countries. This advance comes from rising incomes, which have allowed people to consume greater quantities of goods and services.

To measure economic growth, economists use data on gross domestic product, which measures the total income of everyone in the economy. The real GDP of the United States today is more than fi ve times its 1950 level, and real GDP per person is more than three times its 1950 level. In any given year, we also observe large dif- ferences in the standard of living among countries. Table 8-1 shows the 2010 income per person in the world’s 14 most populous countries. The United States tops the list with an income of $47,140 per person. Bangladesh has an income per person of only $640—less than 2 percent of the fi gure for the United States.

Our goal in this part of the book is to understand what causes these differences in income over time and across countries. In Chapter 3 we identifi ed the factors of production—capital and labor—and the production technology as the sources of the economy’s output and, thus, of its total income. Differences in income, then, must come from differences in capital, labor, and technology.

Our primary task in this chapter and the next is to develop a theory of economic growth called the Solow growth model. Our analysis in Chap- ter 3 enabled us to describe how the economy produces and uses its output at one point in time. The analysis was static—a snapshot of the economy. To explain why our national income grows, and why some economies grow faster than others, we must broaden our analysis so that it describes changes in the economy over time. By developing such a model, we make our analysis

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206 | P A R T I I I Growth Theory: The Economy in the Very Long Run

dynamic—more like a movie than a photograph. The Solow growth model shows how saving, population growth, and technological progress affect the level of an economy’s output and its growth over time. In this chapter we analyze the roles of saving and population growth. In the next chapter we introduce technological progress.1

<h1 The Accumulation of Capital

The Solow growth model is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy as well as how they affect a nation’s total output of goods and services. We will build this model in a series of steps. Our fi rst step is to examine how the supply and demand for goods determine the accumulation of capital. In this fi rst step, we assume that the labor force and technology are fi xed. We then relax these assumptions by introducing changes in the labor force later in this chapter and by introducing changes in technology in the next.

The Supply and Demand for Goods

The supply and demand for goods played a central role in our static model of the closed economy in Chapter 3. The same is true for the Solow model. By considering the supply and demand for goods, we can see what determines how much output is produced at any given time and how this output is allocated among alternative uses.

8-1

Income per Income per Country person (2010) Country person (2010)

United States $47,140 Indonesia 2,580 Germany 43,330 Philippines 2,050 Japan 42,150 India 1,340 Russia 9,910 Nigeria 1,180 Brazil 9,390 Vietnam 1,100 Mexico 9,330 Pakistan 1,050 China 4,260 Bangladesh 640

Source: The World Bank.

International Differences in the Standard of Living

TABLE 8-1

1The Solow growth model is named after economist Robert Solow and was developed in the 1950s and 1960s. In 1987 Solow won the Nobel Prize in economics for his work on economic growth. The model was introduced in Robert M. Solow, “A Contribution to the Theory of Economic Growth,’’ Quarterly Journal of Economics (February 1956): 65−94.

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 207

The Supply of Goods and the Production Function The supply of goods in the Solow model is based on the production function, which states that output depends on the capital stock and the labor force:

Y = F(K, L).

The Solow growth model assumes that the production function has constant returns to scale. This assumption is often considered realistic, and, as we will see shortly, it helps simplify the analysis. Recall that a production function has constant returns to scale if

zY = F(zK, zL)

for any positive number z. That is, if both capital and labor are multiplied by z, the amount of output is also multiplied by z.

Production functions with constant returns to scale allow us to analyze all quan- tities in the economy relative to the size of the labor force. To see that this is true, set z = 1/L in the preceding equation to obtain

Y/L = F(K/L, 1).

This equation shows that the amount of output per worker Y/L is a function of the amount of capital per worker K/L. (The number 1 is constant and thus can be ignored.) The assumption of constant returns to scale implies that the size of the economy—as measured by the number of workers—does not affect the relation- ship between output per worker and capital per worker.

Because the size of the economy does not matter, it will prove convenient to denote all quantities in per-worker terms. We designate quantities per worker with lowercase letters, so y = Y/L is output per worker, and k = K/L is capital per worker. We can then write the production function as

y = f(k),

where we defi ne f(k) = F(k, 1). Figure 8-1 illustrates this production function. The slope of this production function shows how much extra output a worker

produces when given an extra unit of capital. This amount is the marginal product of capital MPK. Mathematically, we write

MPK = f(k + 1) − f(k).

Note that in Figure 8-1, as the amount of capital increases, the production func- tion becomes fl atter, indicating that the production function exhibits diminishing marginal product of capital. When k is low, the average worker has only a little capital to work with, so an extra unit of capital is very useful and produces a lot of additional output. When k is high, the average worker has a lot of capital already, so an extra unit increases production only slightly.

The Demand for Goods and the Consumption Function The demand for goods in the Solow model comes from consumption and investment. In other words, output per worker y is divided between consumption per worker c and investment per worker i:

y = c + i.

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208 | P A R T I I I Growth Theory: The Economy in the Very Long Run

This equation is the per-worker version of the national income accounts identity for an economy. Notice that it omits government purchases (which for present pur- poses we can ignore) and net exports (because we are assuming a closed economy).

The Solow model assumes that each year people save a fraction s of their income and consume a fraction (1 − s). We can express this idea with the following con- sumption function:

c = (1 − s)y,

where s, the saving rate, is a number between zero and one. Keep in mind that various government policies can potentially infl uence a nation’s saving rate, so one of our goals is to fi nd what saving rate is desirable. For now, however, we just take the saving rate s as given.

To see what this consumption function implies for investment, substitute (1 − s)y for c in the national income accounts identity:

y = (1 − s)y + i.

Rearrange the terms to obtain

i = sy.

This equation shows that investment equals saving, as we fi rst saw in Chapter 3. Thus, the rate of saving s is also the fraction of output devoted to investment.

We have now introduced the two main ingredients of the Solow model— the production function and the consumption function—which describe the economy at any moment in time. For any given capital stock k, the produc- tion function y = f(k) determines how much output the economy produces,

8-1FIGURE

The Production Function The production function shows how the amount of capital per worker k determines the amount of output per worker y = f (k). The slope of the production function is the marginal product of capital: if k increases by 1 unit, y increases by MPK units. The production func- tion becomes fl atter as k increases, indicating diminishing marginal product of capital.

Output per worker, y

MPK

Capital per worker, k

1

Output, f (k)

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 209

and the saving rate s determines the allocation of that output between con- sumption and investment.

Growth in the Capital Stock and the Steady State

At any moment, the capital stock is a key determinant of the economy’s output, but the capital stock can change over time, and those changes can lead to economic growth. In particular, two forces infl uence the capital stock: investment and depreciation. Investment is expenditure on new plant and equipment, and it causes the capital stock to rise. Depreciation is the wearing out of old capital, and it causes the capital stock to fall. Let’s consider each of these forces in turn.

As we have already noted, investment per worker i equals sy. By substituting the production function for y, we can express investment per worker as a function of the capital stock per worker:

i = sf (k).

This equation relates the existing stock of capital k to the accumulation of new capital i. Figure 8-2 shows this relationship. This fi gure illustrates how, for any value of k, the amount of output is determined by the production function f(k), and the allocation of that output between consumption and investment is determined by the saving rate s.

To incorporate depreciation into the model, we assume that a certain fraction � of the capital stock wears out each year. Here � (the lowercase Greek letter delta) is called the depreciation rate. For example, if capital lasts an average of 25 years, then the depreciation rate is 4 percent per year (� = 0.04). The amount of capital

8-2FIGURE

Output, Consumption, and Investment The saving rate s determines the allocation of output between consumption and investment. For any level of capital k, output is f (k), invest- ment is sf (k), and consumption is f (k) − sf (k).

Output per worker, y

y

c

Investment, sf(k)

Output, f(k)

i

Capital per worker, k

Consumption per worker

Output per worker

Investment per worker

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210 | P A R T I I I Growth Theory: The Economy in the Very Long Run

that depreciates each year is �k. Figure 8-3 shows how the amount of depreciation depends on the capital stock.

We can express the impact of investment and depreciation on the capital stock with this equation:

Change in Capital Stock = Investment − Depreciation

�k = i − �k,

where �k is the change in the capital stock between one year and the next. Because investment i equals sf(k), we can write this as

�k = sf (k) − �k.

Figure 8-4 graphs the terms of this equation—investment and depreciation—for different levels of the capital stock k. The higher the capital stock, the greater the amounts of output and investment. Yet the higher the capital stock, the greater also the amount of depreciation.

As Figure 8-4 shows, there is a single capital stock k∗ at which the amount of investment equals the amount of depreciation. If the economy fi nds itself at this level of the capital stock, the capital stock will not change because the two forces acting on it—investment and depreciation—just balance. That is, at k∗, �k = 0, so the capital stock k and output f(k) are steady over time (rather than growing or shrinking). We therefore call k∗ the steady-state level of capital.

The steady state is signifi cant for two reasons. As we have just seen, an economy at the steady state will stay there. In addition, and just as important, an economy not at the steady state will go there. That is, regardless of the level of capital with which the economy begins, it ends up with the steady-state level of capital. In this sense, the steady state represents the long-run equilibrium of the economy.

To see why an economy always ends up at the steady state, suppose that the economy starts with less than the steady-state level of capital, such as level k1 in Figure 8-4. In this case, the level of investment exceeds the amount of depreciation.

8-3FIGURE

Depreciation A constant frac- tion � of the capital stock wears out every year. Depreciation is therefore proportional to the capital stock.

Depreciation per worker, �k Depreciation, �k

Capital per worker, k

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Over time, the capital stock will rise and will continue to rise—along with output f(k)—until it approaches the steady state k∗.

Similarly, suppose that the economy starts with more than the steady-state level of capital, such as level k2. In this case, investment is less than deprecia- tion: capital is wearing out faster than it is being replaced. The capital stock will fall, again approaching the steady-state level. Once the capital stock reaches the steady state, investment equals depreciation, and there is no pressure for the capi- tal stock to either increase or decrease.

Approaching the Steady State: A Numerical Example

Let’s use a numerical example to see how the Solow model works and how the economy approaches the steady state. For this example, we assume that the production function is

Y = K1/2L1/2.

From Chapter 3, you will recognize this as the Cobb−Douglas production func- tion with the capital-share parameter � equal to 1/2. To derive the per-worker production function f(k), divide both sides of the production function by the labor force L:

Y L

= K1/2L1/2

L .

Rearrange to obtain

Y L

= aK L b1/2.

8-4FIGURE

Investment, Depreciation, and the Steady State The steady-state level of capital k* is the level at which investment equals depreciation, indicating that the amount of capital will not change over time. Below k* investment exceeds depre- ciation, so the capital stock grows. Above k* investment is less than depreciation, so the capital stock shrinks.

Steady-state level of capital per worker

Capital stock decreases because depreciation exceeds investment.

Capital stock increases because investment exceeds depreciation.

�k2

Depreciation, �k

Investment, sf(k)

i2 i*� �k*

i1

k1

Inv estment and depreciation

k* k2 Capital per worker, k

�k1

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212 | P A R T I I I Growth Theory: The Economy in the Very Long Run

Because y = Y/L and k = K/L, this equation becomes

y = k1/2,

which can also be written as

y = "k. This form of the production function states that output per worker equals the square root of the amount of capital per worker.

To complete the example, let’s assume that 30 percent of output is saved (s = 0.3), that 10 percent of the capital stock depreciates every year (� = 0.1), and that the economy starts off with 4 units of capital per worker (k = 4). Given these numbers, we can now examine what happens to this economy over time.

We begin by looking at the production and allocation of output in the fi rst year, when the economy has 4 units of capital per worker. Here are the steps we follow.

■ According to the production function y = "k, the 4 units of capital per worker (k) produce 2 units of output per worker (y).

■ Because 30 percent of output is saved and invested and 70 percent is con- sumed, i = 0.6 and c = 1.4.

■ Because 10 percent of the capital stock depreciates, �k = 0.4. ■ With investment of 0.6 and depreciation of 0.4, the change in the capital

stock is �k = 0.2.

Thus, the economy begins its second year with 4.2 units of capital per worker. We can do the same calculations for each subsequent year. Table 8-2 shows how

the economy progresses. Every year, because investment exceeds depreciation, new capital is added and output grows. Over many years, the economy approaches a steady state with 9 units of capital per worker. In this steady state, investment of 0.9 exactly offsets depreciation of 0.9, so the capital stock and output are no longer growing.

Following the progress of the economy for many years is one way to fi nd the steady-state capital stock, but there is another way that requires fewer calculations. Recall that

�k = sf(k) − �k. This equation shows how k evolves over time. Because the steady state is (by defi ni- tion) the value of k at which �k = 0, we know that

0 = sf(k∗) − �k∗, or, equivalently,

k* f 1k* 2 =

s d .

This equation provides a way of fi nding the steady-state level of capital per worker k∗. Substituting in the numbers and production function from our example, we obtain

k*

"k* = 0.3 0.1

.

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 213

Now square both sides of this equation to fi nd

k∗ = 9.

The steady-state capital stock is 9 units per worker. This result confi rms the calcula- tion of the steady state in Table 8-2.

Assumptions: y = " k ; s = 0.3; � = 0.1; initial k = 4.0 Year k y c i �k �k

1 4.000 2.000 1.400 0.600 0.400 0.200 2 4.200 2.049 1.435 0.615 0.420 0.195 3 4.395 2.096 1.467 0.629 0.440 0.189 4 4.584 2.141 1.499 0.642 0.458 0.184 5 4.768 2.184 1.529 0.655 0.477 0.178 . . . 10 5.602 2.367 1.657 0.710 0.560 0.150 . . . 25 7.321 2.706 1.894 0.812 0.732 0.080 . . . 100 8.962 2.994 2.096 0.898 0.896 0.002 . . . ` 9.000 3.000 2.100 0.900 0.900 0.000

Approaching the Steady State: A Numerical Example

TABLE 8-2

The Miracle of Japanese and German Growth

Japan and Germany are two success stories of economic growth. Although today they are economic superpowers, in 1945 the economies of both countries were in shambles. World War II had destroyed much of their capital stocks. In the decades after the war, however, these two countries experienced some of the most rapid growth rates on record. Between 1948 and 1972, output per person grew at 8.2 percent per year in Japan and 5.7 percent per year in Ger- many, compared to only 2.2 percent per year in the United States.

CASE STUDY

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214 | P A R T I I I Growth Theory: The Economy in the Very Long Run

Are the postwar experiences of Japan and Germany so surprising from the standpoint of the Solow growth model? Consider an economy in steady state. Now suppose that a war destroys some of the capital stock. (That is, suppose the capital stock drops from k∗ to k1 in Figure 8-4.) Not surprisingly, the level of output falls immediately. But if the saving rate—the fraction of output devoted to saving and investment—is unchanged, the economy will then experience a period of high growth. Output grows because, at the lower capital stock, more capital is added by investment than is removed by depreciation. This high growth continues until the economy approaches its former steady state. Hence, although destroying part of the capital stock immediately reduces output, it is followed by higher-than-normal growth. The “miracle’’ of rapid growth in Japan and Germany, as it is often described in the business press, is what the Solow model predicts for countries in which war has greatly reduced the capital stock. ■

How Saving Affects Growth

The explanation of Japanese and German growth after World War II is not quite as simple as suggested in the preceding Case Study. Another relevant fact is that both Japan and Germany save and invest a higher fraction of their output than does the United States. To understand more fully the international differences in economic performance, we must consider the effects of different saving rates.

Consider what happens to an economy when its saving rate increases. Fig- ure 8-5 shows such a change. The economy is assumed to begin in a steady state

8-5FIGURE

An Increase in the Saving Rate An increase in the saving rate s implies that the amount of investment for any given capital stock is higher. It therefore shifts the saving function upward. At the initial steady state k1*, investment now exceeds depreciation. The capital stock rises until the economy reaches a new steady state k2* with more capital and output.

�k

s2f(k)

s1f(k)

k*2k*1

Investment and depreciation

Capital per worker, k

2. ... causing the capital stock to grow toward a new steady state.

1. An increase in the saving rate raises investment, ...

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 215

with saving rate s1 and capital stock k1 ∗. When the saving rate increases from s1

to s2, the sf(k) curve shifts upward. At the initial saving rate s1 and the initial capital stock k1

∗, the amount of investment just offsets the amount of deprecia- tion. Immediately after the saving rate rises, investment is higher, but the capital stock and depreciation are unchanged. Therefore, investment exceeds deprecia- tion. The capital stock gradually rises until the economy reaches the new steady state k2

∗, which has a higher capital stock and a higher level of output than the old steady state.

The Solow model shows that the saving rate is a key determinant of the steady- state capital stock. If the saving rate is high, the economy will have a large capital stock and a high level of output in the steady state. If the saving rate is low, the economy will have a small capital stock and a low level of output in the steady state. This conclusion sheds light on many discussions of fi scal policy. As we saw in Chapter 3, a govern- ment budget defi cit can reduce national saving and crowd out investment. Now we can see that the long-run consequences of a reduced saving rate are a lower capital stock and lower national income. This is why many economists are critical of persistent budget defi cits.

What does the Solow model say about the relationship between saving and economic growth? Higher saving leads to faster growth in the Solow model, but only temporarily. An increase in the rate of saving raises growth only until the economy reaches the new steady state. If the economy maintains a high saving rate, it will maintain a large capital stock and a high level of output, but it will not maintain a high rate of growth forever. Policies that alter the steady-state growth rate of income per person are said to have a growth effect; we will see examples of such policies in the next chapter. By contrast, a higher saving rate is said to have a level effect, because only the level of income per person—not its growth rate—is infl uenced by the saving rate in the steady state.

Now that we understand how saving and growth interact, we can more fully explain the impressive economic performance of Germany and Japan after World War II. Not only were their initial capital stocks low because of the war, but their steady-state capital stocks were also high because of their high saving rates. Both of these facts help explain the rapid growth of these two countries in the 1950s and 1960s.

Saving and Investment Around the World

We started this chapter with an important question: Why are some countries so rich while others are mired in poverty? Our analysis has taken us a step closer to the answer. According to the Solow model, if a nation devotes a large fraction of its income to saving and investment, it will have a high steady-state capital stock and a high level of income. If a nation saves and invests only a small fraction of its income, its steady-state capital and income will be low.

Let’s now look at some data to see if this theoretical result in fact helps explain the large international variation in standards of living. Figure 8-6 is a scatterplot

CASE STUDY

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216 | P A R T I I I Growth Theory: The Economy in the Very Long Run

of data from about 100 countries. (The fi gure includes most of the world’s economies. It excludes major oil-producing countries and countries that were communist during much of this period, because their experiences are explained by their special circumstances.) The data show a positive relationship between the fraction of output devoted to investment and the level of income per person. That is, countries with high rates of investment, such as South Korea and Japan, usually have high incomes, whereas countries with low rates of investment, such as Nigeria and Burundi, have low incomes. Thus, the data are consistent with the Solow model’s prediction that the investment rate is a key determinant of whether a country is rich or poor.

The positive correlation shown in this fi gure is an important fact, but it raises as many questions as it resolves. One might naturally ask, why do rates of saving and investment vary so much from country to country? There are many potential answers, such as tax policy, retirement patterns, the devel- opment of fi nancial markets, and cultural differences. In addition, political

Argentina Barbados

Burundi

Cameroon

China

Republic of Congo

Ecuador

El Salvador

Ethiopia

Finland

Ghana

Greece

Guinea-Bissau

India

Japan South Korea

Luxembourg

Mexico

Nigeria

Norway

Pakistan

Peru

Rwanda

South Africa

Spain

Switzerland

Thailand

Togo

U.K. U.S.

Zambia

Zimbabwe

100,000

10,000

1,000

100

Income per person in 2009 (logarithmic scale)

0 5 10 15 20 25 30 4035 Investment as percentage of output (average 1961–2009)

8-6FIGURE

International Evidence on Investment Rates and Income per Person This scatterplot shows the experience of about 100 countries, each represented by a single point. The horizontal axis shows the country’s rate of investment, and the vertical axis shows the country’s income per person. High investment is associated with high income per person, as the Solow model predicts. The correlation between these two variables is 0.25.

Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 7.0, Center for International Comparisons of Production, Income, and Prices at the University of Pennsylvania, May 2011.

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 217

stability may play a role: not surprisingly, rates of saving and investment tend to be low in countries with frequent wars, revolutions, and coups. Saving and investment also tend to be low in countries with poor political institutions, as measured by estimates of offi cial corruption. A fi nal interpretation of the evidence in Figure 8-6 is reverse causation: perhaps high levels of income somehow foster high rates of saving and investment. Unfortunately, there is no consensus among economists about which of the many possible explana- tions is most important.

The association between investment rates and income per person is an impor- tant clue as to why some countries are rich and others poor, but it is not the whole story. The correlation between these two variables is far from perfect. There must be other determinants of living standards beyond saving and investment. Later in this chapter and in the next one, we return to the international differences in income per person to see what other variables enter the picture. ■

<h1 The Golden Rule Level of Capital

So far, we have used the Solow model to examine how an economy’s rate of saving and investment determines its steady-state levels of capital and income. This analysis might lead you to think that higher saving is always a good thing because it always leads to greater income. Yet suppose a nation had a saving rate of 100 percent. That would lead to the largest possible capital stock and the larg- est possible income. But if all of this income is saved and none is ever consumed, what good is it?

This section uses the Solow model to discuss the optimal amount of capital accumulation from the standpoint of economic well-being. In the next chapter, we discuss how government policies infl uence a nation’s saving rate. But fi rst, in this section, we present the theory behind these policy decisions.

Comparing Steady States

To keep our analysis simple, let’s assume that a policymaker can set the economy’s saving rate at any level. By setting the saving rate, the policymaker determines the economy’s steady state. What steady state should the policymaker choose?

The policymaker’s goal is to maximize the well-being of the individuals who make up the society. Individuals themselves do not care about the amount of capi- tal in the economy or even the amount of output. They care about the amount of goods and services they can consume. Thus, a benevolent policymaker would want to choose the steady state with the highest level of consumption. The steady- state value of k that maximizes consumption is called the Golden Rule level of capital and is denoted kgold

* .2

8-2

2Edmund Phelps, “The Golden Rule of Accumulation: A Fable for Growthmen,’’ American Economic Review 51 (September 1961): 638−643.

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218 | P A R T I I I Growth Theory: The Economy in the Very Long Run

How can we tell whether an economy is at the Golden Rule level? To answer this question, we must fi rst determine steady-state consumption per worker. Then we can see which steady state provides the most consumption.

To fi nd steady-state consumption per worker, we begin with the national income accounts identity

y = c + i

and rearrange it as

c = y − i.

Consumption is output minus investment. Because we want to fi nd steady-state consumption, we substitute steady-state values for output and investment. Steady-state output per worker is f(k∗), where k∗ is the steady-state capital stock per worker. Furthermore, because the capital stock is not changing in the steady state, investment equals depreciation �k∗. Substituting f(k∗) for y and �k∗ for i, we can write steady-state consumption per worker as

c∗ = f(k∗) − �k∗.

According to this equation, steady-state consumption is what’s left of steady-state output after paying for steady-state depreciation. This equation shows that an increase in steady-state capital has two opposing effects on steady-state consumption. On the one hand, more capital means more output. On the other hand, more capital also means that more output must be used to replace capital that is wearing out.

Figure 8-7 graphs steady-state output and steady-state depreciation as a func- tion of the steady-state capital stock. Steady-state consumption is the gap between

8-7FIGURE

Steady-State Consumption The economy’s output is used for consumption or investment. In the steady state, investment equals depreciation. Therefore, steady-state consumption is the difference between output f(k*) and depreciation �k*. Steady- state consumption is maximized at the Golden Rule steady state. The Golden Rule capital stock is denoted k* gold, and the Golden Rule level of consumption is denoted c* gold.

Below the Golden Rule steady state, increases in steady-state capital raise steady-state consumption.

Above the Golden Rule steady state, increases in steady-state capital reduce steady-state consumption.

Steady-state output and depreciation

Steady-state depreciation (and investment), �k*

Steady-state output, f(k*)

c*gold

Steady-state capital per worker, k*

k*gold

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 219

output and depreciation. This fi gure shows that there is one level of the capital stock—the Golden Rule level kgold

* —that maximizes consumption. When comparing steady states, we must keep in mind that higher levels of

capital affect both output and depreciation. If the capital stock is below the Golden Rule level, an increase in the capital stock raises output more than depreciation, so consumption rises. In this case, the production function is steeper than the �k∗ line, so the gap between these two curves—which equals consumption—grows as k∗ rises. By contrast, if the capital stock is above the Golden Rule level, an increase in the capital stock reduces consumption, because the increase in output is smaller than the increase in depreciation. In this case, the production function is fl atter than the �k∗ line, so the gap between the curves—consumption—shrinks as k∗ rises. At the Golden Rule level of capital, the production function and the �k∗ line have the same slope, and consumption is at its greatest level.

We can now derive a simple condition that characterizes the Golden Rule level of capital. Recall that the slope of the production function is the marginal product of capital MPK. The slope of the �k∗ line is �. Because these two slopes are equal at kgold

* , the Golden Rule is described by the equation

MPK = �.

At the Golden Rule level of capital, the marginal product of capital equals the depreciation rate.

To make the point somewhat differently, suppose that the economy starts at some steady-state capital stock k∗ and that the policymaker is considering increasing the capital stock to k∗ + 1. The amount of extra output from this increase in capital would be f(k∗ + 1) − f(k∗), the marginal product of capital MPK. The amount of extra depreciation from having 1 more unit of capital is the depreciation rate �. Thus, the net effect of this extra unit of capital on consumption is MPK − �. If MPK − � > 0, then increases in capital increase consumption, so k∗ must be below the Golden Rule level. If MPK − � < 0, then increases in capital decrease consumption, so k∗ must be above the Golden Rule level. Therefore, the following condition describes the Golden Rule:

MPK − � = 0.

At the Golden Rule level of capital, the marginal product of capital net of deprecia- tion (MPK − �) equals zero. As we will see, a policymaker can use this condition to fi nd the Golden Rule capital stock for an economy.3

Keep in mind that the economy does not automatically gravitate toward the Golden Rule steady state. If we want any particular steady-state capital stock, such as the Golden Rule, we need a particular saving rate to support it. Figure 8-8 shows

3Mathematical note: Another way to derive the condition for the Golden Rule uses a bit of calculus. Recall that c∗ = f(k∗) − �k∗. To fi nd the k∗ that maximizes c∗, differentiate to fi nd dc∗/dk∗ = f �(k∗) − � and set this derivative equal to zero. Noting that f �(k∗) is the marginal product of capital, we obtain the Golden Rule condition in the text.

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220 | P A R T I I I Growth Theory: The Economy in the Very Long Run

the steady state if the saving rate is set to produce the Golden Rule level of capital. If the saving rate is higher than the one used in this fi gure, the steady-state capital stock will be too high. If the saving rate is lower, the steady-state capital stock will be too low. In either case, steady-state consumption will be lower than it is at the Golden Rule steady state.

Finding the Golden Rule Steady State: A Numerical Example

Consider the decision of a policymaker choosing a steady state in the following economy. The production function is the same as in our earlier example:

y = "k. Output per worker is the square root of capital per worker. Depreciation � is again 10 percent of capital. This time, the policymaker chooses the saving rate s and thus the economy’s steady state.

To see the outcomes available to the policymaker, recall that the following equa- tion holds in the steady state:

k* f 1k* 2 =

s d

8-8FIGURE

The Saving Rate and the Golden Rule There is only one saving rate that produces the Golden Rule level of capital k* gold. Any change in the saving rate would shift the sf(k) curve and would move the economy to a steady state with a lower level of consumption.

1. To reach the Golden Rule steady state ...

2. ...the economy needs the right saving rate.

Steady-state output, depreciation, and investment per worker �k*

f(k*)

sgoldf(k*) c*gold

i*gold

k*gold Steady-state capital per worker, k*

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In this economy, this equation becomes

k*

"k* = s

0.1 .

Squaring both sides of this equation yields a solution for the steady-state capital stock. We fi nd

k∗ = 100s2.

Using this result, we can compute the steady-state capital stock for any saving rate. Table 8-3 presents calculations showing the steady states that result from

various saving rates in this economy. We see that higher saving leads to a higher capital stock, which in turn leads to higher output and higher depreciation. Steady-state consumption, the difference between output and depreciation, fi rst rises with higher saving rates and then declines. Consumption is highest when the saving rate is 0.5. Hence, a saving rate of 0.5 produces the Golden Rule steady state.

Recall that another way to identify the Golden Rule steady state is to fi nd the capital stock at which the net marginal product of capital (MPK − �) equals zero. For this production function, the marginal product is4

MPK = 1

2"k. Using this formula, the last two columns of Table 8-3 present the values of MPK and MPK − � in the different steady states. Note that the net marginal product

4Mathematical note: To derive this formula, note that the marginal product of capital is the derivative of the production function with respect to k.

Assumptions: y = " k ; � = 0.1 s k* y* �k* c* MPK MPK − �

0.0 0.0 0.0 0.0 0.0 � � 0.1 1.0 1.0 0.1 0.9 0.500 0.400 0.2 4.0 2.0 0.4 1.6 0.250 0.150 0.3 9.0 3.0 0.9 2.1 0.167 0.067 0.4 16.0 4.0 1.6 2.4 0.125 0.025 0.5 25.0 5.0 2.5 2.5 0.100 0.000 0.6 36.0 6.0 3.6 2.4 0.083 −0.017 0.7 49.0 7.0 4.9 2.1 0.071 −0.029 0.8 64.0 8.0 6.4 1.6 0.062 −0.038 0.9 81.0 9.0 8.1 0.9 0.056 −0.044 1.0 100.0 10.0 10.0 0.0 0.050 −0.050

Finding the Golden Rule Steady State: A Numerical Example

TABLE 8-3

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of capital is exactly zero when the saving rate is at its Golden Rule value of 0.5. Because of diminishing marginal product, the net marginal product of capital is greater than zero whenever the economy saves less than this amount, and it is less than zero whenever the economy saves more.

This numerical example confi rms that the two ways of fi nding the Golden Rule steady state—looking at steady-state consumption or looking at the mar- ginal product of capital—give the same answer. If we want to know whether an actual economy is currently at, above, or below its Golden Rule capital stock, the second method is usually more convenient, because it is relatively straight- forward to estimate the marginal product of capital. By contrast, evaluating an economy with the fi rst method requires estimates of steady-state consumption at many different saving rates; such information is harder to obtain. Thus, when we apply this kind of analysis to the U.S. economy in the next chapter, we will evaluate U.S. saving by examining the marginal product of capital. Before engaging in that policy analysis, however, we need to proceed further in our development and understanding of the Solow model.

The Transition to the Golden Rule Steady State

Let’s now make our policymaker’s problem more realistic. So far, we have been assuming that the policymaker can simply choose the economy’s steady state and jump there immediately. In this case, the policymaker would choose the steady state with the highest consumption—the Golden Rule steady state. But now suppose that the economy has reached a steady state other than the Golden Rule. What happens to consumption, investment, and capital when the economy makes the transition between steady states? Might the impact of the transition deter the policymaker from trying to achieve the Golden Rule?

We must consider two cases: the economy might begin with more capital than in the Golden Rule steady state, or with less. It turns out that the two cases offer very different problems for policymakers. (As we will see in the next chapter, the second case—too little capital—describes most actual economies, including that of the United States.)

Starting With Too Much Capital We fi rst consider the case in which the economy begins at a steady state with more capital than it would have in the Golden Rule steady state. In this case, the policymaker should pursue poli- cies aimed at reducing the rate of saving in order to reduce the capital stock. Suppose that these policies succeed and that at some point—call it time t0—the saving rate falls to the level that will eventually lead to the Golden Rule steady state.

Figure 8-9 shows what happens to output, consumption, and investment when the saving rate falls. The reduction in the saving rate causes an immediate increase in consumption and a decrease in investment. Because investment and depreciation were equal in the initial steady state, investment will now be less than depreciation, which means the economy is no longer in a steady state. Gradually, the capital stock falls, leading to reductions in output, consumption, and investment. These variables

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 223

continue to fall until the economy reaches the new steady state. Because we are assuming that the new steady state is the Golden Rule steady state, consumption must be higher than it was before the change in the saving rate, even though output and investment are lower.

Note that, compared to the old steady state, consumption is higher not only in the new steady state but also along the entire path to it. When the capital stock exceeds the Golden Rule level, reducing saving is clearly a good policy, for it increases consumption at every point in time.

Starting With Too Little Capital When the economy begins with less capi- tal than in the Golden Rule steady state, the policymaker must raise the saving rate to reach the Golden Rule. Figure 8-10 shows what happens. The increase in the saving rate at time t0 causes an immediate fall in consumption and a rise in investment. Over time, higher investment causes the capital stock to rise. As capital accumulates, output, consumption, and investment gradually increase, eventually approaching the new steady-state levels. Because the initial steady state was below the Golden Rule, the increase in saving eventually leads to a higher level of consumption than that which prevailed initially.

Does the increase in saving that leads to the Golden Rule steady state raise eco- nomic welfare? Eventually it does, because the new steady-state level of consump- tion is higher than the initial level. But achieving that new steady state requires an initial period of reduced consumption. Note the contrast to the case in which the economy begins above the Golden Rule. When the economy begins above the Golden Rule, reaching the Golden Rule produces higher consumption at all points in time. When the economy begins below the Golden Rule, reaching the Golden Rule requires initially reducing consumption to increase consumption in the future.

8-9FIGURE

Reducing Saving When Starting With More Capital Than in the Golden Rule Steady State This fi gure shows what hap- pens over time to output, consumption, and investment when the economy begins with more capital than the Golden Rule level and the saving rate is reduced. The reduction in the saving rate (at time t0) causes an immedi- ate increase in consumption and an equal decrease in investment. Over time, as the capital stock falls, output, consumption, and investment fall together. Because the economy began with too much capital, the new steady state has a higher level of consumption than the initial steady state.

Output, y

t0

The saving rate is reduced.

Time

Consumption, c

Investment, i

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224 | P A R T I I I Growth Theory: The Economy in the Very Long Run

When deciding whether to try to reach the Golden Rule steady state, policymak- ers have to take into account that current consumers and future consumers are not always the same people. Reaching the Golden Rule achieves the highest steady-state level of consumption and thus benefi ts future generations. But when the economy is initially below the Golden Rule, reaching the Golden Rule requires raising invest- ment and thus lowering the consumption of current generations. Thus, when choos- ing whether to increase capital accumulation, the policymaker faces a tradeoff among the welfare of different generations. A policymaker who cares more about current generations than about future ones may decide not to pursue policies to reach the Golden Rule steady state. By contrast, a policymaker who cares about all generations equally will choose to reach the Golden Rule. Even though current generations will consume less, an infi nite number of future generations will benefi t by moving to the Golden Rule.

Thus, optimal capital accumulation depends crucially on how we weigh the interests of current and future generations. The biblical Golden Rule tells us, “Do unto others as you would have them do unto you.’’ If we heed this advice, we give all generations equal weight. In this case, it is optimal to reach the Golden Rule level of capital—which is why it is called the “Golden Rule.’’

Population Growth

The basic Solow model shows that capital accumulation, by itself, cannot explain sustained economic growth: high rates of saving lead to high growth temporar- ily, but the economy eventually approaches a steady state in which capital and

8-3

8-10FIGURE

Increasing Saving When Starting With Less Capital Than in the Golden Rule Steady State This fi gure shows what hap- pens over time to output, consumption, and investment when the economy begins with less capital than the Golden Rule level and the sav- ing rate is increased. The increase in the saving rate (at time t0) causes an immediate drop in consumption and an equal jump in invest- ment. Over time, as the capital stock grows, output, consumption, and investment increase together. Because the economy began with less capital than the Golden Rule level, the new steady state has a higher level of consumption than the initial steady state.

Output, y

Timet0

Consumption, c

Investment, i

The saving rate is increased.

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 225

output are constant. To explain the sustained economic growth that we observe in most parts of the world, we must expand the Solow model to incorporate the other two sources of economic growth—population growth and technological progress. In this section we add population growth to the model.

Instead of assuming that the population is fi xed, as we did in Sections 8-1 and 8-2, we now suppose that the population and the labor force grow at a constant rate n. For example, the U.S. population grows about 1 percent per year, so n = 0.01. This means that if 150 million people are working one year, then 151.5 million (1.01 × 150) are working the next year, and 153.015 million (1.01 × 151.5) the year after that, and so on.

The Steady State With Population Growth

How does population growth affect the steady state? To answer this question, we must discuss how population growth, along with investment and depreciation, infl uences the accumulation of capital per worker. As we noted before, invest- ment raises the capital stock, and depreciation reduces it. But now there is a third force acting to change the amount of capital per worker: the growth in the number of workers causes capital per worker to fall.

We continue to let lowercase letters stand for quantities per worker. Thus, k = K/L is capital per worker, and y = Y/L is output per worker. Keep in mind, however, that the number of workers is growing over time.

The change in the capital stock per worker is

�k = i − (� + n)k.

This equation shows how investment, depreciation, and population growth infl u- ence the per-worker capital stock. Investment increases k, whereas depreciation and population growth decrease k. We saw this equation earlier in this chapter for the special case of a constant population (n = 0).

We can think of the term (� + n)k as defi ning break-even investment—the amount of investment necessary to keep the capital stock per worker constant. Break-even investment includes the depreciation of existing capital, which equals �k. It also includes the amount of investment necessary to provide new workers with capital. The amount of investment necessary for this purpose is nk, because there are n new workers for each existing worker and because k is the amount of capital for each worker. The equation shows that population growth reduces the accumulation of capital per worker much the way depreciation does. Depre- ciation reduces k by wearing out the capital stock, whereas population growth reduces k by spreading the capital stock more thinly among a larger population of workers.5

5Mathematical note: Formally deriving the equation for the change in k requires a bit of calculus. Note that the change in k per unit of time is dk/dt = d(K/L)/dt. After applying the standard rules of calculus, we can write this as dk/dt = (1/L)(dK/dt) − (K/L2)(dL/dt). Now use the following facts to substitute in this equation: dK/dt = I − �K and (dL/dt)/L = n. After a bit of manipulation, this produces the equation in the text.

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226 | P A R T I I I Growth Theory: The Economy in the Very Long Run

Our analysis with population growth now proceeds much as it did previously. First, we substitute sf(k) for i. The equation can then be written as

�k = sf (k) − (� + n)k.

To see what determines the steady-state level of capital per worker, we use Figure 8-11, which extends the analysis of Figure 8-4 to include the effects of population growth. An economy is in a steady state if capital per worker k is unchanging. As before, we designate the steady-state value of k as k∗. If k is less than k∗, investment is greater than break-even investment, so k rises. If k is greater than k∗, investment is less than break-even investment, so k falls.

In the steady state, the positive effect of investment on the capital stock per worker exactly balances the negative effects of depreciation and population growth. That is, at k∗, �k = 0 and i∗ = �k∗ + nk∗. Once the economy is in the steady state, investment has two purposes. Some of it (�k∗) replaces the depreciated capital, and the rest (nk∗) provides the new workers with the steady-state amount of capital.

The Effects of Population Growth

Population growth alters the basic Solow model in three ways. First, it brings us closer to explaining sustained economic growth. In the steady state with popula- tion growth, capital per worker and output per worker are constant. Because the number of workers is growing at rate n, however, total capital and total output must also be growing at rate n. Hence, although population growth cannot explain sus- tained growth in the standard of living (because output per worker is constant in the steady state), it can help explain sustained growth in total output.

Second, population growth gives us another explanation for why some countries are rich and others are poor. Consider the effects of an increase in population growth. Figure 8-12 shows that an increase in the rate of population growth from n1 to n2

8-11FIGURE

Population Growth in the Solow Model Depreciation and population growth are two rea- sons the capital stock per worker shrinks. If n is the rate of popu- lation growth and � is the rate of depreciation, then (� + n)k is break-even investment—the amount of investment necessary to keep constant the capital stock per worker k. For the economy to be in a steady state, investment sf (k) must offset the effects of depreciation and population growth (� + n)k. This is repre- sented by the crossing of the two curves.

Investment, break-even investment

k* Capital per worker, k

Break-even investment, (� + n)k

Investment, sf (k)

The steady state

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 227

reduces the steady-state level of capital per worker from k*1 to k2*. Because k∗ is lower and because y∗ = f(k∗), the level of output per worker y∗ is also lower. Thus, the Solow model predicts that countries with higher population growth will have lower levels of GDP per person. Notice that a change in the population growth rate, like a change in the saving rate, has a level effect on income per person but does not affect the steady-state growth rate of income per person.

Finally, population growth affects our criterion for determining the Golden Rule (consumption-maximizing) level of capital. To see how this criterion changes, note that consumption per worker is

c = y − i.

Because steady-state output is f(k∗) and steady-state investment is (� + n)k∗, we can express steady-state consumption as

c∗ = f (k∗) − (� + n)k∗.

Using an argument largely the same as before, we conclude that the level of k∗ that maximizes consumption is the one at which

MPK = � + n,

or equivalently,

MPK − � = n.

In the Golden Rule steady state, the marginal product of capital net of deprecia- tion equals the rate of population growth.

8-12FIGURE

The Impact of Population Growth An increase in the rate of population growth from n1 to n2 shifts the line representing population growth and depre- ciation upward. The new steady state k2* has a lower level of capi- tal per worker than the initial steady state k1*. Thus, the Solow model predicts that economies with higher rates of population growth will have lower levels of capital per worker and therefore lower incomes.

Investment, break-even investment

k*2 Capital per worker, k

(� + n1)k

(� + n2)k

sf(k)

k*1

1. An increase in the rate of population growth ...

2. ... reduces the steady- state capital stock.

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228 | P A R T I I I Growth Theory: The Economy in the Very Long Run

Population Growth Around the World

Let’s return now to the question of why standards of living vary so much around the world. The analysis we have just completed suggests that population growth may be one of the answers. According to the Solow model, a nation with a high rate of population growth will have a low steady-state capital stock per worker and thus also a low level of income per worker. In other words, high population growth tends to impoverish a country because it is hard to maintain a high level of capital per worker when the number of workers is growing quickly. To see whether the evidence supports this conclusion, we again look at cross-country data.

Figure 8-13 is a scatterplot of data for the same countries examined in the previous Case Study (and in Figure 8-6). The fi gure shows that countries with high rates of population growth tend to have low levels of income per person. The international evidence is consistent with our model’s prediction that the rate of population growth is one determinant of a country’s standard of living.

CASE STUDY

8-13FIGURE

International Evidence on Population Growth and Income per Person This fi gure is a scatterplot of data from about 100 countries. It shows that countries with high rates of population growth tend to have low levels of income per person, as the Solow model predicts. The correlation between these variables is −0.74. Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 7.0, Center for International Comparisons of Production, Income, and Prices at the University of Pennsylvania, May 2011.

Australia

Brazil

Burundi

Canada

China

Costa Rica

Cote d`Ivoire

Denmark

Ethiopia

Gambia

Guatemala

Guinea-Bissau

Hong Kong

India

Israel

Jamaica

Jordan

South Korea

Lesotho

Luxembourg

Niger

Norway

Pakistan

Portugal

U.K. U. S.

Uruguay

Zimbabwe

100,000

10,000

1,000

100 1 2 3 4 50

Income per person in 2009 (logarithmic scale)

Population growth (percent per year; average 1960–2009)

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 229

This conclusion is not lost on policymakers. Those trying to pull the world’s poorest nations out of poverty, such as the advisers sent to developing nations by the World Bank, often advocate reducing fertility by increasing education about birth- control methods and expanding women’s job opportunities. Toward the same end, China has followed the totalitarian policy of allowing only one child for most urban couples. These policies to reduce population growth should, if the Solow model is right, raise income per person in the long run.

In interpreting the cross-country data, however, it is important to keep in mind that correlation does not imply causation. The data show that low population growth is typically associated with high levels of income per person, and the Solow model offers one possible explanation for this fact, but other explanations are also possible. It is conceivable that high income encourages low population growth, perhaps because birth-control techniques are more readily available in richer countries. The international data can help us evaluate a theory of growth, such as the Solow model, because they show us whether the theory’s predictions are borne out in the world. But often more than one theory can explain the same facts. ■

Alternative Perspectives on Population Growth

The Solow growth model highlights the interaction between population growth and capital accumulation. In this model, high population growth reduces output per worker because rapid growth in the number of workers forces the capital stock to be spread more thinly, so in the steady state, each worker is equipped with less capital. The model omits some other potential effects of population growth. Here we consider two—one emphasizing the interaction of population with natural resources, the other emphasizing the interaction of population with technology.

The Malthusian Model In his book An Essay on the Principle of Population as It Affects the Future Improvement of Society, the early economist Thomas Robert Malthus (1766−1834) offered what may be history’s most chilling forecast. Malthus argued that an ever-increasing population would continually strain society’s ability to provide for itself. Mankind, he predicted, would forever live in poverty.

Malthus began by noting that “food is necessary to the existence of man” and that “the passion between the sexes is necessary and will remain nearly in its pres- ent state.” He concluded that “the power of population is infi nitely greater than the power in the earth to produce subsistence for man.” According to Malthus, the only check on population growth was “misery and vice.” Attempts by charities or governments to alleviate poverty were counterproductive, he argued, because they merely allowed the poor to have more children, placing even greater strains on society’s productive capabilities.

The Malthusian model may have described the world when Malthus lived, but its prediction that mankind would remain in poverty forever has proven very wrong. The world population has increased about sixfold over the past two centuries, but average living standards are much higher. Because of economic growth, chronic hunger and malnutrition are less common now than they were in Malthus’s day. Famines occur from time to time, but they are more often

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the result of unequal income distribution or political instability than the inad- equate production of food.

Malthus failed to foresee that growth in mankind’s ingenuity would more than offset the effects of a larger population. Pesticides, fertilizers, mechanized farm equipment, new crop varieties, and other technological advances that Malthus never imagined have allowed each farmer to feed ever-greater numbers of peo- ple. Even with more mouths to feed, fewer farmers are necessary because each farmer is so productive. Today, fewer than 2 percent of Americans work on farms, producing enough food to feed the nation and some excess to export as well.

In addition, although the “passion between the sexes” is just as strong now as it was in Malthus’s day, the link between passion and population growth that Malthus assumed has been broken by modern birth control. Many advanced nations, such as those in western Europe, are now experiencing fertility below replacement rates. Over the next century, shrinking populations may be more likely than rapidly expanding ones. There is now little reason to think that an ever-expanding population will overwhelm food production and doom mankind to poverty.6

The Kremerian Model While Malthus saw population growth as a threat to rising living standards, economist Michael Kremer has suggested that world population growth is a key driver of advancing economic prosperity. If there are more people, Kremer argues, then there are more scientists, inventors, and engi- neers to contribute to innovation and technological progress.

As evidence for this hypothesis, Kremer begins by noting that over the broad span of human history, world growth rates have increased together with world population. For example, world growth was more rapid when the world popula- tion was 1 billion (which occurred around the year 1800) than it was when the population was only 100 million (around 500 B.C.). This fact is consistent with the hypothesis that having more people induces more technological progress.

Kremer’s second, more compelling piece of evidence comes from comparing regions of the world. The melting of the polar ice caps at the end of the ice age around 10,000 B.C. fl ooded the land bridges and separated the world into several distinct regions that could not communicate with one another for thousands of years. If technological progress is more rapid when there are more people to discover things, then the more populous regions should have experienced more rapid growth.

And, indeed, they did. The most successful region of the world in 1500 (when Columbus reestablished technological contact) included the “Old World” civi- lizations of the large Eurasia−Africa region. Next in technological development were the Aztec and Mayan civilizations in the Americas, followed by the hunter- gatherers of Australia, and then the primitive people of Tasmania, who lacked even fi re-making and most stone and bone tools. The least populous isolated region was Flinders Island, a tiny island between Tasmania and Australia. With

6For modern analyses of the Malthusian model, see Oded Galor and David N. Weil, “Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and Beyond,” American Economic Review 90 (September 2000): 806−828; and Gary D. Hansen and Edward C. Prescott, “Malthus to Solow,” American Economic Review 92 (September 2002): 1205−1217.

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 231

few people to contribute new innovations, Flinders Island had the least techno- logical advance and, in fact, seemed to regress. Around 3000 B.C., human society on Flinders Island died out completely.

Kremer concludes from this evidence that a large population is a prerequisite for technological advance.7

Conclusion

This chapter has started the process of building the Solow growth model. The model as developed so far shows how saving and population growth determine the economy’s steady-state capital stock and its steady-state level of income per person. As we have seen, it sheds light on many features of actual growth experiences—why Germany and Japan grew so rapidly after being devastated by World War II, why countries that save and invest a high fraction of their output are richer than countries that save and invest a smaller fraction, and why countries with high rates of popula- tion growth are poorer than countries with low rates of population growth.

What the model cannot do, however, is explain the persistent growth in living standards we observe in most countries. In the model we have developed so far, output per worker stops growing when the economy reaches its steady state. To explain persistent growth, we need to introduce technological progress into the model. That is our fi rst job in the next chapter.

Summary

1. The Solow growth model shows that in the long run, an economy’s rate of saving determines the size of its capital stock and thus its level of produc- tion. The higher the rate of saving, the higher the stock of capital and the higher the level of output.

2. In the Solow model, an increase in the rate of saving has a level effect on income per person: it causes a period of rapid growth, but eventually that growth slows as the new steady state is reached. Thus, although a high sav- ing rate yields a high steady-state level of output, saving by itself cannot generate persistent economic growth.

3. The level of capital that maximizes steady-state consumption is called the Golden Rule level. If an economy has more capital than in the Golden Rule steady state, then reducing saving will increase consumption at all points in time. By contrast, if the economy has less capital than in the Golden Rule steady state, then reaching the Golden Rule requires increased investment and thus lower consumption for current generations.

8-4

7Michael Kremer, “Population Growth and Technological Change: One Million B.C. to 1990,” Quarterly Journal of Economics 108 (August 1993): 681−716.

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232 | P A R T I I I Growth Theory: The Economy in the Very Long Run

4. The Solow model shows that an economy’s rate of population growth is another long-run determinant of the standard of living. According to the Solow model, the higher the rate of population growth, the lower the steady-state levels of capital per worker and output per worker. Other theo- ries highlight other effects of population growth. Malthus suggested that population growth will strain the natural resources necessary to produce food; Kremer suggested that a large population may promote technological progress.

K E Y C O N C E P T S

Solow growth model Steady state Golden Rule level of capital

1. In the Solow model, how does the saving rate affect the steady-state level of income? How does it affect the steady-state rate of growth?

2. Why might an economic policymaker choose the Golden Rule level of capital?

3. Might a policymaker choose a steady state with more capital than in the Golden Rule steady

Q U E S T I O N S F O R R E V I E W

state? With less capital than in the Golden Rule steady state? Explain your answers.

4. In the Solow model, how does the rate of popu- lation growth affect the steady-state level of income? How does it affect the steady-state rate of growth?

P R O B L E M S A N D A P P L I C A T I O N S

1. Country A and country B both have the pro- duction function

Y = F(K, L) = K1/2L1/2. a. Does this production function have constant

returns to scale? Explain.

b. What is the per-worker production function, y = f(k)?

c. Assume that neither country experiences popula- tion growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of out- put each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, fi nd the steady-state level of capital per worker for each country. Then fi nd the steady-state levels of income per worker and consumption per worker.

d. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calcu- late income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A?

2. In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not directly affect the capital stock, but that casualties reduce the labor force. Assume the economy was in a steady state before the war, the saving rate

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C H A P T E R 8 Economic Growth I: Capital Accumulation and Population Growth | 233

is unchanged, and the rate of population growth after the war is the same as it was before.

a. What is the immediate impact of the war on total output and on output per person?

b. What happens subsequently to output per worker in the postwar economy? Is the growth rate of output per worker after the war smaller or greater than it was before the war?

3. Consider an economy described by the produc- tion function: Y = F(K, L) = K0.3L0.7. a. What is the per-worker production function?

b. Assuming no population growth or techno- logical progress, fi nd the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.

c. Assume that the depreciation rate is 10 per- cent per year. Make a table showing steady- state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 per- cent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What sav- ing rate maximizes consumption per worker?

d. (Harder) Use calculus to fi nd the marginal product of capital. Add to your table from part (c) the marginal product of capital net of depreciation for each of the saving rates. What does your table show about the relationship between the net marginal product of capital and steady-state consumption?

4. “Devoting a larger share of national output to investment would help restore rapid productivity growth and rising living standards.’’ Do you agree with this claim? Explain, using the Solow model.

5. Draw a well-labeled graph that illustrates the steady state of the Solow model with population growth. Use the graph to fi nd what happens to steady-state capital per worker and income per worker in response to each of the following exogenous changes.

a. A change in consumer preferences increases the saving rate.

b. A change in weather patterns increases the depreciation rate.

c. Better birth-control methods reduce the rate of population growth.

d. A one-time, permanent improvement in tech- nology increases the amount of output that can be produced from any given amount of capital and labor.

6. Many demographers predict that the United States will have zero population growth in the twenty-fi rst century, in contrast to average popu- lation growth of about 1 percent per year in the twentieth century. Use the Solow model to forecast the effect of this slowdown in popula- tion growth on the growth of total output and the growth of output per person. Consider the effects both in the steady state and in the transi- tion between steady states.

7. In the Solow model, population growth leads to steady-state growth in total output, but not in output per worker. Do you think this would still be true if the production function exhib- ited increasing or decreasing returns to scale? Explain. (For the defi nitions of increasing and decreasing returns to scale, see Chapter 3, “Prob- lems and Applications,” Problem 3.)

8. Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = K�[(1 − u)L]1 − �, where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate �.

a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u).

b. Write an equation that describes the steady state of this economy. Illustrate the steady state graphically, as we did in this chapter for the standard Solow model.

c. Suppose that some change in government policy reduces the natural rate of unemploy- ment. Using the graph you drew in part (b), describe how this change affects output both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect? Explain.

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235

Economic Growth II: Technology, Empirics, and Policy

9C H A P T E R

Is there some action a government of India could take that would lead the

Indian economy to grow like Indonesia’s or Egypt’s? If so, what, exactly? If

not, what is it about the “nature of India” that makes it so? The consequences

for human welfare involved in questions like these are simply staggering: Once

one starts to think about them, it is hard to think about anything else.

—Robert E. Lucas, Jr.

The quotation that opens this chapter was written in 1988. Since then, India has grown rapidly, a phenomenon that has pulled millions of people out of extreme poverty. At the same time, some other poor nations, includ- ing many in sub-Saharan Africa, have experienced little growth, and their citizens continue to live meager existences. It is the job of growth theory to explain such disparate outcomes. The reasons why some nations succeed while others fail at promoting long-run economic growth are not easily apparent, but as Robert Lucas suggests, the consequences for human welfare are indeed staggering.

This chapter continues our analysis of the forces governing long-run growth. With the basic version of the Solow model as our starting point, we take on four new tasks.

Our fi rst task is to make the Solow model more general and realistic. In Chapter 3 we saw that capital, labor, and technology are the key determinants of a nation’s pro- duction of goods and services. In Chapter 8 we developed the Solow model to show how changes in capital (through saving and investment) and changes in the labor force (through population growth) affect the economy’s output. We are now ready to add the third source of growth—changes in technology—to the mix. The Solow model does not explain technological progress but, instead, takes it as exogenously given and shows how it interacts with other variables in the process of economic growth.

Our second task is to move from theory to empirics. That is, we consider how well the Solow model fi ts the facts. Over the past two decades, a large literature has examined the predictions of the Solow model and other models of economic growth. It turns out that the glass is both half full and half empty. The Solow model can shed much light on international growth experiences, but it is far from the last word on the subject.

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236 | P A R T I I I Growth Theory: The Economy in the Very Long Run

Our third task is to examine how a nation’s public policies can infl uence the level and growth of its citizens’ standard of living. In particular, we address fi ve questions: Should our society save more or less? How can policy infl uence the rate of saving? Are there some types of investment that policy should especially encourage? What institutions ensure that the economy’s resources are put to their best use? How can policy increase the rate of technological progress? The Solow growth model provides the theoretical framework within which we consider these policy issues.

Our fourth and fi nal task is to consider what the Solow model leaves out. As we have discussed previously, models help us understand the world by simplifying it. After completing an analysis of a model, therefore, it is important to consider whether we have oversimplifi ed matters. In the last section, we examine a new set of theories, called endogenous growth theories, which help to explain the tech- nological progress that the Solow model takes as exogenous.

9-1 Technological Progress in the Solow Model

So far, our presentation of the Solow model has assumed an unchanging relation- ship between the inputs of capital and labor and the output of goods and services. Yet the model can be modifi ed to include exogenous technological progress, which over time expands society’s production capabilities.

The Efficiency of Labor

To incorporate technological progress, we must return to the production func- tion that relates total capital K and total labor L to total output Y. Thus far, the production function has been

Y = F(K, L).

We now write the production function as

Y = F(K, L × E ),

where E is a new (and somewhat abstract) variable called the effi ciency of labor. The effi ciency of labor is meant to refl ect society’s knowledge about production methods: as the available technology improves, the effi ciency of labor rises, and each hour of work contributes more to the production of goods and services. For instance, the effi ciency of labor rose when assembly-line production transformed manufacturing in the early twentieth century, and it rose again when computeriza- tion was introduced in the late twentieth century. The effi ciency of labor also rises when there are improvements in the health, education, or skills of the labor force.

The term L × E can be interpreted as measuring the effective number of workers. It takes into account the number of actual workers L and the effi ciency of each worker E. In other words, L measures the number of workers in the labor force, whereas L × E measures both the workers and the technology with which the typi- cal worker comes equipped. This new production function states that total output Y depends on the inputs of capital K and effective workers L × E.

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The essence of this approach to modeling technological progress is that increases in the effi ciency of labor E are analogous to increases in the labor force L. Suppose, for example, that an advance in production methods makes the effi ciency of labor E double between 1980 and 2012. This means that a single worker in 2012 is, in effect, as productive as two workers were in 1980. That is, even if the actual number of workers (L) stays the same from 1980 to 2012, the effective number of workers (L × E ) doubles, and the economy benefi ts from the increased production of goods and services.

The simplest assumption about technological progress is that it causes the effi ciency of labor E to grow at some constant rate g. For example, if g = 0.02, then each unit of labor becomes 2 percent more effi cient each year: output increases as if the labor force had increased by 2 percent more than it really did. This form of technological progress is called labor augmenting, and g is called the rate of labor-augmenting technological progress. Because the labor force L is growing at rate n, and the effi ciency of each unit of labor E is growing at rate g, the effective number of workers L × E is growing at rate n + g.

The Steady State With Technological Progress

Because technological progress is modeled here as labor augmenting, it fi ts into the model in much the same way as population growth. Technological progress does not cause the actual number of workers to increase, but because each worker in effect comes with more units of labor over time, technological progress causes the effective number of workers to increase. Thus, the analytic tools we used in Chapter 8 to study the Solow model with population growth are easily adapted to studying the Solow model with labor-augmenting tech- nological progress.

We begin by reconsidering our notation. Previously, when there was no tech- nological progress, we analyzed the economy in terms of quantities per worker; now we can generalize that approach by analyzing the economy in terms of quantities per effective worker. We now let k = K/(L × E ) stand for capital per effective worker and y = Y/(L × E ) stand for output per effective worker. With these defi nitions, we can again write y = f(k).

Our analysis of the economy proceeds just as it did when we examined popula- tion growth. The equation showing the evolution of k over time becomes

�k = sf(k) − (� + n + g)k.

As before, the change in the capital stock �k equals investment sf(k) minus break-even investment (� + n + g)k. Now, however, because k = K/(L × E ), break-even investment includes three terms: to keep k constant, �k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new “effective workers” created by technological progress.1

1Mathematical note: This model with technological progress is a strict generalization of the model analyzed in Chapter 8. In particular, if the effi ciency of labor is constant at E = 1, then g = 0, and the defi nitions of k and y reduce to our previous defi nitions. In this case, the more general model considered here simplifi es precisely to the Chapter 8 version of the Solow model.

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As shown in Figure 9-1, the inclusion of technological progress does not substantially alter our analysis of the steady state. There is one level of k, denoted k∗, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of the economy.

The Effects of Technological Progress

Table 9-1 shows how four key variables behave in the steady state with techno- logical progress. As we have just seen, capital per effective worker k is constant in the steady state. Because y = f(k), output per effective worker is also constant. It is these quantities per effective worker that are steady in the steady state.

From this information, we can also infer what is happening to variables that are not expressed in units per effective worker. For instance, consider output per actual

FIGURE 9-1

Technological Progress and the Solow Growth Model Labor-augmenting technologi- cal progress at rate g enters our analysis of the Solow growth model in much the same way as did population growth at rate n. Now that k is defi ned as the amount of capital per effective worker, increases in the effective number of workers because of technological prog- ress tend to decrease k. In the steady state, investment sf(k) exactly offsets the reductions in k attributable to depreciation, population growth, and tech- nological progress.

Investment, break-even investment

k* Capital per effective worker, k

Break-even investment, (� � n � g)k

Investment, sf(k)

The steady state

Variable Symbol Steady-State Growth Rate

Capital per effective worker k = K/(E × L) 0 Output per effective worker y = Y/(E × L) = f(k) 0 Output per worker Y/L = y × E g Total output Y = y × (E × L) n + g

Steady-State Growth Rates in the Solow Model With Technological Progress

TABLE 9-1

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worker Y/L = y × E. Because y is constant in the steady state and E is growing at rate g, output per worker must also be growing at rate g in the steady state. Similarly, the economy’s total output is Y = y × (E × L). Because y is constant in the steady state, E is growing at rate g, and L is growing at rate n, total output grows at rate n + g in the steady state.

With the addition of technological progress, our model can fi nally explain the sustained increases in standards of living that we observe. That is, we have shown that technological progress can lead to sustained growth in output per worker. By contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. According to the Solow model, only technological progress can explain sustained growth and persis- tently rising living standards.

The introduction of technological progress also modifi es the criterion for the Golden Rule. The Golden Rule level of capital is now defi ned as the steady state that maximizes consumption per effective worker. Following the same arguments that we have used before, we can show that steady-state consumption per effective worker is

c∗ = f(k∗) − (� + n + g)k∗.

Steady-state consumption is maximized if

MPK = � + n + g,

or

MPK − � = n + g.

That is, at the Golden Rule level of capital, the net marginal product of capital, MPK − �, equals the rate of growth of total output, n + g. Because actual econo- mies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than they would at the Golden Rule steady state.

9-2 From Growth Theory to Growth Empirics

So far in this chapter we have introduced exogenous technological progress into the Solow model to explain sustained growth in standards of living. Let’s now discuss what happens when this theory is forced to confront the facts.

Balanced Growth

According to the Solow model, technological progress causes the values of many variables to rise together in the steady state. This property, called balanced growth, does a good job of describing the long-run data for the U.S. economy.

Consider fi rst output per worker Y/L and the capital stock per worker K/L. According to the Solow model, in the steady state both of these variables grow

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240 | P A R T I I I Growth Theory: The Economy in the Very Long Run

at g, the rate of technological progress. U.S. data for the past half century show that output per worker and the capital stock per worker have in fact grown at approximately the same rate—about 2 percent per year. To put it another way, the capital–output ratio has remained approximately constant over time.

Technological progress also affects factor prices. Problem 3(d) at the end of the chapter asks you to show that, in the steady state, the real wage grows at the rate of technological progress. The real rental price of capital, however, is constant over time. Again, these predictions hold true for the United States. Over the past 50 years, the real wage has increased about 2 percent per year; it has increased at about the same rate as real GDP per worker. Yet the real rental price of capital (measured as real capital income divided by the capital stock) has remained about the same.

The Solow model’s prediction about factor prices—and the success of this prediction—is especially noteworthy when contrasted with Karl Marx’s theory of the development of capitalist economies. Marx predicted that the return to capital would decline over time and that this would lead to economic and politi- cal crisis. Economic history has not supported Marx’s prediction, which partly explains why we now study Solow’s theory of growth rather than Marx’s.

Convergence

If you travel around the world, you will see tremendous variation in living stan- dards. The world’s poor countries have average levels of income per person that are less than one-tenth the average levels in the world’s rich countries. These differences in income are refl ected in almost every measure of the quality of life—from the number of televisions and telephones per household to the infant mortality rate and life expectancy.

Much research has been devoted to the question of whether economies con- verge over time to one another. In particular, do economies that start off poor sub- sequently grow faster than economies that start off rich? If they do, then the world’s poor economies will tend to catch up with the world’s rich economies. This process of catch-up is called convergence. If convergence does not occur, then countries that start off behind are likely to remain poor.

The Solow model makes clear predictions about when convergence should occur. According to the model, whether two economies will converge depends on why they differ in the fi rst place. On the one hand, suppose two economies happen by historical accident to start off with different capital stocks, but they have the same steady state, as determined by their saving rates, population growth rates, and effi ciency of labor. In this case, we should expect the two economies to converge; the poorer economy with the smaller capital stock will naturally grow more quickly to reach the steady state. (In a Case Study in Chapter 8, we applied this logic to explain rapid growth in Germany and Japan after World War II.) On the other hand, if two economies have different steady states, perhaps because the economies have different rates of saving, then we should not expect conver- gence. Instead, each economy will approach its own steady state.

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Experience is consistent with this analysis. In samples of economies with simi- lar cultures and policies, studies fi nd that economies converge to one another at a rate of about 2 percent per year. That is, the gap between rich and poor economies closes by about 2 percent each year. An example is the economies of individual American states. For historical reasons, such as the Civil War of the 1860s, income levels varied greatly among states at the end of the nineteenth century. Yet these differences have slowly disappeared over time.

In international data, a more complex picture emerges. When researchers examine only data on income per person, they fi nd little evidence of conver- gence: countries that start off poor do not grow faster on average than countries that start off rich. This fi nding suggests that different countries have different steady states. If statistical techniques are used to control for some of the deter- minants of the steady state, such as saving rates, population growth rates, and accumulation of human capital (education), then once again the data show con- vergence at a rate of about 2 percent per year. In other words, the economies of the world exhibit conditional convergence: they appear to be converging to their own steady states, which in turn are determined by such variables as saving, population growth, and human capital.2

Factor Accumulation Versus Production Efficiency

As a matter of accounting, international differences in income per person can be attributed to either (1) differences in the factors of production, such as the quantities of physical and human capital, or (2) differences in the effi ciency with which economies use their factors of production. That is, a worker in a poor country may be poor because he lacks tools and skills or because the tools and skills he has are not being put to their best use. To describe this issue in terms of the Solow model, the question is whether the large gap between rich and poor is explained by differences in capital accumulation (including human capital) or differences in the production function.

Much research has attempted to estimate the relative importance of these two sources of income disparities. The exact answer varies from study to study, but both factor accumulation and production effi ciency appear important. Moreover, a common fi nding is that they are positively correlated: nations with high levels of physical and human capital also tend to use those factors effi ciently.3

2Robert Barro and Xavier Sala-i-Martin, “Convergence Across States and Regions,” Brookings Papers on Economic Activity 1 (1991): 107–182; N. Gregory Mankiw, David Romer, and David N. Weil, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics (May 1992): 407–437. 3Robert E. Hall and Charles I. Jones, “Why Do Some Countries Produce So Much More Output per Worker Than Others?” Quarterly Journal of Economics 114 (February 1999): 83–116; Peter J. Klenow and Andres Rodriguez-Clare, “The Neoclassical Revival in Growth Economics: Has It Gone Too Far?” NBER Macroeconomics Annual (1997): 73–103.

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There are several ways to interpret this positive correlation. One hypothesis is that an effi cient economy may encourage capital accumulation. For example, a person in a well-functioning economy may have greater resources and incentive to stay in school and accumulate human capital. Another hypothesis is that capital accumulation may induce greater effi ciency. If there are positive externalities to physical and human capital, then countries that save and invest more will appear to have better production functions (unless the research study accounts for these externalities, which is hard to do). Thus, greater production effi ciency may cause greater factor accumulation, or the other way around.

A fi nal hypothesis is that both factor accumulation and production effi ciency are driven by a common third variable. Perhaps the common third variable is the quality of the nation’s institutions, including the government’s policymaking process. As one economist put it, when governments screw up, they screw up big time. Bad policies, such as high infl ation, excessive budget defi cits, widespread market interference, and rampant corruption, often go hand in hand. We should not be surprised that economies exhibiting these maladies both accumulate less capital and fail to use the capital they have as effi ciently as they might.

Is Free Trade Good for Economic Growth?

At least since Adam Smith, economists have advocated free trade as a policy that promotes national prosperity. Here is how Smith put the argument in his 1776 classic, The Wealth of Nations:

It is a maxim of every prudent master of a family, never to attempt to make at home what it will cost him more to make than to buy. The tailor does not attempt to make his own shoes, but buys them of the shoemaker. The shoemaker does not attempt to make his own clothes but employs a tailor. . . .

What is prudence in the conduct of every private family can scarce be folly in that of a great kingdom. If a foreign country can supply us with a commod- ity cheaper than we ourselves can make it, better buy it of them with some part of the produce of our own industry employed in a way in which we have some advantage.

Today, economists make the case with greater rigor, relying on David Ricardo’s theory of comparative advantage as well as more modern theories of interna- tional trade. According to these theories, a nation open to trade can achieve greater production effi ciency and a higher standard of living by specializing in those goods for which it has a comparative advantage.

A skeptic might point out that this is just a theory. What about the evidence? Do nations that permit free trade in fact enjoy greater prosperity? A large body of literature addresses precisely this question.

One approach is to look at international data to see if countries that are open to trade typically enjoy greater prosperity. The evidence shows that they do. Economists Andrew Warner and Jeffrey Sachs studied this question for the period from 1970 to 1989. They report that among developed nations, the

CASE STUDY

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open economies grew at 2.3 percent per year, while the closed economies grew at 0.7 percent per year. Among developing nations, the open economies grew at 4.5 percent per year, while the closed economies again grew at 0.7 percent per year. These fi ndings are consistent with Smith’s view that trade enhances prosper- ity, but they are not conclusive. Correlation does not prove causation. Perhaps being closed to trade is correlated with various other restrictive government policies, and it is those other policies that retard growth.

A second approach is to look at what happens when closed economies remove their trade restrictions. Once again, Smith’s hypothesis fares well. Throughout history, when nations open themselves up to the world economy, the typical result is a subsequent increase in economic growth. This occurred in Japan in the 1850s, South Korea in the 1960s, and Vietnam in the 1990s. But once again, correlation does not prove causation. Trade liberalization is often accompanied by other reforms, and it is hard to disentangle the effects of trade from the effects of the other reforms.

A third approach to measuring the impact of trade on growth, proposed by economists Jeffrey Frankel and David Romer, is to look at the impact of geography. Some countries trade less simply because they are geographi- cally disadvantaged. For example, New Zealand is disadvantaged compared to Belgium because it is farther from other populous countries. Similarly, land- locked countries are disadvantaged compared to countries with their own sea- ports. Because these geographical characteristics are correlated with trade, but arguably uncorrelated with other determinants of economic prosperity, they can be used to identify the causal impact of trade on income. (The statistical tech- nique, which you may have studied in an econometrics course, is called instru- mental variables.) After analyzing the data, Frankel and Romer conclude that “a rise of one percentage point in the ratio of trade to GDP increases income per person by at least one-half percentage point. Trade appears to raise income by spurring the accumulation of human and physical capital and by increasing output for given levels of capital.”

The overwhelming weight of the evidence from this body of research is that Adam Smith was right. Openness to international trade is good for economic growth.4 ■

9-3 Policies to Promote Growth

So far we have used the Solow model to uncover the theoretical relationships among the different sources of economic growth, and we have discussed some of the empirical work that describes actual growth experiences. We can now use the theory and evidence to help guide our thinking about economic policy.

4Jeffrey D. Sachs and Andrew Warner, “Economic Reform and the Process of Global Integration,” Brookings Papers on Economic Activity (1995): 1–95; Jeffrey A. Frankel and David Romer, “Does Trade Cause Growth?” American Economics Review 89 (June 1999): 379–399.

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Evaluating the Rate of Saving

According to the Solow growth model, how much a nation saves and invests is a key determinant of its citizens’ standard of living. So let’s begin our policy discussion with a natural question: is the rate of saving in the U.S. economy too low, too high, or about right?

As we have seen, the saving rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker and thus economic well-being. The Golden Rule provides the benchmark against which we can compare the U.S. economy.

To decide whether the U.S. economy is at, above, or below the Golden Rule steady state, we need to compare the marginal product of capital net of deprecia- tion (MPK − �) with the growth rate of total output (n + g). As we established in Section 9-1, at the Golden Rule steady state, MPK − � = n + g. If the economy is operating with less capital than in the Golden Rule steady state, then diminishing marginal product tells us that MPK − � > n + g. In this case, increasing the rate of saving will increase capital accumulation and economic growth and, eventually, lead to a steady state with higher consumption (although consumption will be lower for part of the transition to the new steady state). On the other hand, if the economy has more capital than in the Golden Rule steady state, then MPK − � < n + g. In this case, capital accumulation is excessive: reducing the rate of saving will lead to higher consumption both immediately and in the long run.

To make this comparison for a real economy, such as the U.S. economy, we need an estimate of the growth rate of output (n + g) and an estimate of the net marginal product of capital (MPK − �). Real GDP in the United States grows an average of 3 percent per year, so n + g = 0.03. We can estimate the net marginal product of capital from the following three facts:

1. The capital stock is about 2.5 times one year’s GDP.

2. Depreciation of capital is about 10 percent of GDP.

3. Capital income is about 30 percent of GDP.

Using the notation of our model (and the result from Chapter 3 that capital owners earn income of MPK for each unit of capital), we can write these facts as

1. k = 2.5y. 2. �k = 0.1y. 3. MPK × k = 0.3y.

We solve for the rate of depreciation � by dividing equation 2 by equation 1:

�k/k = (0.1y)/(2.5y)

� = 0.04.

And we solve for the marginal product of capital MPK by dividing equation 3 by equation 1:

(MPK × k)/k = (0.3y)/(2.5y)

MPK = 0.12.

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Thus, about 4 percent of the capital stock depreciates each year, and the marginal product of capital is about 12 percent per year. The net marginal product of capital, MPK − �, is about 8 percent per year.

We can now see that the return to capital (MPK − � = 8 percent per year) is well in excess of the economy’s average growth rate (n + g = 3 percent per year). This fact, together with our previous analysis, indicates that the capital stock in the U.S. economy is well below the Golden Rule level. In other words, if the United States saved and invested a higher fraction of its income, it would grow more rapidly and eventually reach a steady state with higher consumption.

This conclusion is not unique to the U.S. economy. When calculations similar to those above are done for other economies, the results are similar. The possibil- ity of excessive saving and capital accumulation beyond the Golden Rule level is intriguing as a matter of theory, but it appears not to be a problem that actual economies face. In practice, economists are more often concerned with insuffi - cient saving. It is this kind of calculation that provides the intellectual foundation for this concern.5

Changing the Rate of Saving

The preceding calculations show that to move the U.S. economy toward the Golden Rule steady state, policymakers should increase national saving. But how can they do that? We saw in Chapter 3 that, as a matter of sheer accounting, higher national saving means higher public saving, higher private saving, or some combination of the two. Much of the debate over policies to increase growth centers on which of these options is likely to be most effective.

The most direct way in which the government affects national saving is through public saving—the difference between what the government receives in tax revenue and what it spends. When its spending exceeds its revenue, the government runs a budget defi cit, which represents negative public saving. As we saw in Chapter 3, a budget defi cit raises interest rates and crowds out investment; the resulting reduction in the capital stock is part of the burden of the national debt on future generations. Conversely, if it spends less than it raises in revenue, the government runs a budget surplus, which it can use to retire some of the national debt and stimulate investment.

The government also affects national saving by infl uencing private saving—the saving done by households and fi rms. In particular, how much people decide to save depends on the incentives they face, and these incentives are altered by a variety of public policies. Many economists argue that high tax rates on capital— including the corporate income tax, the federal income tax, the estate tax, and many state income and estate taxes—discourage private saving by reducing the rate of return that savers earn. On the other hand, tax-exempt retirement accounts, such as IRAs, are designed to encourage private saving by giving preferential treatment to income saved in these accounts. Some economists have proposed increasing the incentive to save by replacing the current system of income taxation with a system of consumption taxation.

5For more on this topic and some international evidence, see Andrew B. Abel, N. Gregory Mankiw, Lawrence H. Summers, and Richard J. Zeckhauser, “Assessing Dynamic Effi ciency: Theory and Evidence,” Review of Economic Studies 56 (1989): 1–19.

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Many disagreements over public policy are rooted in different views about how much private saving responds to incentives. For example, suppose that the gov- ernment increased the amount that people could put into tax-exempt retirement accounts. Would people respond to this incentive by saving more? Or, instead, would people merely transfer saving already done in other forms into these accounts— reducing tax revenue and thus public saving without any stimulus to private saving? The desirability of the policy depends on the answers to these questions. Unfortu- nately, despite much research on this issue, no consensus has emerged.

Allocating the Economy’s Investment

The Solow model makes the simplifying assumption that there is only one type of capital. In the world, of course, there are many types. Private businesses invest in traditional types of capital, such as bulldozers and steel plants, and newer types of capital, such as computers and robots. The government invests in various forms of public capital, called infrastructure, such as roads, bridges, and sewer systems.

In addition, there is human capital—the knowledge and skills that workers acquire through education, from early-childhood programs such as Head Start to on-the- job training for adults in the labor force. Although the capital variable in the Solow model is usually interpreted as including only physical capital, in many ways human capital is analogous to physical capital. Like physical capital, human capital increases our ability to produce goods and services. Raising the level of human capital requires investment in the form of teachers, libraries, and student time. Research on economic growth has emphasized that human capital is at least as important as physical capital in explaining international differences in standards of living. One way of modeling this fact is to give the variable we call “capital” a broader defi ni- tion that includes both human and physical capital.6

Policymakers trying to promote economic growth must confront the issue of what kinds of capital the economy needs most. In other words, what kinds of capital yield the highest marginal products? To a large extent, policymakers can rely on the marketplace to allocate the pool of saving to alternative types of investment. Those industries with the highest marginal products of capital will naturally be most willing to borrow at market interest rates to fi nance new investment. Many economists advocate that the government should merely cre- ate a “level playing fi eld” for different types of capital—for example, by ensuring that the tax system treats all forms of capital equally. The government can then rely on the market to allocate capital effi ciently.

Other economists have suggested that the government should actively encour- age particular forms of capital. Suppose, for instance, that technological advance

6Earlier in this chapter, when we were interpreting K as only physical capital, human capital was folded into the effi ciency-of-labor parameter E. The alternative approach suggested here is to include human capital as part of K instead, so E represents technology but not human capital. If K is given this broader interpretation, then much of what we call labor income is really the return to human capital. As a result, the true capital share is much larger than the traditional Cobb–Douglas value of about 1/3. For more on this topic, see N. Gregory Mankiw, David Romer, and David N. Weil, “A Contribution to the Empirics of Economic Growth,’’ Quarterly Journal of Economics (May 1992): 407–437.

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occurs as a by-product of certain economic activities. This would happen if new and improved production processes are devised during the process of building capital (a phenomenon called learning by doing) and if these ideas become part of society’s pool of knowledge. Such a by-product is called a technological externality (or a knowledge spillover). In the presence of such externalities, the social returns to capital exceed the private returns, and the benefi ts of increased capital accumula- tion to society are greater than the Solow model suggests.7 Moreover, some types of capital accumulation may yield greater externalities than others. If, for example, installing robots yields greater technological externalities than building a new steel mill, then perhaps the government should use the tax laws to encourage investment in robots. The success of such an industrial policy, as it is sometimes called, requires that the government be able to accurately measure the externalities of different economic activities so it can give the correct incentive to each activity.

Most economists are skeptical about industrial policies for two reasons. First, measuring the externalities from different sectors is virtually impossible. If policy is based on poor measurements, its effects might be close to random and, thus, worse than no policy at all. Second, the political process is far from perfect. Once the government gets into the business of rewarding specifi c industries with subsidies and tax breaks, the rewards are as likely to be based on political clout as on the magnitude of externalities.

One type of capital that necessarily involves the government is public capital. Local, state, and federal governments are always deciding if and when they should borrow to fi nance new roads, bridges, and transit systems. In 2009, one of Presi- dent Barack Obama’s fi rst economic proposals was to increase spending on such infrastructure. This policy was motivated by a desire partly to increase short-run aggregate demand (a goal we will examine later in this book) and partly to pro- vide public capital and enhance long-run economic growth. Among economists, this policy had both defenders and critics. Yet all of them agree that measuring the marginal product of public capital is diffi cult. Private capital generates an eas- ily measured rate of profi t for the fi rm owning the capital, whereas the benefi ts of public capital are more diffuse. Furthermore, while private capital investment is made by investors spending their own money, the allocation of resources for public capital involves the political process and taxpayer funding. It is all too common to see “bridges to nowhere” being built simply because the local sena- tor or congressman has the political muscle to get funds approved.

7Paul Romer, “Crazy Explanations for the Productivity Slowdown,’’ NBER Macroeconomics Annual 2 (1987): 163–201.

Industrial Policy in Practice

Policymakers and economists have long debated whether the government should promote certain industries and fi rms because they are strategically important for the economy. In the United States, the debate goes back over two centuries.

CASE STUDY

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Alexander Hamilton, the fi rst U.S. Secretary of the Treasury, favored tariffs on certain imports to encourage the development of domestic manufacturing. The Tariff of 1789 was the second act passed by the new federal government. The tariff helped manufacturers, but it hurt farmers, who had to pay more for foreign-made products. Because the North was home to most of the manu- facturers, while the South had more farmers, the tariff was one source of the regional tensions that eventually led to the Civil War.

Advocates of a signifi cant government role in promoting technology can point to some recent successes. For example, the precursor of the modern Internet is a system called Arpanet, which was established by an arm of the U.S. Depart- ment of Defense as a way for information to fl ow among military installations. There is little doubt that the Internet has been associated with large advances in productivity and that the government had a hand in its creation. According to proponents of industrial policy, this example illustrates how the government can help jump-start an emerging technology.

Yet governments can also make mistakes when they try to supplant private business decisions. Japan’s Ministry of International Trade and Industry (MITI) is sometimes viewed as a successful practitioner of industrial policy, but it once tried to stop Honda from expanding its business from motorcycles to auto- mobiles. MITI thought that the nation already had enough car manufacturers. Fortunately, the government lost this battle, and Honda turned into one of the world’s largest and most profi table car companies. Soichiro Honda, the company’s founder, once said, “Probably I would have been even more successful had we not had MITI.”

Over the past several years, government policy has aimed to promote “green technologies.” In particular, the U.S. federal government has subsidized the pro- duction of energy in ways that yield lower carbon emissions, which are thought to contribute to global climate change. It is too early to judge the long-run suc- cess of this policy, but there have been some short-run embarrassments. In 2011, a manufacturer of solar panels called Solyndra declared bankruptcy two years after the federal government granted it a $535 million loan guarantee. Moreover, there were allegations that the decision to grant the loan guarantee had been politically motivated rather than based on an objective evaluation of Solyndra’s business plan. As this book was going to press, the Solyndra case was under inves- tigation by congressional committees and the FBI.

The debate over industrial policy will surely continue in the years to come. The fi nal judgment about this kind of government intervention in the market requires evaluating both the effi ciency of unfettered markets and the ability of governmental institutions to identify technologies worthy of support. ■

Establishing the Right Institutions

As we discussed earlier, economists who study international differences in the standard of living attribute some of these differences to the inputs of physical and human capital and some to the productivity with which these inputs are used. One reason nations may have different levels of production effi ciency is that they

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have different institutions guiding the allocation of scarce resources. Creating the right institutions is important for ensuring that resources are allocated to their best use.

A nation’s legal tradition is an example of such an institution. Some countries, such as the United States, Australia, India, and Singapore, are former colonies of the United Kingdom and, therefore, have English-style common-law systems. Other nations, such as Italy, Spain, and most of those in Latin America, have legal tradi- tions that evolved from the French Napoleonic Code. Studies have found that legal protections for shareholders and creditors are stronger in English-style than French- style legal systems. As a result, the English-style countries have better-developed capital markets. Nations with better-developed capital markets, in turn, experience more rapid growth because it is easier for small and start-up companies to fi nance investment projects, leading to a more effi cient allocation of the nation’s capital.8

Another important institutional difference across countries is the quality of gov- ernment itself. Ideally, governments should provide a “helping hand” to the market system by protecting property rights, enforcing contracts, promoting competition, prosecuting fraud, and so on. Yet governments sometimes diverge from this ideal and act more like a “grabbing hand” by using the authority of the state to enrich a few powerful individuals at the expense of the broader community. Empirical studies have shown that the extent of corruption in a nation is indeed a signifi cant determinant of economic growth.9

Adam Smith, the great eighteenth-century economist, was well aware of the role of institutions in economic growth. He once wrote, “Little else is requisite to carry a state to the highest degree of opulence from the lowest barbarism but peace, easy taxes, and a tolerable administration of justice: all the rest being brought about by the natural course of things.” Sadly, many nations do not enjoy these three simple advantages.

The Colonial Origins of Modern Institutions

International data show a remarkable correlation between latitude and economic prosperity: nations closer to the equator typically have lower levels of income per person than nations farther from the equator. This fact is true in both the northern and southern hemispheres.

What explains the correlation? Some economists have suggested that the tropical climates near the equator have a direct negative impact on productivity. In the heat of the tropics, agriculture is more diffi cult, and disease is more preva- lent. This makes the production of goods and services more diffi cult.

CASE STUDY

8Rafael La Porta, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert Vishny, “Law and Finance,” Journal of Political Economy 106 (1998): 1113–1155; Ross Levine and Robert G. King, “Finance and Growth: Schumpeter Might Be Right,” Quarterly Journal of Economics 108 (1993): 717–737. 9Paulo Mauro, “Corruption and Growth,” Quarterly Journal of Economics 110 (1995): 681–712.

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Although the direct impact of geography is one reason tropical nations tend to be poor, it is not the whole story. Research by Daron Acemoglu, Simon John- son, and James Robinson has suggested an indirect mechanism—the impact of geography on institutions. Here is their explanation, presented in several steps:

1. In the seventeenth, eighteenth, and nineteenth centuries, tropical climates presented European settlers with an increased risk of disease, especially malaria and yellow fever. As a result, when Europeans were colonizing much of the rest of the world, they avoided settling in tropical areas, such as most of Africa and Central America. The European settlers preferred areas with more moderate climates and better health conditions, such as the regions that are now the United States, Canada, and New Zealand.

2. In those areas where Europeans settled in large numbers, the settlers estab- lished European-like institutions that protected individual property rights and limited the power of government. By contrast, in tropical climates, the colonial powers often set up “extractive” institutions, including authoritarian governments, so they could take advantage of the area’s natural resources. These institutions enriched the colonizers, but they did little to foster eco- nomic growth.

3. Although the era of colonial rule is now long over, the early institutions that the European colonizers established are strongly correlated with the modern institutions in the former colonies. In tropical nations, where the colonial powers set up extractive institutions, there is typically less protection of prop- erty rights even today. When the colonizers left, the extractive institutions remained and were simply taken over by new ruling elites.

4. The quality of institutions is a key determinant of economic performance. Where property rights are well protected, people have more incentive to make the investments that lead to economic growth. Where property rights are less respected, as is typically the case in tropical nations, investment and growth tend to lag behind.

This research suggests that much of the international variation in living standards that we observe today is a result of the long reach of history.10 ■

Encouraging Technological Progress

The Solow model shows that sustained growth in income per worker must come from technological progress. The Solow model, however, takes technological progress as exogenous; it does not explain it. Unfortunately, the determinants of technological progress are not well understood.

Despite this limited understanding, many public policies are designed to stimu- late technological progress. Most of these policies encourage the private sector to devote resources to technological innovation. For example, the patent system gives

10Daron Acemoglu, Simon Johnson, and James A. Robinson, “The Colonial Origins of Comparative Development: An Empirical Investigation,” American Economic Review 91 (December 2001): 1369–1401.

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a temporary monopoly to inventors of new products; the tax code offers tax breaks for fi rms engaging in research and development; and government agencies, such as the National Science Foundation, directly subsidize basic research in universities. In addition, as discussed above, proponents of industrial policy argue that the govern- ment should take a more active role in promoting specifi c industries that are key for rapid technological advance.

In recent years, the encouragement of technological progress has taken on an international dimension. Many of the companies that engage in research to advance technology are located in the United States and other developed nations. Developing nations such as China have an incentive to “free ride” on this research by not strictly enforcing intellectual property rights. That is, Chi- nese companies often use the ideas developed abroad without compensating the patent holders. The United States has strenuously objected to this practice, and China has promised to step up enforcement. If intellectual property rights were better enforced around the world, fi rms would have more incentive to engage in research, and this would promote worldwide technological progress.

The Worldwide Slowdown in Economic Growth

Beginning in the early 1970s, world policymakers faced a perplexing prob- lem: a global slowdown in economic growth. Table 9-2 presents data on the growth in real GDP per person for the seven major economies. Growth in the United States fell from 2.2 percent before 1972 to 1.5 percent after 1972. Other countries experienced similar or more severe declines. Accumulated over many years, even a small change in the rate of growth has a large effect on economic

CASE STUDY

GROWTH IN OUTPUT PER PERSON (PERCENT PER YEAR)

Country 1948–1972 1972–1995 1995–2010

Canada 2.9 1.8 1.6 France 4.3 1.6 1.1 West Germany 5.7 2.0 Germany 1.3 Italy 4.9 2.3 0.6 Japan 8.2 2.6 0.6 United Kingdom 2.4 1.8 1.7 United States 2.2 1.5 1.5

Source: Angus Maddison, Phases of Capitalist Development (Oxford: Oxford University Press, 1982); OECD National Accounts; and World Bank: World Development Indicators.

Growth Around the World

TABLE 9-2

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well-being. Real income in the United States today is almost 25 percent lower than it would have been had growth remained at its previous level.

Why did this slowdown occur? Studies have shown that it was attributable to a fall in the rate at which the production function was improving over time. The appendix to this chapter explains how economists measure changes in the produc- tion function with a variable called total factor productivity, which is closely related to the effi ciency of labor in the Solow model. There are many hypotheses to explain this fall in productivity growth. Here are four of them.

Measurement Problems One possibility is that the productivity slowdown did not really occur and that it shows up in the data because the data are fl awed. As you may recall from Chapter 2, one problem in measuring infl ation is correct- ing for changes in the quality of goods and services. The same issue arises when measuring output and productivity. For instance, if technological advance leads to more computers being built, then the increase in output and productivity is easy to measure. But if technological advance leads to faster computers being built, then output and productivity have increased, but that increase is more subtle and harder to measure. Government statisticians try to correct for changes in quality, but despite their best efforts, the resulting data are far from perfect.

Unmeasured quality improvements mean that our standard of living is rising more rapidly than the offi cial data indicate. This issue should make us suspicious of the data, but by itself it cannot explain the productivity slowdown. To explain a slowdown in growth, one must argue that the measurement problems got worse. There is some indication that this might be so. As history passes, fewer people work in industries with tangible and easily measured output, such as agriculture, and more work in industries with intangible and less easily measured output, such as medical services. Yet few economists believe that measurement problems were the full story.

Oil Prices When the productivity slowdown began around 1973, the obvious hypothesis to explain it was the large increase in oil prices caused by the actions of the OPEC oil cartel. The primary piece of evidence was the timing: productivity growth slowed at the same time that oil prices skyrocketed. Over time, however, this explanation has appeared less likely. One reason is that the accumulated short- fall in productivity seems too large to be explained by an increase in oil prices; petroleum-based products are not that large a fraction of a typical fi rm’s costs. In addition, if this explanation were right, productivity should have sped up when political turmoil in OPEC caused oil prices to plummet in 1986. Unfortunately, that did not happen.

Worker Quality Some economists suggest that the productivity slowdown might have been caused by changes in the labor force. In the early 1970s, the large baby-boom generation started leaving school and taking jobs. At the same time, changing social norms encouraged many women to leave full-time housework and enter the labor force. Both of these developments lowered the average level of experience among workers, which in turn lowered average productivity.

Other economists point to changes in worker quality as gauged by human capital. Although the educational attainment of the labor force continued to rise throughout this period, it was not increasing as rapidly as it had in the past.

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Moreover, declining performance on some standardized tests suggests that the qual- ity of education was declining. If so, this could explain slowing productivity growth.

The Depletion of Ideas Still other economists suggest that in the early 1970s the world started running out of new ideas about how to produce, pushing the economy into an age of slower technological progress. These economists often argue that the anomaly is not the period since 1970 but the preceding two decades. In the late 1940s, the economy had a large backlog of ideas that had not been fully implemented because of the Great Depression of the 1930s and World War II in the fi rst half of the 1940s. After the economy used up this backlog, the argument goes, a slowdown in productivity growth was likely. Indeed, although the growth rates after 1972 were disappointing compared to those of the 1950s and 1960s, they were not lower than average growth rates from 1870 to 1950.

As any good doctor will tell you, sometimes a patient’s illness goes away on its own, even if the doctor has failed to come up with a convincing diagnosis and remedy. This seems to be the outcome of the productivity slowdown. In the middle of the 1990s, economic growth took off, at least in the English-speaking countries of the United States, Canada, and the United Kingdom, in large part because of advances in computer and information technology, including the Inter- net. Yet this period of rapid growth was then offset by the fi nancial crisis and deep recession in 2008–2009 (a topic we will discuss in Chapters 12 and 20). Overall, the period from 1995 to 2010 shows a continuation of the relatively slow growth experienced from 1972 to 1995.11 ■

9-4 Beyond the Solow Model: Endogenous Growth Theory

A chemist, a physicist, and an economist are all trapped on a desert island, trying to fi gure out how to open a can of food.

“Let’s heat the can over the fi re until it explodes,” says the chemist. “No, no,” says the physicist, “let’s drop the can onto the rocks from the top

of a high tree.” “I have an idea,” says the economist. “First, we assume a can opener . . .”

This old joke takes aim at how economists use assumptions to simplify—and sometimes oversimplify—the problems they face. It is particularly apt when evaluating the theory of economic growth. One goal of growth theory is to explain the persistent rise in living standards that we observe in most parts of the world. The Solow growth model shows that such persistent growth must come from technological progress. But where does technological progress come from? In the Solow model, it is just assumed!

11For various views on the growth slowdown, see “Symposium: The Slowdown in Productivity Growth’’ in the Fall 1988 issue of The Journal of Economic Perspectives. For a discussion of the subsequent growth acceleration and the role of information technology, see “Symposium: Computers and Productivity” in the Fall 2000 issue of The Journal of Economic Perspectives.

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The preceding Case Study on the productivity slowdown of the 1970s and speed-up of the 1990s suggests that changes in the pace of technological prog- ress are tremendously important. To fully understand the process of economic growth, we need to go beyond the Solow model and develop models that explain technological advance. Models that do this often go by the label endogenous growth theory because they reject the Solow model’s assumption of exogenous technological change. Although the fi eld of endogenous growth theory is large and sometimes complex, here we get a quick taste of this modern research.12

The Basic Model

To illustrate the idea behind endogenous growth theory, let’s start with a particu- larly simple production function:

Y = AK,

where Y is output, K is the capital stock, and A is a constant measuring the amount of output produced for each unit of capital. Notice that this production function does not exhibit the property of diminishing returns to capital. One extra unit of capital produces A extra units of output, regardless of how much capital there is. This absence of diminishing returns to capital is the key difference between this endogenous growth model and the Solow model.

Now let’s see what this production function says about economic growth. As before, we assume a fraction s of income is saved and invested. We therefore describe capital accumulation with an equation similar to those we used previously:

�K = sY − �K.

This equation states that the change in the capital stock (�K) equals investment (sY) minus depreciation (�K). Combining this equation with the Y = AK produc- tion function, we obtain, after a bit of manipulation,

�Y/Y = �K/K = sA − �.

This equation shows what determines the growth rate of output �Y/Y. Notice that, as long as sA > �, the economy’s income grows forever, even without the assumption of exogenous technological progress.

Thus, a simple change in the production function can dramatically alter the predictions about economic growth. In the Solow model, saving temporarily leads to growth, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, in this endogenous growth model, saving and investment can lead to persistent growth.

12This section provides a brief introduction to the large and fascinating literature on endogenous growth theory. Early and important contributions to this literature include Paul M. Romer, “Increasing Returns and Long-Run Growth,” Journal of Political Economy 94 (October 1986): 1002– 1037; and Robert E. Lucas, Jr., “On the Mechanics of Economic Development,’’ Journal of Monetary Economics 22 (1988): 3–42. The reader can learn more about this topic in the undergraduate textbook by David N. Weil, Economic Growth, 2nd ed. (Pearson, 2008).

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But is it reasonable to abandon the assumption of diminishing returns to capital? The answer depends on how we interpret the variable K in the production func- tion Y = AK. If we take the traditional view that K includes only the economy’s stock of plants and equipment, then it is natural to assume diminishing returns. Giv- ing 10 computers to a worker does not make that worker 10 times as productive as he or she is with one computer.

Advocates of endogenous growth theory, however, argue that the assumption of constant (rather than diminishing) returns to capital is more palatable if K is interpreted more broadly. Perhaps the best case can be made for the endogenous growth model by viewing knowledge as a type of capital. Clearly, knowledge is a key input into the economy’s production—both its production of goods and services and its production of new knowledge. Compared to other forms of capital, however, it is less natural to assume that knowledge exhibits the property of diminishing returns. (Indeed, the increasing pace of scientifi c and technologi- cal innovation over the past few centuries has led some economists to argue that there are increasing returns to knowledge.) If we accept the view that knowledge is a type of capital, then this endogenous growth model with its assumption of constant returns to capital becomes a more plausible description of long-run economic growth.

A Two-Sector Model

Although the Y = AK model is the simplest example of endogenous growth, the theory has gone well beyond this. One line of research has tried to develop mod- els with more than one sector of production in order to offer a better description of the forces that govern technological progress. To see what we might learn from such models, let’s sketch out an example.

The economy has two sectors, which we can call manufacturing fi rms and research universities. Firms produce goods and services, which are used for con- sumption and investment in physical capital. Universities produce a factor of production called “knowledge,” which is then freely used in both sectors. The economy is described by the production function for fi rms, the production func- tion for universities, and the capital-accumulation equation:

Y = F[K, (1 − u)LE] (production function in manufacturing fi rms),

�E = g(u)E (production function in research universities),

�K = sY − �K (capital accumulation),

where u is the fraction of the labor force in universities (and 1 − u is the fraction in manufacturing), E is the stock of knowledge (which in turn determines the effi ciency of labor), and g is a function that shows how the growth in knowledge depends on the fraction of the labor force in universities. The rest of the notation is standard. As usual, the production function for the manufacturing fi rms is assumed to have constant returns to scale: if we double both the amount of physical capital (K ) and the effective number of workers in manufacturing [(1 − u)LE], we double the output of goods and services (Y ).

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This model is a cousin of the Y = AK model. Most important, this economy exhibits constant (rather than diminishing) returns to capital, as long as capital is broadly defi ned to include knowledge. In particular, if we double both physical capital K and knowledge E, then we double the output of both sectors in the economy. As a result, like the Y = AK model, this model can generate persistent growth without the assumption of exogenous shifts in the production function. Here persistent growth arises endogenously because the creation of knowledge in universities never slows down.

At the same time, however, this model is also a cousin of the Solow growth model. If u, the fraction of the labor force in universities, is held constant, then the effi ciency of labor E grows at the constant rate g(u). This result of constant growth in the effi ciency of labor at rate g is precisely the assumption made in the Solow model with technological progress. Moreover, the rest of the model—the manufac- turing production function and the capital-accumulation equation—also resembles the rest of the Solow model. As a result, for any given value of u, this endogenous growth model works just like the Solow model.

There are two key decision variables in this model. As in the Solow model, the fraction of output used for saving and investment, s, determines the steady- state stock of physical capital. In addition, the fraction of labor in universities, u, determines the growth in the stock of knowledge. Both s and u affect the level of income, although only u affects the steady-state growth rate of income. Thus, this model of endogenous growth takes a small step in the direction of showing which societal decisions determine the rate of technological change.

The Microeconomics of Research and Development

The two-sector endogenous growth model just presented takes us closer to understanding technological progress, but it still tells only a rudimentary story about the creation of knowledge. If one thinks about the process of research and development for even a moment, three facts become apparent. First, although knowledge is largely a public good (that is, a good freely available to everyone), much research is done in fi rms that are driven by the profi t motive. Second, research is profi table because innovations give fi rms temporary monopolies, either because of the patent system or because there is an advantage to being the fi rst fi rm on the market with a new product. Third, when one fi rm innovates, other fi rms build on that innovation to produce the next generation of innova- tions. These (essentially microeconomic) facts are not easily connected with the (essentially macroeconomic) growth models we have discussed so far.

Some endogenous growth models try to incorporate these facts about research and development. Doing this requires modeling both the decisions that fi rms face as they engage in research and the interactions among fi rms that have some degree of monopoly power over their innovations. Going into more detail about these models is beyond the scope of this book, but it should be clear already that one virtue of these endogenous growth models is that they offer a more complete description of the process of technological innovation.

One question these models are designed to address is whether, from the stand- point of society as a whole, private profi t-maximizing fi rms tend to engage in too

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little or too much research. In other words, is the social return to research (which is what society cares about) greater or smaller than the private return (which is what motivates individual fi rms)? It turns out that, as a theoretical matter, there are effects in both directions. On the one hand, when a fi rm creates a new technology, it makes other fi rms better off by giving them a base of knowledge on which to build in future research. As Isaac Newton famously remarked, “If I have seen further, it is by standing on the shoulders of giants.” On the other hand, when one fi rm invests in research, it can also make other fi rms worse off if it does little more than become the fi rst to discover a technology that another fi rm would have invented in due course. This duplication of research effort has been called the “stepping on toes” effect. Whether fi rms left to their own devices do too little or too much research depends on whether the positive “standing on shoulders” externality or the nega- tive “stepping on toes” externality is more prevalent.

Although theory alone is ambiguous about whether research effort is more or less than optimal, the empirical work in this area is usually less so. Many studies have suggested the “standing on shoulders” externality is important and, as a result, the social return to research is large—often in excess of 40 percent per year. This is an impressive rate of return, especially when compared to the return to physical capital, which we earlier estimated to be about 8 percent per year. In the judgment of some economists, this fi nding justifi es substantial government subsidies to research.13

The Process of Creative Destruction

In his 1942 book Capitalism, Socialism, and Democracy, economist Joseph Schumpeter suggested that economic progress comes through a process of creative destruc- tion. According to Schumpeter, the driving force behind progress is the entre- preneur with an idea for a new product, a new way to produce an old product, or some other innovation. When the entrepreneur’s fi rm enters the market, it has some degree of monopoly power over its innovation; indeed, it is the prospect of monopoly profi ts that motivates the entrepreneur. The entry of the new fi rm is good for consumers, who now have an expanded range of choices, but it is often bad for incumbent producers, who may fi nd it hard to compete with the entrant. If the new product is suffi ciently better than old ones, the incumbents may even be driven out of business. Over time, the process keeps renewing itself. The entrepreneur’s fi rm becomes an incumbent, enjoying high profi tability until its product is displaced by another entrepreneur with the next generation of innovation.

History confi rms Schumpeter’s thesis that there are winners and losers from technological progress. For example, in England in the early nineteenth century, an important innovation was the invention and spread of machines that could pro- duce textiles using unskilled workers at low cost. This technological advance was good for consumers, who could clothe themselves more cheaply. Yet skilled knitters in England saw their jobs threatened by new technology, and they responded by

13For an overview of the empirical literature on the effects of research, see Zvi Griliches, “The Search for R&D Spillovers,” Scandinavian Journal of Economics 94 (1991): 29–47.

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258 | P A R T I I I Growth Theory: The Economy in the Very Long Run

organizing violent revolts. The rioting workers, called Luddites, smashed the weav- ing machines used in the wool and cotton mills and set the homes of the mill owners on fi re (a less than creative form of destruction). Today, the term “Luddite” refers to anyone who opposes technological progress.

A more recent example of creative destruction involves the retailing giant Walmart. Although retailing may seem like a relatively static activity, in fact it is a sector that has seen sizable rates of technological progress over the past several decades. Through better inventory-control, marketing, and personnel-management techniques, for example, Walmart has found ways to bring goods to consumers at lower cost than traditional retailers. These changes benefi t consumers, who can buy goods at lower prices, and the stockholders of Walmart, who share in its profi tability. But they adversely affect small mom-and-pop stores, which fi nd it hard to compete when a Walmart opens nearby.

Faced with the prospect of being the victims of creative destruction, incumbent producers often look to the political process to stop the entry of new, more effi cient competitors. The original Luddites wanted the British government to save their jobs by restricting the spread of the new textile technology; instead, Parliament sent troops to suppress the Luddite riots. Similarly, in recent years, local retailers have sometimes tried to use local land-use regulations to stop Walmart from entering their market. The cost of such entry restrictions, however, is a slower pace of tech- nological progress. In Europe, where entry regulations are stricter than they are in the United States, the economies have not seen the emergence of retailing giants like Walmart; as a result, productivity growth in retailing has been much lower.14

Schumpeter’s vision of how capitalist economies work has merit as a matter of economic history. Moreover, it has inspired some recent work in the theory of economic growth. One line of endogenous growth theory, pioneered by economists Philippe Aghion and Peter Howitt, builds on Schumpeter’s insights by modeling technological advance as a process of entrepreneurial innovation and creative destruction.15

9-5 Conclusion

Long-run economic growth is the single most important determinant of the economic well-being of a nation’s citizens. Everything else that macroeconomists study—unemployment, infl ation, trade defi cits, and so on—pales in comparison.

Fortunately, economists know quite a lot about the forces that govern economic growth. The Solow growth model and the more recent endogenous growth mod- els show how saving, population growth, and technological progress interact in determining the level and growth of a nation’s standard of living. These theories

14Robert J. Gordon, “Why Was Europe Left at the Station When America’s Productivity Locomotive Departed?” NBER Working Paper No. 10661, 2004. 15Philippe Aghion and Peter Howitt, “A Model of Growth Through Creative Destruction,” Econometrica 60 (1992): 323–351.

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offer no magic recipe to ensure that an economy achieves rapid growth, but they give much insight, and they provide the intellectual framework for much of the debate over public policy aimed at promoting long-run economic growth.

Summary

1. In the steady state of the Solow growth model, the growth rate of income per person is determined solely by the exogenous rate of technological progress.

2. Many empirical studies have examined the extent to which the Solow model can help explain long-run economic growth. The model can explain much of what we see in the data, such as balanced growth and conditional convergence. Recent studies have also found that international variation in standards of living is attributable to a combination of capital accumulation and the effi ciency with which capital is used.

3. In the Solow model with population growth and technological progress, the Golden Rule (consumption-maximizing) steady state is characterized by equality between the net marginal product of capital (MPK − �) and the steady-state growth rate of total income (n + g). In the U.S. economy, the net marginal product of capital is well in excess of the growth rate, indicat- ing that the U.S. economy has a lower saving rate and less capital than it would have in the Golden Rule steady state.

4. Policymakers in the United States and other countries often claim that their nations should devote a larger percentage of their output to saving and investment. Increased public saving and tax incentives for private sav- ing are two ways to encourage capital accumulation. Policymakers can also promote economic growth by setting up the appropriate legal and fi nancial institutions to allocate resources effi ciently and by ensuring proper incen- tives to encourage research and technological progress.

5. In the early 1970s, the rate of growth of income per person fell substantially in most industrialized countries, including the United States. The cause of this slowdown is not well understood. In the mid-1990s, the U.S. growth rate increased, most likely because of advances in information technology.

6. Modern theories of endogenous growth attempt to explain the rate of technological progress, which the Solow model takes as exogenous. These models try to explain the decisions that determine the creation of knowl- edge through research and development.

K E Y C O N C E P T S

Effi ciency of labor

Labor-augmenting technological progress

Endogenous growth theory Creative destruction

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1. Suppose an economy described by the Solow model has the following production function:

Y = K1/2(LE)1/2.

a. For this economy, what is f(k)?

b. Use your answer to part (a) to solve for the steady-state value of y as a function of s, n, g, and �.

c. Two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28 percent and a population growth rate of 1 percent per year. Xanadu has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g = 0.02 and � = 0.04. Find the steady-state value of y for each country.

2. In the United States, the capital share of GDP is about 30 percent, the average growth in out- put is about 3 percent per year, the depreciation rate is about 4 percent per year, and the capital– output ratio is about 2.5. Suppose that the pro- duction function is Cobb–Douglas, so that the capital share in output is constant, and that the United States has been in a steady state. (For a discussion of the Cobb–Douglas production function, see Chapter 3.)

a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state rela- tionship, sy = (� + n + g)k.]

b. What is the marginal product of capital in the initial steady state?

P R O B L E M S A N D A P P L I C A T I O N S

1. In the Solow model, what determines the steady-state rate of growth of income per worker?

2. In the steady state of the Solow model, at what rate does output per person grow? At what rate does capital per person grow? How does this compare with the U.S. experience?

3. What data would you need to determine whether an economy has more or less capital than in the Golden Rule steady state?

Q U E S T I O N S F O R R E V I E W

4. How can policymakers infl uence a nation’s saving rate?

5. What has happened to the rate of productivity growth over the past 50 years? How might you explain this phenomenon?

6. How does endogenous growth theory explain persistent growth without the assumption of exogenous technological progress? How does this differ from the Solow model?

c. Suppose that public policy raises the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal prod- uct at the Golden Rule steady state to the marginal product in the initial steady state. Explain.

d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of capital.)

e. What must the saving rate be to reach the Golden Rule steady state?

3. Prove each of the following statements about the steady state of the Solow model with population growth and technological progress.

a. The capital–output ratio is constant.

b. Capital and labor each earn a constant share of an economy’s income. [Hint: Recall the defi nition MPK = f(k + 1) − f(k).]

c. Total capital income and total labor income both grow at the rate of population growth plus the rate of technological progress, n + g.

d. The real rental price of capital is constant, and the real wage grows at the rate of tech- nological progress g. (Hint: The real rental price of capital equals total capital income divided by the capital stock, and the real wage equals total labor income divided by the labor force.)

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4. Two countries, Richland and Poorland, are described by the Solow growth model. They have the same Cobb–Douglas production function, F(K, L) = A K�L1−�, but with different quantities of capital and labor. Richland saves 32 percent of its income, while Poorland saves 10 percent. Richland has population growth of 1 percent per year, while Poorland has population growth of 3 percent. (The numbers in this problem are cho- sen to be approximately realistic descriptions of rich and poor nations.) Both nations have tech- nological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year.

a. What is the per-worker production function f(k)?

b. Solve for the ratio of Richland’s steady-state income per worker to Poorland’s. (Hint: The parameter � will play a role in your answer.)

c. If the Cobb–Douglas parameter � takes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland?

d. Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing the value of the parameter �? What must it be? Can you think of any way of justifying such a value for this parameter? How else might you explain the large difference in income between Richland and Poorland?

5. The amount of education the typical person receives varies substantially among countries. Suppose you were to compare a country with a highly educated labor force and a country with a less educated labor force. Assume that educa- tion affects only the level of the effi ciency of labor. Also assume that the countries are other- wise the same: they have the same saving rate, the same depreciation rate, the same population growth rate, and the same rate of technological progress. Both countries are described by the Solow model and are in their steady states. What would you predict for the following variables?

a. The rate of growth of total income

b. The level of income per worker

c. The real rental price of capital

d. The real wage

6. This question asks you to analyze in more detail the two-sector endogenous growth model pre- sented in the text.

a. Rewrite the production function for manu- factured goods in terms of output per effec- tive worker and capital per effective worker.

b. In this economy, what is break-even invest- ment (the amount of investment needed to keep capital per effective worker constant)?

c. Write down the equation of motion for k, which shows �k as saving minus break-even investment. Use this equation to draw a graph showing the determination of steady-state k. (Hint: This graph will look much like those we used to analyze the Solow model.)

d. In this economy, what is the steady-state growth rate of output per worker Y/L? How do the saving rate s and the fraction of the labor force in universities u affect this steady- state growth rate?

e. Using your graph, show the impact of an increase in u. (Hint: This change affects both curves.) Describe both the immediate and the steady-state effects.

f. Based on your analysis, is an increase in u an unambiguously good thing for the economy? Explain.

7. Choose two countries that interest you—one rich and one poor. What is the income per per- son in each country? Find some data on country characteristics that might help explain the dif- ference in income: investment rates, population growth rates, educational attainment, and so on. (Hint: The Web site of the World Bank, www. worldbank.org, is one place to fi nd such data.) How might you fi gure out which of these fac- tors is most responsible for the observed income difference? In your judgment, how useful is the Solow model as an analytic tool for understand- ing the difference between the two countries you chose?

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Real GDP in the United States has grown an average of about 3 percent per year over the past 50 years. What explains this growth? In Chapter 3 we linked the output of the economy to the factors of production—capital and labor—and to the production technology. Here we develop a technique called growth accounting that divides the growth in output into three different sources: increases in capital, increases in labor, and advances in technology. This breakdown provides us with a measure of the rate of technological change.

Increases in the Factors of Production

We fi rst examine how increases in the factors of production contribute to increases in output. To do this, we start by assuming there is no technological change, so the production function relating output Y to capital K and labor L is constant over time:

Y = F(K, L). In this case, the amount of output changes only because the amount of capital or labor changes.

Increases in Capital First, consider changes in capital. If the amount of capi- tal increases by �K units, by how much does the amount of output increase? To answer this question, we need to recall the defi nition of the marginal product of capital MPK:

MPK = F(K + 1, L) − F(K, L). The marginal product of capital tells us how much output increases when capital increases by 1 unit. Therefore, when capital increases by �K units, output increases by approximately MPK × �K.16

For example, suppose that the marginal product of capital is 1/5; that is, an addi- tional unit of capital increases the amount of output produced by one-fi fth of a unit. If we increase the amount of capital by 10 units, we can compute the amount of additional output as follows:

�Y = MPK × �K

= 1/5 units of output

unit of capital × 10 units of capital

= 2 units of output.

Accounting for the Sources of Economic Growth

A P P E N D I X

16Note the word “approximately’’ here. This answer is only an approximation because the marginal product of capital varies: it falls as the amount of capital increases. An exact answer would take into account the fact that each unit of capital has a different marginal product. If the change in K is not too large, however, the approximation of a constant marginal product is very accurate.

262 |

C H A P T E R

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C H A P T E R 9 Economic Growth II: Technology, Empirics, and Policy | 263

By increasing capital by 10 units, we obtain 2 more units of output. Thus, we use the marginal product of capital to convert changes in capital into changes in output.

Increases in Labor Next, consider changes in labor. If the amount of labor increases by �L units, by how much does output increase? We answer this ques- tion the same way we answered the question about capital. The marginal prod- uct of labor MPL tells us how much output changes when labor increases by 1 unit—that is,

MPL = F(K, L + 1) − F(K, L).

Therefore, when the amount of labor increases by �L units, output increases by approximately MPL × �L.

For example, suppose that the marginal product of labor is 2; that is, an additional unit of labor increases the amount of output produced by 2 units. If we increase the amount of labor by 10 units, we can compute the amount of additional output as follows:

�Y = MPL × �L

= 2 units of output

unit of labor × 10 units of labor

= 20 units of output.

By increasing labor by 10 units, we obtain 20 more units of output. Thus, we use the marginal product of labor to convert changes in labor into changes in output.

Increases in Capital and Labor Finally, let’s consider the more realistic case in which both factors of production change. Suppose that the amount of capital increases by �K and the amount of labor increases by �L. The increase in output then comes from two sources: more capital and more labor. We can divide this increase into the two sources using the marginal products of the two inputs:

�Y = (MPK × �K) + (MPL × �L).

The fi rst term in parentheses is the increase in output resulting from the increase in capital; the second term in parentheses is the increase in output resulting from the increase in labor. This equation shows us how to attribute growth to each factor of production.

We now want to convert this last equation into a form that is easier to interpret and apply to the available data. First, with some algebraic rearrangement, the equa- tion becomes17

DY Y

= aMPK 3 K Y

bDK K

+ aMPL 3 L Y

bDL L

.

17Mathematical note: To see that this is equivalent to the previous equation, note that we can multiply both sides of this equation by Y and thereby cancel Y from three places in which it appears. We can cancel the K in the top and bottom of the fi rst term on the right-hand side and the L in the top and bottom of the second term on the right-hand side. These algebraic manipulations turn this equation into the previous one.

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264 | P A R T I I I Growth Theory: The Economy in the Very Long Run

This form of the equation relates the growth rate of output, �Y/Y, to the growth rate of capital, �K/K, and the growth rate of labor, �L/L.

Next, we need to fi nd some way to measure the terms in parentheses in the last equation. In Chapter 3 we showed that the marginal product of capital equals its real rental price. Therefore, MPK × K is the total return to capital, and (MPK × K)/Y is capital’s share of output. Similarly, the marginal product of labor equals the real wage. Therefore, MPL × L is the total compensation that labor receives, and (MPL × L)/Y is labor’s share of output. Under the assumption that the production function has constant returns to scale, Euler’s theorem (which we discussed in Chapter 3) tells us that these two shares sum to 1. In this case, we can write

DY Y

= a DK K

+ 11 2 a 2DL L

,

where � is capital’s share and (1 − �) is labor’s share. This last equation gives us a simple formula for showing how changes in

inputs lead to changes in output. It shows, in particular, that we must weight the growth rates of the inputs by the factor shares. As we discussed in Chapter 3, capital’s share in the United States is about 30 percent, that is, � = 0.30. Therefore, a 10 percent increase in the amount of capital (�K/K = 0.10) leads to a 3 percent increase in the amount of output (�Y/Y = 0.03). Similarly, a 10 percent increase in the amount of labor (�L/L = 0.10) leads to a 7 percent increase in the amount of output (�Y/Y = 0.07).

Technological Progress

So far in our analysis of the sources of growth, we have been assuming that the production function does not change over time. In practice, of course, techno- logical progress improves the production function. For any given amount of inputs, we can produce more output today than we could in the past. We now extend the analysis to allow for technological progress.

We include the effects of the changing technology by writing the production function as

Y = AF(K, L),

where A is a measure of the current level of technology called total factor productiv- ity. Output now increases not only because of increases in capital and labor but also because of increases in total factor productivity. If total factor productivity increases by 1 percent and if the inputs are unchanged, then output increases by 1 percent.

Allowing for a changing level of technology adds another term to our equation accounting for economic growth:

DY Y

= a DK K

+ 11 2 a 2DL L

+ DA A

Growth in = Contribution + Contribution + Growth in Total Output of Capital of Labor Factor Productivity .

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This is the key equation of growth accounting. It identifi es and allows us to mea- sure the three sources of growth: changes in the amount of capital, changes in the amount of labor, and changes in total factor productivity.

Because total factor productivity is not directly observable, it is measured indi- rectly. We have data on the growth in output, capital, and labor; we also have data on capital’s share of output. From these data and the growth-accounting equation, we can compute the growth in total factor productivity to make sure that every- thing adds up:

DA A

= DY Y 2 a

DK K 2 11 2 a 2DL

L .

�A/A is the change in output that cannot be explained by changes in inputs. Thus, the growth in total factor productivity is computed as a residual—that is, as the amount of output growth that remains after we have accounted for the determi- nants of growth that we can measure directly. Indeed, �A/A is sometimes called the Solow residual, after Robert Solow, who fi rst showed how to compute it.18

Total factor productivity can change for many reasons. Changes most often arise because of increased knowledge about production methods, so the Solow residual is often used as a measure of technological progress. Yet other factors, such as education and government regulation, can affect total factor productivity as well. For example, if higher public spending raises the quality of education, then workers may become more productive and output may rise, which implies higher total factor productivity. As another example, if government regulations require fi rms to purchase capital to reduce pollu- tion or increase worker safety, then the capital stock may rise without any increase in measured output, which implies lower total factor productivity. Total factor productivity captures anything that changes the relation between measured inputs and measured output.

The Sources of Growth in the United States

Having learned how to measure the sources of economic growth, we now look at the data. Table 9-3 uses U.S. data to measure the contributions of the three sources of growth between 1948 and 2010.

This table shows that output in the non-farm business sector grew an average of 3.4 percent per year during this time. Of this 3.4 percent, 1.0 percent was attribut- able to increases in the capital stock, 1.2 percent to increases in the labor input, and 1.2 percent to increases in total factor productivity. These data show that increases in capital, labor, and productivity have contributed almost equally to economic growth in the United States.

18Robert M. Solow, “Technical Change and the Aggregate Production Function,’’ Review of Economics and Statistics 39 (1957): 312–320. It is natural to ask how growth in labor effi ciency E relates to growth in total factor productivity. One can show that �A/A = (1 – �)�E/E, where � is capital’s share. Thus, technological change as measured by growth in the effi ciency of labor is proportional to technological change as measured by the Solow residual.

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Table 9-3 also shows that the growth in total factor productivity slowed sub- stantially during the period from 1972 to 1995. In a Case Study in this chapter, we discussed some hypotheses to explain this productivity slowdown.

Growth in the East Asian Tigers

Perhaps the most spectacular growth experiences in recent history have been those of the “Tigers” of East Asia: Hong Kong, Singapore, South Korea, and Taiwan. From 1966 to 1990, while real income per person was growing about 2 percent per year in the United States, it grew more than 7 percent per year in each of these countries. In the course of a single generation, real income per person increased fi vefold, moving the Tigers from among the world’s poorest countries to among the richest. (In the late 1990s, a period of pronounced fi nancial turmoil tarnished the reputation of some of these economies. But this short-run problem, which we examine in a Case Study in Chapter 13 doesn’t come close to reversing the spec- tacular long-run growth that the Asian Tigers have experienced.)

What accounts for these growth miracles? Some commentators have argued that the success of these four countries is hard to reconcile with basic growth theory, such as the Solow growth model, which takes technology as growing at a constant, exogenous rate. They have suggested that these countries’ rapid growth is explained by their ability to imitate foreign technologies. By adopting technol- ogy developed abroad, the argument goes, these countries managed to improve their production functions substantially in a relatively short period of time. If this argument is correct, these countries should have experienced unusually rapid growth in total factor productivity.

One study shed light on this issue by examining in detail the data from these four countries. The study found that their exceptional growth can be traced to large

CASE STUDY

SOURCES OF GROWTH

Output Total Factor Growth Capital Labor Productivity Years �Y/Y = ��K/K + (1 - �)�L/L + �A/A

(average percentage increase per year) 1948–2010 3.4 1.0 1.2 1.2

1948–1972 4.1 1.0 1.2 1.9 1972–1995 3.4 1.4 1.3 0.7 1995–2010 2.8 0.4 1.1 1.3

Source: US Department of Labor. Data are for the non-farm business sector.

Accounting for Economic Growth in the United States

TABLE 9-3

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increases in measured factor inputs: increases in labor-force participation, increases in the capital stock, and increases in educational attainment. In South Korea, for example, the investment–GDP ratio rose from about 5 percent in the 1950s to about 30 percent in the 1980s; the percentage of the working population with at least a high school education went from 26 percent in 1966 to 75 percent in 1991.

Once we account for growth in labor, capital, and human capital, little of the growth in output is left to explain. None of these four countries experienced unusually rapid growth in total factor productivity. Indeed, the average growth in total factor productivity in the East Asian Tigers was almost exactly the same as in the United States. Thus, although these countries’ rapid growth has been truly impressive, it is easy to explain using the tools of basic growth theory.19 ■

The Solow Residual in the Short Run

When Robert Solow introduced his famous residual, his aim was to shed light on the forces that determine technological progress and economic growth in the long run. But economist Edward Prescott has looked at the Solow residual as a measure of technological change over shorter periods of time. He concludes that fl uctuations in technology are a major source of short-run changes in economic activity.

Figure 9-2 shows the Solow residual and the growth in output using annual data for the United States during the period 1960 to 2010. Notice that the Solow residual fl uctuates substantially. If Prescott’s interpretation is correct, then we can draw conclusions from these short-run fl uctuations, such as that tech- nology worsened in 1982 and improved in 1984. Notice also that the Solow residual moves closely with output: in years when output falls, technology tends to worsen. In Prescott’s view, this fact implies that recessions are driven by adverse shocks to technology. The hypothesis that technological shocks are the driving force behind short-run economic fl uctuations, and the complementary hypothesis that monetary policy has no role in explaining these fl uctuations, is the foundation for an approach called real-business-cycle theory.

Prescott’s interpretation of these data is controversial, however. Many economists believe that the Solow residual does not accurately represent changes in technology over short periods of time. The standard explanation of the cyclical behavior of the Solow residual is that it results from two measurement problems.

First, during recessions, fi rms may continue to employ workers they do not need so that they will have these workers on hand when the economy recovers. This phenomenon, called labor hoarding, means that labor input is overestimated in recessions because the hoarded workers are probably not working as hard as usual. As a result, the Solow residual is more cyclical than the available production tech- nology. In a recession, productivity as measured by the Solow residual falls even if technology has not changed simply because hoarded workers are sitting around waiting for the recession to end.

Second, when demand is low, fi rms may produce things that are not easily measured. In recessions, workers may clean the factory, organize the inventory, get

19Alwyn Young, “The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience,” Quarterly Journal of Economics 101 (August 1995): 641–680.

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268 | P A R T I I I Growth Theory: The Economy in the Very Long Run

some training, and do other useful tasks that standard measures of output fail to include. If so, then output is underestimated in recessions, which would also make the measured Solow residual cyclical for reasons other than technology.

Thus, economists can interpret the cyclical behavior of the Solow residual in different ways. Some economists point to the low productivity in recessions as evidence for adverse technology shocks. Others believe that measured produc- tivity is low in recessions because workers are not working as hard as usual and because more of their output is not measured. Unfortunately, there is no clear evidence on the importance of labor hoarding and the cyclical mismeasurement of output. Therefore, different interpretations of Figure 9-2 persist.20

FIGURE 9-2

Growth in Output and the Solow Residual The Solow residual, which some economists interpret as a measure of technology shocks, fl uctuates with the economy’s output of goods and services.

Sources: U.S. Department of Commerce, U.S. Department of Labor, and author’s calculations.

Output growth

Solow residual

1960

6

Percent per year

1965 1970 1975 1980 Year

1985 1990 1995 2000 2010

8

2005

4

2

0

–2

–4

20To read more about this topic, see Edward C. Prescott, “Theory Ahead of Business Cycle Measurement,’’ and Lawrence H. Summers, “Some Skeptical Observations on Real Business Cycle Theory,’’ both in Quarterly Review, Federal Reserve Bank of Minneapolis (Fall 1986); N. Gregory Mankiw, “Real Business Cycles: A New Keynesian Perspective,’’ Journal of Economic Perspectives 3 (Summer 1989): 79–90; Bennett T. McCallum, “Real Business Cycle Models,’’ in R. Barro, ed., Modern Business Cycle Theory (Cambridge, Mass.: Harvard University Press, 1989), 16–50; and Charles I. Plosser, “Understanding Real Business Cycles,’’ Journal of Economic Perspectives 3 (Summer 1989): 51–77.

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1. In the economy of Solovia, the owners of capi- tal get two-thirds of national income, and the workers receive one-third.

a. The men of Solovia stay at home performing household chores, while the women work in factories. If some of the men started work- ing outside the home so that the labor force increased by 5 percent, what would happen to the measured output of the economy? Does labor productivity—defi ned as output per worker—increase, decrease, or stay the same? Does total factor productivity increase, decrease, or stay the same?

b. In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the labor input was 4, and output was 14. What happened to total factor productivity between the two years?

2. Labor productivity is defi ned as Y/L, the amount of output divided by the amount of labor input. Start with the growth-accounting equation and show that the growth in labor productivity depends on growth in total factor

M O R E P R O B L E M S A N D A P P L I C A T I O N S

productivity and growth in the capital–labor ratio. In particular, show that

D 1Y/L 2 Y/L

= DA A

+ a D 1K/L 2

K/L .

Hint: You may fi nd the following mathematical trick helpful. If z = wx, then the growth rate of z is approximately the growth rate of w plus the growth rate of x. That is,

�z/z ≈ �w/w + �x/x.

3. Suppose an economy described by the Solow model is in a steady state with population growth n of 1.8 percent per year and technological prog- ress g of 1.8 percent per year. Total output and total capital grow at 3.6 percent per year. Sup- pose further that the capital share of output is 1/3. If you used the growth-accounting equation to divide output growth into three sources— capital, labor, and total factor productivity—how much would you attribute to each source? Compare your results to the fi gures we found for the United States in Table 9-3.

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Business Cycle Theory: The Economy in the Short Run

P A R T I V

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273

Introduction to Economic Fluctuations

The modern world regards business cycles much as the ancient Egyptians

regarded the overfl owing of the Nile. The phenomenon recurs at intervals, it is

of great importance to everyone, and natural causes of it are not in sight.

— John Bates Clark, 1898

Economic fl uctuations present a recurring problem for economists and policymakers. On average, the real GDP of the United States grows about 3 percent per year. But this long-run average hides the fact that the economy’s output of goods and services does not grow smoothly. Growth is higher in some years than in others; sometimes the economy loses ground, and growth turns negative. These fl uctuations in the economy’s output are closely associated with fl uctuations in employment. When the economy experiences a period of falling output and rising unemployment, the economy is said to be in recession.

A recent recession began in late 2007. From the third quarter of 2007 to the third quarter of 2008, the economy’s production of goods and services was approx- imately fl at, in contrast to its normal growth. Real GDP then plunged sharply in the fourth quarter of 2008 and fi rst quarter of 2009. The unemployment rate rose from 4.7 percent in November 2007 to 10.1 percent in October 2009. The recession offi cially ended in June 2009 when positive growth resumed, but the recovery was weak, and unemployment remained high even a few years later. Not surprisingly, the recession dominated the economic news, and addressing the problem was high on the agenda of President Barack Obama.

Economists call these short-run fl uctuations in output and employment the business cycle. Although this term suggests that economic fl uctuations are regular and predictable, they are not. Recessions are actually as irregular as they are com- mon. Sometimes they occur close together, while at other times they are much farther apart. For example, the United States fell into recession in 1982, only two years after the previous downturn. By the end of that year, the unemployment rate had reached 10.8 percent—the highest level since the Great Depression of the 1930s. But after the 1982 recession, it was eight years before the economy experienced another one.

C H A P T E R 10

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274 | P A R T I V Business Cycle Theory: The Economy in the Short Run

These historical events raise a variety of related questions: What causes short- run fl uctuations? What model should we use to explain them? Can policymakers avoid recessions? If so, what policy levers should they use?

In Parts Two and Three of this book, we developed theories to explain how the economy behaves in the long run. Here, in Part Four, we see how economists explain short-run fl uctuations. We begin in this chapter with three tasks. First, we examine the data that describe short-run economic fl uctuations. Second, we discuss the key differences between how the economy behaves in the long run and how it behaves in the short run. Third, we introduce the model of aggregate supply and aggregate demand, which most economists use to explain short-run fl uctuations. Developing this model in more detail will be our primary job in the chapters that follow.

Just as Egypt now controls the fl ooding of the Nile Valley with the Aswan Dam, modern society tries to control the business cycle with appropriate eco- nomic policies. The model we develop over the next several chapters shows how monetary and fi scal policies infl uence the business cycle. We will see how these policies can potentially stabilize the economy or, if poorly conducted, make the problem of economic instability even worse.

10-1 The Facts About the Business Cycle

Before thinking about the theory of business cycles, let’s look at some of the facts that describe short-run fl uctuations in economic activity.

GDP and Its Components

The economy’s gross domestic product measures total income and total expen- diture in the economy. Because GDP is the broadest gauge of overall economic conditions, it is the natural place to start in analyzing the business cycle. Fig-

ure 10-1 shows the growth of real GDP from 1970 to 2011. The horizontal line shows the average growth rate of 3 percent per year over this period. You can see that economic growth is not at all steady and that, occasionally, it turns negative.

The shaded areas in the fi gure indicate periods of recession. The offi cial arbiter of when reces- sions begin and end is the National Bureau of Economic Research (NBER), a nonprofi t eco- nomic research group. The NBER’s Business Cycle Dating Committee (of which the author of this book was once a member) chooses the stating date of each recession, called the business cycle peak, and the ending date, called the business cycle trough. “Well, so long Eddie, the recession’s over.’’

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; © 1

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C H A P T E R 1 0 Introduction to Economic Fluctuations | 275

What determines whether a downturn in the economy is suffi ciently severe to be deemed a recession? There is no simple answer. According to an old rule of thumb, a recession is a period of at least two consecutive quarters of declin- ing real GDP. This rule, however, does not always hold. In the most recently revised data, for example, the recession of 2001 had two quarters of negative growth, but those quarters were not consecutive. In fact, the NBER’s Business Cycle Dating Committee does not follow any fi xed rule but, instead, looks at a variety of economic time series and uses its judgment when picking the starting and ending dates of recessions. As this book was going to press, the economy was recovering from the recession of 2008–2009, but the recovery was weak by historical standards.1

Figure 10-2 shows the growth in two major components of GDP— consumption in panel (a) and investment in panel (b). Growth in both of these

Real GDP Growth in the United States Growth in real GDP averages about 3 percent per year, but there are substantial fl uctuations around this average. The shaded areas represent periods of recession.

Source: U.S. Department of Commerce.

Percentage change from 4 quarters earlier

10

8

6

4

2

0

�2

�4

�6 1970

Year 1975 1980 1985 1990 1995 2000 2005

Average growth rate

Real GDP growth rate

2010

FIGURE 10-1

1Note that Figure 10-1 plots growth in real GDP from four quarters earlier, rather than from the immediately preceding quarter. During the 2001 recession, this measure declined but never turned negative.

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276 | P A R T I V Business Cycle Theory: The Economy in the Short Run

Growth in Consumption and Investment When the economy heads into a recession, growth in real consumption and investment spending both decline. Investment spending, shown in panel (b), is considerably more volatile than consumption spending, shown in panel (a). The shaded areas represent periods of recession.

Source: U.S. Department of Commerce.

1970 1975 1980 1985 1990 1995 2000 2005 Year

(b) Growth in Investment

Percentage change from 4 quarters earlier

Investment growth

1970 1975 1980 1985 1990 1995 2000 2005 Year

8

6

4

2

0

–2

(a) Growth in Consumption

2010

Percentage change from 4 quarters earlier

Consumption growth

–4

2010

20

30

40

50

10

0

–10

–20

–30

–40

FIGURE 10-2

variables declines during recessions. Take note, however, of the scales for the vertical axes. Investment is far more volatile than consumption over the busi- ness cycle. When the economy heads into a recession, households respond to the fall in their incomes by consuming less, but the decline in spending on business equipment, structures, new housing, and inventories is even more substantial.

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C H A P T E R 1 0 Introduction to Economic Fluctuations | 277

Unemployment and Okun’s Law

The business cycle is apparent not only in data from the national income accounts but also in data that describe conditions in the labor market. Figure 10-3 shows the unemployment rate from 1970 to 2011 again with the shaded areas representing periods of recession. You can see that unemployment rises in each recession. Other labor-market measures tell a similar story. For example, job vacancies, as measured by the number of help-wanted ads that com- panies have posted, decline during recessions. Put simply, during an economic downturn, jobs are harder to fi nd.

What relationship should we expect to fi nd between unemployment and real GDP? Because employed workers help to produce goods and services and unemployed workers do not, increases in the unemployment rate should be associated with decreases in real GDP. This negative relationship between unem- ployment and GDP is called Okun’s law, after Arthur Okun, the economist who fi rst studied it.2

Figure 10-4 uses annual data for the United States to illustrate Okun’s law. In this scatterplot, each point represents the data for one year. The horizontal axis represents the change in the unemployment rate from the previous year, and the vertical axis represents the percentage change in GDP. This fi gure shows clearly

Unemployment The unemployment rate rises signifi cantly during periods of recession, shown here by the shaded areas.

Source: U.S. Department of Labor.

Unemployment rate

1970 1975 1980 1985 1990 1995 2000 2005 Year

12

10

8

6

4

2

0

Percentage of labor force

2010

FIGURE 10-3

2Arthur M. Okun, “Potential GNP: Its Measurement and Signifi cance,’’ in Proceedings of the Business and Economics Statistics Section, American Statistical Association (Washington, D.C.: American Statistical Association, 1962): 98–103; reprinted in Arthur M. Okun, Economics for Policymaking (Cambridge, Mass.: MIT Press, 1983), 145–158.

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278 | P A R T I V Business Cycle Theory: The Economy in the Short Run

that year-to-year changes in the unemployment rate are closely associated with year-to-year changes in real GDP.

We can be more precise about the magnitude of the Okun’s law relationship. The line drawn through the scatter of points tells us that

Percentage Change in Real GDP

= 3% − 2 × Change in Unemployment Rate.

If the unemployment rate remains the same, real GDP grows by about 3 percent; this normal growth in the production of goods and services is due to growth in the labor force, capital accumulation, and technological progress. In addition, for every percentage point the unemployment rate rises, real GDP growth typically falls by 2 percent. Hence, if the unemployment rate rises from 5 to 7 percent, then real GDP growth would be

Percentage Change in Real GDP = 3% − 2 × (7% − 5%)

= −1%.

In this case, Okun’s law says that GDP would fall by 1 percent, indicating that the economy is in a recession.

Okun’s Law This fi gure is a scatterplot of the change in the unemployment rate on the horizontal axis and the percentage change in real GDP on the vertical axis, using data on the U.S economy. Each point represents one year. The fi gure shows that increases in unemployment tend to be associated with lower-than-normal growth in real GDP. The correlation between these two variables is –0.89.

Sources: U.S. Department of Commerce, U.S. Department of Labor.

−3% −2 −1 0 1 2 43

10

8

6

4

2

0

−2 2008

2003

2001

1991

1987

1984

1982 2009

1975

1971

1966

1963

1951

Change in unemployment rate

Percentage change in real GDP

FIGURE 10-4

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Okun’s law is a reminder that the forces that govern the short-run business cycle are very different from those that shape long-run economic growth. As we saw in Chapters 8 and 9, long-run growth in GDP is determined primarily by technological progress. The long-run trend leading to higher standards of living from generation to generation is not associated with any long-run trend in the rate of unemployment. By contrast, short-run movements in GDP are highly correlated with the utilization of the economy’s labor force. The declines in the production of goods and services that occur during recessions are always associ- ated with increases in joblessness.

Leading Economic Indicators

Many economists, particularly those working in business and government, are engaged in the task of forecasting short-run fl uctuations in the economy. Busi- ness economists are interested in forecasting to help their companies plan for changes in the economic environment. Government economists are interested in forecasting for two reasons. First, the economic environment affects the gov- ernment; for example, the state of the economy infl uences how much tax rev- enue the government collects. Second, the government can affect the economy through its use of monetary and fi scal policy. Economic forecasts are, therefore, an input into policy planning.

One way that economists arrive at their forecasts is by looking at leading indicators, which are variables that tend to fl uctuate in advance of the overall economy. Forecasts can differ in part because economists hold varying opinions about which leading indicators are most reliable.

Each month the Conference Board, a private economics research group, announces the index of leading economic indicators. This index includes ten data series that are often used to forecast changes in economic activity about six to nine months into the future. Here is a list of the series:

■ Average workweek of production workers in manufacturing. Because businesses often adjust the work hours of existing employees before making new hires or laying off workers, average weekly hours is a leading indicator of employment changes. A longer workweek indicates that fi rms are ask- ing their employees to work long hours because they are experiencing strong demand for their products; thus, it indicates that fi rms are likely to increase hiring and production in the future. A shorter workweek indi- cates weak demand, suggesting that fi rms are more likely to lay off workers and cut back production.

■ Average initial weekly claims for unemployment insurance. The number of people making new claims on the unemployment-insurance system is one of the most quickly available indicators of conditions in the labor market. This series is inverted in computing the index of leading indi- cators, so that an increase in the series lowers the index. An increase in the number of people making new claims for unemployment insurance indicates that fi rms are laying off workers and cutting back production;

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280 | P A R T I V Business Cycle Theory: The Economy in the Short Run

these layoffs and cutbacks will soon show up in data on employment and production.

■ New orders for consumer goods and materials, adjusted for infl ation. This indicator is a direct measure of the demand that fi rms are experienc- ing. Because an increase in orders depletes a fi rm’s inventories, this statistic typically predicts subsequent increases in production and employment.

■ New orders for nondefense capital goods. This series is the counterpart to the previous one, but for investment goods rather than consumer goods.

■ Index of supplier deliveries. This variable, sometimes called vendor per- formance, is a measure of the number of companies receiving slower deliveries from suppliers. Vendor performance is a leading indicator because deliveries slow down when companies are experiencing increased demand for their products. Slower deliveries therefore indicate a future increase in economic activity.

■ New building permits issued. Construction of new buildings is part of investment—a particularly volatile component of GDP. An increase in building permits means that planned construction is increasing, which indicates a rise in overall economic activity.

■ Index of stock prices. The stock market refl ects expectations about future economic conditions because stock market investors bid up prices when they expect companies to be profi table. An increase in stock prices indicates that investors expect the economy to grow rapidly; a decrease in stock prices indicates that investors expect an economic slowdown.

■ Money supply (M2), adjusted for infl ation. Because the money supply is related to total spending, more money predicts increased spending, which in turn means higher production and employment.

■ Interest rate spread: the yield spread between 10-year Treasury notes and 3-month Treasury bills. This spread, sometimes called the slope of the yield curve, refl ects the market’s expectation about future interest rates, which in turn refl ect the condition of the economy. A large spread means that interest rates are expected to rise, which typically occurs when economic activity increases.

■ Index of consumer expectations. This is a direct measure of expectations, based on a survey conducted by the University of Michigan’s Survey Research Center. Increased optimism about future economic conditions among consumers suggests increased consumer demand for goods and services, which in turn will encourage businesses to expand production and employment to meet the demand.

The index of leading indicators is far from a precise forecast of the future, as short-run economic fl uctuations are largely unpredictable. Nonetheless, the index is a useful input into planning by both businesses and the government.

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10-2 Time Horizons in Macroeconomics

Now that we have some sense about the facts that describe short-run economic fl uctuations, we can turn to our basic task in this part of the book: building a theory to explain these fl uctuations. That job, it turns out, is not a simple one. It will take us not only the rest of this chapter but also the next four chapters to develop the model of short-run fl uctuations in its entirety.

Before we start building the model, however, let’s step back and ask a fun- damental question: why do economists need different models for different time horizons? Why can’t we stop the course here and be content with the classical models developed in Chapters 3 through 9? The answer, as this book has consis- tently reminded its reader, is that classical macroeconomic theory applies to the long run but not to the short run. But why is this so?

How the Short Run and Long Run Differ

Most macroeconomists believe that the key difference between the short run and the long run is the behavior of prices. In the long run, prices are fl exible and can respond to changes in supply or demand. In the short run, many prices are “sticky’’ at some predetermined level. Because prices behave differently in the short run than in the long run, various economic events and policies have different effects over different time horizons.

To see how the short run and the long run differ, consider the effects of a change in monetary policy. Suppose that the Federal Reserve suddenly reduces the money supply by 5 percent. According to the classical model, the money supply affects nominal variables—variables measured in terms of money—but not real variables. As you may recall from Chapter 5, the theo- retical separation of real and nominal variables is called the classical dichotomy, and the irrelevance of the money supply for the determination of real vari- ables is called monetary neutrality. Most economists believe that these classical ideas describe how the economy works in the long run: a 5 percent reduction in the money supply lowers all prices (including nominal wages) by 5 percent, while output, employment, and other real variables remain the same. Thus, in the long run, changes in the money supply do not cause fl uctuations in output and employment.

In the short run, however, many prices do not respond to changes in monetary policy. A reduction in the money supply does not immediately cause all fi rms to cut the wages they pay, all stores to change the price tags on their goods, all mail-order fi rms to issue new catalogs, and all restaurants to print new menus. Instead, there is little immediate change in many prices; that is, many prices are sticky. This short-run price stickiness implies that the short-run impact of a change in the money supply is not the same as the long-run impact.

A model of economic fl uctuations must take into account this short-run price stickiness. We will see that the failure of prices to adjust quickly and completely

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The Frequency of Price Adjustment

This table is based on answers to the question: How often do the prices of your most important products change in a typical year?

TABLE 10-1

Frequency Percentage of Firms

Less than once 10.2 Once 39.3 1.01 to 2 15.6 2.01 to 4 12.9 4.01 to 12 7.5 12.01 to 52 4.3 52.01 to 365 8.6 More than 365 1.6

Source: Table 4.1, Alan S. Blinder, “On Sticky Prices: Academic Theories Meet the Real World,’’ in N. G. Mankiw, ed., Monetary Policy (Chicago: University of Chicago Press, 1994), 117–154.

If You Want to Know Why Firms Have Sticky Prices, Ask Them

How sticky are prices, and why are they sticky? In an intriguing study, economist Alan Blinder attacked these questions directly by surveying fi rms about their price-adjustment decisions.

Blinder began by asking fi rm managers how often they changed prices. The answers, summarized in Table 10-1, yielded two conclusions. First, sticky prices are common. The typical fi rm in the economy adjusts its prices once or twice a year. Second, there are large differences among fi rms in the frequency of price adjustment. About 10 percent of fi rms changed prices more often than once a week, and about the same number changed prices less often than once a year.

Blinder then asked the fi rm managers why they didn’t change prices more often. In particular, he explained to the managers several economic theories of sticky prices and asked them to judge how well each of these theories described their

CASE STUDY

to changes in the money supply (as well as to other exogenous changes in eco- nomic conditions) means that, in the short run, real variables such as output and employment must do some of the adjusting instead. In other words, during the time horizon over which prices are sticky, the classical dichotomy no longer holds: nominal variables can infl uence real variables, and the economy can devi- ate from the equilibrium predicted by the classical model.

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C H A P T E R 1 0 Introduction to Economic Fluctuations | 283

Theory and Percentage of Managers Brief Description Who Accepted Theory

Coordination failure: 60.6 Firms hold back on price changes, waiting for others to go fi rst

Cost-based pricing with lags: 55.5 Price increases are delayed until costs rise

Delivery lags, service, etc.: 54.8 Firms prefer to vary other product attributes, such as delivery lags, service, or product quality

Implicit contracts: 50.4 Firms tacitly agree to stabilize prices, perhaps out of “fairness” to customers

Nominal contracts: 35.7 Prices are fi xed by explicit contracts

Costs of price adjustment: 30.0 Firms incur costs of changing prices

Procyclical elasticity: 29.7 Demand curves become less elastic as they shift in

Pricing points: 24.0 Certain prices (like $9.99) have special psychological signifi cance

Inventories: 20.9 Firms vary inventory stocks instead of prices

Constant marginal cost: 19.7 Marginal cost is fl at and markups are constant

Hierarchical delays: 13.6 Bureaucratic delays slow down decisions

Judging quality by price: 10.0 Firms fear customers will mistake price cuts for reductions in quality

Source: Tables 4.3 and 4.4, Alan S. Blinder, “On Sticky Prices: Academic Theories Meet the Real World,’’ in N. G. Mankiw, ed., Monetary Policy (Chicago: University of Chicago Press, 1994), 117–154.

Theories of Price Stickiness

TABLE 10-2

fi rms. Table 10-2 summarizes the theories and ranks them by the percentage of managers who accepted the theory as an accurate description of their fi rms’ pricing decisions. Notice that each of the theories was endorsed by some of the managers, but each was rejected by a large number as well. One interpretation is that differ- ent theories apply to different fi rms, depending on industry characteristics, and that price stickiness is a macroeconomic phenomenon without a single microeconomic explanation.

Among the dozen theories, coordination failure tops the list. According to Blinder, this is an important fi nding because it suggests that the inabil- ity of fi rms to coordinate price changes plays a key role in explaining price

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284 | P A R T I V Business Cycle Theory: The Economy in the Short Run

stickiness and, thus, short-run economic fl uctuations. He writes, “The most obvious policy implication of the model is that more coordinated wage and price setting—somehow achieved—could improve welfare. But if this proves diffi cult or impossible, the door is opened to activist monetary policy to cure recessions.”3 ■

The Model of Aggregate Supply and Aggregate Demand

How does the introduction of sticky prices change our view of how the economy works? We can answer this question by considering economists’ two favorite words—supply and demand.

In classical macroeconomic theory, the amount of output depends on the economy’s ability to supply goods and services, which in turn depends on the supplies of capital and labor and on the available production technology. This is the essence of the basic classical model in Chapter 3, as well as of the Solow growth model in Chapters 8 and 9. Flexible prices are a crucial assumption of classical theory. The theory posits, sometimes implicitly, that prices adjust to ensure that the quantity of output demanded equals the quantity supplied.

The economy works quite differently when prices are sticky. In this case, as we will see, output also depends on the economy’s demand for goods and ser- vices. Demand, in turn, depends on a variety of factors: consumers’ confi dence about their economic prospects, fi rms’ perceptions about the profi tability of new investments, and monetary and fi scal policy. Because monetary and fi scal policy can infl uence demand, and demand in turn can infl uence the economy’s output over the time horizon when prices are sticky, price stickiness provides a rationale for why these policies may be useful in stabilizing the economy in the short run.

In the rest of this chapter, we begin developing a model that makes these ideas more precise. The place to start is the model of supply and demand, which we used in Chapter 1 to discuss the market for pizza. This basic model offers some of the most fundamental insights in economics. It shows how the supply and demand for any good jointly determine the good’s price and the quantity sold, as well as how shifts in supply and demand affect the price and quantity. We now introduce the “economy-size” version of this model—the model of aggregate

3To read more about this study, see Alan S. Blinder, “On Sticky Prices: Academic Theories Meet the Real World,’’ in N. G. Mankiw, ed., Monetary Policy (Chicago: University of Chicago Press, 1994), 117–154. For more recent evidence about the frequency of price adjustment, see Emi Nakamura and Jón Steinsson, “Five Facts About Prices: A Reevaluation of Menu Cost Models,” Quarterly Journal of Economics, 123, no. 4 (November 2008):1415–1464. Nakamura and Steinsson examine the microeconomic data that underlie the consumer and producer price indexes. They report that, including temporary sales, 19 to 20 percent of prices change every month. If sales are excluded, however, the frequency of price adjustment falls to about 9 to 12 percent per month. This latter fi nding is broadly consistent with Blinder’s conclusion that the typical fi rm adjusts its prices about once a year.

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supply and aggregate demand. This macroeconomic model allows us to study how the aggregate price level and the quantity of aggregate output are determined in the short run. It also provides a way to contrast how the economy behaves in the long run and how it behaves in the short run.

Although the model of aggregate supply and aggregate demand resembles the model of supply and demand for a single good, the analogy is not exact. The model of supply and demand for a single good considers only one good within a large economy. By contrast, as we will see in the coming chapters, the model of aggregate supply and aggregate demand is a sophisticated model that incor- porates the interactions among many markets. In the remainder of this chapter we get a fi rst glimpse at those interactions by examining the model in its most simplifi ed form. Our goal here is not to explain the model fully but, instead, to introduce its key elements and illustrate how it can help explain short-run eco- nomic fl uctuations.

10-3 Aggregate Demand

Aggregate demand (AD) is the relationship between the quantity of output demanded and the aggregate price level. In other words, the aggregate demand curve tells us the quantity of goods and services people want to buy at any given level of prices. We examine the theory of aggregate demand in detail in Chapters 11 through 13. Here we use the quantity theory of money to provide a simple, although incomplete, derivation of the aggregate demand curve.

The Quantity Equation as Aggregate Demand

Recall from Chapter 5 that the quantity theory says that

MV = PY,

where M is the money supply, V is the velocity of money, P is the price level, and Y is the amount of output. If the velocity of money is constant, then this equation states that the money supply determines the nominal value of output, which in turn is the product of the price level and the amount of output.

When interpreting this equation, it is useful to recall that the quantity equation can be rewritten in terms of the supply and demand for real money balances:

M/P = (M/P)d = kY,

where k = 1/V is a parameter representing how much money people want to hold for every dollar of income. In this form, the quantity equation states that the supply of real money balances M/P equals the demand for real money balances (M/P)d and that the demand is proportional to output Y. The velocity of money V is the fl ip side of the money demand parameter k. The assumption of constant velocity

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is equivalent to the assumption of a constant demand for real money balances per unit of output.

If we assume that velocity V is constant and the money supply M is fi xed by the central bank, then the quantity equation yields a negative relationship between the price level P and output Y. Figure 10-5 graphs the combinations of P and Y that satisfy the quantity equation holding M and V constant. This downward-sloping curve is called the aggregate demand curve.

Why the Aggregate Demand Curve Slopes Downward

As a strictly mathematical matter, the quantity equation explains the downward slope of the aggregate demand curve very simply. The money supply M and the velocity of money V determine the nominal value of output PY. Once PY is fi xed, if P goes up, Y must go down.

What is the economic intuition that lies behind this mathematical relationship? For a complete explanation of the downward slope of the aggregate demand curve, we have to wait for a couple of chapters. For now, however, consider the following logic: Because we have assumed the velocity of money is fi xed, the money supply determines the dollar value of all transactions in the economy. (This conclusion should be familiar from Chapter 5) If the price level rises, each transaction requires more dollars, so the number of transactions and thus the quantity of goods and services purchased must fall.

We can also explain the downward slope of the aggregate demand curve by thinking about the supply and demand for real money balances. If output is higher, people engage in more transactions and need higher real balances M/P.

The Aggregate Demand Curve The aggregate demand curve AD shows the relationship between the price level P and the quantity of goods and services demanded Y. It is drawn for a given value of the money supply M. The aggregate demand curve slopes downward: the higher the price level P, the lower the level of real balances M/P, and therefore the lower the quantity of goods and services demanded Y.

Price level, P

Income, output, Y

Aggregate demand, AD

FIGURE 10-5

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For a fi xed money supply M, higher real balances imply a lower price level. Con- versely, if the price level is lower, real money balances are higher; the higher level of real balances allows a greater volume of transactions, which means a greater quantity of output is demanded.

Shifts in the Aggregate Demand Curve

The aggregate demand curve is drawn for a fi xed value of the money supply. In other words, it tells us the possible combinations of P and Y for a given value of M. If the Fed changes the money supply, then the possible combinations of P and Y change, which means the aggregate demand curve shifts.

For example, consider what happens if the Fed reduces the money supply. The quantity equation, MV = PY, tells us that the reduction in the money sup- ply leads to a proportionate reduction in the nominal value of output PY. For any given price level, the amount of output is lower, and for any given amount of output, the price level is lower. As in Figure 10-6(a), the aggregate demand curve relating P and Y shifts inward.

The opposite occurs if the Fed increases the money supply. The quantity equa- tion tells us that an increase in M leads to an increase in PY. For any given price level, the amount of output is higher, and for any given amount of output, the price level is higher. As shown in Figure 10-6(b), the aggregate demand curve shifts outward.

Shifts in the Aggregate Demand Curve Changes in the money supply shift the aggregate demand curve. In panel (a), a decrease in the money supply M reduces the nominal value of output PY. For any given price level P, output Y is lower. Thus, a decrease in the money supply shifts the aggregate demand curve inward from AD1 to AD2. In panel (b), an increase in the money supply M raises the nominal value of output PY. For any given price level P, output Y is higher. Thus, an increase in the money supply shifts the aggregate demand curve outward from AD1 to AD2.

FIGURE 10-6

Price level, P Price level, P

Income, output, Y Income, output, Y

(a) Inward Shifts in the Aggregate Demand Curve

AD2

AD1

Reductions in the money supply shift the aggregate demand curve to the left.

(b) Outward Shifts in the Aggregate Demand Curve

AD1

AD2

Increases in the money supply shift the aggregate demand curve to the right.

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Although the quantity theory of money provides a very simple basis for understanding the aggregate demand curve, be forewarned that reality is more complicated. Fluctuations in the money supply are not the only source of fl uc- tuations in aggregate demand. Even if the money supply is held constant, the aggregate demand curve shifts if some event causes a change in the velocity of money. Over the next two chapters, we develop a more general model of aggre- gate demand, called the IS–LM model, which will allow us to consider many possible reasons for shifts in the aggregate demand curve.

10-4 Aggregate Supply

By itself, the aggregate demand curve does not tell us the price level or the amount of output that will prevail in the economy; it merely gives a relation- ship between these two variables. To accompany the aggregate demand curve, we need another relationship between P and Y that crosses the aggregate demand curve—an aggregate supply curve. The aggregate demand and aggre- gate supply curves together pin down the economy’s price level and quantity of output.

Aggregate supply (AS) is the relationship between the quantity of goods and services supplied and the price level. Because the fi rms that supply goods and services have fl exible prices in the long run but sticky prices in the short run, the aggregate supply relationship depends on the time horizon. We need to dis- cuss two different aggregate supply curves: the long-run aggregate supply curve LRAS and the short-run aggregate supply curve SRAS. We also need to discuss how the economy makes the transition from the short run to the long run.

The Long Run: The Vertical Aggregate Supply Curve

Because the classical model describes how the economy behaves in the long run, we derive the long-run aggregate supply curve from the classical model. Recall from Chapter 3 that the amount of output produced depends on the fi xed amounts of capital and labor and on the available technology. To show this, we write

Y = F( _ K,

_ L)

= _ Y.

According to the classical model, output does not depend on the price level. To show that output is fi xed at this level, regardless of the price level, we draw a vertical aggregate supply curve, as in Figure 10-7. In the long run, the intersec- tion of the aggregate demand curve with this vertical aggregate supply curve determines the price level.

If the aggregate supply curve is vertical, then changes in aggregate demand affect prices but not output. For example, if the money supply falls, the aggregate demand curve shifts downward, as in Figure 10-8. The economy moves from the old

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intersection of aggregate supply and aggregate demand, point A, to the new inter- section, point B. The shift in aggregate demand affects only prices.

The vertical aggregate supply curve satisfi es the classical dichotomy because it implies that the level of output is independent of the money supply. This long-run level of output,

_ Y, is called the full-employment, or natural, level of output.

It is the level of output at which the economy’s resources are fully employed or, more realistically, at which unemployment is at its natural rate.

The Long-Run Aggregate Supply Curve In the long run, the level of output is determined by the amounts of capital and labor and by the available tech- nology; it does not depend on the price level. The long-run aggregate supply curve, LRAS, is vertical.

Price level, P

Income, output, Y

Long-run aggregate supply, LRAS

Y

FIGURE 10-7

Shifts in Aggregate Demand in the Long Run A reduc- tion in the money supply shifts the aggregate demand curve downward from AD1 to AD2. The equilibrium for the economy moves from point A to point B. Because the aggregate supply curve is vertical in the long run, the reduction in aggregate demand affects the price level but not the level of output.

Price level, P

Income, output, YY

AD1

AD2

LRAS

A

B

1. A fall in aggregate demand ...

3. ... but leaves output the same.

2. ... lowers the price level in the long run ...

FIGURE 10-8

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The Short Run: The Horizontal Aggregate Supply Curve

The classical model and the vertical aggregate supply curve apply only in the long run. In the short run, some prices are sticky and therefore do not adjust to changes in demand. Because of this price stickiness, the short-run aggregate supply curve is not vertical.

In this chapter, we will simplify things by assuming an extreme example. Sup- pose that all fi rms have issued price catalogs and that it is too costly for them to issue new ones. Thus, all prices are stuck at predetermined levels. At these prices, fi rms are willing to sell as much as their customers are willing to buy, and they hire just enough labor to produce the amount demanded. Because the price level is fi xed, we represent this situation in Figure 10-9 with a horizontal aggregate supply curve.

The short-run equilibrium of the economy is the intersection of the aggregate demand curve and this horizontal short-run aggregate supply curve. In this case, changes in aggregate demand do affect the level of output. For example, if the Fed suddenly reduces the money supply, the aggregate demand curve shifts inward, as in Figure 10-10. The economy moves from the old intersection of aggregate demand and aggregate supply, point A, to the new intersection, point B. The movement from point A to point B represents a decline in output at a fi xed price level.

Thus, a fall in aggregate demand reduces output in the short run because prices do not adjust instantly. After the sudden fall in aggregate demand, fi rms are stuck with prices that are too high. With demand low and prices high, fi rms sell less of their product, so they reduce production and lay off workers. The economy experi- ences a recession.

Once again, be forewarned that reality is a bit more complicated than illus- trated here. Although many prices are sticky in the short run, some prices are able to respond quickly to changing circumstances. As we will see in Chap- ter 14, in an economy with some sticky prices and some fl exible prices, the short-run aggregate supply curve is upward sloping rather than horizontal.

The Short-Run Aggregate Supply Curve In this extreme example, all prices are fi xed in the short run. Therefore, the short-run aggregate supply curve, SRAS, is horizontal.

Price level, P

Income, output, Y

Short-run aggregate supply, SRAS

FIGURE 10-9

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Figure 10-10 illustrates the extreme case in which all prices are stuck. Because this case is simpler, it is a useful starting point for thinking about short-run aggregate supply.

From the Short Run to the Long Run

We can summarize our analysis so far as follows: Over long periods of time, prices are fl exible, the aggregate supply curve is vertical, and changes in aggregate demand affect the price level but not output. Over short periods of time, prices are sticky, the aggregate supply curve is fl at, and changes in aggregate demand do affect the economy’s output of goods and services.

How does the economy make the transition from the short run to the long run? Let’s trace the effects over time of a fall in aggregate demand. Suppose that the economy is initially in long-run equilibrium, as shown in Figure 10-11. In this fi gure, there are three curves: the aggregate demand curve, the long-run aggregate supply curve, and the short-run aggregate supply curve. The long-run equilibrium is the point at which aggregate demand crosses the long-run aggregate supply curve. Prices have adjusted to reach this equilibrium. Therefore, when the economy is in its long-run equilibrium, the short-run aggregate supply curve must cross this point as well.

Now suppose that the Fed reduces the money supply and the aggregate demand curve shifts downward, as in Figure 10-12. In the short run, prices are sticky, so the economy moves from point A to point B. Output and

Shifts in Aggregate Demand in the Short Run A reduction in the money supply shifts the aggre- gate demand curve downward from AD1 to AD2. The equilibrium for the economy moves from point A to point B. Because the aggregate supply curve is horizon- tal in the short run, the reduction in aggregate demand reduces the level of output.

Price level, P

Income, output, Y

3. ... lowers the level of output.

2. ... a fall in aggregate demand ...

AD1

AD2

SRAS A B

1. In the short run when prices are sticky...

FIGURE 10-10

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employment fall below their natural levels, which means the economy is in a recession. Over time, in response to the low demand, wages and prices fall. The gradual reduction in the price level moves the economy downward along the aggregate demand curve to point C, which is the new long-run equilibrium. In the new long-run equilibrium (point C), output and employment are back to their natural levels, but prices are lower than in the old long-run equilibrium (point A). Thus, a shift in aggregate demand affects output in the short run, but this effect dissipates over time as fi rms adjust their prices.

A Reduction in Aggregate Demand The economy begins in long-run equilibrium at point A. A reduction in aggregate demand, perhaps caused by a decrease in the money supply, moves the economy from point A to point B, where output is below its natural level. As prices fall, the economy gradu- ally recovers from the recession, moving from point B to point C.

Price level, P

Income, output, YY

AD1

AD2

SRAS

LRAS

A

C

B

2. ... lowers output in the short run ...

3. ... but in the long run affects only the price level.

1. A fall in aggregate demand ...

FIGURE 10-12

Long-Run Equilibrium In the long run, the economy fi nds itself at the intersection of the long-run aggregate supply curve and the aggregate demand curve. Because prices have adjusted to this level, the short-run aggregate supply curve crosses this point as well.

Price level, P

Income, output, Y

AD

Y

SRAS

LRAS

Long-run equilibrium

FIGURE 10-11

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A Monetary Lesson From French History

Finding modern examples to illustrate the lessons from Figure 10-12 is hard. Mod- ern central banks are too smart to engineer a substantial reduction in the money supply for no good reason. They know that a recession would ensue, and they usu- ally do their best to prevent that from happening. Fortunately, history often fi lls in the gap when recent experience fails to produce the right experiment.

A vivid example of the effects of monetary contraction occurred in eighteenth-century France. In 2009, François Velde, an economist at the Federal Reserve Bank of Chicago, studied this episode in French economic history.

The story begins with the unusual nature of French money at the time. The money stock in this economy included a variety of gold and silver coins that, in contrast to modern money, did not indicate a specifi c monetary value. Instead, the monetary value of each coin was set by government decree, and the government could easily change the monetary value and thus the money supply. Sometimes this would occur literally overnight. It is almost as if, while you were sleeping, every $1 bill in your wallet was replaced by a bill worth only 80 cents.

Indeed, that is what happened on September 22, 1724. Every person in France woke up with 20 percent less money than he or she had the night before. Over the course of seven months, the nominal value of the money stock was reduced by about 45 percent. The goal of these changes was to reduce prices in the economy to what the government considered an appropriate level.

What happened as a result of this policy? Velde reports the following consequences:

Although prices and wages did fall, they did not do so by the full 45 percent; moreover, it took them months, if not years, to fall that far. Real wages in fact rose, at least initially. Interest rates rose. The only market that adjusted instanta- neously and fully was the foreign exchange market. Even markets that were as close to fully competitive as one can imagine, such as grain markets, failed to react initially. . . .

At the same time, the industrial sector of the economy (or at any rate the textile industry) went into a severe contraction, by about 30 percent. The onset of the recession may have occurred before the defl ationary policy began, but it was widely believed at the time that the severity of the contraction was due to monetary policy, in particular to a resulting “credit crunch” as holders of money stopped providing credit to trade in anticipation of further price declines (the “scarcity of money” frequently blamed by observers). Likewise, it was widely believed (on the basis of past experience) that a policy of infl ation would halt the recession, and coincidentally or not, the economy rebounded once the nominal money supply was increased by 20 percent in May 1726.

This description of events from French history fi ts well with the lessons from modern macroeconomic theory.4 ■

CASE STUDY

4François R. Velde, “Chronicles of a Defl ation Unforetold,” Journal of Political Economy 117 (August 2009): 591–634.

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10-5 Stabilization Policy

Fluctuations in the economy as a whole come from changes in aggregate sup- ply or aggregate demand. Economists call exogenous events that shift these curves shocks to the economy. A shock that shifts the aggregate demand curve is called a demand shock, and a shock that shifts the aggregate supply curve is called a supply shock. These shocks disrupt the economy by pushing out- put and employment away from their natural levels. One goal of the model of aggregate supply and aggregate demand is to show how shocks cause economic fl uctuations.

Another goal of the model is to evaluate how macroeconomic policy can respond to these shocks. Economists use the term stabilization policy to refer to policy actions aimed at reducing the severity of short-run economic fl uctuations. Because output and employment fl uctuate around their long-run natural levels, stabilization policy dampens the business cycle by keeping output and employment as close to their natural levels as possible.

As noted in Chapter 5, many of the central ideas of monetary theory have a long history. The clas- sical theory of money we discussed in that chap- ter dates back as far as the eighteenth-century philosopher and economist David Hume. While Hume understood that changes in the money supply ultimately led to infl ation, he also knew that money had real effects in the short run. Here is how Hume described a monetary injection in his 1752 essay Of Money:

To account, then, for this phenomenon, we must consider, that though the high price of commodities be a necessary consequence of the increase of gold and silver, yet it follows not immediately upon that increase; but some time is required before the money circulates through the whole state, and makes its effect be felt on all ranks of people. At fi rst, no alteration is perceived; by degrees the price rises, fi rst of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom. In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the increasing quantity of gold and silver is favorable to industry. When any quantity of money is imported into a nation, it is not at fi rst dispersed into many hands; but is confi ned to the coffers of a

David Hume on the Real Effects of Money few persons, who immediately seek to employ it to advantage. Here are a set of manufacturers or mer- chants, we shall suppose, who have received returns of gold and silver for goods which they sent to Cadiz. They are thereby enabled to employ more work- men than formerly, who never dream of demanding higher wages, but are glad of employment from such good paymasters. If workmen become scarce, the manufacturer gives higher wages, but at fi rst requires an increase of labor; and this is willingly submitted to by the artisan, who can now eat and drink better, to compensate his additional toil and fatigue. He carries his money to market, where he fi nds every- thing at the same price as formerly, but returns with greater quantity and of better kinds, for the use of his family. The farmer and gardener, fi nding that all their commodities are taken off, apply themselves with alacrity to the raising more; and at the same time can afford to take better and more cloths from their tradesmen, whose price is the same as formerly, and their industry only whetted by so much new gain. It is easy to trace the money in its progress through the whole commonwealth; where we shall fi nd, that it must fi rst quicken the diligence of every individual, before it increases the price of labor.

It is likely that when writing these words, Hume was well aware of the French experience described in the preceding Case Study.

F Y I

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In the coming chapters, we examine in detail how stabilization policy works and what practical problems arise in its use. Here we begin our analysis of stabili- zation policy using our simplifi ed version of the model of aggregate demand and aggregate supply. In particular, we examine how monetary policy might respond to shocks. Monetary policy is an important component of stabilization policy because, as we have seen, the money supply has a powerful impact on aggregate demand.

Shocks to Aggregate Demand

Consider an example of a demand shock: the introduction and expanded avail- ability of credit cards. Because credit cards are often a more convenient way to make purchases than using cash, they reduce the quantity of money that people choose to hold. This reduction in money demand is equivalent to an increase in the velocity of money. When each person holds less money, the money demand parameter k falls. This means that each dollar of money moves from hand to hand more quickly, so velocity V (= 1/k) rises.

If the money supply is held constant, the increase in velocity causes nomi- nal spending to rise and the aggregate demand curve to shift outward, as in Figure 10-13. In the short run, the increase in demand raises the output of the economy—it causes an economic boom. At the old prices, fi rms now sell more output. Therefore, they hire more workers, ask their existing workers to work lon- ger hours, and make greater use of their factories and equipment.

Over time, the high level of aggregate demand pulls up wages and prices. As the price level rises, the quantity of output demanded declines, and the economy gradually approaches the natural level of production. But during the transition to the higher price level, the economy’s output is higher than its natural level.

An Increase in Aggregate Demand The economy begins in long-run equilibrium at point A. An increase in aggregate demand, perhaps due to an increase in the velocity of money, moves the economy from point A to point B, where output is above its natural level. As prices rise, output gradually returns to its natural level, and the economy moves from point B to point C.

Price level, P

Income, output, YY

AD2

AD1

SRAS

LRAS

A

C

B

2. ... raises output in the short run ...

1. A rise in aggregate demand ...

3. ... but in the long run affects only the price level.

FIGURE 10-13

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What can the Fed do to dampen this boom and keep output closer to the natural level? The Fed might reduce the money supply to offset the increase in velocity. Offsetting the change in velocity would stabilize aggregate demand. Thus, the Fed can reduce or even eliminate the impact of demand shocks on output and employment if it can skillfully control the money supply. Whether the Fed in fact has the necessary skill is a more diffi cult question, which we take up in Chapter 18.

Shocks to Aggregate Supply

Shocks to aggregate supply can also cause economic fl uctuations. A supply shock is a shock to the economy that alters the cost of producing goods and services and, as a result, the prices that fi rms charge. Because supply shocks have a direct impact on the price level, they are sometimes called price shocks. Here are some examples:

■ A drought that destroys crops. The reduction in food supply pushes up food prices.

■ A new environmental protection law that requires fi rms to reduce their emissions of pollutants. Firms pass on the added costs to customers in the form of higher prices.

■ An increase in union aggressiveness. This pushes up wages and the prices of the goods produced by union workers.

■ The organization of an international oil cartel. By curtailing competition, the major oil producers can raise the world price of oil.

All these events are adverse supply shocks, which means they push costs and prices upward. A favorable supply shock, such as the breakup of an international oil cartel, reduces costs and prices.

Figure 10-14 shows how an adverse supply shock affects the economy. The short-run aggregate supply curve shifts upward. (The supply shock may also lower the natural level of output and thus shift the long-run aggregate supply curve to the left, but we ignore that effect here.) If aggregate demand is held constant, the economy moves from point A to point B: the price level rises and the amount of output falls below its natural level. An experience like this is called stagfl ation because it combines economic stagnation (falling output and, from Okun’s law, rising unemployment) with infl ation (rising prices).

Faced with an adverse supply shock, a policymaker with the ability to infl uence aggregate demand, such as the Fed, has a diffi cult choice between two options. The fi rst option, implicit in Figure 10-14, is to hold aggregate demand constant. In this case, output and employment are lower than the natural level. Eventually, prices will fall to restore full employment at the old price level (point A), but the cost of this adjustment process is a painful recession.

The second option, illustrated in Figure 10-15, is to expand aggregate demand to bring the economy toward the natural level of output more quickly. If the

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increase in aggregate demand coincides with the shock to aggregate supply, the economy goes immediately from point A to point C. In this case, the Fed is said to accommodate the supply shock. The drawback of this option, of course, is that the price level is permanently higher. There is no way to adjust aggregate demand to maintain full employment and keep the price level stable.

An Adverse Supply Shock An adverse supply shock pushes up costs and thus prices. If aggregate demand is held constant, the econ- omy moves from point A to point B, leading to stagfl ation—a combina- tion of increasing prices and falling output. Eventually, as prices fall, the economy returns to the natural level of output, point A.

Price level, P

Income, output, YY

AD

SRAS1

LRAS

A

B SRAS2

3. ... and output to fall.

1. An adverse supply shock shifts the short- run aggregate supply curve upward, ...

2. ... which causes the price level to rise ...

FIGURE 10-14

Accommodating an Adverse Supply Shock In response to an adverse supply shock, the Fed can increase aggregate demand to prevent a reduction in output. The economy moves from point A to point C. The cost of this policy is a perma- nently higher level of prices.

Price level, P

Income, output, YY

AD1

AD2

SRAS1

LRAS

A

C SRAS2

3. ... resulting in a permanently higher price level ...

2. ... but the Fed accommodates the shock by raising aggregate demand, ...

4. ... but no change in output.

1. An adverse supply shock shifts the short- run aggregate supply curve upward, ...

FIGURE 10-15

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The increases in oil prices in 1979, 1980, and 1981 again led to double-digit infl ation and higher unemployment.

Change in Infl ation Unemployment Year Oil Prices Rate (CPI) Rate

1973 11.0% 6.2% 4.9% 1974 68.0 11.0 5.6 1975 16.0 9.1 8.5 1976 3.3 5.8 7.7 1977 8.1 6.5 7.1

Change in Infl ation Unemployment Year Oil Prices Rate (CPI) Rate

1978 9.4% 7.7% 6.1% 1979 25.4 11.3 5.8 1980 47.8 13.5 7.0 1981 44.4 10.3 7.5 1982 –8.7 6.1 9.5

How OPEC Helped Cause Stagflation in the 1970s and Euphoria in the 1980s

The most disruptive supply shocks in recent history were caused by OPEC, the Organization of Petroleum Exporting Countries. OPEC is a cartel, which is an organization of suppliers that coordinate production levels and prices. In the early 1970s, OPEC’s reduction in the supply of oil nearly doubled the world price. This increase in oil prices caused stagfl ation in most industrial countries. These statistics show what happened in the United States:

CASE STUDY

The 68 percent increase in the price of oil in 1974 was an adverse supply shock of major proportions. As one would have expected, this shock led to both higher infl ation and higher unemployment.

A few years later, when the world economy had nearly recovered from the fi rst OPEC recession, almost the same thing happened again. OPEC raised oil prices, causing further stagfl ation. Here are the statistics for the United States:

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C H A P T E R 1 0 Introduction to Economic Fluctuations | 299

In 1986 oil prices fell by nearly half. This favorable supply shock led to one of the lowest infl ation rates experienced during that era and to falling unemployment.

More recently, OPEC has not been a major cause of economic fl uctuations. Conservation efforts and technological changes have made the U.S. economy less susceptible to oil shocks. The economy today is more service-based and less manufacturing-based, and services typically require less energy to produce than do manufactured goods. Because the amount of oil consumed per unit of real GDP has fallen by more than half over the previous three decades, it takes a much larger oil-price change to have the impact on the economy that we observed in the 1970s and 1980s. Thus, when oil prices fl uctuate substantially, as they have in recent years, these price changes have a smaller macroeconomic impact than they would have had in the past.5 ■

10-6 Conclusion

This chapter introduced a framework to study economic fl uctuations: the model of aggregate supply and aggregate demand. The model is built on the assump- tion that prices are sticky in the short run and fl exible in the long run. It shows how shocks to the economy cause output to deviate temporarily from the level implied by the classical model.

The model also highlights the role of monetary policy. On the one hand, poor monetary policy can be a source of destabilizing shocks to the economy. On the other hand, a well-run monetary policy can respond to shocks and stabilize the economy.

Changes in Infl ation Unemployment Year Oil Prices Rate (CPI) Rate

1983 −7.1% 3.2% 9.5% 1984 −1.7 4.3 7.4 1985 −7.5 3.6 7.1 1986 −44.5 1.9 6.9 1987 18.3 3.6 6.1

In the mid-1980s, political turmoil among the Arab countries weakened OPEC’s ability to restrain supplies of oil. Oil prices fell, reversing the stagfl ation of the 1970s and the early 1980s. Here’s what happened:

5Some economists have suggested that changes in oil prices played a major role in economic fl uctuations even before the 1970s. See James D. Hamilton, “Oil and the Macroeconomy Since World War II,’’ Journal of Political Economy 91 (April 1983): 228–248.

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300 | P A R T I V Business Cycle Theory: The Economy in the Short Run

In the chapters that follow, we refi ne our understanding of this model and our analysis of stabilization policy. Chapters 11 through 13 go beyond the quantity equation to refi ne our theory of aggregate demand. Chapter 14 examines aggre- gate supply in more detail. The remainder of the book then uses this model as the platform from which to dive into more advanced topics in macroeconomic theory and policy.

Summary

1. Economies experience short-run fl uctuations in economic activity, mea- sured most broadly by real GDP. These fl uctuations are associated with movement in many macroeconomic variables. In particular, when GDP growth declines, consumption growth falls (typically by a smaller amount), investment growth falls (typically by a larger amount), and unemployment rises. Although economists look at various leading indicators to forecast movements in the economy, these short-run fl uctuations are largely unpredictable.

2. The crucial difference between how the economy works in the long run and how it works in the short run is that prices are fl exible in the long run but sticky in the short run. The model of aggregate supply and aggregate demand provides a framework to analyze economic fl uctuations and see how the impact of policies and events varies over different time horizons.

3. The aggregate demand curve slopes downward. It tells us that the lower the price level, the greater the aggregate quantity of goods and services demanded.

4. In the long run, the aggregate supply curve is vertical because output is determined by the amounts of capital and labor and by the available tech- nology but not by the level of prices. Therefore, shifts in aggregate demand affect the price level but not output or employment.

5. In the short run, the aggregate supply curve is horizontal, because wages and prices are sticky at predetermined levels. Therefore, shifts in aggregate demand affect output and employment.

6. Shocks to aggregate demand and aggregate supply cause economic fl uctua- tions. Because the Fed can shift the aggregate demand curve, it can attempt to offset these shocks to maintain output and employment at their natural levels.

K E Y C O N C E P T S

Okun’s law

Leading indicators

Aggregate demand

Aggregate supply

Shocks

Demand shocks

Supply shocks

Stabilization policy

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C H A P T E R 1 0 Introduction to Economic Fluctuations | 301

1. When real GDP declines during a recession, what typically happens to consumption, invest- ment, and the unemployment rate?

2. Give an example of a price that is sticky in the short run but fl exible in the long run.

3. Why does the aggregate demand curve slope downward?

Q U E S T I O N S F O R R E V I E W

4. Explain the impact of an increase in the money supply in the short run and in the long run.

5. Why is it easier for the Fed to deal with demand shocks than with supply shocks?

1. An economy begins in long-run equilibrium, and then a change in government regulations allows banks to start paying interest on check- ing accounts. Recall that the money stock is the sum of currency and demand deposits, includ- ing checking accounts, so this regulatory change makes holding money more attractive.

a. How does this change affect the demand for money?

b. What happens to the velocity of money?

c. If the Fed keeps the money supply constant, what will happen to output and prices in the short run and in the long run?

d. If the goal of the Fed is to stabilize the price level, should the Fed keep the money sup- ply constant in response to this regulatory change? If not, what should it do? Why?

e. If the goal of the Fed is to stabilize output, how would your answer to part (d) change?

2. Suppose the Fed reduces the money supply by 5 percent. Assume the velocity of money is constant.

a. What happens to the aggregate demand curve?

b. What happens to the level of output and the price level in the short run and in the long run?

P R O B L E M S A N D A P P L I C A T I O N S

c. In light of your answer to part (b), what hap- pens to unemployment in the short run and in the long run according to Okun’s law?

d. What happens to the real interest rate in the short run and in the long run? (Hint: Use the model of the real interest rate in Chapter 3 to see what happens when output changes.)

3. Let’s examine how the goals of the Fed infl u- ence its response to shocks. Suppose that in scenario A the Fed cares only about keeping the price level stable and in scenario B the Fed cares only about keeping output and employment at their natural levels. Explain how in each scenario the Fed would respond to the following.

a. An exogenous decrease in the velocity of money.

b. An exogenous increase in the price of oil.

4. The offi cial arbiter of when recessions begin and end is the National Bureau of Economic Research, a nonprofi t economics research group. Go to the NBER’s Web site (www.nber.org) and fi nd the latest turning point in the busi- ness cycle. When did it occur? Was this a switch from expansion to contraction or the other way around? List all the recessions (contractions) that have occurred during your lifetime and the dates when they began and ended.

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303

Aggregate Demand I: Building the IS–LM Model

11C H A P T E R

I shall argue that the postulates of the classical theory are applicable to a

special case only and not to the general case. . . . Moreover, the characteristics

of the special case assumed by the classical theory happen not to be those of

the economic society in which we actually live, with the result that its teaching

is misleading and disastrous if we attempt to apply it to the facts of experience.

—John Maynard Keynes, The General Theory

Of all the economic fl uctuations in world history, the one that stands out as particularly large, painful, and intellectually signifi cant is the Great Depression of the 1930s. During this time, the United States and many other countries experienced massive unemployment and greatly reduced incomes. In the worst year, 1933, one-fourth of the U.S. labor force was unem- ployed, and real GDP was 30 percent below its 1929 level.

This devastating episode caused many economists to question the validity of classical economic theory—the theory we examined in Chapters 3 through 7. Classical theory seemed incapable of explaining the Depression. According to that theory, national income depends on factor supplies and the available technology, neither of which changed substantially from 1929 to 1933. After the onset of the Depression, many economists believed that a new model was needed to explain such a large and sudden economic downturn and to suggest government policies that might reduce the economic hardship so many people faced.

In 1936 the British economist John Maynard Keynes revolutionized econom- ics with his book The General Theory of Employment, Interest, and Money. Keynes proposed a new way to analyze the economy, which he presented as an alterna- tive to classical theory. His vision of how the economy works quickly became a center of controversy. Yet, as economists debated The General Theory, a new understanding of economic fl uctuations gradually developed.

Keynes proposed that low aggregate demand is responsible for the low income and high unemployment that characterize economic downturns. He criticized classical theory for assuming that aggregate supply alone—capital, labor, and technology—determines national income. Economists today reconcile these two views with the model of aggregate demand and aggregate supply introduced in

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Chapter 10. In the long run, prices are fl exible, and aggregate supply determines income. But in the short run, prices are sticky, so changes in aggregate demand infl uence income.

Keynes’s ideas about short-run fl uctuations have been prominent since he pro- posed them in the 1930s, but they have commanded renewed attention in recent years. In the aftermath of the fi nancial crisis of 2008–2009, the United States and Europe descended into a deep recession, followed by a weak recovery. As unemploy- ment lingered at high levels, policymakers around the world debated how best to increase aggregate demand. Many of the issues that gripped economists during the Great Depression were once again at the center of the economic policy debate.

In this chapter and the next, we continue our study of economic fl uctua- tions by looking more closely at aggregate demand. Our goal is to identify the variables that shift the aggregate demand curve, causing fl uctuations in national income. We also examine more fully the tools policymakers can use to infl uence aggregate demand. In Chapter 10 we derived the aggregate demand curve from the quantity theory of money, and we showed that monetary policy can shift the aggregate demand curve. In this chapter we see that the government can infl u- ence aggregate demand with both monetary and fi scal policy.

The model of aggregate demand developed in this chapter, called the IS–LM model, is the leading interpretation of Keynes’s theory. The goal of the model is to show what determines national income for a given price level. There are two ways to interpret this exercise. We can view the IS–LM model as showing what causes income to change in the short run when the price level is fi xed because all prices are sticky. Or we can view the model as showing what causes the aggregate demand curve to shift. These two interpretations of the model are equivalent: as Figure 11-1 shows, in the short run when the price level is fi xed,

Shifts in Aggregate Demand For a given price level, national income fl uctuates because of shifts in the aggregate demand curve. The IS–LM model takes the price level as given and shows what causes income to change. The model therefore shows what causes aggregate demand to shift.

Price level, P

Income, output, YY1 Y2 Y3

AD1 AD2 AD3

Fixed price level (SRAS)

FIGURE 11-1

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shifts in the aggregate demand curve lead to changes in the equilibrium level of national income.

The two parts of the IS–LM model are, not surprisingly, the IS curve and the LM curve. IS stands for “investment’’ and “saving,’’ and the IS curve represents what’s going on in the market for goods and services (which we fi rst discussed in Chapter 3). LM stands for “liquidity’’ and “money,’’ and the LM curve represents what’s happening to the supply and demand for money (which we fi rst discussed in Chapter 5). Because the interest rate infl uences both investment and money demand, it is the variable that links the two halves of the IS–LM model. The model shows how interactions between the goods and money markets determine the position and slope of the aggregate demand curve and, therefore, the level of national income in the short run.1

11-1 The Goods Market and the IS Curve

The IS curve plots the relationship between the interest rate and the level of income that arises in the market for goods and services. To develop this relation- ship, we start with a basic model called the Keynesian cross. This model is the simplest interpretation of Keynes’s theory of how national income is determined and is a building block for the more complex and realistic IS–LM model.

The Keynesian Cross

In The General Theory Keynes proposed that an economy’s total income is, in the short run, determined largely by the spending plans of households, businesses, and government. The more people want to spend, the more goods and services fi rms can sell. The more fi rms can sell, the more output they will choose to produce and the more workers they will choose to hire. Keynes believed that the problem during recessions and depressions is inadequate spending. The Keynesian cross is an attempt to model this insight.

Planned Expenditure We begin our derivation of the Keynesian cross by drawing a distinction between actual and planned expenditure. Actual expenditure is the amount households, fi rms, and the government spend on goods and ser- vices, and as we fi rst saw in Chapter 2, it equals the economy’s gross domestic product (GDP). Planned expenditure is the amount households, fi rms, and the government would like to spend on goods and services.

Why would actual expenditure ever differ from planned expenditure? The answer is that fi rms might engage in unplanned inventory investment because their sales do not meet their expectations. When fi rms sell less of their product than they planned, their stock of inventories automatically rises; conversely,

1The IS–LM model was introduced in a classic article by the Nobel Prize–winning economist John R. Hicks, “Mr. Keynes and the Classics: A Suggested Interpretation,’’ Econometrica 5 (1937): 147–159.

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306 | P A R T I V Business Cycle Theory: The Economy in the Short Run

when fi rms sell more than planned, their stock of inventories falls. Because these unplanned changes in inventory are counted as investment spending by fi rms, actual expenditure can be either above or below planned expenditure.

Now consider the determinants of planned expenditure. Assuming that the economy is closed, so that net exports are zero, we write planned expendi- ture PE as the sum of consumption C, planned investment I, and government purchases G:

PE = C + I + G.

To this equation, we add the consumption function:

C = C(Y − T ).

This equation states that consumption depends on disposable income (Y − T ), which is total income Y minus taxes T. To keep things simple, for now we take planned investment as exogenously fi xed:

I = I−.

Finally, as in Chapter 3, we assume that fi scal policy—the levels of government purchases and taxes—is fi xed:

G = G−. T = T−.

Combining these fi ve equations, we obtain

PE = C(Y − T− ) + I− + G−.

This equation shows that planned expenditure is a function of income Y, the level of planned investment I−, and the fi scal policy variables G− and T−.

Figure 11-2 graphs planned expenditure as a function of the level of income. This line slopes upward because higher income leads to higher consumption and

Planned Expenditure as a Function of Income Planned expenditure PE depends on income because higher income leads to higher consumption, which is part of planned expenditure. The slope of the planned-expenditure function is the marginal propensity to consume, MPC.

Planned expenditure, PE

Income, output, Y

Planned expenditure, PE � C(Y � T) � I � G

$1

MPC

FIGURE 11-2

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thus higher planned expenditure. The slope of this line is the marginal propen- sity to consume, MPC: it shows how much planned expenditure increases when income rises by $1. This planned-expenditure function is the fi rst piece of the Keynesian cross.

The Economy in Equilibrium The next piece of the Keynesian cross is the assumption that the economy is in equilibrium when actual expenditure equals planned expenditure. This assumption is based on the idea that when people’s plans have been realized, they have no reason to change what they are doing. Recalling that Y as GDP equals not only total income but also total actual expenditure on goods and services, we can write this equilibrium condition as

Actual Expenditure = Planned Expenditure Y = PE.

The 45-degree line in Figure 11-3 plots the points where this condition holds. With the addition of the planned-expenditure function, this diagram becomes the Keynesian cross. The equilibrium of this economy is at point A, where the planned-expenditure function crosses the 45-degree line.

How does the economy get to equilibrium? In this model, inventories play an important role in the adjustment process. Whenever an economy is not in equilibrium, fi rms experience unplanned changes in inventories, and this induces them to change production levels. Changes in production in turn infl uence total income and expenditure, moving the economy toward equilibrium.

The Keynesian Cross The equilibrium in the Keynesian cross is the point at which income (actual expenditure) equals planned expenditure (point A).

Expenditure (Planned, PE Actual, Y)

Income, output, Y

Actual expenditure, Y � PE

Planned expenditure, PE � C � I � GA

45º

Equilibrium income

FIGURE 11-3

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308 | P A R T I V Business Cycle Theory: The Economy in the Short Run

For example, suppose the economy fi nds itself with GDP at a level greater than the equilibrium level, such as the level Y1 in Figure 11-4. In this case, planned expenditure PE1 is less than production Y1, so fi rms are selling less than they are producing. Firms add the unsold goods to their stock of inventories. This unplanned rise in inventories induces fi rms to lay off workers and reduce production; these actions in turn reduce GDP. This process of unintended inven- tory accumulation and falling income continues until income Y falls to the equilibrium level.

Similarly, suppose GDP is at a level lower than the equilibrium level, such as the level Y2 in Figure 11-4. In this case, planned expenditure PE2 is greater than pro- duction Y2. Firms meet the high level of sales by drawing down their inventories. But when fi rms see their stock of inventories dwindle, they hire more workers and increase production. GDP rises, and the economy approaches equilibrium.

In summary, the Keynesian cross shows how income Y is determined for given levels of planned investment I and fi scal policy G and T. We can use this model to show how income changes when one of these exogenous variables changes.

Fiscal Policy and the Multiplier: Government Purchases Consider how changes in government purchases affect the economy. Because government purchases are one component of expenditure, higher government purchases result in higher planned expenditure for any given level of income. If government pur- chases rise by �G, then the planned-expenditure schedule shifts upward by �G, as in Figure 11-5. The equilibrium of the economy moves from point A to point B.

This graph shows that an increase in government purchases leads to an even greater increase in income. That is, �Y is larger than �G. The ratio �Y/�G is called the government-purchases multiplier; it tells us how much income

The Adjustment to Equilibrium in the Keynesian Cross If fi rms are producing at level Y1, then planned expenditure PE1 falls short of pro- duction, and fi rms accumulate inventories. This inventory accu- mulation induces fi rms to decrease production. Similarly, if fi rms are producing at level Y2, then planned expenditure PE2 exceeds production, and fi rms run down their invento- ries. This fall in inventories induces fi rms to increase production. In both cases, the fi rms’ decisions drive the economy toward equilibrium.

Expenditure (Planned, PE, Actual, Y)

Income, output, Y

Y1

PE1

PE2

Y2

Y2 Y1

Actual expenditure

Planned expenditure

Equilibrium income

Unplanned drop in inventory causes income to rise.

Unplanned inventory accumulation causes income to fall.

45º

FIGURE 11-4

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rises in response to a $1 increase in government purchases. An implication of the Keynesian cross is that the government-purchases multiplier is larger than 1.

Why does fi scal policy have a multiplied effect on income? The reason is that, according to the consumption function C = C(Y − T ), higher income causes higher consumption. When an increase in government purchases raises income, it also raises consumption, which further raises income, which further raises consumption, and so on. Therefore, in this model, an increase in government purchases causes a greater increase in income.

How big is the multiplier? To answer this question, we trace through each step of the change in income. The process begins when expenditure rises by �G, which implies that income rises by �G as well. This increase in income in turn raises consumption by MPC × �G, where MPC is the marginal propensity to consume. This increase in consumption raises expenditure and income once again. This second increase in income of MPC × �G again raises consumption, this time by MPC × (MPC × �G), which again raises expenditure and income, and so on. This feedback from consumption to income to consumption contin- ues indefi nitely. The total effect on income is

Initial Change in Government Purchases = �G First Change in Consumption = MPC × �G Second Change in Consumption = MPC2 × �G Third Change in Consumption = MPC3 × �G . . . . . .

�Y = (1 + MPC + MPC2 + MPC3 + . . .)�G.

An Increase in Government Purchases in the Keynesian Cross An increase in government purchases of �G raises planned expenditure by that amount for any given level of income. The equilibri- um moves from point A to point B, and income rises from Y1 to Y2. Note that the increase in income �Y exceeds the increase in government purchases �G. Thus, fi scal policy has a multiplied effect on income.

Expenditure

Income, output, Y

2. ...which increases equilibrium income.

�G

�Y

�Y

Actual expenditure Planned expenditure

PE2 � Y2

PE1 � Y1 PE2 � Y2

PE1 � Y1

B

A

45º

1. An increase in government purchases shifts planned expenditure upward, ...

FIGURE 11-5

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310 | P A R T I V Business Cycle Theory: The Economy in the Short Run

The government-purchases multiplier is

�Y/�G = 1 + MPC + MPC2 + MPC3 + . . .

This expression for the multiplier is an example of an infi nite geometric series. A result from algebra allows us to write the multiplier as2

�Y/�G = 1/(1 − MPC ).

For example, if the marginal propensity to consume is 0.6, the multiplier is

�Y/�G = 1 + 0.6 + 0.62 + 0.63 + . . .

= 1/(1 − 0.6) = 2.5.

In this case, a $1.00 increase in government purchases raises equilibrium income by $2.50.3

Fiscal Policy and the Multiplier: Taxes Now consider how changes in taxes affect equilibrium income. A decrease in taxes of �T immediately raises disposable income Y − T by �T and, therefore, increases consumption by MPC × �T. For any given level of income Y, planned expenditure is now higher. As Figure 11-6 shows, the planned-expenditure schedule shifts upward by MPC × �T. The equilibrium of the economy moves from point A to point B.

2Mathematical note: We prove this algebraic result as follows. For |x| � 1, let

z = 1 + x + x2 + . . . .

Multiply both sides of this equation by x:

xz = x + x2 + x3 + . . . .

Subtract the second equation from the fi rst:

z − xz = 1.

Rearrange this last equation to obtain

z(1 − x) = 1,

which implies

z = 1/(1 − x).

This completes the proof. 3Mathematical note: The government-purchases multiplier is most easily derived using a little calculus. Begin with the equation

Y = C(Y − T ) + I + G.

Holding T and I fi xed, differentiate to obtain

dY = C ′dY + dG,

and then rearrange to fi nd

dY/dG = 1/(1 − C ′).

This is the same as the equation in the text.

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Just as an increase in government purchases has a multiplied effect on income, so does a decrease in taxes. As before, the initial change in expenditure, now MPC × �T, is multiplied by 1/(1 − MPC). The overall effect on income of the change in taxes is

�Y/�T = −MPC/(1 − MPC ).

This expression is the tax multiplier, the amount income changes in response to a $1 change in taxes. (The negative sign indicates that income moves in the opposite direction from taxes.) For example, if the marginal propensity to con- sume is 0.6, then the tax multiplier is

�Y/�T = −0.6/(1 − 0.6) = −1.5.

In this example, a $1.00 cut in taxes raises equilibrium income by $1.50.4

A Decrease in Taxes in the Keynesian Cross A decrease in taxes of �T raises planned expenditure by MPC × �T for any given level of income. The equilibrium moves from point A to point B, and income rises from Y1 to Y2. Again, fi scal policy has a multiplied effect on income.

Expenditure

Income, output, Y

2. ...which increases equilibrium income.

�Y

�Y

PE2 � Y2

PE1 � Y1 PE2 � Y2

PE1 � Y1

MPC � �T

B

A

45º

1. A tax cut shifts planned expenditure upward, ...

Actual expenditure Planned

expenditure

FIGURE 11-6

4Mathematical note: As before, the multiplier is most easily derived using a little calculus. Begin with the equation

Y = C(Y − T ) + I + G.

Holding I and G fi xed, differentiate to obtain

dY = C′(dY − dT ),

and then rearrange to fi nd

dY/dT = −C′/(1 − C′).

This is the same as the equation in the text.

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Cutting Taxes to Stimulate the Economy: The Kennedy and Bush Tax Cuts

When John F. Kennedy became president of the United States in 1961, he brought to Washington some of the brightest young economists of the day to work on his Council of Economic Advisers. These economists, who had been schooled in the economics of Keynes, brought Keynesian ideas to discussions of economic policy at the highest level.

One of the council’s fi rst proposals was to expand national income by reducing taxes. This eventually led to a substantial cut in personal and corporate income taxes in 1964. The tax cut was intended to stimulate expenditure on consumption and investment and thus lead to higher levels of income and employment. When a reporter asked Kennedy why he advocated a tax cut, Kennedy replied, “To stimu- late the economy. Don’t you remember your Economics 101?”

As Kennedy’s economic advisers predicted, the passage of the tax cut was fol- lowed by an economic boom. Growth in real GDP was 5.3 percent in 1964 and 6.0 percent in 1965. The unemployment rate fell from 5.7 percent in 1963 to 5.2 percent in 1964 and then to 4.5 percent in 1965.

Economists continue to debate the source of this rapid growth in the early 1960s. A group called supply-siders argue that the economic boom resulted from the incen- tive effects of the cut in income tax rates. According to supply-siders, when workers are allowed to keep a higher fraction of their earnings, they supply substantially more labor and expand the aggregate supply of goods and services. Keynesians, however, emphasize the impact of tax cuts on aggregate demand. Most likely, there is some truth to both views: Tax cuts stimulate aggregate supply by improving workers’ incentives and expand aggregate demand by raising households’ disposable income.

When George W. Bush was elected president in 2000, a major element of his platform was a cut in income taxes. Bush and his advisers used both supply-side and Keynesian rhetoric to make the case for their policy. (Full disclosure: The author of this textbook was one of Bush’s economic advisers from 2003 to 2005.) During the campaign, when the economy was doing fi ne, they argued that lower marginal tax rates would improve work incentives. But when the economy started to slow, and unemployment started to rise, the argument shifted to emphasize that the tax cut would stimulate spending and help the economy recover from the recession.

Congress passed major tax cuts in 2001 and 2003. After the second tax cut, the weak recovery from the 2001 recession turned into a robust one. Growth in real GDP was 4.4 percent in 2004. The unemployment rate fell from its peak of 6.3 percent in June 2003 to 5.4 percent in December 2004.

When President Bush signed the 2003 tax bill, he explained the measure using the logic of aggregate demand: “When people have more money, they can spend it on goods and services. And in our society, when they demand an additional good or a service, somebody will produce the good or a service. And when somebody produces that good or a service, it means somebody is more likely to be able to fi nd a job.” The explanation could have come from an exam in Economics 101. ■

CASE STUDY

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Increasing Government Purchases to Stimulate the Economy: The Obama Spending Plan

When President Barack Obama took offi ce in January 2009, the economy was suffering from a signifi cant recession. (The causes of this recession are discussed in a Case Study in the next chapter and in more detail in Chapter 20.) Even before he was inaugurated, the president and his advisers proposed a sizable stim- ulus package to increase aggregate demand. As proposed, the package would cost the federal government about $800 billion, or about 5 percent of annual GDP. The package included some tax cuts and higher transfer payments, but much of it was made up of increases in government purchases of goods and services.

Professional economists debated the merits of the plan. Advocates of the Obama plan argued that increased spending was better than reduced taxes because, according to standard Keynesian theory, the government- purchases multiplier exceeds the tax multiplier. The reason for this difference is simple: when the government spends a dollar, that dollar gets spent, whereas when the government gives households a tax cut of a dollar, some of that dollar might be saved. According to an analysis by Obama administration economists, the government purchases multiplier is 1.57, whereas the tax multiplier is only 0.99. Thus, they argued that increased government spending on roads, schools, and other infrastructure was the better route to increase aggregate demand and create jobs. The logic here is quintessentially Keynesian: as the economy sinks into recession, the government is acting as the demander of last resort.

The Obama stimulus proposal was controversial among economists for vari- ous reasons. One criticism was that the stimulus was not large enough given the apparent depth of the economic downturn. In March 2008, economist Paul Krugman wrote in the New York Times:

The plan was too small and too cautious. . . . Employment has already fallen more in this recession than in the 1981–82 slump, considered the worst since the Great Depression. As a result, Mr. Obama’s promise that his plan will create or save 3.5 million jobs by the end of 2010 looks underwhelming, to say the least. It’s a credible promise—his economists used solidly mainstream estimates of the impacts of tax and spending policies. But 3.5 million jobs almost two years from now isn’t enough in the face of an economy that has already lost 4.4 million jobs, and is losing 600,000 more each month.

Still other economists argued that despite the predictions of conventional Keynesian models, spending-based fi scal stimulus is not as effective as tax-based

CASE STUDY

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314 | P A R T I V Business Cycle Theory: The Economy in the Short Run

initiatives. A recent study of fi scal policy since 1970 in countries that are mem- bers of the Organization for Economic Cooperation and Development (OECD) examined which kinds of fi scal stimulus have historically been most successful at promoting growth in economic activity. It found that successful fi scal stimulus relies almost entirely on cuts in business and income taxes, whereas failed fi scal stimulus relies primarily on increases in government spending.5

In addition, some economists thought that using infrastructure spending to promote employment might confl ict with the goal of obtaining the infrastruc- ture that was most needed. Here is how economist Gary Becker explained the concern on his blog:

Putting new infrastructure spending in depressed areas like Detroit might have a big stimulating effect since infrastructure building projects in these areas can utilize some of the considerable unemployed resources there. However, many of these areas are also declining because they have been producing goods and services that are not in great demand, and will not be in demand in the future. Therefore, the overall value added by improving their roads and other infrastructure is likely to be a lot less than if the new infrastructure were located in growing areas that might have relatively little unemployment, but do have great demand for more roads, schools, and other types of long-term infrastructure.

In the end, Congress went ahead with President Obama’s proposed stimulus plans with relatively minor modifi cations. The president signed the $787 billion bill on February 17, 2009. Did it work? The economy did recover from the recession, but much more slowly than the Obama administration economists initially forecast. Whether the slow recovery refl ects the failure of stimulus policy or a sicker economy than the economists fi rst appreciated is a question of continuing debate. ■

The Interest Rate, Investment, and the IS Curve

The Keynesian cross is only a stepping-stone on our path to the IS–LM model, which explains the economy’s aggregate demand curve. The Keynesian cross is use- ful because it shows how the spending plans of households, fi rms, and the govern- ment determine the economy’s income. Yet it makes the simplifying assumption that the level of planned investment I is fi xed. As we discussed in Chapter 3, an important macroeconomic relationship is that planned investment depends on the interest rate r.

To add this relationship between the interest rate and investment to our model, we write the level of planned investment as

I = I(r).

This investment function is graphed in panel (a) of Figure 11-7. Because the interest rate is the cost of borrowing to fi nance investment projects, an increase in the interest rate reduces planned investment. As a result, the investment function slopes downward.

To determine how income changes when the interest rate changes, we can combine the investment function with the Keynesian-cross diagram. Because

5Alberto Alesina and Silvia Ardagna, “Large Changes in Fiscal Policy: Taxes Versus Spending,” Tax Policy and the Economy 24 (2010): 35-68.

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investment is inversely related to the interest rate, an increase in the interest rate from r1 to r2 reduces the quantity of investment from I(r1) to I(r2). The reduction in planned investment, in turn, shifts the planned-expenditure function down- ward, as in panel (b) of Figure 11-7. The shift in the planned-expenditure func- tion causes the level of income to fall from Y1 to Y2. Hence, an increase in the interest rate lowers income.

The IS curve, shown in panel (c) of Figure 11-7, summarizes this relation- ship between the interest rate and the level of income. In essence, the IS curve combines the interaction between r and I expressed by the investment function and the interaction between I and Y demonstrated by the Keynesian cross. Each point on the IS curve represents equilibrium in the goods market, and the curve illustrates how the equilibrium level of income depends on the interest rate. Because an increase in the interest rate causes planned investment to fall, which in turn causes equilibrium income to fall, the IS curve slopes downward.

Expenditure

Interest rate, r

Interest rate, r

Income, output, Y

Investment, I Income, output, Y

IS

Y1 Y2

r2

r1

�I

I(r1)

I(r)

I(r2)

Actual expenditure

Planned expenditure �I

45º

r2

r1

(a) The Investment Function

(b) The Keynesian Cross

(c) The IS Curve

Y1 Y2

3. ...which shifts planned expenditure downward ...

5. The IS curve summarizes these changes in the goods market equilibrium.

4. ...and lowers income.

2. ... lowers planned investment, ...

1. An increase in the interest rate ...

FIGURE 11-7

Deriving the IS Curve Panel (a) shows the investment function: an increase in the interest rate from r1 to r2 reduces planned investment from I(r1) to I(r2). Panel (b) shows the Keynesian cross: a decrease in planned investment from I(r1) to I(r2) shifts the planned-expenditure function down- ward and thereby reduces income from Y1 to Y2. Panel (c) shows the IS curve summa- rizing this relationship between the interest rate and income: the higher the interest rate, the lower the level of income.

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How Fiscal Policy Shifts the IS Curve

The IS curve shows us, for any given interest rate, the level of income that brings the goods market into equilibrium. As we learned from the Keynesian cross, the equilibrium level of income also depends on government spending G and taxes T. The IS curve is drawn for a given fi scal policy; that is, when we construct the IS curve, we hold G and T fi xed. When fi scal policy changes, the IS curve shifts.

Figure 11-8 uses the Keynesian cross to show how an increase in govern- ment purchases �G shifts the IS curve. This fi gure is drawn for a given interest rate r− and thus for a given level of planned investment. The Keynesian cross in

An Increase in Government Purchases Shifts the IS Curve Outward Panel (a) shows that an increase in government pur- chases raises planned expendi- ture. For any given interest rate, the upward shift in planned expenditure of �G leads to an increase in income Y of �G/(1 – MPC). Therefore, in panel (b), the IS curve shifts to the right by this amount.

Income, output, Y

Income, output, Y

Actual expenditure

Y2

Y1 Y2

Y1

45º

Planned expenditure

r

Y1 Y2

IS1

IS2

Expenditure

Interest rate, r

3. ... and shifts the IS curve to the right by

�G 1 � MPC

.

(a) The Keynesian Cross

(b) The IS Curve

2. ...which raises income by

�G 1 � MPC

1. An increase in government purchases shifts planned expenditure upward by �G, ...

...

FIGURE 11-8

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panel (a) shows that this change in fi scal policy raises planned expenditure and thereby increases equilibrium income from Y1 to Y2. Therefore, in panel (b), the increase in government purchases shifts the IS curve outward.

We can use the Keynesian cross to see how other changes in fi scal policy shift the IS curve. Because a decrease in taxes also expands expenditure and income, it, too, shifts the IS curve outward. A decrease in government purchases or an increase in taxes reduces income; therefore, such a change in fi scal policy shifts the IS curve inward.

In summary, the IS curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for goods and services. The IS curve is drawn for a given fi scal policy. Changes in fi scal policy that raise the demand for goods and services shift the IS curve to the right. Changes in fi scal policy that reduce the demand for goods and services shift the IS curve to the left.

The Money Market and the LM Curve

The LM curve plots the relationship between the interest rate and the level of income that arises in the market for money balances. To understand this relation- ship, we begin by looking at a theory of the interest rate called the theory of liquidity preference.

The Theory of Liquidity Preference

In his classic work The General Theory, Keynes offered his view of how the inter- est rate is determined in the short run. His explanation is called the theory of liquidity preference because it posits that the interest rate adjusts to balance the supply and demand for the economy’s most liquid asset—money. Just as the Keynesian cross is a building block for the IS curve, the theory of liquidity pref- erence is a building block for the LM curve.

To develop this theory, we begin with the supply of real money balances. If M stands for the supply of money and P stands for the price level, then M/P is the supply of real money balances. The theory of liquidity preference assumes there is a fi xed supply of real money balances. That is,

(M/P)s = M−/P−.

The money supply M is an exogenous policy variable chosen by a central bank, such as the Federal Reserve. The price level P is also an exogenous variable in this model. (We take the price level as given because the IS–LM model—our ultimate goal in this chapter—explains the short run when the price level is fi xed.) These assump- tions imply that the supply of real money balances is fi xed and, in particular, does not depend on the interest rate. Thus, when we plot the supply of real money balances against the interest rate in Figure 11-9, we obtain a vertical supply curve.

Next, consider the demand for real money balances. The theory of liquidity preference posits that the interest rate is one determinant of how much money people choose to hold. The underlying reason is that the interest rate is the

11-2

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opportunity cost of holding money: it is what you forgo by holding some of your assets as money, which does not bear interest, instead of as interest-bearing bank deposits or bonds. When the interest rate rises, people want to hold less of their wealth in the form of money. We can write the demand for real money balances as

(M/P)d = L(r),

where the function L( ) shows that the quantity of money demanded depends on the interest rate. The demand curve in Figure 11-9 slopes downward because higher interest rates reduce the quantity of real money balances demanded.6

According to the theory of liquidity preference, the supply and demand for real money balances determine what interest rate prevails in the economy. That is, the interest rate adjusts to equilibrate the money market. As the fi gure shows, at the equilibrium interest rate, the quantity of real money balances demanded equals the quantity supplied.

How does the interest rate get to this equilibrium of money supply and money demand? The adjustment occurs because whenever the money market is not in equilibrium, people try to adjust their portfolios of assets and, in the process, alter the interest rate. For instance, if the interest rate is above the equilibrium level, the quantity of real money balances supplied exceeds the quantity demanded. Individuals holding the excess supply of money try to convert some of their

The Theory of Liquidity Preference The supply and demand for real money balances determine the interest rate. The supply curve for real money balances is vertical because the supply does not depend on the interest rate. The demand curve is downward sloping because a higher interest rate raises the cost of holding money and thus lowers the quantity demanded. At the equilibrium interest rate, the quantity of real money bal- ances demanded equals the quantity supplied.

Interest rate, r

Real money balances, M/P

Demand, L(r)

Supply

M/P

Equilibrium interest rate

FIGURE 11-9

6Note that r is being used to denote the interest rate here, as it was in our discussion of the IS curve. More accurately, it is the nominal interest rate that determines money demand and the real interest rate that determines investment. To keep things simple, we are ignoring expected infl ation, which creates the difference between the real and nominal interest rates. For short-run analysis, it is often realistic to assume that expected infl ation is constant, in which case real and nominal interest rates move together. The role of expected infl ation in the IS–LM model is explored in Chapter 12.

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non-interest-bearing money into interest-bearing bank deposits or bonds. Banks and bond issuers, which prefer to pay lower interest rates, respond to this excess supply of money by lowering the interest rates they offer. Conversely, if the inter- est rate is below the equilibrium level, so that the quantity of money demanded exceeds the quantity supplied, individuals try to obtain money by selling bonds or making bank withdrawals. To attract now-scarcer funds, banks and bond issu- ers respond by increasing the interest rates they offer. Eventually, the interest rate reaches the equilibrium level, at which people are content with their portfolios of monetary and nonmonetary assets.

Now that we have seen how the interest rate is determined, we can use the theory of liquidity preference to show how the interest rate responds to changes in the supply of money. Suppose, for instance, that the Fed suddenly decreases the money supply. A fall in M reduces M/P because P is fi xed in the model. The sup- ply of real money balances shifts to the left, as in Figure 11-10. The equilibrium interest rate rises from r1 to r2, and the higher interest rate makes people satisfi ed to hold the smaller quantity of real money balances. The opposite would occur if the Fed had suddenly increased the money supply. Thus, according to the theory of liquidity preference, a decrease in the money supply raises the interest rate, and an increase in the money supply lowers the interest rate.

Does a Monetary Tightening Raise or Lower Interest Rates?

How does a tightening of monetary policy infl uence nominal interest rates? According to the theories we have been developing, the answer depends on the time horizon. Our analysis of the Fisher effect in Chapter 5 suggests that,

CASE STUDY

A Reduction in the Money Supply in the Theory of Liquidity Preference If the price level is fi xed, a reduction in the money supply from M1 to M2 reduces the supply of real money balances. The equilib- rium interest rate therefore rises from r1 to r2.

Interest rate, r

Real money balances, M/P

L(r)

M2/P

r1

r2

M1/P

2. ... raises the interest rate.

1. A fall in the money supply ...

FIGURE 11-10

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320 | P A R T I V Business Cycle Theory: The Economy in the Short Run

in the long run when prices are fl exible, a reduction in money growth would lower infl ation, and this in turn would lead to lower nominal interest rates. Yet the theory of liquidity preference predicts that, in the short run when prices are sticky, anti-infl ationary monetary policy would lead to falling real money bal- ances and higher interest rates.

Both conclusions are consistent with experience. A good illustration occurred during the early 1980s, when the U.S. economy saw the largest and quickest reduction in infl ation in recent history.

Here’s the background: By the late 1970s, infl ation in the U.S. economy had reached the double-digit range and was a major national problem. In 1979 con- sumer prices were rising at a rate of 11.3 percent per year. In October of that year, only two months after becoming the chairman of the Federal Reserve, Paul Volcker decided that it was time to change course. He announced that monetary policy would aim to reduce the rate of infl ation. This announcement began a period of tight money that, by 1983, brought the infl ation rate down to about 3 percent.

Let’s look at what happened to nominal interest rates. If we look at the period immediately after the October 1979 announcement of tighter monetary policy, we see a fall in real money balances and a rise in the interest rate—just as the theory of liquidity preference predicts. Nominal interest rates on three-month Treasury bills rose from 10 percent just before the October 1979 announcement to 12 percent in 1980 and 14 percent in 1981. Yet these high interest rates were only temporary. As Volcker’s change in monetary policy lowered infl ation and expectations of infl ation, nominal interest rates gradually fell, reaching 6 percent in 1986.

This episode illustrates a general lesson: to understand the link between monetary policy and nominal interest rates, we need to keep in mind both the theory of liquidity preference and the Fisher effect. A monetary tightening leads to higher nominal interest rates in the short run and lower nominal interest rates in the long run. ■

Income, Money Demand, and the LM Curve

Having developed the theory of liquidity preference as an explanation for how the interest rate is determined, we can now use the theory to derive the LM curve. We begin by considering the following question: how does a change in the economy’s level of income Y affect the market for real money balances? The answer (which should be familiar from Chapter 5) is that the level of income affects the demand for money. When income is high, expenditure is high, so people engage in more transactions that require the use of money. Thus, greater income implies greater money demand. We can express these ideas by writing the money demand function as

(M/P)d = L(r, Y ).

The quantity of real money balances demanded is negatively related to the interest rate and positively related to income.

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Using the theory of liquidity preference, we can fi gure out what happens to the equilibrium interest rate when the level of income changes. For example, consider what happens in Figure 11-11 when income increases from Y1 to Y2. As panel (a) illustrates, this increase in income shifts the money demand curve to the right. With the supply of real money balances unchanged, the inter- est rate must rise from r1 to r2 to equilibrate the money market. Therefore, according to the theory of liquidity preference, higher income leads to a higher interest rate.

The LM curve shown in panel (b) of Figure 11-11 summarizes this relation- ship between the level of income and the interest rate. Each point on the LM curve represents equilibrium in the money market, and the curve illustrates how the equilibrium interest rate depends on the level of income. The higher the level of income, the higher the demand for real money balances, and the higher the equilibrium interest rate. For this reason, the LM curve slopes upward.

How Monetary Policy Shifts the LM Curve

The LM curve tells us the interest rate that equilibrates the money market at any level of income. Yet, as we saw earlier, the equilibrium interest rate also depends on the supply of real money balances M/P. This means that the LM curve is drawn for a given supply of real money balances. If real money balances change— for example, if the Fed alters the money supply—the LM curve shifts.

We can use the theory of liquidity preference to understand how monetary policy shifts the LM curve. Suppose that the Fed decreases the money supply

Interest rate, r Interest rate, r

Real money balances, M/P

Income, output, Y

r2

M/P

L(r, Y1)

L(r, Y2) r1

Y1 Y2

LM

2. ... increasing the interest rate.

r2

r1

1. An increase in income raises money demand, ...

3. The LM curve summarizes these changes in the money market equilibrium.

(a) The Market for Real Money Balances (b) The LM Curve

FIGURE 11-11

Deriving the LM Curve Panel (a) shows the market for real money balances: an increase in income from Y1 to Y2 raises the demand for money and thus raises the interest rate from r1 to r2. Panel (b) shows the LM curve summarizing this rela- tionship between the interest rate and income: the higher the level of income, the higher the interest rate.

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322 | P A R T I V Business Cycle Theory: The Economy in the Short Run

from M1 to M2, which causes the supply of real money balances to fall from M1/P to M2/P. Figure 11-12 shows what happens. Holding constant the amount of income and thus the demand curve for real money balances, we see that a reduction in the supply of real money balances raises the interest rate that equili- brates the money market. Hence, a decrease in the money supply shifts the LM curve upward.

In summary, the LM curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for real money balances. The LM curve is drawn for a given supply of real money balances. Decreases in the supply of real money balances shift the LM curve upward. Increases in the supply of real money balances shift the LM curve downward.

Conclusion: The Short-Run Equilibrium

We now have all the pieces of the IS–LM model. The two equations of this model are

Y = C(Y − T ) + I(r) + G IS, M/P = L(r, Y ) LM.

Interest rate, r Interest rate, r

Real money balances, M/P

Income, output, Y M2/P M1/P

L(r, Y)

r2

r1

Y

LM1

LM2

r2

r1

3. ... and shifting the LM curve upward.

(a) The Market for Real Money Balances (b) The LM Curve

1. The Fed reduces the money supply, ... 2. ...

raising the interest rate ...

FIGURE 11-12

A Reduction in the Money Supply Shifts the LM Curve Upward Panel (a) shows that for any given level of income Y−, a reduction in the money supply raises the interest rate that equilibrates the money market. Therefore, the LM curve in panel (b) shifts upward.

11-3

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The model takes fi scal policy G and T, monetary policy M, and the price level P as exogenous. Given these exogenous variables, the IS curve provides the combinations of r and Y that satisfy the equation representing the goods market, and the LM curve provides the combinations of r and Y that satisfy the equation representing the money market. These two curves are shown together in Figure 11-13.

The equilibrium of the economy is the point at which the IS curve and the LM curve cross. This point gives the interest rate r and the level of income Y that satisfy conditions for equilibrium in both the goods market and the money market. In other words, at this intersection, actual expendi- ture equals planned expenditure, and the demand for real money balances equals the supply.

As we conclude this chapter, let’s recall that our ultimate goal in developing the IS–LM model is to analyze short-run fl uctuations in economic activity. Figure 11-14 illustrates how the different pieces of our theory fi t together. In this chapter we developed the Keynesian cross and the theory of liquidity preference as building blocks for the IS–LM model. As we see more fully in the next chapter, the IS–LM model helps explain the position and slope of the aggregate demand curve. The aggregate demand curve, in turn, is a piece of the model of aggregate supply and aggregate demand, which economists use to explain the short-run effects of policy changes and other events on national income.

Equilibrium in the IS–LM Model The intersection of the IS and LM curves represents simultaneous equilibrium in the market for goods and services and in the market for real money balances for given values of government spending, taxes, the money supply, and the price level.

Interest rate, r

Income, output, Y

Equilibrium interest rate

LM

IS

Equilibrium level of income

FIGURE 11-13

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324 | P A R T I V Business Cycle Theory: The Economy in the Short Run

Summary

1. The Keynesian cross is a basic model of income determination. It takes fi s- cal policy and planned investment as exogenous and then shows that there is one level of national income at which actual expenditure equals planned expenditure. It shows that changes in fi scal policy have a multiplied impact on income.

2. Once we allow planned investment to depend on the interest rate, the Keynesian cross yields a relationship between the interest rate and national income. A higher interest rate lowers planned investment, and this in turn lowers national income. The downward-sloping IS curve summarizes this negative relationship between the interest rate and income.

3. The theory of liquidity preference is a basic model of the determination of the interest rate. It takes the money supply and the price level as exog- enous and assumes that the interest rate adjusts to equilibrate the supply and demand for real money balances. The theory implies that increases in the money supply lower the interest rate.

4. Once we allow the demand for real money balances to depend on national income, the theory of liquidity preference yields a relationship between

Keynesian Cross

Theory of Liquidity Preference

Model of Aggregate Supply and Aggregate Demand

IS–LM Model

LM Curve

IS Curve

Explanation of Short-Run Economic Fluctuations

Aggregate Demand Curve

Aggregate Supply Curve

FIGURE 11-14

The Theory of Short-Run Fluctuations This schematic diagram shows how the different pieces of the theory of short-run fl uctuations fi t together. The Keynesian cross explains the IS curve, and the theory of liquidity preference explains the LM curve. The IS and LM curves together yield the IS–LM model, which explains the aggregate demand curve. The aggregate demand curve is part of the model of aggregate supply and aggregate demand, which economists use to explain short- run fl uctuations in economic activity.

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income and the interest rate. A higher level of income raises the demand for real money balances, and this in turn raises the interest rate. The upward- sloping LM curve summarizes this positive relationship between income and the interest rate.

5. The IS–LM model combines the elements of the Keynesian cross and the elements of the theory of liquidity preference. The IS curve shows the points that satisfy equilibrium in the goods market, and the LM curve shows the points that satisfy equilibrium in the money market. The inter- section of the IS and LM curves shows the interest rate and income that satisfy equilibrium in both markets for a given price level.

K E Y C O N C E P T S

IS–LM model

IS curve

LM curve

Keynesian cross

Government-purchases multiplier

Tax multiplier

Theory of liquidity preference

1. Use the Keynesian cross to explain why fi s- cal policy has a multiplied effect on national income.

2. Use the theory of liquidity preference to explain why an increase in the money supply lowers the

Q U E S T I O N S F O R R E V I E W

interest rate. What does this explanation assume about the price level?

3. Why does the IS curve slope downward?

4. Why does the LM curve slope upward?

P R O B L E M S A N D A P P L I C A T I O N S

1. Use the Keynesian cross to predict the impact on equilibrium GDP of the following. In each case, state the direction of the change and give a formula for the size of the impact.

a. An increase in government purchases

b. An increase in taxes

c. Equal-sized increases in both government purchases and taxes

2. In the Keynesian cross, assume that the con- sumption function is given by

C = 200 + 0.75 (Y − T ).

Planned investment is 100; government purchases and taxes are both 100.

a. Graph planned expenditure as a function of income.

b. What is the equilibrium level of income?

c. If government purchases increase to 125, what is the new equilibrium income?

d. What level of government purchases is needed to achieve an income of 1,600?

3. Although our development of the Keynesian cross in this chapter assumes that taxes are a

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fi xed amount, most countries levy some taxes that rise automatically with national income. (Examples in the United States include the income tax and the payroll tax.) Let’s represent the tax system by writing tax revenue as

T = T− + tY,

where T− and t are parameters of the tax code. The parameter t is the marginal tax rate: if income rises by $1, taxes rise by t × $1. a. How does this tax system change the way

consumption responds to changes in GDP?

b. In the Keynesian cross, how does this tax system alter the government-purchases multiplier?

c. In the IS–LM model, how does this tax system alter the slope of the IS curve?

4. Consider the impact of an increase in thriftiness in the Keynesian cross. Suppose the consump- tion function is

C = C− + c (Y − T ),

where C− is a parameter called autonomous consumption and c is the marginal propensity to consume.

a. What happens to equilibrium income when the society becomes more thrifty, as repre- sented by a decline in C−?

b. What happens to equilibrium saving?

c. Why do you suppose this result is called the paradox of thrift?

d. Does this paradox arise in the classical model of Chapter 3? Why or why not?

5. Suppose that the money demand function is

(M/P)d = 1,000 − 100r,

where r is the interest rate in percent. The money supply M is 1,000 and the price level P is 2.

a. Graph the supply and demand for real money balances.

b. What is the equilibrium interest rate?

c. Assume that the price level is fi xed. What happens to the equilibrium interest rate if the supply of money is raised from 1,000 to 1,200?

d. If the Fed wishes to raise the interest rate to 7 percent, what money supply should it set?

6. The following equations describe an economy.

Y = C + I + G. C = 120 + 0.5(Y − T ). I = 100 − 10r. G = 50. T = 40. (M/P)d = Y − 20r. M = 600. P = 2.

a. Identify each of the variables and briefl y explain their meaning.

b. From the above list, use the relevant set of equations to derive the IS curve. Graph the IS curve on an appropriately labeled graph.

c. From the above list, use the relevant set of equations to derive the LM curve. Graph the LM curve on the same graph you used in part (b).

d. What are the equilibrium level of income and equilibrium interest rate?

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327

Aggregate Demand II: Applying the IS–LM Model

12C H A P T E R

Science is a parasite: the greater the patient population the better the advance in

physiology and pathology; and out of pathology arises therapy. The year 1932

was the trough of the great depression, and from its rotten soil was belatedly

begot a new subject that today we call macroeconomics.

—Paul Samuelson

In Chapter 11 we assembled the pieces of the IS–LM model as a step toward understanding short-run economic fl uctuations. We saw that the IS curve represents the equilibrium in the market for goods and services, that the LM curve represents the equilibrium in the market for real money balances, and that the IS and LM curves together determine the interest rate and national income in the short run when the price level is fi xed. Now we turn our attention to applying the IS–LM model to analyze three issues.

First, we examine the potential causes of fl uctuations in national income. We use the IS–LM model to see how changes in the exogenous variables (govern- ment purchases, taxes, and the money supply) infl uence the endogenous variables (the interest rate and national income) for a given price level. We also examine how various shocks to the goods market (the IS curve) and the money market (the LM curve) affect the interest rate and national income in the short run.

Second, we discuss how the IS–LM model fi ts into the model of aggregate supply and aggregate demand we introduced in Chapter 10. In particular, we examine how the IS–LM model provides a theory to explain the slope and posi- tion of the aggregate demand curve. Here we relax the assumption that the price level is fi xed and show that the IS–LM model implies a negative relationship between the price level and national income. The model can also tell us what events shift the aggregate demand curve and in what direction.

Third, we examine the Great Depression of the 1930s. As this chapter’s open- ing quotation indicates, this episode gave birth to short-run macroeconomic theory, for it led Keynes and his many followers to argue that aggregate demand was the key to understanding fl uctuations in national income. With the benefi t of hindsight, we can use the IS–LM model to discuss the various explanations of this traumatic economic downturn.

The IS–LM model has played a central role in the history of economic thought, and it offers a powerful lens through which to view economic history,

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328 | P A R T I V Business Cycle Theory: The Economy in the Short Run

but it has much modern signifi cance as well. Throughout this chapter we will see that the model can also be used to shed light on more recent fl uctuations in the economy; two case studies in the chapter use it to examine the recessions that began in 2001 and 2008. Moreover, as we will see in Chapter 15, the logic of the IS–LM model provides a good foundation for understanding newer and more sophisticated theories of the business cycle.

12-1 Explaining Fluctuations With the IS–LM Model

The intersection of the IS curve and the LM curve determines the level of national income. When one of these curves shifts, the short-run equilibrium of the economy changes, and national income fl uctuates. In this section we examine how changes in policy and shocks to the economy can cause these curves to shift.

How Fiscal Policy Shifts the IS Curve and Changes the Short-Run Equilibrium

We begin by examining how changes in fi scal policy (government purchases and taxes) alter the economy’s short-run equilibrium. Recall that changes in fi scal policy infl uence planned expenditure and thereby shift the IS curve. The IS–LM model shows how these shifts in the IS curve affect income and the interest rate.

Changes in Government Purchases Consider an increase in government purchases of �G. The government-purchases multiplier in the Keynesian cross tells us that this change in fi scal policy raises the level of income at any given interest rate by �G/(1 � MPC). Therefore, as Figure 12-1 shows, the IS curve

Interest rate, r

Income, output, Y Y1 Y2

r1

r2

IS1

B

A IS2

LM

2. ... which raises income ...

3. ... and the interest rate.

1. The IS curve shifts to the right by �G/(1 � MPC), ...

An Increase in Government Purchases in the IS–LM Model An increase in govern- ment purchases shifts the IS curve to the right. The equilib- rium moves from point A to point B. Income rises from Y1 to Y2, and the interest rate rises from r1 to r2.

FIGURE 12-1

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 329

shifts to the right by this amount. The equilibrium of the economy moves from point A to point B. The increase in government purchases raises both income and the interest rate.

To understand fully what’s happening in Figure 12-1, it helps to keep in mind the building blocks for the IS–LM model from the preceding chapter—the Keynesian cross and the theory of liquidity preference. Here is the story. When the government increases its purchases of goods and services, the economy’s planned expenditure rises. The increase in planned expenditure stimulates the production of goods and services, which causes total income Y to rise. These effects should be familiar from the Keynesian cross.

Now consider the money market, as described by the theory of liquidity preference. Because the economy’s demand for money depends on income, the rise in total income increases the quantity of money demanded at every interest rate. The supply of money, however, has not changed, so higher money demand causes the equilibrium interest rate r to rise.

The higher interest rate arising in the money market, in turn, has ramifi ca- tions back in the goods market. When the interest rate rises, fi rms cut back on their investment plans. This fall in investment partially offsets the expansionary effect of the increase in government purchases. Thus, the increase in income in response to a fi scal expansion is smaller in the IS–LM model than it is in the Keynesian cross (where investment is assumed to be fi xed). You can see this in Figure 12-1. The horizontal shift in the IS curve equals the rise in equilibrium income in the Keynesian cross. This amount is larger than the increase in equi- librium income here in the IS–LM model. The difference is explained by the crowding out of investment due to a higher interest rate.

Changes in Taxes In the IS–LM model, changes in taxes affect the economy much the same as changes in government purchases do, except that taxes affect expenditure through consumption. Consider, for instance, a decrease in taxes of �T. The tax cut encourages consumers to spend more and, therefore, increases planned expenditure. The tax multiplier in the Keynesian cross tells us that this change in policy raises the level of income at any given interest rate by �T × MPC/(1 – MPC). Therefore, as Figure 12-2 illustrates, the IS curve shifts to the right by this amount. The equilibrium of the economy moves from point A to point B. The tax cut raises both income and the interest rate. Once again, because the higher interest rate depresses investment, the increase in income is smaller in the IS–LM model than it is in the Keynesian cross.

How Monetary Policy Shifts the LM Curve and Changes the Short-Run Equilibrium

We now examine the effects of monetary policy. Recall that a change in the money supply alters the interest rate that equilibrates the money market for any given level of income and, thus, shifts the LM curve. The IS–LM model shows how a shift in the LM curve affects income and the interest rate.

Consider an increase in the money supply. An increase in M leads to an increase in real money balances M/P because the price level P is fi xed in the short run. The theory of liquidity preference shows that for any given level of

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330 | P A R T I V Business Cycle Theory: The Economy in the Short Run

income, an increase in real money balances leads to a lower interest rate. There- fore, the LM curve shifts downward, as in Figure 12-3. The equilibrium moves from point A to point B. The increase in the money supply lowers the interest rate and raises the level of income.

Once again, to tell the story that explains the economy’s adjustment from point A to point B, we rely on the building blocks of the IS–LM model—the Keynesian cross and the theory of liquidity preference. This time, we begin with the money market, where the monetary-policy action occurs. When the

Interest rate, r

Income, output, YY1 Y2

r1

r2

IS1

B

A

LM

2. ... which raises income ...

IS23. ... and the interest rate. 1. The IS curve

shifts to the right by �T � MPC , ...

1 � MPC

A Decrease in Taxes in the IS–LM Model A decrease in taxes shifts the IS curve to the right. The equilibrium moves from point A to point B. Income rises from Y1 to Y2, and the interest rate rises from r1 to r2.

FIGURE 12-2

An Increase in the Money Supply in the IS–LM Model An increase in the money supply shifts the LM curve downward. The equi- librium moves from point A to point B. Income rises from Y1 to Y2, and the interest rate falls from r1 to r2.

Interest rate, r

Income, output, Y Y1 Y2

r2

r1

IS

B

A

LM1

LM2

3. ... and lowers the interest rate.

2. ... which raises income ...

1. An increase in the money supply shifts the LM curve downward, ...

FIGURE 12-3

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 331

Federal Reserve increases the supply of money, people have more money than they want to hold at the prevailing interest rate. As a result, they start depositing this extra money in banks or using it to buy bonds. The interest rate r then falls until people are willing to hold all the extra money that the Fed has created; this brings the money market to a new equilibrium. The lower interest rate, in turn, has ramifi cations for the goods market. A lower interest rate stimulates planned investment, which increases planned expenditure, production, and income Y.

Thus, the IS–LM model shows that monetary policy infl uences income by changing the interest rate. This conclusion sheds light on our analysis of monetary policy in Chapter 10. In that chapter we showed that in the short run, when prices are sticky, an expansion in the money supply raises income. But we did not discuss how a monetary expansion induces greater spending on goods and services—a process called the monetary transmission mechanism. The IS–LM model shows an important part of that mechanism: An increase in the money supply lowers the interest rate, which stimulates investment and thereby expands the demand for goods and services. The next chapter shows that in open economies, the exchange rate also has a role in the monetary transmission mechanism; for large economies such as that of the United States, however, the interest rate has the leading role.

The Interaction Between Monetary and Fiscal Policy

When analyzing any change in monetary or fi scal policy, it is important to keep in mind that the policymakers who control these policy tools are aware of what the other policymakers are doing. A change in one policy, therefore, may infl u- ence the other, and this interdependence may alter the impact of a policy change.

For example, suppose Congress raises taxes. What effect will this policy have on the economy? According to the IS–LM model, the answer depends on how the Fed responds to the tax increase.

Figure 12-4 shows three of the many possible outcomes. In panel (a), the Fed holds the money supply constant. The tax increase shifts the IS curve to the left. Income falls (because higher taxes reduce consumer spending), and the interest rate falls (because lower income reduces the demand for money). The fall in income indicates that the tax hike causes a recession.

In panel (b), the Fed wants to hold the interest rate constant. In this case, when the tax increase shifts the IS curve to the left, the Fed must decrease the money supply to keep the interest rate at its original level. This fall in the money supply shifts the LM curve upward. The interest rate does not fall, but income falls by a larger amount than if the Fed had held the money supply constant. Whereas in panel (a) the lower interest rate stimulated investment and partially offset the contractionary effect of the tax hike, in panel (b) the Fed deepens the recession by keeping the interest rate high.

In panel (c), the Fed wants to prevent the tax increase from lowering income. It must, therefore, raise the money supply and shift the LM curve downward enough to offset the shift in the IS curve. In this case, the tax increase does not cause a recession, but it does cause a large fall in the interest rate. Although the level of income is not changed, the combination of a tax increase and a monetary expansion does change the allocation of the economy’s resources. The higher

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The Response of the Economy to a Tax Increase How the economy responds to a tax increase depends on how the central bank responds. In panel (a) the Fed holds the money supply constant. In panel (b) the Fed holds the interest rate constant by reducing the money supply. In panel (c) the Fed holds the level of income constant by raising the money supply. In each case, the economy moves from point A to point B.

Interest rate, r

Interest rate, r

Interest rate, r

Income, output, Y

Income, output, Y

Income, output, Y

LM2

IS1

IS2

LM1

2. ... but because the Fed holds the money supply constant, the LM curve stays the same.

2. ... and to hold the interest rate constant, the Fed contracts the money supply.

LM

IS1

IS2

1. A tax increase shifts the IS curve . . .

1. A tax increase shifts the IS curve . . .

2. ... and to hold income constant, the Fed expands the money supply.

1. A tax increase shifts the IS curve . . .

LM1

IS1

IS2

LM2

A

A

A

B

B

B

(a) Fed Holds Money Supply Constant

(b) Fed Holds Interest Rate Constant

(c) Fed Holds Income Constant

FIGURE 12-4

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 333

taxes depress consumption, while the lower interest rate stimulates investment. Income is not affected because these two effects exactly balance.

From this example we can see that the impact of a change in fi scal policy depends on the policy the Fed pursues—that is, on whether it holds the money supply, the interest rate, or the level of income constant. More generally, whenever analyzing a change in one policy, we must make an assumption about its effect on the other policy. The most appropriate assumption depends on the case at hand and the many political considerations that lie behind economic policymaking.

Policy Analysis With Macroeconometric Models

The IS–LM model shows how monetary and fi scal policy infl uence the equilib- rium level of income. The predictions of the model, however, are qualitative, not quantitative. The IS–LM model shows that increases in government purchases raise GDP and that increases in taxes lower GDP. But when economists analyze specifi c policy proposals, they need to know not only the direction of the effect but also the size. For example, if Congress increases taxes by $100 billion and if monetary policy is not altered, how much will GDP fall? To answer this question, economists need to go beyond the graphical representation of the IS–LM model.

Macroeconometric models of the economy provide one way to evaluate policy proposals. A macroeconometric model is a model that describes the economy quan- titatively, rather than just qualitatively. Many of these models are essentially more complicated and more realistic versions of our IS–LM model. The economists who build macroeconometric models use historical data to estimate parameters such as the marginal propensity to consume, the sensitivity of investment to the interest rate, and the sensitivity of money demand to the interest rate. Once a model is built, economists can simulate the effects of alternative policies with the help of a computer.

When interpreting such an exercise, it is important to keep in mind that the results of such a computer simulation are only as good as the macroeconometric model being simulated. In judging such a model, various questions arise. What assumptions did the model builders make in constructing the model? Are these assumptions appropriate for the issue at hand, or were crucial factors ignored? What data were used to estimate the key parameters? How reliable are these data? Were the statistical techniques used to analyze the data and estimate the parameters the right ones for the task? How precise are the results? Only after addressing these questions can an economist judge how much confi dence to put in a model’s output.

Table 12-1 shows the fi scal-policy multipliers implied by one prominent mac- roeconometric model, the Data Resources Incorporated (DRI) model, named for the economic forecasting fi rm that developed it. The multipliers are given for two assumptions about how the Fed might respond to changes in fi scal policy.

One assumption about monetary policy is that the Fed keeps the nominal inter- est rate constant. That is, when fi scal policy shifts the IS curve to the right or to the left, the Fed adjusts the money supply to shift the LM curve in the same direction. Because there is no crowding out of investment due to a changing interest rate, the fi scal-policy multipliers are similar to those from the Keynesian cross. The DRI

CASE STUDY

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334 | P A R T I V Business Cycle Theory: The Economy in the Short Run

model indicates that, in this case, the government-purchases multiplier is 1.93, and the tax multiplier is –1.19. That is, a $100 billion increase in government purchases raises GDP by $193 billion, and a $100 billion increase in taxes lowers GDP by $119 billion.

The second assumption about monetary policy is that the Fed keeps the money supply constant so that the LM curve does not shift. In this case, the interest rate rises, and investment is crowded out, so the multipliers are much smaller. The government-purchases multiplier is only 0.60, and the tax multiplier is only –0.26. That is, a $100 billion increase in government purchases raises GDP by $60 billion, and a $100 billion increase in taxes lowers GDP by $26 billion.

Table 12-1 shows that the fi scal-policy multipliers are very different under the two assumptions about monetary policy. The impact of any change in fi scal policy depends crucially on how the Fed responds to that change. ■

Shocks in the IS–LM Model

Because the IS–LM model shows how national income is determined in the short run, we can use the model to examine how various economic disturbances affect income. So far we have seen how changes in fi scal policy shift the IS curve and how changes in monetary policy shift the LM curve. Similarly, we can group other disturbances into two categories: shocks to the IS curve and shocks to the LM curve.

Shocks to the IS curve are exogenous changes in the demand for goods and services. Some economists, including Keynes, have emphasized that such changes in demand can arise from investors’ animal spirits—exogenous and perhaps self- fulfi lling waves of optimism and pessimism. For example, suppose that fi rms become pessimistic about the future of the economy and that this pessimism causes them to build fewer new factories. This reduction in the demand for investment goods causes a contractionary shift in the investment function: at every interest rate, fi rms want to invest less. The fall in investment reduces planned expenditure and shifts the IS curve to the left, reducing income and employment. This fall in equilibrium income in part validates the fi rms’ initial pessimism.

Shocks to the IS curve may also arise from changes in the demand for consumer goods. Suppose, for instance, that the election of a popular president increases

The Fiscal-Policy Multipliers in the DRI Model

TABLE 12-1

Value of Multipliers

Assumption About Monetary Policy �Y/�G �Y/�T

Nominal interest rate held constant 1.93 �1.19 Money supply held constant 0.60 �0.26

Note: This table gives the fi scal-policy multipliers for a sustained change in government purchases or in personal income taxes. These multipliers are for the fourth quarter after the policy change is made. Source: Otto Eckstein, The DRI Model of the U.S. Economy (New York: McGraw-Hill, 1983), 169.

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 335

consumer confi dence in the economy. This induces consumers to save less for the future and consume more today. We can interpret this change as an upward shift in the consumption function. This shift in the consumption function increases planned expenditure and shifts the IS curve to the right, and this raises income.

Shocks to the LM curve arise from exogenous changes in the demand for money. For example, suppose that new restrictions on credit card availability increase the amount of money people choose to hold. According to the theory of liquidity preference, when money demand rises, the interest rate necessary to equilibrate the money market is higher (for any given level of income and money supply). Hence, an increase in money demand shifts the LM curve upward, which tends to raise the interest rate and depress income.

In summary, several kinds of events can cause economic fl uctuations by shift- ing the IS curve or the LM curve. Remember, however, that such fl uctuations are not inevitable. Policymakers can try to use the tools of monetary and fi scal policy to offset exogenous shocks. If policymakers are suffi ciently quick and skillful (admittedly, a big if), shocks to the IS or LM curves need not lead to fl uctuations in income or employment.

The U.S. Recession of 2001

In 2001, the U.S. economy experienced a pronounced slowdown in economic activ- ity. The unemployment rate rose from 3.9 percent in September 2000 to 4.9 percent in August 2001, and then to 6.3 percent in June 2003. In many ways, the slowdown looked like a typical recession driven by a fall in aggregate demand.

Three notable shocks explain this event. The fi rst was a decline in the stock mar- ket. During the 1990s, the stock market experienced a boom of historic propor- tions, as investors became optimistic about the prospects of the new information technology. Some economists viewed the optimism as excessive at the time, and in hindsight this proved to be the case. When the optimism faded, average stock prices fell by about 25 percent from August 2000 to August 2001. The fall in the market reduced household wealth and thus consumer spending. In addition, the declining perceptions of the profi tability of the new technologies led to a fall in investment spending. In the language of the IS–LM model, the IS curve shifted to the left.

CASE STUDY

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336 | P A R T I V Business Cycle Theory: The Economy in the Short Run

The second shock was the terrorist attacks on New York City and Washing- ton, D.C., on September 11, 2001. In the week after the attacks, the stock market fell another 12 percent, which at the time was the biggest weekly loss since the Great Depression of the 1930s. Moreover, the attacks increased uncertainty about what the future would hold. Uncertainty can reduce spending because house- holds and fi rms postpone some of their plans until the uncertainty is resolved. Thus, the terrorist attacks shifted the IS curve farther to the left.

The third shock was a series of accounting scandals at some of the nation’s most prominent corporations, including Enron and WorldCom. The result of these scan- dals was the bankruptcy of some companies that had fraudulently represented them- selves as more profi table than they truly were, criminal convictions for the executives who had been responsible for the fraud, and new laws aimed at regulating corporate accounting standards more thoroughly. These events further depressed stock prices and discouraged business investment—a third leftward shift in the IS curve.

Fiscal and monetary policymakers responded quickly to these events. Con- gress passed a major tax cut in 2001, including an immediate tax rebate, and a second major tax cut in 2003. One goal of these tax cuts was to stimulate consumer spending. (See the Case Study on Cutting Taxes in Chapter 11.) In addition, after the terrorist attacks, Congress increased government spending by appropriating funds to assist in New York’s recovery and to bail out the ailing airline industry. These fi scal measures shifted the IS curve to the right.

At the same time, the Federal Reserve pursued expansionary monetary policy, shifting the LM curve to the right. Money growth accelerated, and interest rates fell. The interest rate on three-month Treasury bills fell from 6.4 percent in November 2000 to 3.3 percent in August 2001, just before the terrorist attacks. After the attacks and corporate scandals hit the economy, the Fed increased its monetary stimulus, and the Treasury bill rate fell to 0.9 percent in July 2003—the lowest level in many decades.

Expansionary monetary and fi scal policy had the intended effects. Economic growth picked up in the second half of 2003 and was strong throughout 2004. By July 2005, the unemployment rate was back down to 5.0 percent, and it stayed at or below that level for the next several years. Unemployment would begin rising again in 2008, however, when the economy experienced another recession. The causes of the 2008 recession are examined in another Case Study later in this chapter. ■

What Is the Fed’s Policy Instrument— The Money Supply or the Interest Rate?

Our analysis of monetary policy has been based on the assumption that the Fed infl uences the economy by controlling the money supply. By contrast, when the media report on changes in Fed policy, they often just say that the Fed has raised or lowered interest rates. Which is right? Even though these two views may seem different, both are correct, and it is important to understand why.

In recent years, the Fed has used the federal funds rate—the interest rate that banks charge one another for overnight loans—as its short-term policy instrument. When the Federal Open Market Committee meets every six weeks to set monetary policy,

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 337

it votes on a target for this interest rate that will apply until the next meeting. After the meeting is over, the Fed’s bond traders (who are located in New York) are told to conduct the open-market operations necessary to hit that target. These open-market operations change the money supply and shift the LM curve so that the equilibrium interest rate (determined by the intersection of the IS and LM curves) equals the target interest rate that the Federal Open Market Committee has chosen.

As a result of this operating procedure, Fed policy is often discussed in terms of changing interest rates. Keep in mind, however, that behind these changes in interest rates are the necessary changes in the money supply. A newspaper might report, for instance, that “the Fed has lowered interest rates.” To be more precise, we can translate this statement as meaning “the Federal Open Market Commit- tee has instructed the Fed bond traders to buy bonds in open-market operations so as to increase the money supply, shift the LM curve, and reduce the equilib- rium interest rate to hit a new lower target.”

Why has the Fed chosen to use an interest rate, rather than the money supply, as its short-term policy instrument? One possible answer is that shocks to the LM curve are more prevalent than shocks to the IS curve. When the Fed targets interest rates, it automatically offsets LM shocks by adjusting the money supply, although this policy exacerbates IS shocks. If LM shocks are the more prevalent type, then a policy of targeting the interest rate leads to greater economic stability than a policy of targeting the money supply. (Problem 7 at the end of this chapter asks you to analyze this issue more fully.)

In Chapter 15 we extend our theory of short-run fl uctuations to explicitly include a monetary policy that targets the interest rate and that changes its target in response to economic conditions. The IS–LM model presented here is a useful foundation for that more complicated and realistic analysis. One lesson from the IS–LM model is that when a central bank sets the money supply, it determines the equilibrium interest rate. Thus, in some ways, setting the money supply and setting the interest rate are two sides of the same coin.

12-2 IS–LM as a Theory of Aggregate Demand

We have been using the IS–LM model to explain national income in the short run when the price level is fi xed. To see how the IS–LM model fi ts into the model of aggregate supply and aggregate demand introduced in Chapter 10, we now examine what happens in the IS–LM model if the price level is allowed to change. By examining the effects of changing the price level, we can fi nally deliver what was promised when we began our study of the IS–LM model: a theory to explain the position and slope of the aggregate demand curve.

From the IS–LM Model to the Aggregate Demand Curve

Recall from Chapter 10 that the aggregate demand curve describes a relation- ship between the price level and the level of national income. In Chapter 10 this relationship was derived from the quantity theory of money. That analysis showed

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that for a given money supply, a higher price level implies a lower level of income. Increases in the money supply shift the aggregate demand curve to the right, and decreases in the money supply shift the aggregate demand curve to the left.

To understand the determinants of aggregate demand more fully, we now use the IS–LM model, rather than the quantity theory, to derive the aggregate demand curve. First, we use the IS–LM model to show why national income falls as the price level rises—that is, why the aggregate demand curve is downward sloping. Second, we examine what causes the aggregate demand curve to shift.

To explain why the aggregate demand curve slopes downward, we examine what happens in the IS–LM model when the price level changes. This is done in Figure 12-5. For any given money supply M, a higher price level P reduces the supply of real money balances M/P. A lower supply of real money balances shifts the LM curve upward, which raises the equilibrium interest rate and lowers the equilibrium level of income, as shown in panel (a). Here the price level rises from P1 to P2, and income falls from Y1 to Y2. The aggregate demand curve in panel (b) plots this negative relationship between national income and the price level. In other words, the aggregate demand curve shows the set of equilibrium points that arise in the IS–LM model as we vary the price level and see what happens to income.

What causes the aggregate demand curve to shift? Because the aggregate demand curve summarizes the results from the IS–LM model, events that shift the IS curve or the LM curve (for a given price level) cause the aggregate demand curve to shift. For instance, an increase in the money supply raises income in the

Deriving the Aggregate Demand Curve with the IS–LM Model Panel (a) shows the IS–LM model: an increase in the price level from P1 to P2 lowers real money balances and thus shifts the LM curve upward. The shift in the LM curve lowers income from Y1 to Y2. Panel (b) shows the aggregate demand curve summarizing this relationship between the price level and income: the higher the price level, the lower the level of income.

Interest rate, r Price level, P

Income, output, Y

Income, output, Y

Y1

IS

LM(P1)

LM(P2)

Y2

P2

P1

Y1

AD

Y2

(a) The IS–LM Model (b) The Aggregate Demand Curve

2. ... lowering income Y.

1. A higher price level P shifts the LM curve upward, ...

3. The AD curve summarizes the relationship between P and Y.

FIGURE 12-5

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IS–LM model for any given price level; it thus shifts the aggregate demand curve to the right, as shown in panel (a) of Figure 12-6. Similarly, an increase in govern- ment purchases or a decrease in taxes raises income in the IS–LM model for a given price level; it also shifts the aggregate demand curve to the right, as shown in panel (b) of Figure 12-6. Conversely, a decrease in the money supply, a decrease in government purchases, or an increase in taxes lowers income in the IS–LM

How Monetary and Fiscal Policies Shift the Aggregate Demand Curve Panel (a) shows a monetary expansion. For any given price level, an increase in the money supply raises real money balances, shifts the LM curve downward, and raises income. Hence, an increase in the money supply shifts the aggregate demand curve to the right. Panel (b) shows a fi scal expansion, such as an increase in government purchases or a decrease in taxes. The fi scal expansion shifts the IS curve to the right and, for any given price level, raises income. Hence, a fi scal expansion shifts the aggregate demand curve to the right.

Interest rate, r

Price level, P

Interest rate, r

Price level, P

Income, output, Y

Income, output, Y

Income, output, Y

Income, output, Y

IS

LM2 (P � P1)

Y1 Y2 Y1 Y2

Y1 Y2 Y1 Y2

LM1(P � P1)

AD2

AD1

IS1

IS2 AD2

AD1

P1

LM(P � P1)

P1

1. A fiscal expansion shifts the IS curve, ...

(a) Expansionary Monetary Policy

(b) Expansionary Fiscal Policy

1. A monetary expansion shifts the LM curve, ... 2. ... increasing

aggregate demand at any given price level.

2. ... increasing aggregate demand at any given price level.

FIGURE 12-6

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340 | P A R T I V Business Cycle Theory: The Economy in the Short Run

model and shifts the aggregate demand curve to the left. Anything that changes income in the IS–LM model other than a change in the price level causes a shift in the aggregate demand curve. The factors shifting aggregate demand include not only monetary and fi scal policy but also shocks to the goods market (the IS curve) and shocks to the money market (the LM curve).

We can summarize these results as follows: A change in income in the IS–LM model resulting from a change in the price level represents a movement along the aggregate demand curve. A change in income in the IS–LM model for a given price level represents a shift in the aggregate demand curve.

The IS–LM Model in the Short Run and Long Run

The IS–LM model is designed to explain the economy in the short run when the price level is fi xed. Yet, now that we have seen how a change in the price level infl uences the equilibrium in the IS–LM model, we can also use the model to describe the economy in the long run when the price level adjusts to ensure that the economy produces at its natural rate. By using the IS–LM model to describe the long run, we can show clearly how the Keynesian model of income determination differs from the classical model of Chapter 3.

Panel (a) of Figure 12-7 shows the three curves that are necessary for under- standing the short-run and long-run equilibria: the IS curve, the LM curve, and the vertical line representing the natural level of output Y–. The LM curve is, as always, drawn for a fi xed price level P1. The short-run equilibrium of the

Interest rate, r

Price level, P

Income, output, Y Income, output, Y Y

P1 P2

LRAS

SRAS1

SRAS2

AD

K

C

Y

LM(P1)

LM(P2)

LRAS

IS

K

C

(a) The IS–LM Model (b) The Model of Aggregate Supply and

Aggregate Demand

The Short-Run and Long-Run Equilibria We can compare the short-run and long-run equilibria using either the IS–LM diagram in panel (a) or the aggregate supply–aggregate demand diagram in panel (b). In the short run, the price level is stuck at P1. The short-run equilibrium of the economy is therefore point K. In the long run, the price level adjusts so that the economy is at the natural level of output. The long-run equilibrium is therefore point C.

FIGURE 12-7

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economy is point K, where the IS curve crosses the LM curve. Notice that in this short-run equilibrium, the economy’s income is less than its natural level.

Panel (b) of Figure 12-7 shows the same situation in the diagram of aggregate supply and aggregate demand. At the price level P1, the quantity of output demanded is below the natural level. In other words, at the existing price level, there is insuffi - cient demand for goods and services to keep the economy producing at its potential.

In these two diagrams we can examine the short-run equilibrium at which the economy fi nds itself and the long-run equilibrium toward which the economy gravitates. Point K describes the short-run equilibrium, because it assumes that the price level is stuck at P1. Eventually, the low demand for goods and services causes prices to fall, and the economy moves back toward its natural rate. When the price level reaches P2, the economy is at point C, the long-run equilibrium. The diagram of aggregate supply and aggregate demand shows that at point C, the quantity of goods and services demanded equals the natural level of output. This long-run equi- librium is achieved in the IS–LM diagram by a shift in the LM curve: the fall in the price level raises real money balances and therefore shifts the LM curve to the right.

We can now see the key difference between the Keynesian and classical approaches to the determination of national income. The Keynesian assumption (represented by point K) is that the price level is stuck. Depending on monetary policy, fi scal policy, and the other determinants of aggregate demand, output may deviate from its natural level. The classical assumption (represented by point C) is that the price level is fully fl exible. The price level adjusts to ensure that national income is always at its natural level.

To make the same point somewhat differently, we can think of the economy as being described by three equations. The fi rst two are the IS and LM equations:

Y = C(Y – T ) + I(r) + G IS,

M/P = L(r, Y ) LM.

The IS equation describes the equilibrium in the goods market, and the LM equation describes the equilibrium in the money market. These two equations contain three endogenous variables: Y, P, and r. To complete the system, we need a third equation. The Keynesian approach completes the model with the assump- tion of fi xed prices, so the Keynesian third equation is

P = P1.

This assumption implies that the remaining two variables r and Y must adjust to satisfy the remaining two equations IS and LM. The classical approach completes the model with the assumption that output reaches its natural level, so the clas- sical third equation is

Y = Y–.

This assumption implies that the remaining two variables r and P must adjust to satisfy the remaining two equations IS and LM. Thus, the classical approach fi xes output and allows the price level to adjust to satisfy the goods and money market equilibrium conditions, whereas the Keynesian approach fi xes the price level and lets output move to satisfy the equilibrium conditions.

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342 | P A R T I V Business Cycle Theory: The Economy in the Short Run

Which assumption is most appropriate? The answer depends on the time hori- zon. The classical assumption best describes the long run. Hence, our long-run analysis of national income in Chapter 3 and prices in Chapter 5 assumes that output equals its natural level. The Keynesian assumption best describes the short run. Therefore, our analysis of economic fl uctuations relies on the assumption of a fi xed price level.

12-3 The Great Depression

Now that we have developed the model of aggregate demand, let’s use it to address the question that originally motivated Keynes: what caused the Great Depression? Even today, more than half a century after the event, economists continue to debate the cause of this major economic downturn. The Great Depression provides an extended case study to show how economists use the IS–LM model to analyze economic fl uctuations.1

Before turning to the explanations economists have proposed, look at Table 12-2, which presents some statistics regarding the Depression. These

What Happened During the Great Depression?

TABLE 12-2

Unemployment Real GNP Consumption Investment Government Year Rate (1) (2) (2) (2) Purchases (2)

1929 3.2 203.6 139.6 40.4 22.0 1930 8.9 183.5 130.4 27.4 24.3 1931 16.3 169.5 126.1 16.8 25.4 1932 24.1 144.2 114.8 4.7 24.2 1933 25.2 141.5 112.8 5.3 23.3 1934 22.0 154.3 118.1 9.4 26.6 1935 20.3 169.5 125.5 18.0 27.0 1936 17.0 193.2 138.4 24.0 31.8 1937 14.3 203.2 143.1 29.9 30.8 1938 19.1 192.9 140.2 17.0 33.9 1939 17.2 209.4 148.2 24.7 35.2 1940 14.6 227.2 155.7 33.0 36.4

Source: Historical Statistics of the United States, Colonial Times to 1970, Parts I and II (Washington, DC: U.S. Department of Commerce, Bureau of Census, 1975). Note: (1) The unemployment rate is series D9. (2) Real GNP, consumption, investment, and government purchases are series F3, F48, F52, and F66, and are measured in billions of 1958 dollars. (3) The interest rate is the prime Commercial Paper

1For a fl avor of the debate, see Milton Friedman and Anna J. Schwartz, A Monetary History of the United States, 1867–1960 (Princeton, N.J.: Princeton University Press, 1963); Peter Temin, Did Monetary Forces Cause the Great Depression? (New York: W. W. Norton, 1976); the essays in Karl Brunner, ed., The Great Depression Revisited (Boston: Martinus Nijhoff, 1981); and the symposium on the Great Depression in the Spring 1993 issue of the Journal of Economic Perspectives.

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statistics are the battlefi eld on which debate about the Depression takes place. What do you think happened? An IS shift? An LM shift? Or something else?

The Spending Hypothesis: Shocks to the IS Curve

Table 12-2 shows that the decline in income in the early 1930s coincided with falling interest rates. This fact has led some economists to suggest that the cause of the decline may have been a contractionary shift in the IS curve. This view is sometimes called the spending hypothesis because it places primary blame for the Depression on an exogenous fall in spending on goods and services.

Economists have attempted to explain this decline in spending in several ways. Some argue that a downward shift in the consumption function caused the con- tractionary shift in the IS curve. The stock market crash of 1929 may have been partly responsible for this shift: by reducing wealth and increasing uncertainty about the future prospects of the U.S. economy, the crash may have induced consumers to save more of their income rather than spend it.

Others explain the decline in spending by pointing to the large drop in investment in housing. Some economists believe that the residential investment boom of the 1920s was excessive and that once this “overbuilding” became apparent, the demand for residential investment declined drastically. Another possible explanation for the fall in residential investment is the reduction in immigration in the 1930s: a more slowly growing population demands less new housing.

Nominal Money Supply Price Level Infl ation Real Money Year Interest Rate (3) (4) (5) (6) Balances (7)

1929 5.9 26.6 50.6 – 52.6 1930 3.6 25.8 49.3 −2.6 52.3 1931 2.6 24.1 44.8 −10.1 54.5 1932 2.7 21.1 40.2 −9.3 52.5 1933 1.7 19.9 39.3 −2.2 50.7 1934 1.0 21.9 42.2 7.4 51.8 1935 0.8 25.9 42.6 0.9 60.8 1936 0.8 29.6 42.7 0.2 62.9 1937 0.9 30.9 44.5 4.2 69.5 1938 0.8 30.5 43.9 −1.3 69.5 1939 0.6 34.2 43.2 −1.6 79.1 1940 0.6 39.7 43.9 1.6 90.3

rate, 4–6 months, series ×445. (4) The money supply is series ×414, currency plus demand deposits, measured in billions of dollars. (5) The price level is the GNP defl ator (1958 = 100), series E1. (6) The infl ation rate is the percentage change in the price level series. (7) Real money balances, calculated by dividing the money supply by the price level and multiplying by 100, are in billions of 1958 dollars.

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Once the Depression began, several events occurred that could have reduced spending further. First, many banks failed in the early 1930s, in part because of inadequate bank regulation, and these bank failures may have exacerbated the fall in investment spending. Banks play the crucial role of getting the funds available for investment to those households and fi rms that can best use them. The clos- ing of many banks in the early 1930s may have prevented some businesses from getting the funds they needed for capital investment and, therefore, may have led to a further contraction in investment spending.2

The fi scal policy of the 1930s also contributed to the contractionary shift in the IS curve. Politicians at that time were more concerned with balancing the budget than with using fi scal policy to keep production and employment at their natural levels. The Revenue Act of 1932 increased various taxes, especially those falling on lower- and middle-income consumers.3 The Democratic plat- form of that year expressed concern about the budget defi cit and advocated an “immediate and drastic reduction of governmental expenditures.” In the midst of historically high unemployment, policymakers searched for ways to raise taxes and reduce government spending.

There are, therefore, several ways to explain a contractionary shift in the IS curve. Keep in mind that these different views may all be true. There may be no single explanation for the decline in spending. It is possible that all of these changes coincided and that together they led to a massive reduction in spending.

The Money Hypothesis: A Shock to the LM Curve

Table 12-2 shows that the money supply fell 25 percent from 1929 to 1933, during which time the unemployment rate rose from 3.2 percent to 25.2 per- cent. This fact provides the motivation and support for what is called the money hypothesis, which places primary blame for the Depression on the Federal Reserve for allowing the money supply to fall by such a large amount.4 The best-known advocates of this interpretation are Milton Friedman and Anna Schwartz, who defended it in their treatise on U.S. monetary history. Friedman and Schwartz argue that contractions in the money supply have caused most economic down- turns and that the Great Depression is a particularly vivid example.

Using the IS-LM model, we might interpret the money hypothesis as explain- ing the Depression by a contractionary shift in the LM curve. Seen in this way, however, the money hypothesis runs into two problems.

The fi rst problem is the behavior of real money balances. Monetary policy leads to a contractionary shift in the LM curve only if real money balances fall. Yet from 1929 to 1931 real money balances rose slightly because the fall in the money

2Ben Bernanke, “Non-Monetary Effects of the Financial Crisis in the Propagation of the Great Depression,” American Economic Review 73 (June 1983): 257–276. 3E. Cary Brown, “Fiscal Policy in the ‘Thirties: A Reappraisal,” American Economic Review 46 (December 1956): 857–879. 4We discussed the reasons for this large decrease in the money supply in Chapter 4, where we examined the money supply process in more detail. In particular, see the Case Study on Bank Failures and the Money Supply in the 1930s.

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supply was accompanied by an even greater fall in the price level. Although the monetary contraction may have been responsible for the rise in unemployment from 1931 to 1933, when real money balances did fall, it cannot easily explain the initial downturn from 1929 to 1931.

The second problem for the money hypothesis is the behavior of interest rates. If a contractionary shift in the LM curve triggered the Depression, we should have observed higher interest rates. Yet nominal interest rates fell continuously from 1929 to 1933.

These two reasons appear suffi cient to reject the view that the Depression was instigated by a contractionary shift in the LM curve. But was the fall in the money stock irrelevant? Next, we turn to another mechanism through which monetary policy might have been responsible for the severity of the Depression—the defl ation of the 1930s.

The Money Hypothesis Again: The Effects of Falling Prices

From 1929 to 1933 the price level fell 25 percent. Many economists blame this defl ation for the severity of the Great Depression. They argue that the defl a- tion may have turned what in 1931 was a typical economic downturn into an unprecedented period of high unemployment and depressed income. If correct, this argument gives new life to the money hypothesis. Because the falling money supply was, plausibly, responsible for the falling price level, it could have been responsible for the severity of the Depression. To evaluate this argument, we must discuss how changes in the price level affect income in the IS–LM model.

The Stabilizing Effects of Deflation In the IS–LM model we have developed so far, falling prices raise income. For any given supply of money M, a lower price level implies higher real money balances M/P. An increase in real money balances causes an expansionary shift in the LM curve, which leads to higher income.

Another channel through which falling prices expand income is called the Pigou effect. Arthur Pigou, a prominent classical economist in the 1930s, pointed out that real money balances are part of households’ wealth. As prices fall and real money balances rise, consumers should feel wealthier and spend more. This increase in consumer spending should cause an expansionary shift in the IS curve, also leading to higher income.

These two reasons led some economists in the 1930s to believe that falling prices would help stabilize the economy. That is, they thought that a decline in the price level would automatically push the economy back toward full employ- ment. Yet other economists were less confi dent in the economy’s ability to correct itself. They pointed to other effects of falling prices, to which we now turn.

The Destabilizing Effects of Defl ation Economists have proposed two theo- ries to explain how falling prices could depress income rather than raise it. The fi rst, called the debt-defl ation theory, describes the effects of unexpected falls in the price level. The second explains the effects of expected defl ation.

The debt-defl ation theory begins with an observation from Chapter 5: unanticipated changes in the price level redistribute wealth between debtors

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346 | P A R T I V Business Cycle Theory: The Economy in the Short Run

and creditors. If a debtor owes a creditor $1,000, then the real amount of this debt is $1,000/P, where P is the price level. A fall in the price level raises the real amount of this debt—the amount of purchasing power the debtor must repay the creditor. Therefore, an unexpected defl ation enriches creditors and impoverishes debtors.

The debt-defl ation theory then posits that this redistribution of wealth affects spending on goods and services. In response to the redistribution from debtors to creditors, debtors spend less and creditors spend more. If these two groups have equal spending propensities, there is no aggregate impact. But it seems reasonable to assume that debtors have higher propensities to spend than creditors—perhaps that is why the debtors are in debt in the fi rst place. In this case, debtors reduce their spending by more than creditors raise theirs. The net effect is a reduction in spending, a contractionary shift in the IS curve, and lower national income.

To understand how expected changes in prices can affect income, we need to add a new variable to the IS–LM model. Our discussion of the model so far has not distinguished between the nominal and real interest rates. Yet we know from previous chapters that investment depends on the real interest rate and that money demand depends on the nominal interest rate. If i is the nominal interest rate and E� is expected infl ation, then the ex ante real interest rate is i – E�. We can now write the IS–LM model as

Y � C(Y � T ) � I(i � E�) + G IS,

M/P � L(i, Y ) LM.

Expected infl ation enters as a variable in the IS curve. Thus, changes in expected infl ation shift the IS curve.

Let’s use this extended IS–LM model to examine how changes in expected infl ation infl uence the level of income. We begin by assuming that everyone expects the price level to remain the same. In this case, there is no expected infl ation (E� = 0), and these two equations produce the familiar IS–LM model. Figure 12-8 depicts this initial situation with the LM curve and the IS curve labeled IS1. The intersection of these two curves determines the nominal and real interest rates, which for now are the same.

Now suppose that everyone suddenly expects that the price level will fall in the future, so that E� becomes negative. The real interest rate is now higher at any given nominal interest rate. This increase in the real interest rate depresses planned investment spending, shifting the IS curve from IS1 to IS2. (The vertical distance of the downward shift exactly equals the expected defl ation.) Thus, an expected defl ation leads to a reduction in national income from Y1 to Y2. The nominal interest rate falls from i1 to i2, while the real interest rate rises from r1 to r2.

Here is the story behind this fi gure. When fi rms come to expect defl ation, they become reluctant to borrow to buy investment goods because they believe they will have to repay these loans later in more valuable dollars. The fall in investment depresses planned expenditure, which in turn depresses income. The fall in income reduces the demand for money, and this reduces the nominal interest rate that equilibrates the money market. The nominal interest rate falls by less than the expected defl ation, so the real interest rate rises.

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Note that there is a common thread in these two stories of destabilizing defl a- tion. In both, falling prices depress national income by causing a contractionary shift in the IS curve. Because a defl ation of the size observed from 1929 to 1933 is unlikely except in the presence of a major contraction in the money supply, these two explanations assign some of the responsibility for the Depression— especially its severity—to the Fed. In other words, if falling prices are destabiliz- ing, then a contraction in the money supply can lead to a fall in income, even without a decrease in real money balances or a rise in nominal interest rates.

Could the Depression Happen Again?

Economists study the Depression both because of its intrinsic interest as a major economic event and to provide guidance to policymakers so that it will not hap- pen again. To state with confi dence whether this event could recur, we would need to know why it happened. Because there is not yet agreement on the causes of the Great Depression, it is impossible to rule out with certainty another depression of this magnitude.

Yet most economists believe that the mistakes that led to the Great Depression are unlikely to be repeated. The Fed seems unlikely to allow the money supply to fall by one-fourth. Many economists believe that the defl ation of the early 1930s was responsible for the depth and length of the Depression. And it seems likely that such a prolonged defl ation was possible only in the presence of a fall- ing money supply.

The fi scal-policy mistakes of the Depression are also unlikely to be repeated. Fiscal policy in the 1930s not only failed to help but actually further depressed aggregate demand. Few economists today would advocate such a rigid adherence to a balanced budget in the face of massive unemployment.

In addition, there are many institutions today that would help prevent the events of the 1930s from recurring. The system of Federal Deposit Insurance

Expected Defl ation in the IS–LM Model An expected defl a- tion (a negative value of E�) raises the real interest rate for any given nominal interest rate, and this depresses investment spending. The reduction in investment shifts the IS curve downward. The level of income falls from Y1 to Y2. The nominal interest rate falls from i1 to i2, and the real interest rate rises from r1 to r2.

Y2 Y1

i2

r1 � i1

r2

IS2

IS1

LM

E�

Interest rate, i

Income, output, Y

FIGURE 12-8

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348 | P A R T I V Business Cycle Theory: The Economy in the Short Run

makes widespread bank failures less likely. The income tax causes an automatic reduction in taxes when income falls, which stabilizes the economy. Finally, economists know more today than they did in the 1930s. Our knowledge of how the economy works, limited as it still is, should help policymakers formulate better policies to combat such widespread unemployment.

The Financial Crisis and Economic Downturn of 2008 and 2009

In 2008 the U.S. economy experienced a fi nancial crisis, followed by a deep recession. Several of the developments during this time were reminiscent of events during the 1930s, causing many observers to fear that the economy might experience a second Great Depression.

The story of the 2008 crisis begins a few years earlier with a substantial boom in the housing market. The boom had several sources. In part, it was fueled by low interest rates. As we saw in a previous Case Study in this chapter, the Federal Reserve lowered interest rates to historically low levels in the aftermath of the recession of 2001. Low interest rates helped the economy recover, but by making it less expensive to get a mortgage and buy a home, they also contributed to a rise in housing prices.

In addition, developments in the mortgage market made it easier for subprime borrowers—those borrowers with higher risk of default based on their income and credit history—to get mortgages to buy homes. One of these developments was securitization, the process by which one mortgage originator makes loans and then sells them to an investment bank, which in turn bundles them together into a variety of “mortgage-backed securities” and then sells them to a third fi nancial institution (such as a bank, pension fund, or insurance company). These securities pay a return as long as homeowners continue to repay their loans, but they lose value if homeowners default. Unfortunately, it seems that the ultimate holders of these mortgage-backed securities sometimes failed to fully appreciate the risks they were taking. Some economists blame insuffi cient regulation for these high- risk loans. Others believe the problem was not too little regulation but the wrong kind: some government policies encouraged this high-risk lending to make the goal of homeownership more attainable for low-income families.

Together, these forces drove up housing demand and housing prices. From 1995 to 2006, average housing prices in the United States more than doubled. Some observ- ers view this rise in housing prices as a speculative bubble, as more people bought homes based on the hope and expectation that the prices would continue to rise.

The high price of housing, however, proved unsustainable. From 2006 to 2009, housing prices nationwide fell about 30 percent. Such price fl uctuations should not necessarily be a problem in a market economy. After all, price move- ments are how markets equilibrate supply and demand. But, in this case, the price decline led to a series of problematic repercussions.

The fi rst of these repercussions was a substantial rise in mortgage defaults and home foreclosures. During the housing boom, many homeowners had bought

CASE STUDY

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their homes with mostly borrowed money and minimal down payments. When housing prices declined, these homeowners were underwater: they owed more on their mortgages than their homes were worth. Many of these homeowners stopped paying their loans. The banks servicing the mortgages responded to the defaults by taking the houses away in foreclosure procedures and then selling them off. The banks’ goal was to recoup whatever they could. The increase in the num- ber of homes for sale, however, exacerbated the downward spiral of housing prices.

A second repercussion was large losses at the various fi nancial institutions that owned mortgage-backed securities. In essence, by borrowing large sums to buy high-risk mortgages, these companies had bet that housing prices would keep rising; when this bet turned bad, they found themselves at or near the point of bankruptcy. Even healthy banks stopped trusting one another and avoided inter- bank lending because it was hard to discern which institution would be the next to go out of business. Because of these large losses at fi nancial institutions and the widespread fear and distrust, the ability of the fi nancial system to make loans even to creditworthy customers was impaired. Chapter 20 discusses fi nancial crises, including this one, in more detail.

A third repercussion was a substantial rise in stock market volatility. Many companies rely on the fi nancial system to get the resources they need for busi- ness expansion or to help them manage their short-term cash fl ows. With the fi nancial system less able to perform its normal operations, the profi tability of many companies was called into question. Because it was hard to know how bad things would get, stock market volatility reached levels not seen since the 1930s.

Higher volatility, in turn, led to a fourth repercussion: a decline in consumer con- fi dence. In the midst of all the uncertainty, households started putting off spending plans. In particular, expenditure on durable goods plummeted. As a result of all these events, the economy experienced a large contractionary shift in the IS curve.

The U.S government responded vigorously as the crisis unfolded. First, the Fed cut its target for the federal funds rate from 5.25 percent in September 2007 to about zero in December 2008. Second, in an even more unusual move in October 2008, Congress appropriated $700 billion for the Treasury to use to res- cue the fi nancial system. In large part these funds were used for equity injections into banks. That is, the Treasury put funds into the banking system, which the banks could use to make loans; in exchange for these funds, the U.S. government became a part owner of these banks, at least temporarily. The goal of the rescue (or “bailout,” as it was sometimes called) was to stem the fi nancial crisis on Wall Street and prevent it from causing a depression on every other street in America. Finally, as discussed in Chapter 11, one of Barack Obama’s fi rst acts when he became president in January 2009 was to support a major increase in government spending to expand aggregate demand.

As this book was going to press, the economy was recovering from the reces- sion, albeit very gradually. Economic growth was positive but well below the rate experienced during previous recoveries. Unemployment remained high. Policy- makers could take some credit for having averted another Great Depression. Yet there is no doubt that the fi nancial crisis of 2008–2009 and its aftermath consti- tuted a painful event for many families. ■

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350 | P A R T I V Business Cycle Theory: The Economy in the Short Run

In the United States in the 1930s, interest rates reached very low levels. As Table 12-2 shows, U.S. interest rates were well under 1 percent throughout the second half of the 1930s. A similar situation occurred during the economic downturn of 2008– 2009. In December 2008, the Federal Reserve cut its target for the federal funds rate to the range of zero to 0.25 percent, and it kept the rate at that level for the next several years. On August 9, 2011, the Fed released a statement pledging to keep interest rates low “at least through mid-2013.”

Some economists describe this situation as a liquidity trap. According to the IS–LM model, expansionary monetary policy works by reduc- ing interest rates and stimulating investment spending. But if interest rates have already fallen almost to zero, then perhaps monetary policy is no longer effective. Nominal interest rates can- not fall below zero: rather than making a loan at a negative nominal interest rate, a person would just hold cash. In this environment, expansionary monetary policy increases the supply of money, making the public’s asset portfolio more liquid, but because interest rates can’t fall any farther, the extra liquidity might not have any effect. Aggregate demand, production, and employ- ment may be “trapped” at low levels. The liquid- ity trap is sometimes called the problem of the zero lower bound.

Other economists are skeptical about the rel- evance of liquidity traps and believe that central banks continue to have tools to expand the econ- omy, even after its interest rate target hits the lower bound of zero. One possibility is that the central bank could raise infl ation expectations by committing itself to future monetary expansion. Even if nominal interest rates cannot fall any farther, higher expected infl ation can lower real interest rates by making them negative, which would stimulate investment spending. A second possibility is that monetary expansion could

The Liquidity Trap (Also Known as the Zero Lower Bound) cause the currency to lose value in the market for foreign-currency exchange. This depreciation would make the nation’s goods cheaper abroad, stimulating export demand. (This mechanism goes beyond the closed-economy IS–LM model we have used in this chapter, but it fi ts well with the open-economy version of the model devel- oped in the next chapter.) A third possibility is that the central bank could conduct expansion- ary open-market operations in a larger variety of fi nancial instruments than it normally does. For example, it could buy mortgages and corporate debt and thereby lower the interest rates on these kinds of loans. The Federal Reserve actively pur- sued this last option in response to the downturn of 2008–2009, a policy sometimes called quanti- tative easing.

How much do monetary policymakers need to worry about the liquidity trap? Might the central bank at times lose its power to infl uence the econ- omy? There is no consensus about the answers. Skeptics say we shouldn’t worry about the liquid- ity trap because central banks have various tools at their disposal. But others say the possibility of a liquidity trap argues for a target rate of infl ation greater than zero. Under zero infl ation, the real interest rate, like the nominal interest, can never fall below zero. But if the normal rate of infl ation is, say, 4 percent, then the central bank can easily push the real interest rate to negative 4 percent by lowering the nominal interest rate toward zero. Put differently, a higher target for the infl ation rate means a higher nominal interest rate in nor- mal times (recall the Fisher effect), which in turn gives the central bank more room to cut interest rates when the economy experiences recessionary shocks. Thus, a higher infl ation target gives mon- etary policymakers more room to stimulate the economy when needed, reducing the likelihood that the economy will hit the zero lower bound and fall into a liquidity trap.5

F Y I

5To read more about the liquidity trap, see Paul R. Krugman, “It’s Baaack: Japan’s Slump and the Return of the Liquidity Trap,” Brookings Panel on Economic Activity 2 (1998): 137–205.

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12-4 Conclusion

The purpose of this chapter and the previous one has been to deepen our under- standing of aggregate demand. We now have the tools to analyze the effects of monetary and fi scal policy in the long run and in the short run. In the long run, prices are fl exible, and we use the classical analysis of Parts Two and Three of this book. In the short run, prices are sticky, and we use the IS–LM model to examine how changes in policy infl uence the economy.

The model in this and the previous chapter provides the basic framework for analyzing the economy in the short run, but it is not the whole story. In Chap- ter 13 we examine how international interactions affect the theory of aggregate demand. In Chapter 14 we examine the theory behind short-run aggregate supply. Subsequent chapters further refi ne the theory and examine various issues that arise as the theory is applied to formulate macroeconomic policy. The IS–LM model presented in this and the previous chapter provides the starting point for this further analysis.

Summary

1. The IS–LM model is a general theory of the aggregate demand for goods and services. The exogenous variables in the model are fiscal policy, monetary policy, and the price level. The model explains two endogenous variables: the interest rate and the level of national income.

2. The IS curve represents the negative relationship between the interest rate and the level of income that arises from equilibrium in the market for goods and services. The LM curve represents the positive relationship between the interest rate and the level of income that arises from equi- librium in the market for real money balances. Equilibrium in the IS–LM model—the intersection of the IS and LM curves—represents simultane- ous equilibrium in the market for goods and services and in the market for real money balances.

3. The aggregate demand curve summarizes the results from the IS–LM model by showing equilibrium income at any given price level. The aggre- gate demand curve slopes downward because a lower price level increases real money balances, lowers the interest rate, stimulates investment spending, and thereby raises equilibrium income.

4. Expansionary fi scal policy—an increase in government purchases or a decrease in taxes—shifts the IS curve to the right. This shift in the IS curve increases the interest rate and income. The increase in income represents a rightward shift in the aggregate demand curve. Similarly, contractionary fi s- cal policy shifts the IS curve to the left, lowers the interest rate and income, and shifts the aggregate demand curve to the left.

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5. Expansionary monetary policy shifts the LM curve downward. This shift in the LM curve lowers the interest rate and raises income. The increase in income represents a rightward shift of the aggregate demand curve. Simi- larly, contractionary monetary policy shifts the LM curve upward, raises the interest rate, lowers income, and shifts the aggregate demand curve to the left.

K E Y C O N C E P T S

Monetary transmission mechanism

Pigou effect

1. Explain why the aggregate demand curve slopes downward.

2. What is the impact of an increase in taxes on the interest rate, income, consumption, and investment?

Q U E S T I O N S F O R R E V I E W

3. What is the impact of a decrease in the money supply on the interest rate, income, consump- tion, and investment?

4. Describe the possible effects of falling prices on equilibrium income.

P R O B L E M S A N D A P P L I C A T I O N S

1. According to the IS–LM model, what happens in the short run to the interest rate, income, consumption, and investment under the follow- ing circumstances? Be sure your answer includes an appropriate graph.

a. The central bank increases the money supply.

b. The government increases government purchases.

c. The government increases taxes.

d. The government increases government pur- chases and taxes by equal amounts.

2. Use the IS–LM model to predict the short- run effects of each of the following shocks on income, the interest rate, consumption, and investment. In each case, explain what the Fed should do to keep income at its initial level.

a. After the invention of a new high-speed computer chip, many fi rms decide to upgrade their computer systems.

b. A wave of credit card fraud increases the fre- quency with which people make transactions in cash.

c. A best-seller titled Retire Rich convinces the public to increase the percentage of their income devoted to saving.

d. The appointment of a new “dovish” Federal Reserve chairman increases expected infl ation.

3. Consider the economy of Hicksonia.

a. The consumption function is given by

C = 200 + 0.75(Y – T ).

The investment function is

I = 200 – 25r.

Government purchases and taxes are both 100. For this economy, graph the IS curve for r ranging from 0 to 8.

b. The money demand function in Hicksonia is

(M/P)d = Y – 100r.

The money supply M is 1,000 and the price level P is 2. For this economy, graph the LM curve for r ranging from 0 to 8.

Debt-defl ation theory

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C H A P T E R 1 2 Aggregate Demand II: Applying the IS–LM Model | 353

c. Find the equilibrium interest rate r and the equilibrium level of income Y.

d. Suppose that government purchases are raised from 100 to 150. How does the IS curve shift? What are the new equilibrium interest rate and level of income?

e. Suppose instead that the money supply is raised from 1,000 to 1,200. How does the LM curve shift? What are the new equilib- rium interest rate and level of income?

f. With the initial values for monetary and fi s- cal policy, suppose that the price level rises from 2 to 4. What happens? What are the new equilibrium interest rate and level of income?

g. Derive and graph an equation for the aggre- gate demand curve. What happens to this aggregate demand curve if fi scal or monetary policy changes, as in parts (d) and (e)?

4. Determine whether each of the following state- ments is true or false, and explain why. For each true statement, discuss the impact of monetary and fi scal policy in that special case.

a. If investment does not depend on the interest rate, the LM curve is horizontal.

b. If investment does not depend on the interest rate, the IS curve is vertical.

c. If money demand does not depend on the interest rate, the IS curve is horizontal.

d. If money demand does not depend on the interest rate, the LM curve is vertical.

e. If money demand does not depend on income, the LM curve is horizontal.

f. If money demand is extremely sensitive to the interest rate, the LM curve is horizontal.

5. Monetary policy and fi scal policy often change at the same time.

a. Suppose that the government wants to raise investment but keep output constant. In the IS–LM model, what mix of monetary and fi scal policy will achieve this goal?

b. In the early 1980s, the U.S. government cut taxes and ran a budget defi cit while the Fed pursued a tight monetary policy. What effect should this policy mix have?

6. Use the IS–LM diagram to describe both the short-run effects and the long-run effects of the

following changes on national income, the inter- est rate, the price level, consumption, investment, and real money balances.

a. An increase in the money supply

b. An increase in government purchases

c. An increase in taxes

7. The Fed is considering two alternative monetary policies:

• holding the money supply constant and letting the interest rate adjust, or

• adjusting the money supply to hold the inter- est rate constant.

In the IS–LM model, which policy will better stabilize output under the following conditions? Explain your answer.

a. All shocks to the economy arise from exog- enous changes in the demand for goods and services.

b. All shocks to the economy arise from exogenous changes in the demand for money.

8. Suppose that the demand for real money balances depends on disposable income. That is, the money demand function is

M/P = L(r, Y – T ).

Using the IS–LM model, discuss whether this change in the money demand function alters the following.

a. The analysis of changes in government purchases

b. The analysis of changes in taxes

9. This problem asks you to analyze the IS–LM model algebraically. Suppose consumption is a linear function of disposable income:

C(Y – T ) = a + b(Y – T ),

where a > 0 and 0 < b < 1. The parameter b is the marginal propensity to consume, and the parameter a is a constant sometimes called autonomous consumption. Suppose also that investment is a linear function of the interest rate:

I(r) = c – dr,

where c > 0 and d > 0. The parameter d mea- sures the sensitivity of investment to the interest

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rate, and the parameter c is a constant sometimes called autonomous investment.

a. Solve for Y as a function of r, the exogenous variables G and T, and the model’s parameters a, b, c, and d.

b. How does the slope of the IS curve depend on the parameter d, the interest sensitivity of investment? Refer to your answer to part (a), and explain the intuition.

c. Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or a $100 increase in government spending? Refer to your answer to part (a), and explain the intuition.

Now suppose demand for real money balances is a linear function of income and the interest rate:

L(r, Y ) = eY – fr,

where e > 0 and f > 0. The parameter e measures the sensitivity of money demand to income, while the parameter f measures the sensitivity of money demand to the interest rate.

d. Solve for r as a function of Y, M, and P and the parameters e and f.

e. Using your answer to part (d), determine whether the LM curve is steeper for large or small values of f, and explain the intuition.

f. How does the size of the shift in the LM curve resulting from a $100 increase in M depend on

i. the value of the parameter e, the income sensitivity of money demand?

ii. the value of the parameter f, the interest sensitivity of money demand?

g. Use your answers to parts (a) and (d) to derive an expression for the aggregate demand curve. Your expression should show Y as a function of P; of exogenous policy variables M, G, and T; and of the model’s parameters. This expres- sion should not contain r.

h. Use your answer to part (g) to prove that the aggregate demand curve has a negative slope.

i. Use your answer to part (g) to prove that increases in G and M, and decreases in T, shift the aggregate demand curve to the right. How does this result change if the parameter f, the interest sensitivity of money demand, equals zero? Explain the intuition for your result.

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355

The Open Economy Revisited: The Mundell–Fleming Model and the Exchange-Rate Regime

13C H A P T E R

The world is still a closed economy, but its regions and countries are becoming

increasingly open. . . . The international economic climate has changed in

the direction of fi nancial integration, and this has important implications for

economic policy.

—Robert Mundell, 1963

When conducting monetary and fi scal policy, policymakers often look beyond their own country’s borders. Even if domestic pros-perity is their sole objective, it is necessary for them to consider the rest of the world. The international fl ow of goods and services and the inter- national fl ow of capital can affect an economy in profound ways. Policymakers ignore these effects at their peril.

In this chapter we extend our analysis of aggregate demand to include inter- national trade and fi nance. The model developed in this chapter, called the Mundell–Fleming model, has been described as “the dominant policy para- digm for studying open-economy monetary and fi scal policy.” In 1999, Robert Mundell was awarded the Nobel Prize for his work in open-economy macro- economics, including this model.1

The Mundell–Fleming model is a close relative of the IS–LM model. Both models stress the interaction between the goods market and the money mar- ket. Both models assume that the price level is fi xed and then show what causes short-run fl uctuations in aggregate income (or, equivalently, shifts in the

1The quotation is from Maurice Obstfeld and Kenneth Rogoff, Foundations of International Macroeconomics (Cambridge, Mass.: MIT Press, 1996)—a leading graduate-level textbook in open- economy macroeconomics. The Mundell–Fleming model was developed in the early 1960s. Mundell’s contributions are collected in Robert A. Mundell, International Economics (New York: Macmillan, 1968). For Fleming’s contribution, see J. Marcus Fleming, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates,’’ IMF Staff Papers 9 (November 1962): 369–379. Fleming died in 1976, so he was not eligible to share in the Nobel award.

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aggregate demand curve). The key difference is that the IS–LM model assumes a closed economy, whereas the Mundell–Fleming model assumes an open econ- omy. The Mundell–Fleming model extends the short-run model of national income from Chapters 11 and 12 by including the effects of international trade and fi nance discussed in Chapter 6.

The Mundell–Fleming model makes one important and extreme assumption: it assumes that the economy being studied is a small open economy with perfect capital mobility. That is, the economy can borrow or lend as much as it wants in world fi nancial markets and, as a result, the economy’s interest rate is determined by the world interest rate. Here is how Mundell himself, in his original 1963 article, explained why he made this assumption:

In order to present my conclusions in the simplest possible way and to bring the implications for policy into sharpest relief, I assume the extreme degree of mobility that prevails when a country cannot maintain an interest rate differ- ent from the general level prevailing abroad. This assumption will overstate the case but it has the merit of posing a stereotype towards which international fi nancial relations seem to be heading. At the same time it might be argued that the assumption is not far from the truth in those fi nancial centers, of which Zurich, Amsterdam, and Brussels may be taken as examples, where the authori- ties already recognize their lessening ability to dominate money market con- ditions and insulate them from foreign infl uences. It should also have a high degree of relevance to a country like Canada whose fi nancial markets are dominated to a great degree by the vast New York market.

As we will see, Mundell’s assumption of a small open economy with perfect capital mobility will prove useful in developing a tractable and illuminating model.2

One lesson from the Mundell–Fleming model is that the behavior of an econ- omy depends on the exchange-rate system it has adopted. Indeed, the model was fi rst developed in large part to understand how alternative exchange-rate regimes work and how the choice of exchange-rate regime impinges on monetary and fi scal policy. We begin by assuming that the economy operates with a fl oating exchange rate. That is, we assume that the central bank allows the exchange rate to adjust to changing economic conditions. We then examine how the economy operates under a fi xed exchange rate. After developing the model, we will be in a position to address an important policy question: what exchange-rate system should a nation adopt?

These issues of open-economy macroeconomics have been very much in the news in recent years. As various European nations, most notably Greece, experi- enced severe fi nancial diffi culties, many observers wondered whether it was wise for much of the continent to adopt a common currency—the most extreme

2This assumption—and thus the Mundell–Fleming model—does not apply exactly to a large open economy such as that of the United States. In the conclusion to this chapter (and more fully in the appendix), we consider what happens in the more complex case in which international capital mobility is less than perfect or a nation is so large that it can infl uence world fi nancial markets.

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form of a fi xed exchange rate. If each nation had its own currency, monetary policy and the exchange rate could have adjusted more easily to the changing individual circumstances and needs of each nation. Meanwhile, many American policymakers, including both President George W. Bush and President Barack Obama, were objecting that China did not allow the value of its currency to fl oat freely against the U.S. dollar. They argued that China kept its currency artifi cially cheap, making its goods more competitive on world markets. As we will see, the Mundell–Fleming model offers a useful starting point for understanding and evaluating these often-heated international policy debates.

13-1 The Mundell–Fleming Model

In this section we construct the Mundell–Fleming model, and in the following sections we use the model to examine the impact of various policies. As you will see, the Mundell–Fleming model is built from components we have used in previous chapters. But these pieces are put together in a new way to address a new set of questions.

The Key Assumption: Small Open Economy With Perfect Capital Mobility

Let’s begin with the assumption of a small open economy with perfect capital mobility. As we saw in Chapter 6, this assumption means that the interest rate in this economy r is determined by the world interest rate r ∗. Mathematically, we can write this assumption as

r = r ∗.

This world interest rate is assumed to be exogenously fi xed because the economy is suffi ciently small relative to the world economy that it can borrow or lend as much as it wants in world fi nancial markets without affecting the world interest rate.

Although the idea of perfect capital mobility is expressed with a simple equa- tion, it is important not to lose sight of the sophisticated process that this equa- tion represents. Imagine that some event occurred that would normally raise the interest rate (such as a decline in domestic saving). In a small open economy, the domestic interest rate might rise by a little bit for a short time, but as soon as it did, foreigners would see the higher interest rate and start lending to this country (by, for instance, buying this country’s bonds). The capital infl ow would drive the domestic interest rate back toward r ∗. Similarly, if any event started to drive the domestic interest rate downward, capital would fl ow out of the country to earn a higher return abroad, and this capital outfl ow would drive the domestic interest rate back up to r ∗. Hence, the r = r ∗ equation represents the assumption that the international fl ow of capital is rapid enough to keep the domestic interest rate equal to the world interest rate.

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The Goods Market and the IS* Curve

The Mundell–Fleming model describes the market for goods and services much as the IS–LM model does, but it adds a new term for net exports. In particular, the goods market is represented with the following equation:

Y = C(Y − T ) + I(r) + G + NX(e).

This equation states that aggregate income Y is the sum of consumption C, investment I, government purchases G, and net exports NX. Consumption depends positively on disposable income Y − T. Investment depends negatively on the interest rate. Net exports depend negatively on the exchange rate e. As before, we defi ne the exchange rate e as the amount of foreign currency per unit of domestic currency—for example, e might be 100 yen per dollar.

You may recall that in Chapter 6 we related net exports to the real exchange rate (the relative price of goods at home and abroad) rather than the nominal exchange rate (the relative price of domestic and foreign currencies). If e is the nominal exchange rate, then the real exchange rate � equals eP/P ∗, where P is the domestic price level and P ∗ is the foreign price level. The Mundell–Fleming model, however, assumes that the price levels at home and abroad are fi xed, so the real exchange rate is proportional to the nominal exchange rate. That is, when the domestic currency appreciates and the nominal exchange rate rises (from, say, 100 to 120 yen per dol- lar), the real exchange rate rises as well; thus, foreign goods become cheaper com- pared to domestic goods, and this causes exports to fall and imports to rise.

The goods-market equilibrium condition above has two fi nancial variables that affect expenditure on goods and services (the interest rate and the exchange rate), but we can simplify matters by using the assumption of perfect capital mobility, r = r ∗:

Y = C(Y − T ) + I(r ∗) + G + NX(e).

Let’s call this the IS ∗ equation. (The asterisk reminds us that the equation holds the interest rate constant at the world interest rate r ∗.) We can illustrate this equa- tion on a graph in which income is on the horizontal axis and the exchange rate is on the vertical axis. This curve is shown in panel (c) of Figure 13-1.

The IS ∗ curve slopes downward because a higher exchange rate reduces net exports, which in turn lowers aggregate income. To show how this works, the other panels of Figure 13-1 combine the net-exports schedule and the Keynesian cross to derive the IS ∗ curve. In panel (a), an increase in the exchange rate from e1 to e2 lowers net exports from NX(e1) to NX(e2). In panel (b), the reduction in net exports shifts the planned-expenditure schedule downward and thus lowers income from Y1 to Y2. The IS ∗ curve summarizes this relationship between the exchange rate e and income Y.

The Money Market and the LM* Curve

The Mundell–Fleming model represents the money market with an equation that should be familiar from the IS–LM model:

M/P = L(r, Y ).

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This equation states that the supply of real money balances M/P equals the demand L(r, Y ). The demand for real balances depends negatively on the interest rate and positively on income Y. The money supply M is an exogenous vari- able controlled by the central bank, and because the Mundell–Fleming model is designed to analyze short-run fl uctuations, the price level P is also assumed to be exogenously fi xed.

Once again, we add the assumption that the domestic interest rate equals the world interest rate, so r = r ∗:

M/P = L(r ∗, Y ).

Let’s call this the LM ∗ equation. We can represent it graphically with a verti- cal line, as in panel (b) of Figure 13-2. The LM ∗ curve is vertical because the exchange rate does not enter into the LM ∗ equation. Given the world interest

FIGURE 13-1

Expenditure

Exchange rate, e

Exchange rate, e

Income, output, Y

Income, output, Y

Net exports, NX

Y1 Y2

IS*

NX(e1) NX(e2)

�NX

�NX

e1

e2

Actual expenditure

Planned expenditure

45° Y1 Y2

e1

e2

(a) The Net-Exports Schedule

(b) The Keynesian Cross

(c) The IS* Curve

2. ... lowers net exports, ...

3. ... which shifts planned expenditure downward ...

5. The IS* curve summarizes these changes in the goods- market equilibrium.

1. An increase in the exchange rate ...

4. ... and lowers income.

The IS * Curve The IS* curve is derived from the net-exports schedule and the Keynesian cross. Panel (a) shows the net-exports schedule: an increase in the exchange rate from e1 to e2 low- ers net exports from NX(e1) to NX(e2). Panel (b) shows the Keynesian cross: a decrease in net exports from NX(e1) to NX(e2) shifts the planned-expenditure schedule downward and reduces income from Y1 to Y2. Panel (c) shows the IS* curve summarizing this relation- ship between the exchange rate and income: the higher the exchange rate, the lower the level of income.

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360 | P A R T I V Business Cycle Theory: The Economy in the Short Run

rate, the LM ∗ equation determines aggregate income, regardless of the exchange rate. Figure 13-2 shows how the LM ∗ curve arises from the world interest rate and the LM curve, which relates the interest rate and income.

Putting the Pieces Together

According to the Mundell–Fleming model, a small open economy with perfect capital mobility can be described by two equations:

Y = C(Y − T ) + I(r ∗) + G + NX(e) IS ∗, M/P = L(r ∗, Y ) LM ∗.

The LM * Curve Panel (a) shows the standard LM curve [which graphs the equation M/P = L(r, Y)] together with a horizontal line representing the world interest rate r*. The intersection of these two curves determines the level of income, regardless of the exchange rate. Therefore, as panel (b) shows, the LM* curve is vertical.

Interest rate, r

Exchange rate, e

Income, output, Y

Income, output, Y

1. The money market equilibrium condition ...

2. ... and the world interest rate ...

3. ... determine the level of income.

(a) The LM Curve

(b) The LM* Curve

LM

r � r*

LM*

FIGURE 13-2

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C H A P T E R 1 3 The Open Economy Revisited: The Mundell–Fleming Model and the Exchange-Rate Regime | 361

The fi rst equation describes equilibrium in the goods market; the second describes equilibrium in the money market. The exogenous variables are fi scal policy G and T, monetary policy M, the price level P, and the world interest rate r ∗. The endogenous variables are income Y and the exchange rate e.

Figure 13-3 illustrates these two relationships. The equilibrium for the economy is found where the IS ∗ curve and the LM ∗ curve intersect. This intersection shows the exchange rate and the level of income at which the goods market and the money market are both in equilibrium. With this diagram, we can use the Mundell–Fleming model to show how aggregate income Y and the exchange rate e respond to changes in policy.

13-2 The Small Open Economy Under Floating Exchange Rates

Before analyzing the impact of policies in an open economy, we must specify the international monetary system in which the country has chosen to operate. That is, we must consider how people engaged in international trade and fi nance can convert the currency of one country into the currency of another.

We start with the system relevant for most major economies today: fl oating exchange rates. Under a system of fl oating exchange rates, the exchange rate is set by market forces and is allowed to fl uctuate in response to changing eco- nomic conditions. In this case, the exchange rate e adjusts to achieve simultane- ous equilibrium in the goods market and the money market. When something happens to change that equilibrium, the exchange rate is allowed to move to a new equilibrium value.

The Mundell–Fleming Model This graph of the Mundell– Fleming model plots the goods-market equilibrium condition IS* and the money market equilibrium condition LM*. Both curves are drawn holding the interest rate con- stant at the world interest rate. The intersection of these two curves shows the level of income and the exchange rate that satisfy equilibrium both in the goods market and in the money market.

Exchange rate, e

Income, output, Y

Equilibrium exchange rate

Equilibrium income

LM*

IS*