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Managerial Economics and Business Strategy

NINTH EDITION

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The McGraw-Hill Series Economics

ESSENTIALS OF ECONOMICS

Brue, McConnell, and Flynn Essentials of Economics Third Edition

Mandel M: Economics: The Basics Third Edition

Schiller and Gebhardt Essentials of Economics Tenth Edition

PRINCIPLES OF ECONOMICS

Asarta and Butters Connect Master: Principles of Economics First Edition

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MANAGERIAL ECONOMICS

Baye and Prince Managerial Economics and Business Strategy Ninth Edition

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Managerial Economics and Business Strategy

Michael R. Baye Bert Elwert Professor of Business Economics & Public Policy Kelley School of Business Indiana University

Jeffrey T. Prince Associate Professor of Business Economics & Public Policy Harold A. Poling Chair in Strategic Management Kelley School of Business Indiana University

NINTH EDITION

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MANAGERIAL ECONOMICS AND BUSINESS STRATEGY, NINTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2017 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2014, 2010, 2008 and 2006. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

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DEDICATION

To my former students. —Michael R. Baye

To Annie, Kate, and Elise. —Jeffrey T. Prince

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vi

Michael R. Baye is the Bert Elwert Professor of Business Economics & Public Policy at Indiana University’s Kelley School of Business, and served as the Director of the Bureau of Economics at the Federal Trade Commission from July 2007 to December 2008. He received his BS in economics from Texas A&M University in 1980 and earned a PhD in economics from Purdue University in 1983. Prior to joining Indiana University, he taught graduate and undergraduate courses at The Pennsylvania State University, Texas A&M University, and the University of Kentucky. He has held a variety of editorial posts in economics, mar- keting, and business, and currently serves as a co-editor for the Journal of Economics and Management Strategy.

Professor Baye has won numerous awards for his outstanding teaching and research, and teaches courses in managerial economics and industrial organization at the undergrad- uate, MBA, and PhD levels. His research has been published in the American Economic Review, Journal of Political Economy, Econometrica, Review of Economic Studies, Economic Journal, and Management Science. It has also been featured in The Wall Street Journal, Forbes, the New York Times, and numerous other outlets. When he is not teaching or engaged in research, Mike enjoys activities ranging from camping to shopping for electronic gadgets.

Jeffrey T. Prince is Associate Professor of Business Economics & Public Policy at Indiana University’s Kelley School of Business. He is also the Harold A. Poling Chair in Strategic Management. He received his BA in economics and BS in mathematics and statistics from Miami University in 1998 and earned a PhD in economics from Northwestern University in 2004. Prior to joining Indiana University, he taught graduate and undergraduate courses at Cornell University.

Professor Prince has won top teaching honors as a faculty member at both Indiana University and Cornell, and as a graduate student at Northwestern. He has a broad research agenda within applied economics, having written and published on topics that include demand in technology markets, Internet diffusion, regulation in health care, risk aversion in insurance markets, and quality competition among airlines. He is one of a small number of economists to have published in both the top journal in economics (American Economic Review) and the top journal in management (Academy of Management Journal). He currently serves as a co-editor for the Journal of Economics and Management Strategy and on the editorial board for Information Economics and Policy. In his free time, Jeff enjoys activities ranging from poker and bridge to running and racquetball.

About the Authors

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vii

Thanks to feedback from users around the world, Managerial Economics and Business Strategy remains the best-selling managerial text in the market. We are grateful to all of you for allowing us to provide this updated and improved edition. Before highlighting some of the new features of the ninth edition, we would like to stress that the fundamental goal of the book—providing students with the tools from intermediate microeconomics, game the- ory, and industrial organization that they need to make sound managerial decisions—has not changed. What has changed are the examples used to make managerial economics come to life for this generation of students and the utilization of new technologies (such as Connect) for enhancing the teaching and learning experiences of instructors and their students.

This book begins by teaching managers the practical utility of basic economic tools such as present value analysis, supply and demand, regression, indifference curves, isoquants, pro- duction, costs, and the basic models of perfect competition, monopoly, and monopolistic com- petition. Adopters and reviewers also praise the book for its real-world examples and because it includes modern topics not contained in any other single managerial economics textbook: oligopoly, penetration pricing, multistage and repeated games, foreclosure, contracting, ver- tical and horizontal integration, networks, bargaining, predatory pricing, principal–agent problems, raising rivals’ costs, adverse selection, auctions, screening and signaling, search, limit pricing, and a host of other pricing strategies for firms enjoying market power. This balanced coverage of traditional and modern microeconomic tools makes it appropriate for a wide variety of managerial economics classrooms. An increasing number of business schools are adopting this book to replace (or use alongside) managerial strategy texts laden with anec- dotes but lacking the microeconomic tools needed to identify and implement the business strategies that are optimal in a given situation.

This ninth edition of Managerial Economics and Business Strategy has been revised to include updated examples and problems, but it retains all of the basic content that made pre- vious editions a success. The basic structure of the textbook is unchanged to ensure a smooth transition to this edition.

KEY PEDAGOGICAL FEATURES

The ninth edition retains all of the class-tested features of previous editions that enhance students’ learning experiences and make it easy to teach from this book. But this edition includes a number of new features available to those using McGraw-Hill’s wonderful interac- tive learning products, Connect and SmartBook. McGraw-Hill Connect® offers hundreds of variations of end-of-chapter problems that may be electronically graded and provide students with immediate, detailed, feedback. SmartBook® provides an adaptive reading experience. Students and instructors can access these and other powerful resources directly from their laptops, tablets, and phones. We know how important quality and accuracy is for both instruc- tors and students when utilizing these enhanced features. For this reason, and unlike many

Preface

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viii Preface

competing books, we are directly involved in the generation and editing of material offered through both Connect and SmartBook.

Headlines As in previous editions, each chapter begins with a Headline that is based on a real-world economic problem—a problem that students should be able to address after completing the chapter. These Headlines are essentially hand-picked “mini-cases” designed to motivate stu- dents to learn the material in the chapter. Each Headline is answered at the end of the relevant chapter—when the student is better prepared to deal with the complications of real-world prob- lems. Reviewers as well as users of previous editions praise the Headlines not only because they motivate students to learn the material in the chapter, but also because the answers at the end of each chapter help students learn how to use economics to make business decisions.

Learning Objectives Each chapter includes learning objectives designed to enhance the learning experience. End- of-chapter problems are denoted with the learning objective(s) to which they relate.

Demonstration Problems The best way to learn economics is to practice solving economic problems. So, in addition to the Headlines, each chapter contains many Demonstration Problems sprinkled throughout the text, along with detailed answers. This provides students with a mechanism to verify that they have mastered the material, and reduces the cost to students and instructors of having to meet during office hours to discuss answers to problems. Some of the more challenging demonstration problems have an accompanying video tutorial that walks through the solution step-by-step. These videos are available via Connect and at www.mhhe.com/baye9e.

Inside Business Applications Most chapters contain boxed material (called Inside Business applications) to illustrate how theories explained in the text relate to a host of different business situations. As in previous editions, we have tried to strike a balance between applications drawn from the current eco- nomic literature and the popular press.

Calculus and Non-Calculus Alternatives Users can easily include or exclude calculus-based material without losing content or con- tinuity. That’s because the basic principles and formulae needed to solve a particular class of economic problems (e.g., MR = MC) are first stated without appealing to the notation of calculus. Immediately following each stated principle or formula is a clearly marked Calculus Alternative. Each of these calculus alternatives states the preceding principle or formula in calculus notation, and explains the relation between the calculus-based and non- calculus- based formula. More detailed calculus derivations are relegated to chapter Appendices. Thus, the book is designed for use by instructors who want to integrate calculus into managerial economics and by those who do not require students to use calculus.

Variety of End-of-Chapter Problems Three types of problems are offered. Highly structured but nonetheless challenging Conceptual and Computational Questions stress fundamentals. These are followed by Problems and

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Preface ix

Applications, which are far less structured and, like real-world decision environments, may contain more information than is actually needed to solve the problem. Many of these applied problems are based on actual business events.

Additionally, the Time Warner Cable case that follows Chapter 14 includes 13 problems called Memos that have a “real-world feel” and complement the text. All of these case-based problems may be assigned on a chapter-by-chapter basis as specific skills are introduced, or as part of a capstone experience. 

Detailed answers to all problems can be found among the instructor resource material available via Connect.

Case Study A case study in business strategy—Time Warner Cable—follows Chapter 14 and was pre- pared especially for this text. It can be used either as a capstone case for the course or to supplement individual chapters. The case allows students to apply core elements from man- agerial economics to a remarkably rich business environment. Instructors can use the case as the basis for an “open-ended” discussion of business strategy, or they can assign specific “memos” (contained at the end of the case) that require students to apply specific tools from managerial economics to the case. Teaching notes, as well as solutions to all of the memos, are provided among the instructor resource material available via Connect.

Flexibility Instructors of managerial economics have genuinely heterogeneous textbook needs. Reviewers and users continue to praise the book for its flexibility, and they assure us that sections or even entire chapters can be excluded without losing continuity. For instance, an instructor wishing to stress microeconomic fundamentals might choose to cover Chapters 2, 3, 4, 5, 8, 9, 10, 11, and 12. An instructor teaching a more applied course that stresses business strategy might choose to cover Chapters 1, 2, 3, 5, 6, 7, 8, 10, 11, and 13. Each may choose to include additional chapters (for example, Chapter 14 or the Time Warner Cable case) as time permits. More generally, instructors can easily omit topics such as present value analysis, regression, indifference curves, isoquants, or reaction functions without losing continuity.

CHANGES IN THE NINTH EDITION

We have made every effort to update and improve Managerial Economics and Business Strategy while assuring a smooth transition to the ninth edition. Following is a summary of the pedagogical improvements, enhanced supplements, and content changes that make the ninth edition an even more powerful tool for teaching and learning managerial economics and business strategy.

∙ A brand new Case Study—Time Warner Cable—which introduces a whole new set of managerial challenges beyond those posed in our previous case, Challenges at Time Warner.

∙ New and updated end-of-chapter problems. ∙ Learning objective labels for each end-of-chapter problem, to help foster targeted

learning. ∙ New and updated Headlines. ∙ New and updated Inside Business applications.

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x Preface

Chapter-by-Chapter Changes ∙ Chapter 1 contains new and updated examples, several updated end-of-chapter prob-

lems, and a new end-of-chapter problem that carefully distinguishes total benefits and total costs from marginal benefits and marginal costs in an applied setting.

∙ Chapter 2 contains updated demonstration problems and an expanded discussion of price floors in the text and demonstration problems.

∙ Chapter 3 contains a new Headline and an updated table with accompanying discus- sion. It also has several updated end-of-chapter problems.

∙ Chapter 4 contains an updated Headline and updated Inside Business applications. It also has several updated end-of-chapter problems.

∙ Chapter 5 contains an updated Inside Business application with details about the Affordable Care Act. It also includes a formal definition of the law of diminishing marginal returns and has several updated end-of-chapter problems.

∙ Chapter 6 offers a new Inside Business on the duration of franchise contracts, updated examples, and several updated end-of-chapter problems.

∙ Chapter 7 contains a new Headline, updated examples and industry data, as well as several updated end-of-chapter problems.

∙ Chapter 8 contains an updated Inside Business concerning automobile competition in China, updated examples, and several updated end-of-chapter problems.

∙ Chapter 9 contains an updated end-of-chapter problem, as well as a new end-of- chapter problem looking at contestability within airline markets.

∙ Chapter 10 contains a new Inside Business application examining airline competition, as well as improved Demonstration Problem exposition. It also has several updated end-of-chapter problems.

∙ Chapter 11 contains a new Inside Business application discussing the use of fuel points by major U.S. grocery chains. It also has several updated end-of-chapter problems.

∙ Chapter 12 includes a new discussion of online reviews as a means of attracting risk- averse customers. It also includes a new Inside Business application, as well as several updated end-of-chapter problems.

∙ Chapter 13 contains a new Inside Business on limit pricing and the “Southwest Effect.” It also has two updated end-of-chapter problems.

∙ Chapter 14 contains a new Inside Business application discussing the Small Business Act for Europe as a key distinction in competition policy between Europe and the United States. In addition, it has two updated end-of-chapter problems, including one discussing the Trans-Pacific Partnership (TPP).

ORGANIZED LEARNING IN THE NINTH EDITION

Chapter Learning Objectives Students and instructors can be confident that the organization of each chapter reflects com- mon themes outlined by four to seven learning objectives listed on the first page of each chapter. These objectives, along with AACSB and Bloom’s taxonomy learning categories, are connected to all end-of-chapter material and test bank questions to offer a comprehensive and thorough teaching and learning experience.

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Preface xi

Assurance of Learning Ready Many educational institutions today are focused on the notion of assurance of learning, an important element of some accreditation standards. Managerial Economics and Business Strategy is designed specifically to support your assurance of learning initiatives with a sim- ple, yet powerful solution.

Instructors can use Connect to easily query for learning outcomes/objectives that directly relate to the learning objectives of the course. You can then use the reporting features of Connect to aggregate student results in similar fashion, making the collection and presenta- tion of assurance of learning data simple and easy.

AACSB Statement McGraw-Hill Global Education is a proud corporate member of AACSB International. Understanding the importance and value of AACSB accreditation, Managerial Economics and Business Strategy, 9/e, has sought to recognize the curricula guidelines detailed in the AACSB standards for business accreditation by connecting questions in the test bank and end-of-chapter material to the general knowledge and skill guidelines found in the AACSB standards.

It is important to note that the statements contained in Managerial Economics and Business Strategy, 9/e, are provided only as a guide for the users of this text. The AACSB leaves content coverage and assessment within the purview of individual schools, the mission of the school, and the faculty. While Managerial Economics and Business Strategy, 9/e, and the teaching package make no claim of any specific AACSB qualification or evaluation, we have labeled questions according to the general knowledge and skill areas.

ACKNOWLEDGMENTS

We thank the many users of Managerial Economics and Business Strategy who provided both direct and indirect feedback that has helped improve your book. This includes thousands of students at Indiana University’s Kelley School of Business and instructors worldwide who have used this book in their own classrooms, colleagues who unselfishly gave up their own time to provide comments and suggestions, and reviewers who provided detailed suggestions to improve this and previous editions of the book. We especially thank the following profes- sors, past and present, for enlightening us on the market’s diverse needs and for providing suggestions and constructive criticisms to improve this book.

Contributing reviewers for this edition:

Narine Badasyan, Murray State University Cristanna Cook, Husson University Robert Daffenbach, University of

Oklahoma

Jeffrey Edwards, North Carolina A&T University

Silke Forbes, Case Western Reserve University

Martin Heintzelman, Clarkson University Craig Hovey, Brenau University, Gainesville

Anand Jha, Texas A&M International University

Harlan Platt, Northeastern University Stefan Ruediger, Arizona State University Charles Sebuhara, Virginia Technical

University

Thomas White, Fontbonne University Keith Willett, Oklahoma State University,

Stillwater

Laura Youderian, Xavier University

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xii Preface

Contributing reviewers for previous editions:

Fatma Abdel-Raouf, Goldey-Beacom College

Burton Abrams, University of Delaware Rashid Al-Hmoud, Texas Tech University Anthony Paul Andrews, Governors State

University

Sisay Asefa, Western Michigan University Simon Avenell, Murdoch University Joseph P. Bailey, University of Maryland Dale G. Bails Christian Brothers University Dean Baim, Pepperdine University Sheryl Ball, Virginia Polytechnic University Klaus Becker, Texas Tech University Richard Beil, Auburn University Barbara C. Belivieu, University of

Connecticut

Dan Black, University of Chicago Louis Cain, Northwestern University Kerem Cakirer, Indiana University Leo Chan, University of Kansas Robert L. Chapman, Florida Metropolitan

University

Joni Charles, Texas State University—San Marcos

Basanta Chaudhuri, Rutgers University— New Brunswick

Shuo Chen, State University of New York at Geneseo

Xiujian Chen, State University of New York—Binghamton University

Kwang Soo Cheong, Johns Hopkins University

Christopher B. Colburn, Old Dominion University

Daniel Patrick Condon, Dominican University

Michael Conlin, Syracuse University Cristanna Cook, Husson University Keith Crocker, Penn State University Ian Cromb, University of Western Ontario Dean Croushore, Federal Reserve

Wilffrid W. Csaplar Jr., Bethany College Shah Dabirian, California State University,

Long Beach

Joseph DaBoll-Lavioe, Nazareth College of Rochester

George Darko, Tusculum College Tina Das, Elon University Ron Deiter, Iowa State University Jonathan C. Deming, Seattle Pacific

University

Casey Dirienzo, Appalachian State University

Eric Drabkin, Hawaii Pacific University Martine Duchatelet, Barry University Keven C. Duncan, University of Southern

Colorado

Yvonne Durham, Western Washington University

Eugene F. Elander, Brenau University Ibrahim Elsaify, Goldey-Beacom College David Ely, San Diego State University Mark J. Eschenfelder, Robert Morris

University

Li Feng, Texas State University–San Marcos David Figlio, University of Florida Ray Fisman, Graduate School of Business,

Columbia University

Silke Forbes, University of California—San Diego

David Gerard, Carnegie Mellon University Sharon Gifford, Rutgers University Lynn G. Gillette, Northeast Missouri State

University

Otis Gilley, Louisiana Tech University Roy Gobin, Loyola University Stephan Gohmann, University of Louisville Steven Gold, Rochester Institute of

Technology

Julie Hupton Gonzalez, University of California—Santa Cruz

Thomas A. Gresik, Mendoza College of Business (University of Notre Dame)

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Preface xiii

Andrea Mays Griffith, California State University

Madhurima Gupta, University of Notre Dame

Carl Gwin, Pepperdine University Gail Heyne Hafer, Lindenwood College Karen Hallows, George Mason University William Hamlen Jr., SUNY Buffalo Shawkat Hammoudeh, Drexel University Mehdi Harian, Bloomsburg University Nile W. Hatch, Marriott School (Brigham

Young University)

Clifford Hawley, West Virginia University Ove Hedegaard, Copenhagen Business

School

Steven Hinson, Webster University Hart Hodges, Western Washington

University

Robert L. Holland, Purdue University Jack Hou, California State University—

Long Beach

Lowel R. Jacobsen, William Jewell College

Thomas D. Jeitschko, Michigan State University

Jaswant R. Jindia, Southern University Russell Kashian, University of

Wisconsin—Whitewater

Paul Kattuman, Judge Business School (Cambridge University)

Brian Kench, University of Tampa Kimberley L. Kinsley, University of Mary

Washington

Peter Klein, University of Georgia, University of Missouri—Columbia

Audrey D. Kline, University of Louisville Robert A. Krell, George Mason

University

Paul R. Kutasovic, New York Institute of Technology

W. J. Lane, University of New Orleans Daniel Lee, Shippensburg University

Dick Leiter, American Public University Canlin Li, University of

California—Riverside

Chung-Ping Loh, University of North Florida

Vahe Lskavyan, Ohio University—Athens Heather Luea, Newman University Nancy L. Lumpkin, Georgetown

College

Thomas Lyon, University of Michigan Richard Marcus, University of

Wisconsin—Milwaukee

Vincent Marra, University of Delaware Wade Martin, California State University,

Long Beach

Catherine Matraves, Michigan State University—East Lansing

John Maxwell, Indiana University David May, Oklahoma City University Alan McInnes, California State University,

Fullerton

Christopher McIntosh, University of Minnesota Duluth

Kimberly L. Merritt, Oklahoma Christian University

Edward Millner, Virginia Commonwealth University

John Moran, Syracuse University Shahriar Mostashari, Campbell University John Morgan, Haas Business School

(University of California—Berkeley)

Ram Mudambi, Temple University Francis Mummery, California State

University—Fullerton

Inder Nijhawan, Fayetteville State University Albert A. Okunade, University of Memphis Walton M. Padelford, Union University Darrell Parker, Georgia Southern University Stephen Pollard, California State University,

Los Angeles

Dwight A. Porter, College of St. Thomas Stanko Racic, University of Pittsburgh

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xiv Preface

Eric Rasmusen, Indiana University Matthew Roelofs, Western Washington

University

Christian Roessler, National University of Singapore

Bansi Sawhney, University of Baltimore George L. Schatz, Maine Maritime

Academy

Craig Schulman, University of Arkansas Karen Schultes, University of

Michigan—Dearborn

Peter M. Schwartz, University of North Carolina

Richard Alan Seals Jr., Oklahoma City University

Edward Shinnick, University College Ireland

Dean Showalter, Southwest Texas State University

Chandra Shrestha, Virginia Commonwealth University

Karen Smith, Columbia Southern University John Stapleford, Eastern University Mark Stegeman, University of Arizona

Ed Steinberg, New York University Barbara M. Suleski, Cardinal Stritch

College

Caroline Swartz, University of North Carolina Charlotte

Joseph K. Tanimura, San Diego State University

Bill Taylor, New Mexico Highlands University

Roger Tutterow, Kennesaw State College Nora Underwood, University of Central

Florida

Lskavyan Vahe, Ohio University Lawrence White, Stern School of Business

(New York University)

Leonard White, University of Arkansas Keith Willett, Oklahoma State

University—Stillwater

Mike Williams, Bethune Cookman College Richard Winkelman, Arizona State

University

Eduardo Zambrano, University of Notre Dame Rick Zuber, University of North Carolina,

Charlotte

We thank Katie Hoenicke, Christina Kouvelis, James Heine, and Doug Ruby at McGraw- Hill for all they have done to make this project a success. We also thank Mitchell Baye, Patrick Scholten, Eric Schmidbauer, Susan Kayser, Kyle Anderson, and Vikram Ahuja for sugges- tions and assistance during various stages of the revision, and Ellie Mafi-Kreft, Haizhen Lin, and Steven Kreft, who graciously agreed to class test the Connect features in their classrooms. Finally, we thank our families for their continued love and support.

As always, we welcome your comments and suggestions for the next edition. Please feel free to write to us directly at [email protected] or [email protected].

Michael R. Baye Jeffrey T. Prince

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Preface xv

SUPPLEMENTS 

We know the content and reliability of new editions and book supplements are of utmost impor- tance to users of our book. Because of this, and unlike most other managerial economics books, we personally are involved in crafting and accuracy checking virtually every content update and supplement for our book. Below we discuss popular features of some of the supplements that have been greatly expanded for this edition. The following ancillaries are available for quick download and convenient access via the instructor resource material available through Connect.

Cases In addition to the Time Warner Cable case, nearly a dozen full-length cases were updated and prepared to accompany Managerial Economics and Business Strategy. These cases comple- ment the textbook by showing how real-world businesses use tools like demand elasticities, markup pricing, third-degree price discrimination, bundling, Herfindahl indices, game the- ory, and predatory pricing to enhance profits or shape business strategies. The cases are based on actual decisions by companies that include Microsoft, Heinz, Visa, Staples, American Airlines, and Nasdaq. Expanded teaching notes and solutions for all of the cases—including the Time Warner Cable case—are also provided.

PowerPoint Slides Thoroughly updated and fully editable PowerPoint presentations with animated figures and graphs, make teaching and learning a snap. For instance, a simple mouse click reveals the firm’s demand curve. Another click reveals the associated marginal revenue curve. Another click shows the firm’s marginal cost. A few more clicks, and students see how to determine the profit-maximizing output, price, and maximum profits. Animated graphs and tables are also provided for all other relevant concepts (like Cournot and Stackelberg equilibrium, nor- mal form and extensive form games, and the like).

Solutions Manual We have prepared a solutions manual that provides detailed answers to all end-of-chapter problems, all of which have been class-tested for accuracy.

Test Bank An updated test bank, offers well over 1,000 multiple-choice questions categorized by learning objectives, AACSB learning categories, Bloom’s taxonomy objectives, and level of difficulty.

Computerized Test Bank TestGen is a complete, state-of-the-art test generator and editing application software that allows instructors to quickly and easily select test items from McGraw Hill’s test bank content. The instructors can then organize, edit and customize questions and answers to rapidly generate tests for paper or online administration. Questions can include stylized text, symbols, graphics, and equations that are inserted directly into questions using built-in mathematical templates. TestGen’s random generator provides the option to display different text or calculated number values each time questions are used. With both quick-and-simple test creation and flexible and robust editing tools, TestGen is a complete test generator system for today’s educators.

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Required=Results

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xviii

Brief Contents

1 The Fundamentals of Managerial Economics 1

2 Market Forces: Demand and Supply 30

3 Quantitative Demand Analysis 64

4 The Theory of Individual Behavior 101

5 The Production Process and Costs 135

6 The Organization of the Firm 175

7 The Nature of Industry 203

8 Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets 229

9 Basic Oligopoly Models 270

10 Game Theory: Inside Oligopoly 302

11 Pricing Strategies for Firms with Market Power 340

12 The Economics of Information 372

13 Advanced Topics in Business Strategy 406

14 A Manager’s Guide to Government in the Marketplace 435

Case Study Time Warner Cable 468

Glossary 497

Appendix Additional Readings and References 505

Name Index 525

General Index 534

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xix

CHAPTER 1

The Fundamentals of Managerial Economics 1

HEADLINE: Amcott Loses $3.5 Million; Manager Fired 1

INTRODUCTION 2 The Manager 2 Economics 3 Managerial Economics Defined 3

THE ECONOMICS OF EFFECTIVE MANAGEMENT 4 Identify Goals and Constraints 4 Recognize the Nature and Importance of Profits 4

Economic versus Accounting Profits 4 The Role of Profits 5 The Five Forces Framework and Industry Profitability 7

Understand Incentives 10 Understand Markets 11

Consumer–Producer Rivalry 11 Consumer–Consumer Rivalry 11 Producer–Producer Rivalry 11 Government and the Market 12

Recognize the Time Value of Money 12 Present Value Analysis 12 Present Value of Indefinitely Lived Assets 14

Use Marginal Analysis 16 Discrete Decisions 17 Continuous Decisions 19 Incremental Decisions 20

LEARNING MANAGERIAL ECONOMICS 21

ANSWERING THE HEADLINE 22

KEY TERMS AND CONCEPTS 23 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 23 / PROBLEMS AND APPLICATIONS 25 / SELECTED READINGS 28 / APPENDIX: THE CALCULUS OF MAXIMIZING NET BENEFITS 29

INSIDE BUSINESS 1–1: The Goals of Firms in Our Global Economy 6

INSIDE BUSINESS 1–2: Profits and the Evolution of the Computer Industry 9

INSIDE BUSINESS 1–3: Joining the Jet Set 16

CHAPTER 2

Market Forces: Demand and Supply 30

HEADLINE: Samsung and Hynix Semiconductor to Cut Chip Production 30

INTRODUCTION 31

DEMAND 31 Demand Shifters 33

Income 33 Prices of Related Goods 34 Advertising and Consumer Tastes 35 Population 35 Consumer Expectations 36 Other Factors 36

The Demand Function 36 Consumer Surplus 38

SUPPLY 39 Supply Shifters 40

Input Prices 40 Technology or Government Regulations 40 Number of Firms 40 Substitutes in Production 41 Taxes 41 Producer Expectations 42

The Supply Function 43 Producer Surplus 44

MARKET EQUILIBRIUM 45

PRICE RESTRICTIONS AND MARKET EQUILIBRIUM 47 Price Ceilings 47 Price Floors 51

Contents

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xx Contents

Elasticities for Nonlinear Demand Functions 81

REGRESSION ANALYSIS 84 Evaluating the Statistical Significance of Estimated Coefficients 85

Confidence Intervals 86 The t-Statistic 87

Evaluating the Overall Fit of the Regression Line 88

The R-Square 88 The F-Statistic 89

Regression for Nonlinear Functions and Multiple Regression 89

Regression for Nonlinear Functions 89 Multiple Regression 91

A Caveat 93

ANSWERING THE HEADLINE 94

SUMMARY 94 / KEY TERMS AND CONCEPTS 95 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 95 / PROBLEMS AND APPLICATIONS 97 / SELECTED READINGS 100

INSIDE BUSINESS 3–1: Calculating and Using the Arc Elasticity: An Application to the Housing Market 70

INSIDE BUSINESS 3–2: Inelastic Demand for Prescription Drugs 74

INSIDE BUSINESS 3–3: Using Cross-Price Elasticities to Improve New Car Sales in the Wake of Increasing Gasoline Prices 77

INSIDE BUSINESS 3–4: Shopping Online in Europe: Elasticities of Demand for Personal Digital Assistants Based on Regression Techniques 93

CHAPTER 4

The Theory of Individual Behavior 101

HEADLINE: Packaging Firm Uses Overtime Pay to Overcome Labor Shortage 101

INTRODUCTION 102

CONSUMER BEHAVIOR 102

CONSTRAINTS 106 The Budget Constraint 106 Changes in Income 108 Changes in Prices 110

COMPARATIVE STATICS 53 Changes in Demand 53 Changes in Supply 54 Simultaneous Shifts in Supply and Demand 55

ANSWERING THE HEADLINE 57

SUMMARY 58 / KEY TERMS AND CONCEPTS 58 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 58 / PROBLEMS AND APPLICATIONS 60 / SELECTED READINGS 63

INSIDE BUSINESS 2–1: Asahi Breweries Ltd. and the Asian Recession 34

INSIDE BUSINESS 2–2: The Trade Act of 2002, NAFTA, and the Supply Curve 42

INSIDE BUSINESS 2–3: Unpopular Equilibrium Prices 46

INSIDE BUSINESS 2–4: Price Ceilings and Price Floors around the Globe 50

INSIDE BUSINESS 2–5: Globalization and the Supply of Automobiles 54

INSIDE BUSINESS 2–6: Using a Spreadsheet to Calculate Equilibrium in the Supply and Demand Model 55

CHAPTER 3

Quantitative Demand Analysis 64

HEADLINE: Walmart Hoping for Another Big Holiday Showing 64

INTRODUCTION 65

THE ELASTICITY CONCEPT 65

OWN PRICE ELASTICITY OF DEMAND 66 Elasticity and Total Revenue 67 Factors Affecting the Own Price Elasticity 71

Available Substitutes 71 Time 72 Expenditure Share 72

Marginal Revenue and the Own Price Elasticity of Demand 73

CROSS-PRICE ELASTICITY 75

INCOME ELASTICITY 77

OTHER ELASTICITIES 79

OBTAINING ELASTICITIES FROM DEMAND FUNCTIONS 79 Elasticities for Linear Demand Functions 80

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Contents xxi

THE PRODUCTION FUNCTION 136 Short-Run versus Long-Run Decisions 137 Measures of Productivity 138

Total Product 138 Average Product 138 Marginal Product 138

The Role of the Manager in the Production Process 140

Produce on the Production Function 140 Use the Right Level of Inputs 140

Algebraic Forms of Production Functions 143 Algebraic Measures of Productivity 144 Isoquants 146 Isocosts 148 Cost Minimization 149 Optimal Input Substitution 151

THE COST FUNCTION 152 Short-Run Costs 153 Average and Marginal Costs 156 Relations among Costs 158 Fixed and Sunk Costs 159 Algebraic Forms of Cost Functions 160 Long-Run Costs 160 Economies of Scale 161 A Reminder: Economic Costs versus Accounting Costs 162

MULTIPLE-OUTPUT COST FUNCTIONS 163 Economies of Scope 164 Cost Complementarity 164

ANSWERING THE HEADLINE 166

SUMMARY 166 / KEY TERMS AND CONCEPTS 167 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 167 / PROBLEMS AND APPLICATIONS 169 / SELECTED READINGS 173 / APPENDIX: THE CALCULUS OF PRODUCTION AND COSTS 173

INSIDE BUSINESS 5–1: Where Does Technology Come From? 142

INSIDE BUSINESS 5–2: The Affordable Care Act, Employer Mandate, and Input Substitution 154

INSIDE BUSINESS 5–3: Estimating Production Functions, Cost Functions, and Returns to Scale 162

INSIDE BUSINESS 5–4: International Companies Exploit Economies of Scale 163

CONSUMER EQUILIBRIUM 111

COMPARATIVE STATICS 112 Price Changes and Consumer Behavior 112 Income Changes and Consumer Behavior 114 Substitution and Income Effects 116

APPLICATIONS OF INDIFFERENCE CURVE ANALYSIS 117 Choices by Consumers 117

Buy One, Get One Free 117 Cash Gifts, In-Kind Gifts, and Gift Certificates 118

Choices by Workers and Managers 121 A Simplified Model of Income–Leisure Choice 121 The Decisions of Managers 122

THE RELATIONSHIP BETWEEN INDIFFERENCE CURVE ANALYSIS AND DEMAND CURVES 124 Individual Demand 124 Market Demand 125

ANSWERING THE HEADLINE 126

SUMMARY 127 / KEY TERMS AND CONCEPTS 127 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 128 / PROBLEMS AND APPLICATIONS 130 / SELECTED READINGS 133 / APPENDIX: A CALCULUS APPROACH TO INDIVIDUAL BEHAVIOR 133

INSIDE BUSINESS 4–1: Indifference Curves and Risk Preferences 105

INSIDE BUSINESS 4–2: The Budget Constraints and Credit Cards 109

INSIDE BUSINESS 4–3: Price Changes and Inventory Management for Multiproduct Firms 113

INSIDE BUSINESS 4–4: Income Effects and the Business Cycle 115

INSIDE BUSINESS 4–5: The “Deadweight Loss” of In-Kind Gifts 122

INSIDE BUSINESS 4–6: Public Health Centers and Output-Oriented Incentives 126

CHAPTER 5

The Production Process and Costs 135

HEADLINE: Boeing Loses the Battle but Wins the War 135

INTRODUCTION 136

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xxii Contents

INSIDE BUSINESS 6–1: The Cost of Using an Inefficient Method of Procuring Inputs 182

INSIDE BUSINESS 6–2: What Determines Contract Length in Franchising? 186

INSIDE BUSINESS 6–3: The Evolution of Input Decisions in the Automobile Industry 187

INSIDE BUSINESS 6–4: Paying for Performance 194

CHAPTER 7

The Nature of Industry 203

HEADLINE: AT&T Puts Halt to T-Mobile Merger 203

INTRODUCTION 204

MARKET STRUCTURE 204 Firm Size 204 Industry Concentration 205

Measures of Industry Concentration 206 The Concentration of U.S. Industry 207 Limitations of Concentration Measures 208

Technology 209 Demand and Market Conditions 210 Potential for Entry 212

CONDUCT 214 Pricing Behavior 214 Integration and Merger Activity 215

Vertical Integration 216 Horizontal Integration 216 Conglomerate Mergers 217

Research and Development 217 Advertising 217

PERFORMANCE 218 Profits 218 Social Welfare 218

THE STRUCTURE–CONDUCT–PERFORMANCE PARADIGM 219 The Causal View 220 The Feedback Critique 220 Relation to the Five Forces Framework 220

OVERVIEW OF THE REMAINDER OF THE BOOK 221 Perfect Competition 221 Monopoly 222 Monopolistic Competition 222 Oligopoly 222

ANSWERING THE HEADLINE 224

CHAPTER 6

The Organization of the Firm 175

HEADLINE: Google Buys Motorola Mobility to Vertically Integrate 175

INTRODUCTION 176

METHODS OF PROCURING INPUTS 177 Purchase the Inputs Using Spot Exchange 177 Acquire Inputs Under a Contract 177 Produce the Inputs Internally 178

TRANSACTION COSTS 179 Types of Specialized Investments 179

Site Specificity 179 Physical-Asset Specificity 180 Dedicated Assets 180 Human Capital 180

Implications of Specialized Investments 180 Costly Bargaining 180 Underinvestment 180 Opportunism and the “Hold-Up Problem” 181

OPTIMAL INPUT PROCUREMENT 182 Spot Exchange 182 Contracts 183 Vertical Integration 186 The Economic Trade-Off 186

MANAGERIAL COMPENSATION AND THE PRINCIPAL–AGENT PROBLEM 189

FORCES THAT DISCIPLINE MANAGERS 191 Incentive Contracts 191 External Incentives 192

Reputation 192 Takeovers 192

THE MANAGER–WORKER PRINCIPAL–AGENT PROBLEM 192 Solutions to the Manager–Worker Principal–Agent Problem 192

Profit Sharing 192 Revenue Sharing 193 Piece Rates 193 Time Clocks and Spot Checks 194

ANSWERING THE HEADLINE 195

SUMMARY 195 / KEY TERMS AND CONCEPTS 196 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 196 / PROBLEMS AND APPLICATIONS 197 / SELECTED READINGS 200 / APPENDIX: AN INDIFFERENCE CURVE APPROACH TO MANAGERIAL INCENTIVES 200

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Contents xxiii

OPTIMAL ADVERTISING DECISIONS 260

ANSWERING THE HEADLINE 262

SUMMARY 263 / KEY TERMS AND CONCEPTS 263 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 263 / PROBLEMS AND APPLICATIONS 265 / SELECTED READINGS 268 / APPENDIX: THE CALCULUS OF PROFIT MAXIMIZATION 269 / APPENDIX: THE ALGEBRA OF PERFECTLY COMPETITIVE SUPPLY FUNCTIONS 269

INSIDE BUSINESS 8–1: Peugeot-Citroën of France: A Price-Taker in China’s Auto Market 235

INSIDE BUSINESS 8–2: Patent, Trademark, and Copyright Protection 246

INSIDE BUSINESS 8–3: Product Differentiation, Cannibalization, and Colgate’s Smile 255

CHAPTER 9

Basic Oligopoly Models 270

HEADLINE: Crude Oil Prices Fall, but Consumers in Some Areas See No Relief at the Pump 270

INTRODUCTION 271

CONDITIONS FOR OLIGOPOLY 271

THE ROLE OF BELIEFS AND STRATEGIC INTERACTION 271

PROFIT MAXIMIZATION IN FOUR OLIGOPOLY SETTINGS 273 Sweezy Oligopoly 273 Cournot Oligopoly 274

Reaction Functions and Equilibrium 275 Isoprofit Curves 279 Changes in Marginal Costs 281 Collusion 283

Stackelberg Oligopoly 284 Bertrand Oligopoly 288

COMPARING OLIGOPOLY MODELS 290 Cournot 290 Stackelberg 291 Bertrand 291 Collusion 291

CONTESTABLE MARKETS 292

ANSWERING THE HEADLINE 293

SUMMARY 295 / KEY TERMS AND CONCEPTS 295 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 295 / PROBLEMS AND APPLICATIONS 297 / SELECTED

SUMMARY 224 / KEY TERMS AND CONCEPTS 224 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 225 / PROBLEMS AND APPLICATIONS 226 / SELECTED READINGS 228

INSIDE BUSINESS 7–1: The 2012 North American Industry Classification System (NAICS) 210

INSIDE BUSINESS 7–2: The Elasticity of Demand at the Firm and Market Levels 213

INSIDE BUSINESS 7–3: The Evolution of Market Structure in the Computer Industry 223

CHAPTER 8

Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets 229

HEADLINE: McDonald’s New Buzz: Specialty Coffee 229

INTRODUCTION 230

PERFECT COMPETITION 230 Demand at the Market and Firm Levels 231 Short-Run Output Decisions 232

Maximizing Profits 232 Minimizing Losses 236 The Short-Run Firm and Industry Supply Curves 238

Long-Run Decisions 239

MONOPOLY 241 Monopoly Power 241 Sources of Monopoly Power 242

Economies of Scale 242 Economies of Scope 243 Cost Complementarity 244 Patents and Other Legal Barriers 244

Maximizing Profits 244 Marginal Revenue 245 The Output Decision 248 The Absence of a Supply Curve 251 Multiplant Decisions 251

Implications of Entry Barriers 253

MONOPOLISTIC COMPETITION 255 Conditions for Monopolistic Competition 255 Profit Maximization 256 Long-Run Equilibrium 257 Implications of Product Differentiation 259

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xxiv Contents

MULTISTAGE GAMES 325 Theory 325 Applications of Multistage Games 328

The Entry Game 328 Innovation 329 Sequential Bargaining 330

ANSWERING THE HEADLINE 331

SUMMARY 332 / KEY TERMS AND CONCEPTS 332 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 333 / PROBLEMS AND APPLICATIONS 335 / SELECTED READINGS 339

INSIDE BUSINESS 10–1: Hollywood’s (not so) Beautiful Mind: Nash or “Opie” Equilibrium? 307

INSIDE BUSINESS 10–2: Cola Wars in India 309

INSIDE BUSINESS 10–3: Trigger Strategies in the Waste Industry 318

INSIDE BUSINESS 10–4: Multimarket Contact and Price Competition 320

INSIDE BUSINESS 10–5: Entry Strategies in International Markets: Sprinkler or Waterfall? 327

CHAPTER 11

Pricing Strategies for Firms with Market Power 340

HEADLINE: Mickey Mouse Lets You Ride “for Free” at Disney World 340

INTRODUCTION 341

BASIC PRICING STRATEGIES 341 Review of the Basic Rule of Profit Maximization 341 A Simple Pricing Rule for Monopoly and Monopolistic Competition 342 A Simple Pricing Rule for Cournot Oligopoly 345

STRATEGIES THAT YIELD EVEN GREATER PROFITS 347 Extracting Surplus from Consumers 347

Price Discrimination 347 Two-Part Pricing 351 Block Pricing 354 Commodity Bundling 356

Pricing Strategies for Special Cost and Demand Structures 358

Peak-Load Pricing 358 Cross-Subsidies 359 Transfer Pricing 360

READINGS 300 / APPENDIX: DIFFERENTIATED- PRODUCT BERTRAND OLIGOPOLY 300

INSIDE BUSINESS 9–1: OPEC Members Can’t Help but Cheat 285

INSIDE BUSINESS 9–2: Commitment in Stackelberg Oligopoly 287

INSIDE BUSINESS 9–3: Price Competition and the Number of Sellers: Evidence from Online and Laboratory Markets 289

INSIDE BUSINESS 9–4: Using a Spreadsheet to Calculate Cournot, Stackelberg, and Collusive Outcomes 292

CHAPTER 10

Game Theory: Inside Oligopoly 302

HEADLINE: Bring Back Complimentary Drinks! 302

INTRODUCTION 303

OVERVIEW OF GAMES AND STRATEGIC THINKING 303

SIMULTANEOUS-MOVE, ONE-SHOT GAMES 304 Theory 304 Applications of One-Shot Games 307

Pricing Decisions 307 Advertising and Quality Decisions 309 Coordination Decisions 310 Monitoring Employees 311 Nash Bargaining 312

INFINITELY REPEATED GAMES 314 Theory 314

Review of Present Value 314 Supporting Collusion with Trigger Strategies 314

Factors Affecting Collusion in Pricing Games 317 Number of Firms 317 Firm Size 317 History of the Market 317 Punishment Mechanisms 318

An Application of Infinitely Repeated Games to Product Quality 319

FINITELY REPEATED GAMES 320 Games with an Uncertain Final Period 320 Repeated Games with a Known Final Period: The End-of-Period Problem 323 Applications of the End-of-Period Problem 324

Resignations and Quits 324 The “Snake-Oil” Salesman 325

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Contents xxv

AUCTIONS 390 Types of Auctions 391

English Auction 391 First-Price, Sealed-Bid Auction 391 Second-Price, Sealed-Bid Auction 392 Dutch Auction 392

Information Structures 393 Independent Private Values 393 Correlated Value Estimates 394

Optimal Bidding Strategies for Risk-Neutral Bidders 394

Strategies for Independent Private Values Auctions 394 Strategies for Correlated Values Auctions 396

Expected Revenues in Alternative Types of Auctions 397

ANSWERING THE HEADLINE 399

SUMMARY 400 / KEY TERMS AND CONCEPTS 400 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 400 / PROBLEMS AND APPLICATIONS 402 / SELECTED READINGS 405

INSIDE BUSINESS 12–1: Risk Aversion and the Value of Selling the Firm: The St. Petersburg Paradox 376

INSIDE BUSINESS 12–2: Obfuscation to Counter Low Internet Search Costs 379

INSIDE BUSINESS 12–3: Groucho Marx the Economist? 386

INSIDE BUSINESS 12–4: Second-Price Auctions on eBay 392

INSIDE BUSINESS 12–5: Auctions with Risk-Averse Bidders 399

CHAPTER 13

Advanced Topics in Business Strategy 406

HEADLINE: Local Restaurateur Faces Looming Challenge from Morton’s 406

INTRODUCTION 407

LIMIT PRICING TO PREVENT ENTRY 408 Theoretical Basis for Limit Pricing 408 Limit Pricing May Fail to Deter Entry 409 Linking the Preentry Price to Postentry Profits 410

Commitment Mechanisms 411 Learning Curve Effects 412 Incomplete Information 412 Reputation Effects 413

Dynamic Considerations 413

Pricing Strategies in Markets with Intense Price Competition 362

Price Matching 362 Inducing Brand Loyalty 364 Randomized Pricing 364

ANSWERING THE HEADLINE 366

SUMMARY 366 / KEY TERMS AND CONCEPTS 367 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 367 / PROBLEMS AND APPLICATIONS 369 / SELECTED READINGS 371

INSIDE BUSINESS 11–1: Pricing Markups as Rules of Thumb 343

INSIDE BUSINESS 11–2: Is Price Discrimination Bad for Consumers? 352

INSIDE BUSINESS 11–3: Bundling and “Price Frames” in Online Markets 357

INSIDE BUSINESS 11–4: The Prevalence of Price-Matching Policies and Other Low-Price Guarantees 363

INSIDE BUSINESS 11–5: Kroger Combines Pricing Strategies 364

INSIDE BUSINESS 11–6: Randomized Pricing in the Airline Industry 365

CHAPTER 12

The Economics of Information 372

HEADLINE: Firm Chickens Out in the FCC Spectrum Auction 372

INTRODUCTION 373

THE MEAN AND THE VARIANCE 373

UNCERTAINTY AND CONSUMER BEHAVIOR 375 Risk Aversion 375

Managerial Decisions with Risk-Averse Consumers 376

Consumer Search 378

UNCERTAINTY AND THE FIRM 380 Risk Aversion 381 Producer Search 383 Profit Maximization 383

UNCERTAINTY AND THE MARKET 384 Asymmetric Information 384

Adverse Selection 386 Moral Hazard 387

Signaling and Screening 388

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xxvi Contents

Externalities 444 The Clean Air Act 446

Public Goods 448 Incomplete Information 451

Rules against Insider Trading 452 Certification 452 Truth in Lending 453 Truth in Advertising 454 Enforcing Contracts 454

RENT SEEKING 455

GOVERNMENT POLICY AND INTERNATIONAL MARKETS 457 Quotas 457 Tariffs 459

Lump-Sum Tariffs 459 Excise Tariffs 460

ANSWERING THE HEADLINE 461

SUMMARY 461 / KEY TERMS AND CONCEPTS 461 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 462 / PROBLEMS AND APPLICATIONS 464 / SELECTED READINGS 466

INSIDE BUSINESS 14–1: European Commission Moves to Protect Small Businesses 439

INSIDE BUSINESS 14–2: Electricity Deregulation 443

INSIDE BUSINESS 14–3: Canada’s Competition Bureau 455

CASE STUDY

Time Warner Cable 468

HEADLINE 468

BACKGROUND 469 Time Warner Cable History 469 Cable Television History 469 Broadband Internet 470

BUSINESS AND MARKETS 471 Video Programming 471 Internet Services 473 Telephone 473

COMPETITION 474 Cable Companies 474

Comcast 474 Comcast/Time Warner Cable Proposed Acquisition 475 Charter Communications 475 Other Cable Players 476

PREDATORY PRICING TO LESSEN COMPETITION 415

RAISING RIVALS’ COSTS TO LESSEN COMPETITION 417 Strategies Involving Marginal Cost 418 Strategies Involving Fixed Costs 419 Strategies for Vertically Integrated Firms 419

Vertical Foreclosure 420 The Price–Cost Squeeze 420

PRICE DISCRIMINATION AS A STRATEGIC TOOL 420

CHANGING THE TIMING OF DECISIONS OR THE ORDER OF MOVES 421 First-Mover Advantages 421 Second-Mover Advantages 423

PENETRATION PRICING TO OVERCOME NETWORK EFFECTS 424 What Is a Network? 424 Network Externalities 425 First-Mover Advantages Due to Consumer Lock-In 426 Using Penetration Pricing to “Change the Game” 427

ANSWERING THE HEADLINE 429

SUMMARY 429 / KEY TERMS AND CONCEPTS 430 / CONCEPTUAL AND COMPUTATIONAL QUESTIONS 430 / PROBLEMS AND APPLICATIONS 432 / SELECTED READINGS 434

INSIDE BUSINESS 13–1: Business Strategy at Microsoft 410

INSIDE BUSINESS 13–2: Limit Pricing and the “Southwest Effect” 415

INSIDE BUSINESS 13–3: First to Market, First to Succeed? Or First to Fail? 423

INSIDE BUSINESS 13–4: Network Externalities and Penetration Pricing by Yahoo! Auctions 427

CHAPTER 14

A Manager’s Guide to Government in the Marketplace 435

HEADLINE: FTC Conditionally Approves $10.3 Billion Merger 435

INTRODUCTION 436

MARKET FAILURE 436 Market Power 436

Antitrust Policy 437 Price Regulation 440

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Contents xxvii

REGULATION IN THE CABLE INDUSTRY 483 Carriage of Broadcast Television 484 Cable Pricing Regulation 484 Net Neutrality 484 Connect America Fund 484

CHALLENGES 484

CASE-BASED EXERCISES 485

MEMOS 485

SELECTED READINGS AND REFERENCES 492 / APPENDIX: EXHIBITS 493

Glossary 497

Appendix Additional Readings and References 505

Name Index 525

General Index 534

Satellite 476 AT&T DirecTV 476

Dish Network 477 Telephone Providers 477

Verizon 477 AT&T 477 Other Companies 478

Online Video Distributors 478 Netflix 478 Amazon Prime Video 479 Hulu 479 Google/YouTube 479

SUPPLIERS 480 Cable Networks 480 Broadcast Networks 480 Sports Programming 481 Carriage Disputes 481 Over-the-Top Content 482

MARKET TRENDS AND CONSUMER BEHAVIOR 482 Digital Video Recorders (DVRs) 482 Cutting the Cord 483 Going Mobile 483

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1

headLINE Amcott Loses $3.5 Million; Manager Fired On Tuesday software giant Amcott posted a year-end operating loss of $3.5 million. Reportedly, $1.7 million of the loss stemmed from its foreign language division.

At a time when Amcott was paying First National a hefty 7 percent rate to borrow short-term funds, Amcott decided to use $20 million of its retained earnings to purchase three-year rights to Magicword, a software package that converts generic word proces- sor files saved as French text into English. First-year sales revenue from the software was $7 million, but thereafter sales were halted pending a copyright infringement suit filed by Foreign, Inc. Amcott lost the suit and paid damages of $1.7 million. Industry insiders say that the copyright violation pertained to “a very small component of Magicword.”

Ralph, the Amcott manager who was fired over the incident, was quoted as saying, “I’m a scapegoat for the attorneys [at Amcott] who didn’t do their homework before buy- ing the rights to Magicword. I projected annual sales of $7 million per year for three years. My sales forecasts were right on target.”

Do you know why Ralph was fired?1

The Fundamentals of Managerial Economics

1 LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Summarize how goals, constraints, incentives, and market rivalry affect eco- nomic decisions.

LO2 Distinguish economic versus accounting profits and costs. LO3 Explain the role of profits in a market economy. LO4 Apply the five forces framework to analyze the sustainability of an industry’s profits. LO5 Apply present value analysis to make decisions and value assets. LO6 Apply marginal analysis to determine the optimal level of a managerial

control variable.

LO7 Identify and apply six principles of effective managerial decision making.

1Each chapter concludes with an answer to the question posed in that chapter’s opening headline. After you read each chapter, you should attempt to solve the opening headline on your own and then compare your solution to that presented at the end of the chapter.

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2 CHAPTER 1 The Fundamentals of Managerial Economics

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INTRODUCTION

Many students taking managerial economics ask, “Why should I study economics? Will it tell me what the stock market will do tomorrow? Will it tell me where to invest my money or how to get rich?” Unfortunately, managerial economics by itself is unlikely to provide defini- tive answers to such questions. Obtaining the answers would require an accurate crystal ball. Nevertheless, managerial economics is a valuable tool for analyzing business situations such as the ones raised in the headlines that open each chapter of this book.

In fact, if you surf the Internet, browse a business publication such as Bloomberg Businessweek or The Wall Street Journal, or read a trade publication like Restaurant News or Supermarket Business News, you will find a host of stories that involve managerial econom- ics. A recent search generated the following headlines:

“From iPhones to Automobiles: Apple Car Reportedly Ready to Hit the Streets in 2019” “Ferrari Spinoff Generates $4 Billion Windfall for Fiat Chrysler” “Target to Match Online Prices with Online Rivals” “U.S. Indicts Three in Auto Parts Price-Fixing Probe” “Competition Heats Up for Northwest Wine Shipping” “U.S. Government Steps Up Challenges to Hospital Mergers” “Brands Rethink Social Media Strategy” “Comcast Calls Off Time Warner Cable Merger”

Sadly, billions of dollars are lost each year because many existing managers fail to use basic tools from managerial economics to shape pricing and output decisions, optimize the production process and input mix, choose product quality, guide horizontal and vertical merger decisions, or optimally design internal and external incentives. Happily, if you learn a few basic principles from managerial economics, you will be poised to drive the inept man- agers out of their jobs! You will also understand why the latest recession was great news to some firms and why some software firms spend millions on the development of applications for smartphones but permit consumers to download them for free.

Managerial economics is not only valuable to managers of Fortune 500 companies; it is also valuable to managers of not-for-profit organizations. It is useful to the manager of a food bank who must decide the best means for distributing food to the needy. It is valuable to the coordinator of a shelter for the homeless whose goal is to help the largest possible number of homeless, given a very tight budget. In fact, managerial economics provides useful insights into every facet of the business and nonbusiness world in which we live—including house- hold decision making.

Why is managerial economics so valuable to such a diverse group of decision makers? The answer to this question lies in the meaning of the term managerial economics.

The Manager A manager is a person who directs resources to achieve a stated goal. This definition includes all individuals who (1) direct the efforts of others, including those who delegate tasks within an organization such as a firm, a family, or a club; (2) purchase inputs to be used in the production of goods and services such as the output of a firm, food for the needy, or shelter for the homeless; or (3) are in charge of making other decisions, such as product price or quality.

manager A person who directs resources to achieve a stated goal.

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A manager generally has responsibility for his or her own actions as well as for the actions of individuals, machines, and other inputs under the manager’s control. This control may involve responsibilities for the resources of a multinational corporation or for those of a single household. In each instance, however, a manager must direct resources and the behavior of individuals for the purpose of accomplishing some task. While much of this book assumes the manager’s task is to maximize the profits of the firm that employs the manager, the underly- ing principles are valid for virtually any decision process.

Economics The primary focus of this book is on the second word in managerial economics. Economics is the science of making decisions in the presence of scarce resources. Resources are simply anything used to produce a good or service or, more generally, to achieve a goal. Decisions are important because scarcity implies that by making one choice, you give up another. A com- puter firm that spends more resources on advertising has fewer resources to invest in research and development. A food bank that spends more on soup has less to spend on fruit. Economic decisions thus involve the allocation of scarce resources, and a manager’s task is to allocate resources so as to best meet the manager’s goals.

One of the best ways to comprehend the pervasive nature of scarcity is to imagine that a genie has appeared and offered to grant you three wishes. If resources were not scarce, you would tell the genie you have absolutely nothing to wish for; you already have everything you want. Surely, as you begin this course, you recognize that time is one of the scarcest resources of all. Your primary decision problem is to allocate a scarce resource—time—to achieve a goal—such as mastering the subject matter or earning an A in the course.

Managerial Economics Defined Managerial economics, therefore, is the study of how to direct scarce resources in the way that most efficiently achieves a managerial goal. It is a very broad discipline in that it describes methods useful for directing everything from the resources of a household to maxi- mize household welfare to the resources of a firm to maximize profits.

To understand the nature of decisions that confront managers of firms, imagine that you are the manager of a Fortune 500 company that makes computers. You must make a host of decisions to succeed as a manager: Should you purchase components such as disk drives and chips from other manufacturers or produce them within your own firm? Should you specialize in making one type of computer or produce several different types? How many computers should you produce, and at what price should you sell them? How many employees should you hire, and how should you compensate them? How can you ensure that employees work hard and produce quality products? How will the actions of rival computer firms affect your decisions?

The key to making sound decisions is to know what information is needed to make an informed decision and then to collect and process the data. If you work for a large firm, your legal department can provide data about the legal ramifications of alternative decisions; your accounting department can provide tax advice and basic cost data; your marketing depart- ment can provide you with data on the characteristics of the market for your product; and your firm’s financial analysts can provide summary data for alternative methods of obtaining financial capital. Ultimately, however, the manager must integrate all of this information, pro- cess it, and arrive at a decision. The remainder of this book will show you how to perform this important managerial function by using six principles that comprise effective management.

economics The science of making decisions in the presence of scarce resources.

managerial economics The study of how to direct scarce resources in the way that most efficiently achieves a managerial goal.

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THE ECONOMICS OF EFFECTIVE MANAGEMENT

The nature of sound managerial decisions varies depending on the underlying goals of the manager. Since this course is designed primarily for managers of firms, this book focuses on managerial decisions as they relate to maximizing profits or, more generally, the value of the firm. Before embarking on this special use of managerial economics, we provide an overview of the basic principles that comprise effective management. In particular, an effective man- ager must (1) identify goals and constraints, (2) recognize the nature and importance of prof- its, (3) understand incentives, (4) understand markets, (5) recognize the time value of money, and (6) use marginal analysis.

Identify Goals and Constraints The first step in making sound decisions is to have well-defined goals because achieving dif- ferent goals entails making different decisions. If your goal is to maximize your grade in this course rather than maximize your overall grade point average, your study habits will differ accordingly. Similarly, if the goal of a food bank is to distribute food to needy people in rural areas, its decisions and optimal distribution network will differ from those it would use to distribute food to needy inner-city residents. Notice that, in both instances, the decision maker faces constraints that affect the ability to achieve a goal. The 24-hour day affects your ability to earn an A in this course; a budget affects the ability of the food bank to distribute food to the needy. Constraints are an artifact of scarcity.

Different units within a firm may be given different goals; those in a firm’s marketing department might be instructed to use their resources to maximize sales or market share, while those in the firm’s financial group might focus on earnings growth or risk-reduction strategies. Later in this book we will see how the firm’s overall goal—maximizing profits— can be achieved by giving each unit within the firm an incentive to achieve potentially differ- ent goals.

Unfortunately, constraints make it difficult for managers to achieve goals such as max- imizing profits or increasing market share. These constraints include such things as the available technology and the prices of inputs used in production. The goal of maximizing profits requires the manager to decide the optimal price to charge for a product, how much to produce, which technology to use, how much of each input to use, how to react to deci- sions made by competitors, and so on. This book provides tools for answering these types of questions.

Recognize the Nature and Importance of Profits The overall goal of most firms is to maximize profits or the firm’s value, and the remain- der of this book will detail strategies managers can use to achieve this goal. Before we provide these details, let us examine the nature and importance of profits in a free-market economy.

Economic versus Accounting Profits When most people hear the word profit, they think of accounting profits. Accounting profits are the total amount of money taken in from sales (total revenue, or price times quantity sold) minus the dollar cost of producing goods or services. Accounting profits are what show up on the firm’s income statement and are typically reported to the manager by the firm’s account- ing department.

accounting profits The total amount of money taken in from sales (total revenue, or price times quantity sold) minus the dollar cost of producing goods or services.  

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A more general way to define profits is in terms of what economists refer to as economic profits. Economic profits are the difference between the total revenue and the total opportu- nity cost of producing the firm’s goods or services. The opportunity cost of using a resource includes both the explicit (or accounting) cost of the resource and the implicit cost of giving up the best alternative use of the resource. The opportunity cost of producing a good or ser- vice generally is higher than accounting costs because it includes both the dollar value of costs (explicit, or accounting, costs) and any implicit costs.

Implicit costs are very hard to measure and therefore managers often overlook them. Effective managers, however, continually seek out data from other sources to identify and quantify implicit costs. Managers of large firms can use sources within the company, includ- ing the firm’s finance, marketing, and/or legal departments, to obtain data about the implicit costs of decisions. In other instances managers must collect data on their own. For example, what does it cost you to read this book? The price you paid the bookseller for this book is an explicit (or accounting) cost, while the implicit cost is the value of what you are giving up by reading the book. You could be studying some other subject or watching TV, and each of these alternatives has some value to you. The “best” of these alternatives is your implicit cost of reading this book; you are giving up this alternative to read the book. Similarly, the opportu- nity cost of going to school is much higher than the cost of tuition and books; it also includes the amount of money you would earn had you decided to work rather than go to school.

In the business world, the opportunity cost of opening a restaurant is the best alternative use of the resources used to establish the restaurant—say, opening a hair salon. Again, these resources include not only the explicit financial resources needed to open the business but any implicit costs as well. Suppose you own a building in New York that you use to run a small pizzeria. Food supplies are your only accounting costs. At the end of the year, your accountant informs you that these costs were $20,000 and that your revenues were $100,000. Thus, your accounting profits are $80,000.

However, these accounting profits overstate your economic profits because the costs include only accounting costs. First, the costs do not include the time you spent running the business. Had you not run the business, you could have worked for someone else, and this fact reflects an economic cost not accounted for in accounting profits. To be concrete, suppose you could have worked for someone else for $30,000. Your opportunity cost of time would have been $30,000 for the year. Thus, $30,000 of your accounting profits are not profits at all but one of the implicit costs of running the pizzeria.

Second, accounting costs do not account for the fact that, had you not run the pizzeria, you could have rented the building to someone else. If the rental value of the building is $100,000 per year, you gave up this amount to run your own business. Thus, the costs of running the pizzeria include not only the costs of supplies ($20,000) but the $30,000 you could have earned in some other business and the $100,000 you could have earned in renting the building to someone else. The economic cost of running the pizzeria is $150,000—the amount you gave up to run your business. Considering the revenue of $100,000, you actually lost $50,000 by running the pizzeria; your economic profits were –$50,000.

Throughout this book, when we speak of costs, we mean economic costs. Economic costs are opportunity costs and include not only the explicit (accounting) costs but also the implicit costs of the resources used in production.

The Role of Profits A common misconception is that the firm’s goal of maximizing profits is necessarily bad for society. Individuals who want to maximize profits often are considered self-interested, a

economic profits The difference between total revenue and total opportunity cost.

opportunity cost The explicit cost of a resource plus the implicit cost of giving up its best alternative use.

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Recent trends in globalization have forced businesses around the world to more keenly focus on profitability. This trend is also present in Japan, where historical links between banks and businesses have traditionally blurred the goals of firms. For example, the Japanese busi- ness engineering firm Mitsui & Co. Ltd. launched “Challenge 21,” a plan directed at helping the company emerge as Japan’s leading business engineering group. According to a spokesperson for the company, “[This plan permits us to] create new value and maximize profitability by taking steps such as renewing our management framework and prioritizing the allocation of our resources into strategic areas. We are committed to maximizing shareholder value

through business conduct that balances the pursuit of earn- ings with socially responsible behavior.”

Ultimately, the goal of any continuing company must be to maximize the value of the firm. This goal is often achieved by trying to hit intermediate targets, such as minimizing costs or increasing market share. If you—as a manager— do not maximize your firm’s value over time, you will be in danger of either going out of business, being taken over by other owners (as in a leveraged buyout), or having stock- holders elect to replace you and other managers.

Source: “Mitsui & Co., Ltd. UK Regulatory Announcement: Final Results,” Business Wire, May 13, 2004.

INSIDE BUSINESS 1–1

The Goals of Firms in Our Global Economy

quality that many people view as undesirable. However, consider Adam Smith’s classic line from The Wealth of Nations: “It is not out of the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest.”2

Smith is saying that by pursuing its self-interest—the goal of maximizing profits—a firm ultimately meets the needs of society. If you cannot make a living as a rock singer, it is prob- ably because society does not appreciate your singing; society would more highly value your talents in some other employment. If you break five dishes each time you clean up after din- ner, your talents are perhaps better suited for filing paperwork or mowing the lawn. Similarly, the profits of businesses signal where society’s scarce resources are best allocated. When firms in a given industry earn economic profits, the opportunity cost to resource holders out- side the industry increases. Owners of other resources soon recognize that, by continuing to operate their existing businesses, they are giving up profits. This induces new firms to enter the markets in which economic profits are available. As more firms enter the industry, the market price falls, and economic profits decline.

Thus, profits signal the owners of resources where the resources are most highly valued by society. By moving scarce resources toward the production of goods most valued by soci- ety, the total welfare of society is improved. As Adam Smith first noted, this phenomenon is due not to benevolence on the part of the firms’ managers but to the self-interested goal of maximizing the firms’ profits.

2Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, 1776.

P R I N C I P L E Profits Are a Signal Profits signal to resource holders where resources are most highly valued by society.

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The Five Forces Framework and Industry Profitability A key theme of this textbook is that many interrelated forces and decisions influence the level, growth, and sustainability of profits. If you or other managers in the industry are clever enough to identify strategies that yield a windfall to shareholders this quarter, there is no guarantee that these profits will be sustained in the long run. You must recognize that profits are a signal—if your business earns superior profits, existing and potential competitors will do their best to get a piece of the action. In the remaining chapters, we will examine a variety of business strategies designed to enhance your prospects of earning and sustaining profits. Before we do so, however, it is constructive to provide a conceptual framework for thinking about some of the factors that impact industry profitability.

Figure 1–1 illustrates the “five forces” framework pioneered by Michael Porter.3 This framework organizes many complex managerial economics issues into five categories or “forces” that impact the sustainability of industry profits: (1) entry, (2) power of input sup- pliers, (3) power of buyers, (4) industry rivalry, and (5) substitutes and complements. The following discussion explains how these forces influence industry profitability and highlights the connections among these forces and material covered in the remaining chapters of the text.

Entry. As we will see in Chapters 2, 7, and 8, entry heightens competition and reduces the margins of existing firms in a wide variety of industry settings. For this reason, the ability of existing firms to sustain profits depends on how barriers to entry affect the ease with which other firms can enter the industry. Entry can come from a number of directions, including the formation of new companies (Wendy’s entered the fast-food industry in the 1970s after its founder, Dave Thomas, left KFC); globalization strategies by foreign companies (Toyota has sold vehicles in Japan since the 1930s but waited until the middle of the last century to

3Michael Porter, Competitive Strategy (New York: Free Press, 1980).

Sustainable Industry Profits

∙ Entry costs ∙ Sunk costs ∙ Network effects ∙ Switching costs ∙ Speed of adjustment ∙ Economies of scale ∙ Reputation ∙ Government restraints

Entry

∙ Supplier concentration ∙ Price/productivity of alternative inputs ∙ Relationship-specific investments ∙ Supplier switching costs ∙ Government restraints

Power of Input Suppliers ∙ Buyer concentration ∙ Price/value of substitute products or services ∙ Relationship-specific investments ∙ Customer switching costs ∙ Government restraints

Powe r of Buyers

∙ Concentration ∙ Switching costs ∙ Price, quantity, quality, or ∙ Timing of decisions service competition ∙ Information ∙ Degree of differentiation ∙ Government restraints

Industry Rivalry ∙ Price/value of surrogate ∙ Network effects products or services ∙ Government restraints ∙ Price/value of complementary products or services

Substitutes and Complements

Figure 1–1 The Five Forces Framework

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enter the U.S. automobile market); and the introduction of new product lines by existing firms (computer manufacturer Apple now also sells the popular iPhone).

As shown in Figure 1–1, a number of economic factors affect the ability of entrants to erode existing industry profits. In subsequent chapters, you will learn why entrants are less likely to capture market share quickly enough to justify the costs of entry in environments where there are sizeable sunk costs (Chapters 5 and 9), significant economies of scale (Chapters 5 and 8), or significant network effects (Chapter 13), or where existing firms have invested in strong reputations for providing value to a sizeable base of loyal consumers (Chapter 11) or to aggressively fight entrants (Chapters 10 and 13). In addition, you will gain a better apprecia- tion for the role that governments play in shaping entry through patents and licenses (Chapter 8), trade policies (Chapters 5 and 14), and environmental legislation (Chapter 14). We will also identify a variety of strategies to raise the costs to consumers of “switching” to would-be entrants, thereby lowering the threat that entrants will erode your profits.

Power of Input Suppliers. Industry profits tend to be lower when suppliers have the power to negotiate favorable terms for their inputs. Supplier power tends to be low when inputs are relatively standardized and relationship-specific investments are minimal (Chapter 6), input markets are not highly concentrated (Chapter 7), or alternative inputs are available with similar marginal productivities per dollar spent (Chapter 5). In many countries, the government con- strains the prices of inputs through price ceilings and other controls (Chapters 2 and 14), which limits to some extent the ability of suppliers to expropriate profits from firms in the industry.

Power of Buyers. Similar to the case of suppliers, industry profits tend to be lower when customers or buyers have the power to negotiate favorable terms for the products or services produced in the industry. In most consumer markets, buyers are fragmented and thus buyer con- centration is low. Buyer concentration and hence customer power tend to be higher in industries that serve relatively few “high-volume” customers. Buyer power tends to be lower in industries where the cost to customers of switching to other products is high—as is often the case when there are relationship-specific investments and hold-up problems (Chapter 6), imperfect infor- mation that leads to costly consumer search (Chapter 12), or few close substitutes for the prod- uct (Chapters 2, 3, 4, and 11). Government regulations, such as price floors or price ceilings (Chapters 2 and 14), can also impact the ability of buyers to obtain more favorable terms.

Industry Rivalry. The sustainability of industry profits also depends on the nature and intensity of rivalry among firms competing in the industry. Rivalry tends to be less intense (and hence the likelihood of sustaining profits is higher) in concentrated industries—that is, those with relatively few firms. In Chapter 7 we will take a closer look at various measures that can be used to gauge industry concentration.

The level of product differentiation and the nature of the game being played—whether firms’ strategies involve prices, quantities, capacity, or quality/service attributes, for example— also impact profitability. In later chapters you will learn why rivalry tends to be more intense in industry settings where there is little product differentiation and firms compete in price (Chapters 8, 9, 10, and 11) and where consumer switching costs are low (Chapters 11 and 12). You will also learn how imperfect information and the timing of decisions affect rivalry among firms (Chapters 10, 12, and 13).

Substitutes and Complements. The level and sustainability of industry profits also depend on the price and value of interrelated products and services. Porter’s original five forces framework emphasized that the presence of close substitutes erodes industry profitability.

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When profits in a given industry are higher than in other industries, new firms will attempt to enter that industry. When losses are recorded, some firms will likely leave the industry. This sort of “evolution” has changed the global landscape of personal computer markets.

At the start of the PC era, personal computer makers enjoyed positive economic profits. These higher profits led to new entry and heightened competition. Over the past two decades, entry has led to declines in PC prices and industry profitability despite significant increases in the speed and storage capacities of PCs. Less efficient firms have been forced to exit the market.

In the early 2000s, IBM—the company that launched the PC era when it introduced the IBM PC in the early

1980s—sold its PC business to China-based Lenovo. Compaq—an early leader in the market for PCs—was acquired by Hewlett-Packard. A handful of small PC makers have enjoyed some success competing against the remain- ing traditional players, which include Dell and Hewlett- Packard. By the late 2000s, Dell’s strategy switched from selling computers directly to consumers to entering into relationships with retailers such as Best Buy and Staples. While only time will tell how these strategies will impact the long-run viability of traditional players, competitive pressures continue to push PC prices and industry profits downward as consumers increasingly shift toward tablets and smartphones.

INSIDE BUSINESS 1–2

Profits and the Evolution of the Computer Industry

In Chapters 2, 3, 4, and 11 you will learn how to quantify the degree to which surrogate products are close substitutes by using elasticity analysis and models of consumer behavior. We will also see that government policies (such as restrictions limiting the importation of prescription drugs from Canada into the United States) can directly impact the availability of substitutes and thus industry profits.

More recent work by economists and business strategists emphasizes that complemen- tarities also affect industry profitability.4 For example, Microsoft’s profitability in the market for operating systems is enhanced by the presence of complementary products ranging from relatively inexpensive computer hardware to a plethora of Windows-compatible application software. Analogously, Apple’s profitability in the cell phone market is enhanced by the tens of thousands of complementary applications (“apps”) that are compatible with its iPhone. In Chapters 3, 5, 10, and 13 you will learn how to quantify these complementarities or “syner- gies” and identify strategies to create and exploit complementarities and network effects.

Many forces that impact the level and sustainability of industry profits are interrelated. For instance, the U.S. automobile industry suffered a sharp decline in industry profitability during the 1970s as a result of sharp increases in the price of gasoline (a complement to auto- mobiles). This change in the price of a complementary product enabled Japanese automakers to enter the U.S. market through a differentiation strategy of marketing their fuel-efficient cars, which sold like hotcakes compared to the gas-guzzlers American automakers produced at that time. These events, in turn, have had a profound impact on industry rivalry in the auto- motive industry—not just in the United States, but worldwide.

It is also important to stress that the five forces framework is primarily a tool for helping managers see the “big picture”; it is a schematic you can use to organize various industry conditions that affect industry profitability and assess the efficacy of alternative business

4See, for example, Barry J. Nalebuff and Adam M. Brandenburger, Co-Opetition (New York: Doubleday, 1996), as well as R. Preston McAfee, Competitive Solutions (Princeton: Princeton University Press, 2002).

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strategies. However, it would be a mistake to view it as a comprehensive list of all factors that affect industry profitability. The five forces framework is not a substitute for understanding the economic principles that underlie sound business decisions.

Understand Incentives In our discussion of the role of profits, we emphasized that profits signal the holders of resources when to enter and exit particular industries. In effect, changes in profits provide an incentive to resource holders to alter their use of resources. Within a firm, incentives affect how resources are used and how hard workers work. To succeed as a manager, you must have a clear grasp of the role of incentives within an organization such as a firm and how to con- struct incentives to induce maximal effort from those you manage. Chapter 6 is devoted to this special aspect of managerial decision making, but it is useful here to provide a synopsis of how to construct proper incentives.

The first step in constructing incentives within a firm is to distinguish between the world, or the business place, as it is and the way you wish it were. Many professionals and owners of small establishments have difficulties because they do not fully comprehend the importance of the role incentives play in guiding the decisions of others.

A friend of ours—Mr. O—opened a restaurant and hired a manager to run the business so he could spend time doing the things he enjoys. Recently, we asked him how his business was doing, and he reported that he had been losing money ever since the restaurant opened. When asked whether he thought the manager was doing a good job, he said, “For the $75,000 salary I pay the manager each year, the manager should be doing a good job.”

Mr. O believes the manager “should be doing a good job.” This is the way he wishes the world was. But individuals often are motivated by self-interest. This is not to say that people never act out of kindness or charity, but rather that human nature is such that people naturally tend to look after their own self-interest. Had Mr. O taken a managerial economics course, he would know how to provide the manager with an incentive to do what is in Mr. O’s best interest. The key is to design a mechanism such that if the manager does what is in his own interest, he will indirectly do what is best for Mr. O.

Since Mr. O is not physically present at the restaurant to watch over the manager, he has no way of knowing what the manager is up to. Indeed, his unwillingness to spend time at the restaurant is what induced him to hire the manager in the first place. What type of incentive has he created by paying the manager $75,000 per year? The manager receives $75,000 per year regardless of whether he puts in 12-hour or 2-hour days. The manager receives no reward for working hard and incurs no penalty if he fails to make sound managerial decisions. The manager receives the same $75,000 regardless of the restaurant’s profitability.

Fortunately, most business owners understand the problem just described. The owners of large corporations are shareholders, and most never set foot on company ground. How do they provide incentives for chief executive officers (CEOs) to be effective managers? Very simply, they provide them with “incentive plans” in the form of bonuses. These bonuses are in direct proportion to the firm’s profitability. If the firm does well, the CEO receives a large bonus. If the firm does poorly, the CEO receives no bonus and risks being fired by the stockholders. These types of incentives are also present at lower levels within firms. Some individuals earn commissions based on the revenue they generate for the firm’s owner. If they put forth little effort, they receive little pay; if they put forth much effort and hence generate many sales, they receive a generous commission.

The thrust of managerial economics is to provide you with a broad array of skills that enable you to make sound economic decisions and to structure appropriate incentives within

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your organization. We will begin under the assumption that everyone with whom you come into contact is greedy, that is, interested only in his or her own self-interest. In such a case, understanding incentives is a must. Of course, this is a worst-case scenario; more likely, some of your business contacts will not be so selfishly inclined. If you are so lucky, your job will be all the easier.

Understand Markets In studying microeconomics in general, and managerial economics in particular, it is import- ant to bear in mind that there are two sides to every transaction in a market: For every buyer of a good there is a corresponding seller. The final outcome of the market process, then, depends on the relative power of buyers and sellers in the marketplace. The power, or bargaining posi- tion, of consumers and producers in the market is limited by three sources of rivalry that exist in economic transactions: consumer–producer rivalry, consumer–consumer rivalry, and producer–producer rivalry. Each form of rivalry serves as a disciplining device to guide the market process, and each affects different markets to a different extent. Thus, your ability as a manager to meet performance objectives will depend on the extent to which your product is affected by these sources of rivalry.

Consumer–Producer Rivalry Consumer–producer rivalry occurs because of the competing interests of consumers and producers. Consumers attempt to negotiate or locate low prices, while producers attempt to negotiate high prices. In a very loose sense, consumers attempt to “rip off” producers, and producers attempt to “rip off” consumers. Of course, there are limits to the ability of these parties to achieve their goals. If a consumer offers a price that is too low, the producer will refuse to sell the product to the consumer. Similarly, if the producer asks a price that exceeds the consumer’s valuation of a good, the consumer will refuse to purchase the good. These two forces provide a natural check and balance on the market process even in markets in which the product is offered by a single firm (a monopolist). An illustrative example of this type of rivalry is the common haggling over price between a potential car buyer and salesperson.

Consumer–Consumer Rivalry A second source of rivalry that guides the market process occurs among consumers. Consumer–consumer rivalry reduces the negotiating power of consumers in the marketplace. It arises because of the economic doctrine of scarcity. When limited quantities of goods are available, consumers will compete with one another for the right to purchase the available goods. Consumers who are willing to pay the highest prices for the scarce goods will outbid other consumers for the right to consume the goods. Once again, this source of rivalry is pres- ent even in markets in which a single firm is selling a product. A good example of consumer– consumer rivalry is an auction, a topic we will examine in detail in Chapter 12.

Producer–Producer Rivalry A third source of rivalry in the marketplace is producer–producer rivalry. Unlike the other forms of rivalry, this disciplining device functions only when multiple sellers of a product compete in the marketplace. Given that customers are scarce, producers compete with one another for the right to service the customers available. Those firms that offer the best- quality product at the lowest price earn the right to serve the customers. For example, when two gas stations located across the street from one another compete on price, they are engaged in producer–producer rivalry.

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Government and the Market When agents on either side of the market find themselves disadvantaged in the market process, they attempt to induce government to intervene on their behalf. For example, the market for electricity in some towns is characterized by a sole local supplier of electricity, and thus there is no producer–producer rivalry. Consumer groups may initiate action by a public utility commis- sion to limit the power of utilities in setting prices. Similarly, producers may lobby for govern- ment assistance to place them in a better bargaining position relative to consumers and foreign producers. Thus, in modern economies government also plays a role in disciplining the market process. Chapter 14 explores how government affects managerial decisions.

Recognize the Time Value of Money The timing of many decisions involves a gap between the time when the costs of a project are borne and the time when the benefits of the project are received. In these instances it is important to recognize that $1 today is worth more than $1 received in the future. The reason is simple: The opportunity cost of receiving the $1 in the future is the forgone interest that could be earned were $1 received today. This opportunity cost reflects the time value of money. To properly account for the timing of receipts and expenditures, the manager must understand present value analysis.

Present Value Analysis The present value (PV) of an amount received in the future is the amount that would have to be invested today at the prevailing interest rate to generate the given future value. For exam- ple, suppose someone offered you $1.10 one year from today. What is the value today (the present value) of $1.10 to be received one year from today? Notice that if you could invest $1.00 today at a guaranteed interest rate of 10 percent, one year from now $1.00 would be worth $1.00 × 1.1 = $1.10. In other words, over the course of one year, your $1.00 would earn $.10 in interest. Thus, when the interest rate is 10 percent, the present value of receiving $1.10 one year in the future is $1.00.

A more general formula follows:

Formula (Present Value). The present value (PV) of a future value (FV) received n years in the future is

PV = FV _____

( 1 + i ) n (1−1)

where i is the rate of interest, or the opportunity cost of funds. For example, the present value of $100.00 in 10 years if the interest rate is at 7 percent is

$50.83 since

PV = $100 _______

( 1 + .07 ) 10 =

$100 _____

1.9672 = $50.83

This essentially means that if you invested $50.83 today at a 7 percent interest rate, in 10 years your investment would be worth $100.

Notice that the interest rate appears in the denominator of the expression in Equation 1–1. This means that the higher the interest rate, the lower the present value of a future amount, and conversely. The present value of a future payment reflects the difference between the future value (FV) and the opportunity cost of waiting (OCW): PV = FV − OCW. Intuitively, the higher the interest rate, the higher the opportunity cost of waiting to receive a future

time value of money The fact that $1 today is worth more than $1 received in the future.

present value The amount that would have to be invested today at the prevailing interest rate to generate the given future value.

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amount and thus the lower the present value of the future amount. For example, if the interest rate is zero, the opportunity cost of waiting is zero, and the present value and the future value coincide. This is consistent with Equation 1–1 since PV = FV when the interest rate is zero.

The basic idea of the present value of a future amount can be extended to a series of future payments. For example, if you are promised FV1 one year in the future, FV2 two years in the future, and so on for n years, the present value of this sum of future payments is

PV = F V 1 _____

( 1 + i ) 1 +

F V 2 _____ ( 1 + i ) 2

+ F V 3 _____

( 1 + i ) 3 + · · · +

F V n _____ ( 1 + i ) n

Formula (Present Value of a Stream). When the interest rate is i, the present value of a stream of future payments of FV1, FV2, . . . , FVn is

PV = ∑ t = 1

n

F V t _____

( 1 + i ) t

Given the present value of the income stream that arises from a project, one can easily compute the net present value of the project. The net present value (NPV) of a project is simply the present value (PV) of the income stream generated by the project minus the current cost (C0) of the project: NPV = PV − C0. If the net present value of a project is positive, then the project is profitable because the present value of the earnings from the project exceeds the current cost of the project. On the other hand, a manager should reject a project that has a negative net present value since the cost of such a project exceeds the present value of the income stream that project generates.

Formula (Net Present Value). Suppose that by sinking C0 dollars into a project today, a firm will generate income of FV1 one year in the future, FV2 two years in the future, and so on for n years. If the interest rate is i, the net present value of the project is

NPV = F V 1 _____

( 1 + i ) 1 +

F V 2 _____ ( 1 + i ) 2

+ F V 3 _____

( 1 + i ) 3 + · · · +

F V n _____ ( 1 + i ) n

− C 0

net present value The present value of the income stream generated by a project minus the current cost of the project.

DEMONSTRATION PROBLEM 1–1

The manager of Automated Products is contemplating the purchase of a new machine that will cost $300,000 and has a useful life of five years. The machine will yield (year-end) cost reductions to Automated Products of $50,000 in year 1, $60,000 in year 2, $75,000 in year 3, and $90,000 in years 4 and 5. What is the present value of the cost savings of the machine if the interest rate is 8 percent? Should the manager purchase the machine?

ANSWER: By spending $300,000 today on a new machine, the firm will reduce costs by $365,000 over five years. However, the present value of the cost savings is only

PV = 50,000

______ 1.08

+ 60,000

______ 1.08 2

+ 75,000

______ 1.08 3

+ 90,000

______ 1.08 4

+ 90,000

______ 1.08 5

= $284,679

Consequently, the net present value of the new machine is

NPV = PV − C 0 = $284,679 − $300,000 = −$15,321

Since the net present value of the machine is negative, the manager should not purchase the machine. In other words, the manager could earn more by investing the $300,000 at 8 percent than by spending the money on the cost-saving technology.

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Present Value of Indefinitely Lived Assets Some decisions generate cash flows that continue indefinitely. For instance, consider an asset that generates a cash flow of CF0 today, CF1 one year from today, CF2 two years from today, and so on for an indefinite period of time. If the interest rate is i, the value of the asset is given by the present value of these cash flows:

P V Asset = C F 0 + C F 1 ______

( 1 + i ) +

C F 2 _____ ( 1 + i ) 2

+ C F 3 _____

( 1 + i ) 3 + · · ·

While this formula contains terms that continue indefinitely, for certain patterns of future cash flows one can readily compute the present value of the asset. For instance, suppose that the cur- rent cash flow is zero (CF0 = 0) and that all future cash flows are identical (CF1 = CF2 = . . . ). In this case, the asset generates a perpetual stream of identical cash flows at the end of each period. If each of these future cash flows is CF, the value of the asset is the present value of the perpetuity:

P V Perpetuity =

CF ______

( 1 + i ) +

CF _____

( 1 + i ) 2 +

CF _____

( 1 + i ) 3 + · · ·

=

CF ___

i

Examples of such an asset include perpetual bonds and preferred stocks. Each of these assets pays the owner a fixed amount at the end of each period, indefinitely. Based on this formula, the value of a perpetual bond that pays the owner $100 at the end of each year when the inter- est rate is fixed at 5 percent is given by

P V Perpetual bond = CF

___ i =

$100 ____

.05 = $2,000

Present value analysis is also useful in determining the value of a firm since the value of a firm is the present value of the stream of profits (cash flows) generated by the firm’s physical, human, and intangible assets. In particular, if π0 is the firm’s current level of profits, π1 is next year’s profit, and so on, then the value of the firm is

P V Firm = π 0 + π 1 ______

( 1 + i ) +

π 2 _______ ( 1 + i ) 2

+ π 3 _______

( 1 + i ) 3 + · · ·

In other words, the value of the firm today is the present value of its current and future profits. To the extent that the firm is a “going concern” that lives on even after its founder dies, firm ownership represents a claim to assets with an indefinite profit stream.

Notice that the value of a firm takes into account the long-term impact of managerial decisions on profits. When economists say that the goal of the firm is to maximize profits, it should be understood to mean that the firm’s goal is to maximize its value, which is the pres- ent value of current and future profits.

P R I N C I P L E Profit Maximization Maximizing profits means maximizing the value of the firm, which is the present value of current and future profits.

While it is beyond the scope of this book to present all the tools Wall Street analysts use to estimate the value of firms, it is possible to gain insight into the issues involved by making a few simplifying assumptions. Suppose a firm’s current profits are π0 and that these profits

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have not yet been paid out to stockholders as dividends. Imagine that these profits are expected to grow at a constant rate of g percent each year and that profit growth is less than the interest rate (g < i). In this case, profits one year from today will be (1 + g)π0, profits two years from today will be (1 + g)2π0, and so on. The value of the firm, under these assumptions, is

P V Firm = π 0 + π 0 ( 1 + g ) ______

( 1 + i ) +

π 0 (1 + g) 2 _________

(1 + i) 2 +

π 0 (1 + g) 3 _______

(1 + i) 3 + · · ·

= π 0 ( 1 + i

_ i − g

)

For a given interest rate and growth rate of the firm, it follows that maximizing the lifetime value of the firm (long-term profits) is equivalent to maximizing the firm’s current (short- term) profits of π0.

You may wonder how this formula changes if current profits have already been paid out as dividends. In this case, the present value of the firm is the present value of future profits (since current profits have already been paid out). The value of the firm immediately after its current profits have been paid out as dividends (called the ex-dividend date) may be obtained by simply subtracting π0 from the equation:

P V Firm Ex-dividend = P V Firm − π 0

This may be simplified to yield the following formula:

P V Firm Ex-dividend = π 0 (

1 + g _

i − g )

Thus, so long as the interest rate and growth rate are constant, the strategy of maximizing current profits also maximizes the value of the firm on the ex-dividend date.

P R I N C I P L E Maximizing Short-Term Profits May Maximize Long-Term Profits If the growth rate in profits is less than the interest rate and both are constant, maximizing current (short-term) profits is the same as maximizing long-term profits.

DEMONSTRATION PROBLEM 1–2

Suppose the interest rate is 10 percent and the firm is expected to grow at a rate of 5 percent for the foreseeable future. The firm’s current profits are $100 million.

(a) What is the value of the firm (the present value of its current and future earnings)? (b) What is the value of the firm immediately after it pays a dividend equal to its current profits?

ANSWER: (a) The value of the firm is

P V Firm = π 0 + π 0 ( 1 + g ) ______

( 1 + i ) +

π 0 (1 + g) 2 _______

(1 + i) 2 +

π 0 (1 + g) 3 _______

(1 + i) 3 + · · ·

= π 0 ( 1 + i

_ i − g

)

= $100 ( 1 + .1

_ .1 − .05

) = ($100)(22) = $2,200 million

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(b) The value of the firm on the ex-dividend date is this amount ($2,200 million) less the cur- rent profits paid out as dividends ($100 million), or $2,100 million. Alternatively, this may be calculated as

P V Firm

Ex-dividend = π 0 ( 1 + g

_ i − g

)

= ($100) ( 1 + .05

_ .1 − .05

) = ($100)(21) = $2,100 million

Recently, an airline offered a standard one-year member- ship into its Airline Club for $450. Alternatively, one could purchase a three-month membership for $120. Many man- agers and executives join air clubs because they offer a quiet place to work or relax while on the road; thus, produc- tivity is enhanced.

Let’s assume you wish to join the club for one year. Should you pay the up-front $450 fee for a one-year membership or buy four three-month memberships at $120 each, for total payments of $480? For simplicity, let’s suppose the airline will not change the three-month fee of $120 over the next year.

On the surface it appears that you save $30 by paying for a one-year membership in advance. But this approach ignores the time value of money. Is paying for a full year in advance profitable when you take the time value of money into account?

The present value of the cost of membership if you pay for one year in advance is $450 since all of that money is

paid today. If you pay every three months, you pay $120 today, $120 in three months, $120 in six months, and $120 in nine months. Given an interest rate of 8 percent per year, which translates into a quarterly rate of 2 percent, the pres- ent value of the payments is

PV = $120 + $120

_____ 1.02

+ $120

_____ ( 1.02 ) 2

+ $120

_____ ( 1.02 ) 3

or

 PV = 120 + 117.65 + 115.34 + 113.08

= $466.07

Thus, in present value terms, you save $16.07 if you pay for an annual membership in advance. If you wish to join for one year and expect three-month fees to either remain con- stant or rise over the next year, it is better to pay in advance. Given the current interest rate, the airline is offering a good deal, but the present value of the savings is $16.07, not $30.

INSIDE BUSINESS 1–3

Joining the Jet Set

While the notion of the present value of a firm is very general, the simplified formula presented above is based on the assumption that the growth rate of the firm’s profits is con- stant. In reality, however, the investment and marketing strategies of the firm will affect its growth rate. Moreover, the strategies used by competitors generally will affect the growth rate of the firm. In such instances, there is no substitute for using the general present value formula and understanding strategies that have different impacts on profits over time, discussed in later chapters in this book.

Use Marginal Analysis Marginal analysis is one of the most important managerial tools—a tool we will use repeat- edly throughout this text in alternative contexts. Simply put, marginal analysis states that optimal managerial decisions involve comparing the marginal (or incremental) benefits of a decision with the marginal (or incremental) costs. For example, the optimal amount of study- ing for this course is determined by comparing (1) the improvement in your grade that will

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result from an additional hour of studying and (2) the additional costs of studying an addi- tional hour. So long as the benefits of studying an additional hour exceed the costs of studying an additional hour, it is profitable to continue to study. However, once an additional hour of studying adds more to costs than it does to benefits, you should stop studying.

More generally, let B(Q) denote the total benefits derived from Q units of some variable that is within the manager’s control. This is a very general idea: B(Q) may be the revenue a firm generates from producing Q units of output; it may be the benefits associated with dis- tributing Q units of food to the needy; or, in the context of our previous example, it may rep- resent the benefits derived by studying Q hours for an exam. Let C(Q) represent the total costs of the corresponding level of Q. Depending on the nature of the decision problem, C(Q) may be the total cost to a firm of producing Q units of output, the total cost to a food bank of pro- viding Q units of food to the needy, or the total cost to you of studying Q hours for an exam.

Discrete Decisions We first consider the situation where the managerial control variable is discrete. In this instance, the manager faces a situation like that summarized in columns 1 through 3 in Table 1–1. Notice that the manager cannot use fractional units of Q; only integer values are possible. This reflects the discrete nature of the problem. In the context of a production deci- sion, Q may be the number of gallons of soft drink produced. The manager must decide how many gallons of soft drink to produce (0, 1, 2, and so on), but cannot choose to produce fractional units (for example, one pint). Column 2 of Table 1–1 provides hypothetical data for total benefits; column 3 gives hypothetical data for total costs.

Suppose the objective of the manager is to maximize the net benefits

N ( Q ) = B ( Q ) − C ( Q ) ,

Table 1–1 Determining the Optimal Level of a Control Variable: The Discrete Case

(1) Control Variable

Q

(2) Total

Benefits B(Q)

(3) Total Costs C(Q)

(4) Net

Benefits N(Q)

(5) Marginal Benefit MB(Q)

(6) Marginal

Cost MC(Q)

(7) Marginal

Net Benefits MNB(Q)

Given Given Given (2) − (3) Δ(2) Δ(3)

Δ(4) or

(5) − (6)

0 0 0 0 − − − 1 90 10 80 90 10 80

2 170 30 140 80 20 60

3 240 60 180 70 30 40

4 300 100 200 60 40 20

5 350 150 200 50 50 0

6 390 210 180 40 60 −20 7 420 280 140 30 70 −40 8 440 360 80 20 80 −60 9 450 450 0 10 90 −80 10 450 550 −100 0 100 −100

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which represent the premium of total benefits over total costs of using Q units of the managerial control variable, Q. The net benefits—N(Q)—for our hypothetical example are given in column 4 of Table 1–1. Notice that the net benefits in column 4 are maximized when net benefits equal 200, which occurs when 5 units of Q are chosen by the manager.5

To illustrate the importance of marginal analysis in maximizing net benefits, it is useful to define a few terms. Marginal benefit refers to the additional benefits that arise by using an additional unit of the managerial control variable. For example, the marginal benefit of the first unit of Q is 90 since the first unit of Q increases total benefits from 0 to 90. The marginal benefit of the second unit of Q is 80 since increasing Q from 1 to 2 increases total benefits from 90 to 170. The marginal benefit of each unit of Q—MB(Q)—is presented in column 5 of Table 1–1.

Marginal cost, on the other hand, is the additional cost incurred by using an additional unit of the managerial control variable. Marginal costs—MC(Q)—are given in column 6 of Table 1–1. For example, the marginal cost of the first unit of Q is 10 since the first unit of Q increases total costs from 0 to 10. Similarly, the marginal cost of the second unit of Q is 20 since increasing Q from 1 to 2 increases total costs by 20 (costs rise from 10 to 30).

Finally, the marginal net benefits of Q—MNB(Q)—are the change in net benefits that arise from a one-unit change in Q. For example, by increasing Q from 0 to 1, net benefits rise from 0 to 80 in column 4 of Table 1–1, and thus the marginal net benefit of the first unit of Q is 80. By increasing Q from 1 to 2, net benefits increase from 80 to 140, so the marginal net benefit due to the second unit of Q is 60. Column 7 of Table 1–1 presents marginal net benefits for our hypothetical example. Notice that marginal net benefits may also be obtained as the difference between marginal benefits and marginal costs:

MNB ( Q ) = MB ( Q ) − MC ( Q )

Inspection of Table 1–1 reveals a remarkable pattern in the columns. Notice that by using 5 units of Q, the manager ensures that net benefits are maximized. At the net-benefit- maximizing level of Q (5 units), the marginal net benefits of Q are zero. Furthermore, at the net-benefit-max- imizing level of Q (5 units), marginal benefits equal marginal costs (both are equal to 50 in this example). There is an important reason why MB = MC at the level of Q that maximizes net benefits: So long as marginal benefits exceed marginal costs, an increase in Q adds more to total benefits than it does to total costs. In this instance, it is profitable for the manager to increase the use of the managerial control variable. Expressed differently, when marginal benefits exceed marginal costs, the net benefits of increasing the use of Q are positive; by using more Q, net benefits increase. For example, consider the use of 1 unit of Q in Table 1–1. By increasing Q to 2 units, total benefits increase by 80 and total costs increase by only 20. Increasing the use of Q from 1 to 2 units is profitable because it adds more to total benefits than it does to total costs.

5Actually, net benefits are equal to 200 for either 4 or 5 units of Q. This is due to the discrete nature of the data in the table, which restricts Q to be selected in one-unit increments. In the next section, we show that when Q can be selected in arbitrarily small increments (for example, when the firm can produce fractional gallons of soft drink), net benefits are maximized at a single level of Q. At this level of Q, marginal net benefits are equal to zero, which corresponds to 5 units of Q in Table 1–1.

marginal benefit The change in total benefits arising from a change in the managerial control variable Q.

marginal (incremental) cost (MC) The change in total costs arising from a change in the managerial control variable Q.

P R I N C I P L E

Marginal Principle To maximize net benefits, the manager should increase the managerial control variable up to the point where marginal benefits equal marginal costs. This level of the managerial control variable corresponds to the level at which marginal net benefits are zero; nothing more can be gained by fur- ther changes in that variable.

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Notice in Table 1–1 that while 5 units of Q maximizes net benefits, it does not maximize total benefits. In fact, total benefits are maximized at 10 units of Q, where marginal benefits are zero. The reason the net-benefit-maximizing level of Q is less than the level of Q that maximizes total benefits is that there are costs associated with achieving more total benefits. The goal of maximizing net benefits takes costs into account, while the goal of maximizing total benefits does not. In the context of a firm, maximizing total benefits is equivalent to maximizing revenues without regard for costs. In the context of studying for an exam, max- imizing total benefits requires studying until you maximize your grade, regardless of how much it costs you to study.

Continuous Decisions The basic principles for making decisions when the control variable is discrete also apply to the case of a continuous control variable. The basic relationships in Table 1–1 are depicted graphically in Figure 1–2. The top panel of the figure presents the total benefits and total costs of using different levels of Q under the assumption that Q is infinitely divisible (instead of allowing the firm to produce soft drinks only in one-gallon containers as in Table 1–1, it can now produce fractional units). The middle panel presents the net benefits, B(Q) − C(Q), and represents the vertical difference between B and C in the top panel. Notice that net benefits are maximized at the point where the difference between B(Q) and C(Q) is the greatest in the top panel. Furthermore, the slope of B(Q) is ΔB/ΔQ, or marginal benefit, and the slope of C(Q) is ΔC/ΔQ, or marginal cost. The slopes of the total benefits curve and the total cost curve are equal when net benefits are maximized. This is just another way of saying that when net benefits are maximized, MB = MC.

0

Marginal benefits, costs, and net benefits

0

Net benefits

0

Total benefits

and costs

MC(Q)

N(Q) = B(Q) – C(Q)

Slope = MNB

Maximum net benefits

Slope = MC

B(Q)

Q

Q

Q

C(Q)

Slope = MB

Maximum total benefits

MB(Q)MNB(Q)

Figure 1–2 Determining the Optimal Level of a Control Variable: The Continuous Case

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P R I N C I P L E

Marginal Value Curves Are the Slopes of Total Value Curves When the control variable is infinitely divisible, the slope of a total value curve at a given point is the marginal value at that point. In particular, the slope of the total benefit curve at a given Q is the marginal benefit of that level of Q. The slope of the total cost curve at a given Q is the marginal cost of that level of Q. The slope of the net benefit curve at a given Q is the marginal net benefit of that level of Q.

A C A L C U L U S A L T E R N A T I V E Since the slope of a function is the derivative of that function, the preceding principle means that the derivative of a given function is the marginal value of that function. For example,

MB

=

dB ( Q )

_____ dQ

MC = dC ( Q )

_____ dQ

MNB

=

dN ( Q )

_____ dQ

The bottom panel of Figure 1–2 depicts the marginal benefits, marginal costs, and mar- ginal net benefits. At the level of Q where the marginal benefit curve intersects the marginal cost curve, marginal net benefits are zero. That level of Q maximizes net benefits.

DEMONSTRATION PROBLEM 1–3

An engineering firm recently conducted a study to determine its benefit and cost structure. The results of the study are as follows:

B (Y) = 300Y − 6 Y 2

C (Y) = 4 Y 2

so that MB = 300 − 12Y and MC = 8Y. The manager has been asked to determine the maximum level of net benefits and the level of Y that will yield that result.

ANSWER: Equating MB and MC yields 300 − 12Y = 8Y. Solving this equation for Y reveals that the optimal level of Y is Y* = 15. Plugging Y* = 15 into the net benefit relation yields the maximum level of net benefits:

NB = 300 (15) − (6) ( 15 2 ) − (4) ( 15 2 ) = 2,250

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

Incremental Decisions Sometimes managers are faced with proposals that require a simple thumbs-up or thumbs- down decision. Marginal analysis is the appropriate tool to use for such decisions; the man- ager should adopt a project if the additional revenues that will be earned if the project is adopted exceed the additional costs required to implement the project. In the case of yes-or-no decisions, the additional revenues derived from a decision are called incremental revenues. The additional costs that stem from the decision are called incremental costs.

incremental revenues The additional revenues that stem from a yes- or-no decision.

incremental costs The additional costs that stem from a yes-or-no decision.

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To illustrate, imagine that you are the CEO of Slick Drilling Inc. and you must decide whether or not to drill for crude oil around the Twin Lakes area in Michigan. You are rela- tively certain there are 10,000 barrels of crude oil at this location. An accountant working for you prepared the information in Table 1–2 to help you decide whether or not to adopt the new project.

While the accountant supplied you with a lot of information in Table 1–2, the only data relevant for your decision are the incremental revenues and costs of adopting the new drilling project. In particular, notice that your direct and indirect fixed costs are the same regardless of whether you adopt the project and therefore are irrelevant to your decision. In contrast, note that your revenues increase by $183,200 if you adopt the project. This change in revenues stemming from the adoption of the project represents your incremental revenues. To earn these additional revenues, however, you must spend an additional $90,000 for drill augers and $75,000 for additional temporary workers. The sum of these costs—$165,000—represents the incremental cost of the new drilling project. Since your incremental revenues of $183,200 exceed the incremental costs of $165,000, you should give your “thumbs up” to the new proj- ect. Doing so adds $18,200 to your bottom line.

As another example, suppose the first unit of a control variable adds more to benefits than costs (MB > MC), but the second unit adds more to costs than benefits (MB < MC). In this case, the manager should give a “thumbs down” to the second unit since it adds more to costs than benefits.

LEARNING MANAGERIAL ECONOMICS

Before we continue our analysis of managerial economics, it is useful to provide some hints about how to study economics. Becoming proficient in economics is like learning to play music or ride a bicycle: The best way to learn economics is to practice, practice, and practice

Table 1–2 Incremental Costs and Revenues of the New Drilling Project

  Current

Situation After New

Drilling Project Incremental

Revenues and Costs

Total revenue $1,740,400 $1,923,600   $183,200

Variable cost        

Drill augers     750,000 840,000 90,000  

Temporary workers        500,000        575,000 75,000  

Total variable cost 1,250,000  1,415,000     165,000

Direct fixed costs        

Depreciation—equipment         120,000       120,000    

Total direct fixed cost     120,000     120,000         0  

Indirect fixed costs        

Supervisors’ salaries       240,000     240,000    

Office supplies            30,000           30,000    

Total indirect fixed cost      270,000     270,000         0  

Profit $      100,400 $    118,600   $18,200

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some more. Practicing managerial economics means practicing making decisions, and the best way to do this is to work and rework the problems presented in the text and at the end of each chapter. Before you can be effective at practicing, however, you must understand the language of economics.

The terminology in economics has two purposes. First, the definitions and formulas economists use are needed for precision. Economics deals with very complex issues, and much confusion can be avoided by using the language economists have designed to break down complex issues into manageable components. Second, precise terminology helps prac- titioners of economics communicate more efficiently. It would be difficult to communicate if, like Dr. Seuss, each of us made words mean whatever we wanted them to mean. However, the terminology is not an end in itself but simply a tool that makes it easier to communicate and analyze different economic situations.

Understanding the definitions used in economics is like knowing the difference between a whole note and a quarter note in music. Without such an understanding, it would be very difficult for anyone other than an extremely gifted musician to learn to play an instrument or to communicate to another musician how to play a new song. Given an under- standing of the language of music, anyone who is willing to take the time to practice can make beautiful music. The same is true of economics: Anyone who is willing to learn the language of economics and take the time to practice making decisions can learn to be an effective manager.

ANSWERING THE headLINE Why was Ralph fired from his managerial post at Amcott? As the manager of the foreign language division, he probably relied on his marketing department for sales forecasts and on his legal department for advice on contract and copyright law. The information he obtained about future sales was indeed accurate, but apparently his legal department did not fully anticipate all the legal ramifications of distributing Magicword. Sometimes, man- agers are given misinformation.

The real problem in this case, however, is that Ralph did not properly act on the information that was given him. Ralph’s plan was to generate $7 million per year in sales by sinking $20 million into Magicword. Assuming there were no other costs associated with the project, the projected net present value to Amcott of purchasing Magicword was

NPV = $7,000,000

___________ (1 + .07) 1

+ $7,000,000

___________ (1 + .07) 2

+ $7,000,000

___________ (1 + .07) 3

− $20,000,000

= −$1,629,788

which means that Ralph should have expected Amcott to lose over $1.6 million by pur- chasing Magicword.

Ralph was not fired because of the mistakes of his legal department but for his man- agerial ineptness. The lawsuit publicized to Amcott’s shareholders, among others, that Ralph was not properly processing information given to him: He did not recognize the time value of money.

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23

KEY TERMS AND CONCEPTS

accounting cost accounting profits constraints consumer–consumer rivalry consumer–producer rivalry economic profits economics ex-dividend date explicit cost five forces framework future value (FV)

goals implicit cost incentives incremental cost incremental revenue manager managerial economics marginal analysis marginal benefit marginal cost marginal net benefit

net present value (NPV) opportunity cost perpetuity present value (PV) producer–producer rivalry profit resources time value of money value of a firm

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. Southwest Airlines begins a “Bags Fly Free” campaign, charging no fees for the first and second checked bags. Does this situation best represent producer–producer rivalry, consumer–consumer rivalry, or consumer–producer rivalry? Explain. (LO1, LO7)

2. What is the maximum amount you would pay for an asset that generates an income of $250,000 at the end of each of five years if the opportunity cost of using funds is 8 per- cent? (LO5, LO7)

3. Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations: B(Q) = 100 + 36Q − 4Q2 and C(Q) = 80 + 12Q. [Note: MB(Q) = 36 − 8Q and MC(Q) = 12.] (LO1, LO6, LO7) a. Write out the equation for the net benefits. b. What are the net benefits when Q = 1? Q = 5? c. Write out the equation for the marginal net benefits. d. What are the marginal net benefits when Q = 1? Q = 5? e. What level of Q maximizes net benefits? f. At the value of Q that maximizes net benefits, what is the value of marginal net

benefits? 4. A firm’s current profits are $400,000. These profits are expected to grow indefinitely

at a constant annual rate of 4 percent. If the firm’s opportunity cost of funds is 6 percent, determine the value of the firm: (LO5, LO7) a. The instant before it pays out current profits as dividends. b. The instant after it pays out current profits as dividends.

5. What is the value of a preferred stock that pays a perpetual dividend of $125 at the end of each year when the interest rate is 5 percent? (LO5, LO7)

6. Complete the accompanying table and answer the accompanying questions. (LO1, LO6, LO7) a. At what level of the control variable are net benefits maximized? b. What is the relation between marginal benefit and marginal cost at this level of

the variable?

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24

Control Variable

Q

Total Benefits

B(Q)

Total Cost C(Q)

Net Benefits

N(Q)

Marginal Benefit MB(Q)

Marginal Cost

MC(Q)

Marginal Net

Benefits MNB(Q)

100 1200 950 210   60

101 1400   70

102 1590   80

103 1770   90

104 1940 100

105 2100 110

106 2250 120

107 2390 130

108 2520 140

109 2640 150

110 2750 160

7. It is estimated that over 100,000 students will apply to the top 30 MBA programs in the United States this year. (LO1, LO3, LO5, LO7) a. Using the concept of net present value and opportunity cost, explain when it is ratio-

nal for an individual to pursue an MBA degree. b. What would you expect to happen to the number of applicants if the starting salaries

of managers with MBA degrees remained constant but salaries of managers without such degrees decreased by 20 percent? Why?

8. Jaynet spends $30,000 per year on painting supplies and storage space. She recently received two job offers from a famous marketing firm—one offer was for $110,000 per year and the other was for $80,000. However, she turned both jobs down to continue a painting career. If Jaynet sells 25 paintings per year at a price of $8,000 each, (LO1, LO2, LO3, LO7) a. What are her accounting profits? b. What are her economic profits?

9. Suppose the total benefit derived from a continuous decision, Q, is B(Q) = 20Q − 2Q2 and the corresponding total cost is C(Q) = 4 + 2Q2, so that MB(Q) = 20 − 4Q and MC(Q)= 4Q. (LO1, LO6, LO7) a. What is total benefit when Q = 2? Q = 10? b. What is marginal benefit when Q = 2? Q = 10? c. What level of Q maximizes total benefit? d. What is total cost when Q = 2? Q = 10? e. What is marginal cost when Q = 2? Q = 10? f. What level of Q minimizes total cost? g. What level of Q maximizes net benefits?

10. An owner can lease her building for $120,000 per year for three years. The explicit cost of maintaining the building is $40,000, and the implicit cost is $55,000. All revenues are received, and costs borne, at the end of each year. If the interest rate is 5 percent, deter- mine the present value of the stream of: (LO2, LO5, LO7) a. Accounting profits. b. Economic profits.

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PROBLEMS AND APPLICATIONS

11. You have recently learned that the company where you work is being sold for $300,000. The company’s income statement indicates current profits of $11,000, which have yet to be paid out as dividends. Assuming the company will remain a “going concern” indef- initely and the interest rate will remain constant at 9 percent, at what constant rate does the owner believe that profits will grow? Does this seem reasonable? (LO5, LO7)

12. You are in the market for a new refrigerator for your company’s lounge, and you have narrowed the search down to two models. The energy-efficient model sells for $1,700 and will save you $45 in electricity costs at the end of each of the next five years. The standard model has features similar to the energy-efficient model but provides no future saving in electricity costs. It is priced at only $1,500. Assuming your opportunity cost of funds is 6 percent, which refrigerator should you purchase? (LO1, LO5, LO7)

13. You are the human resources manager for a famous retailer and are trying to convince the president of the company to change the structure of employee compensation. Currently, the company’s retail sales staff is paid a flat hourly wage of $20 per hour for each eight-hour shift worked. You propose a new pay structure whereby each sales- person in a store would be compensated $10 per hour, plus 1 percent of that store’s daily profits. Assume that, when run efficiently, each store’s maximum daily profits are $25,000. Outline the arguments that support your proposed plan. (LO1, LO7)

14. Jamie is considering leaving her current job, which pays $75,000 per year, to start a new company that develops applications for smartphones. Based on market research, she can sell about 50,000 units during the first year at a price of $4 per unit. With annual overhead costs and operating expenses amounting to $145,000, Jamie expects a profit margin of 20 percent. This margin is 5 percent larger than that of her largest competitor, Apps, Inc. (LO2, LO3, LO7) a. If Jamie decides to embark on her new venture, what will her accounting costs be

during the first year of operation? Her implicit costs? Her opportunity costs? b. Suppose that Jamie’s estimated selling price is lower than originally projected during

the first year. How much revenue would she need in order to earn positive account- ing profits? Positive economic profits?

15. Approximately 14 million Americans are addicted to drugs and alcohol. The federal government estimates that these addicts cost the U.S. economy $300 billion in medical expenses and lost productivity. Despite the enormous potential market, many biotech companies have shied away from funding research and development (R&D) initiatives to find a cure for drug and alcohol addiction. Your firm—Drug Abuse Sciences (DAS)— is a notable exception. It has spent $200 million to date working on a cure, but is now at a crossroads. It can either abandon its program or invest another $60 million today. Unfortunately, the firm’s opportunity cost of funds is 5 percent, and it will take another five years before final approval from the Food and Drug Administration is achieved and the product is actually sold. Expected (year-end) profits from selling the drug are pre- sented in the accompanying table. Should DAS continue with its plan to bring the drug to market, or should it abandon the project? Explain. (LO1, LO5, LO6, LO7)

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9

$0 $0 $0 $0 $12,000,000 $13,400,000 $17,200,000 $20,700,000 $22,450,000

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26

16. As a marketing manager for one of the world’s largest automakers, you are responsible for the advertising campaign for a new energy-efficient sports utility vehicle. Your support team has prepared the accompanying table, which summarizes the (year-end) profitabil- ity, estimated number of vehicles sold, and average estimated selling price for alternative levels of advertising. The accounting department projects that the best alternative use for the funds used in the advertising campaign is an investment returning 9 percent. In light of the staggering cost of advertising (which accounts for the lower projected profits in years 1 and 2 for the high and moderate advertising intensities), the team leader rec- ommends a low advertising intensity in order to maximize the value of the firm. Do you agree? Explain. (LO1, LO5, LO6, LO7)

Profitability by Advertising Intensity

  Profits (in millions) Units Sold (in thousands) Average Selling Price

  Year 1 Year 2 Year 3 Year 1 Year 2 Year 3 Year 1 Year 2 Year 3

Advertising Intensity                  

High $20 $    80 $300 10 60 120 $35,000 $36,500 $38,000

Moderate 40 80 135 5 12.5 25 35,800 36,100 36,300

Low 75 110 118 4 6 7.2 35,900 36,250 36,000

17. The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company’s value under several possible growth scenarios and the assumption that the company’s many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm’s competitors are comparatively small, collectively their annual revenue growth has exceeded 50 per- cent over each of the last five years. She has requested that the value projections be based on the firm’s current profits of $3.2 billion (which have yet to be paid out to stockholders) and the average interest rate over the past 20 years (6 percent) in each of the following profit growth scenarios: (LO5, LO7) a. Profits grow at an annual rate of 9 percent. (This one is tricky.) b. Profits grow at an annual rate of 2 percent. c. Profits grow at an annual rate of 0 percent. d. Profits decline at an annual rate of 4 percent.

18. Suppose one of your clients is four years away from retirement and has only $2,500 in pretax income to devote to either a Roth or traditional IRA. The traditional IRA permits investors to contribute the full $2,500 since contributions to these accounts are tax- deductible, but they must pay taxes on all future distributions. In contrast, contributions to a Roth IRA are not tax-deductible. For example, if a person’s tax rate is 25 percent, an investor is able to contribute only $1,875 after taxes; however, the earnings of a Roth IRA grow tax-free. Your company has decided to waive the one-time set-up fee of $50 to open a Roth IRA; however, investors opening a traditional IRA must pay the $50 setup fee. Assuming that your client anticipates that her tax rate will remain at 19 per- cent in retirement and she will earn a stable 7 percent return on her investments, will she prefer a traditional or Roth IRA? (LO1, LO5, LO7)

19. You are the manager in charge of global operations at BankGlobal—a large com- mercial bank that operates in a number of countries around the world. You must decide whether or not to launch a new advertising campaign in the U.S. market. Your accounting department has provided the accompanying statement, which summarizes the financial impact of the advertising campaign on U.S. operations. In addition, you recently received a call from a colleague in charge of foreign operations, and she

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Financial Impact on U.S. Operations

  Pre–Advertising Campaign Post–Advertising Campaign

Total Revenues $18,610,900 $31,980,200

Variable Cost    

TV Airtime     5,750,350     8,610,400

Ad development labor       1,960,580      3,102,450

Total variable costs    7,710,930  11,712,850

Direct Fixed Cost

Depreciation—computer equipment       1,500,000       1,500,000

Total direct fixed cost    1,500,000    1,500,000

Indirect Fixed Cost

Managerial salaries    8,458,100    8,458,100

Office supplies       2,003,500       2,003,500

Total indirect fixed cost $10,461,600 $10,461,600

indicated that her unit would lose $8 million if the U.S. advertising campaign were launched. Your goal is to maximize BankGlobal’s value. Should you launch the new campaign? Explain. (LO1, LO6, LO7)

20. According to The Wall Street Journal, merger and acquisition activity in the first quarter rose to $5.3 billion. Approximately three-fourths of the 78 first-quarter deals occurred between information technology (IT) companies. The largest IT transaction of the quarter was EMC’s $625 million acquisition of VMWare. The VMWare acquisition broadened EMC’s core data storage device business to include software technology enabling multiple operating systems—such as Microsoft’s Windows, Linux, and OS X—to simultaneously and independently run on the same Intel-based server or workstation. Suppose that at the time of the acquisition a weak economy led many analysts to project that VMWare’s profits would grow at a constant rate of 2 percent for the foreseeable future, and that the company’s annual net income was $39.60 million. If EMC’s estimated opportunity cost of funds is 9 percent, as an analyst, how would you view the acquisition? Would your conclusion change if you knew that EMC had credible information that the economy was on the verge of an expansion period that would boost VMWare’s projected annual growth rate to 4 percent for the foreseeable future? Explain. (LO1, LO5, LO6, LO7)

21. Recently, European Union (EU) governments approved a five-year EU trade protec- tion against grain-oriented electrical steel (GOES) from Russia, Japan, China, South Korea, and the United States. The protection would consist of minimum import prices on shipments of GOES from any of the five listed countries. This measure was enacted as a punishment for exporters in these countries for allegedly dumping their product (i.e., selling below cost) on the European market. The European Steel Association lauded the plan, noting it would help protect an important subdivision of the steel industry. However, transformer manufacturers, who use GOES as an input to their pro- duction, have protested the minimum prices. They argue minimum prices will result in prices for GOES that are too high and lead some of these manufacturers to downsize or move production facilities outside the EU. Describe the various rivalries depicted in this scenario, and then use the five forces framework to analyze the industry. (LO1, LO3, LO4, LO7)

22. You are the manager of Local Electronics Shop (LES), a small brick-and-mortar retail camera and electronics store. One of your employees proposed a new online strategy

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A

Price ($)

Number of salespeople

Total sales revenue

Total sales force salaries

SELECTED READINGS

Anders, Gary C.; Ohta, Hiroshi; and Sailors, Joel, “A Note on the Marginal Efficiency of Investment and Related Concepts.” Journal of Economic Studies 17(2), 1990, pp. 50–57.

Clark, Gregory, “Factory Discipline.” Journal of Economic History 54(1), March 1994, pp. 128–63.

Fizel, John L., and Nunnikhoven, Thomas S., “Technical Efficiency of For-Profit and Nonprofit Nursing Homes.” Managerial and Decision Economics 13(5), September– October 1992, pp. 429–39.

Gifford, Sharon, “Allocation of Entrepreneurial Attention.” Journal of Economic Behavior and Organization 19(3), December 1992, pp. 265–84.

McNamara, John R., “The Economics of Decision Making in the New Manufacturing Firm.” Managerial and Decision Economics 13(4), July–August 1992, pp. 287–93.

Mercuro, Nicholas; Sourbis, Haralambos; and Whitney, Gerald, “Ownership Structure, Value of the Firm and the Bargaining Power of the Manager.” Southern Economic Journal 59(2), October 1992, pp. 273–83.

Parsons, George R., and Wu, Yangru, “The Opportunity Cost of Coastal Land-Use Controls: An Empirical Analysis.” Land Economics 67, August 1991, pp. 308–16.

Phillips, Owen R.; Battalio, Raymond C.; and Kogut, Carl A., “Sunk Costs and Opportunity Costs in Valuation and Bidding.” Southern Economic Journal 58, July 1991, pp. 112–28.

Pindyck, Robert S., “Irreversibility, Uncertainty, and Investment.” Journal of Economic Literature 29, September 1991, pp. 1110–48.

whereby LES lists its products at Pricesearch.com—a price comparison Web site that allows consumers to view the prices of dozens of retailers selling the same items. Would you expect this strategy to enable LES to achieve sustainable economic profits? Explain. (LO1, LO4, LO7)

23. Two months ago, the owner of a car dealership (and a current football star) signifi- cantly changed his sales manager’s compensation plan. Under the old plan, the manager was paid a salary of $6,000 per month; under the new plan, she receives 2 percent of the sales price of each car sold. During the past two months, the number of cars sold increased by 40 percent, but the dealership’s margins (and profits) significantly declined. According to the sales manager, “Consumers are driving harder bargains and I have had to authorize significantly lower prices to remain competitive.” What advice would you give the owner of the dealership? (LO1, LO7)

24. Last year, MedSupplies—a national supplier of medical devices—posted its first loss in six years. The loss was a surprise to investors since the industry as a whole has been growing. Analysts have reached a consensus that at least part of the blame for the loss falls on Heidi Stevens, the national sales manager for MedSupplies. Ms. Stevens is responsible for determining the size of the firm’s sales force, and over the past year, she engaged in a significant expansion. In this industry, it is well understood that rev- enues generally increase as the sales force grows. However, each new hire generally adds less new revenue than the last, as the best sales opportunities already have been

exhausted. At the same time, the salaries for medical device salespeople essentially have been constant. Analysts sum- marize the problem in the accompanying figure. They note that Ms. Stevens appears to have expanded her sales force to point A and argue that her sales force is too big. When approached for comment, Ms. Stevens replied, “Of course I would choose point A in that graph! Anything less means the company underperforms.” Both the analysts and Ms. Stevens agree that she has chosen point A in the graph as the size of her sales force but disagree on the wisdom of this decision. Who is right? (LO6, LO7)

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29

APPENDIX

THE CALCULUS OF MAXIMIZING NET BENEFITS

This appendix provides a calculus-based derivation of the important rule that to maximize net benefits, a manager must equate marginal benefits and marginal costs.

Let B(Q) denote the benefits of using Q units of the managerial control variable, and let C(Q) denote the cor- responding costs. The net benefits are N(Q) = B(Q) − C(Q). The objective is to choose Q so as to maximize

N ( Q ) = B ( Q ) − C ( Q )

The first-order condition for a maximum is

dN

___ dQ

= dB

___ dQ

− dC

___ dQ

= 0

But

dB

___ dQ

= MB

is nothing more than marginal benefits, while

dC

___ dQ

= MC

is simply marginal costs. Thus, the first-order condition for a maximum implies that

dB

___ dQ

= dC

___ dQ

or MB = MC. The second-order condition requires that the func-

tion N(Q) be concave in Q or, in mathematical terms, that the second derivative of the net benefit function be negative:

d 2 N

___ d Q 2

= d 2 B

___ d Q 2

− d 2 C

___ d Q 2

< 0

Notice that d2B/dQ2 = d(MB)/dQ, while d2C/dQ2 = d(MC)/dQ. Thus, the second-order condition may be rewritten as

d 2 N

___ d Q 2

= d ( MB )

_____ dQ

− d ( MC )

_____ dQ

< 0

In other words, the slope of the marginal benefit curve must be less than the slope of the marginal cost curve.

DEMONSTRATION PROBLEM 1–4

Suppose B(Q) = 10Q − 2Q2 and C(Q) = 2 + Q2. What value of the managerial control variable, Q, maximizes net benefits?

ANSWER: Net benefits are

N (Q) = B (Q) − C (Q) = 10Q − 2 Q 2 − 2 − Q 2

Taking the derivative of N(Q) and setting it equal to zero gives

dN

___ dQ

= 10 − 4Q − 2Q = 0

Solving for Q gives Q = 10/6. To verify that this is indeed a maximum, we must check that the sec- ond derivative of N(Q) is negative:

d 2 N

___ d Q 2

= −4 − 2 = −6 < 0

Therefore, Q = 10/6 indeed maximizes net benefits.

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30

Market Forces: Demand and Supply

2

headLINE Samsung and Hynix Semiconductor to Cut Chip Production Sam Robbins, owner and CEO of PC Solutions, arrived at the office and glanced at the front page of The Wall Street Journal waiting on his desk. One of the articles contained statements from executives of two of South Korea’s largest semiconductor manufacturers— Samsung Electronic Company and Hynix Semiconductor—indicating that they would sus- pend all their memory chip production for one week. The article went on to say that another large semiconductor manufacturer was likely to follow suit. Collectively, these three chip manufacturers produce about 30 percent of the world’s basic semiconductor chips.

PC Solutions is a small but growing company that assembles PCs and sells them in the highly competitive market for “clones.” PC Solutions experienced 100 percent growth last year and is in the process of interviewing recent graduates in an attempt to double its workforce.

After reading the article, Sam picked up the phone and called a few of his business contacts to verify for himself the information contained in the Journal. Satisfied that the information was correct, he called the director of personnel, Jane Remak.

What do you think Sam and Jane discussed?

LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Explain the laws of demand and supply, and identify factors that cause demand and supply to shift.

LO2 Calculate consumer surplus and producer surplus, and describe what they mean.

LO3 Explain price determination in a competitive market, and show how equilib- rium changes in response to changes in determinants of demand and supply.

LO4 Explain and illustrate how excise taxes, ad valorem taxes, price floors, and price ceilings impact the functioning of a market.

LO5 Apply supply and demand analysis as a qualitative forecasting tool to see the “big picture” in competitive markets.

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INTRODUCTION

This chapter describes supply and demand, which are the driving forces behind the market economies that exist in the United States and around the globe. As suggested in this chapter’s opening headline, supply and demand analysis is a tool that managers can use to visualize the “big picture.” Many companies fail because their managers get bogged down in the day-to- day decisions of the business without having a clear picture of market trends and changes that are on the horizon.

To illustrate, imagine that you manage a small retail outlet that sells PCs. A magic genie appears and says, “Over the next month, the market price of PCs will decline and consumers will purchase fewer PCs.” The genie revealed the big picture: PC prices and sales will decline. If you worry about the details of your business without knowledge of these future trends in prices and sales, you will be at a significant competitive disadvantage. Absent a view of the big picture, you are likely to negotiate the wrong prices with suppliers and customers, carry too much inventory, hire too many employees, and—if your business spends money on infor- mative advertising—purchase ads in which your prices are no longer competitive by the time they reach print.

Supply and demand analysis is a qualitative tool that, like the genie, empowers managers by enabling them to see the “big picture.” It is a qualitative forecasting tool you can use to predict trends in competitive markets, including changes in the prices of your firm’s products, related products (both substitutes and complements), and the prices of inputs (such as labor services) that are necessary for your operations. As we will see in subsequent chapters, after you use supply and demand analysis to see the big picture, additional tools are available to assist with details—determining how much the price will change, how much sales and reve- nues will change, and so on.

For those of you who have taken a principles-level course in economics, some parts of this chapter will be a review. However, make sure you have complete mastery of the tools of supply and demand. The rest of this book will assume you have a thorough working knowl- edge of the material in this chapter.

DEMAND

Suppose a clothing manufacturer desires information about the impact of its pricing decisions on the demand for its jeans in a small foreign market. To obtain this information, it might engage in market research to determine how many pairs of jeans consumers would purchase each year at alternative prices per unit. The numbers from such a market survey would look something like those in Table 2–1. The market research reveals that if jeans were priced at $10 per pair, 60,000 pairs of jeans would be sold per year; at $30 per pair, 20,000 pairs of jeans would be sold annually.

When there is no ambiguity, it is sometimes convenient to say simply “price” rather than “price per pair” or “price per unit.” For instance, if one of your classmates says gas- oline is priced at $3.99 in Indianapolis, you understand that she means $3.99 per gallon. Looking at the rows in Table 2–1, notice that the only difference in the entries is the price of jeans and the quantity of jeans sold. Everything else that might influence buyer deci- sions, such as consumer income, advertising, and the prices of other goods such as shirts, is held constant. In effect, the market survey does not ask consumers how much they would buy at alternative levels of income or advertising; it simply seeks to determine how much

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would be purchased at alternative prices. The market research reveals that, holding all other things constant, the quantity of jeans consumers are willing and able to purchase goes down as the price rises. This fundamental economic principle is known as the law of demand: Price and quantity demanded are inversely related. That is, as the price of a good rises (falls) and all other things remain constant, the quantity demanded of the good falls (rises).

Figure 2–1 plots the data in Table 2–1. The straight line connecting those points, called the market demand curve, interpolates the quantities consumers would be willing and able to purchase at prices not explicitly dealt with in the market research. For example, using this market demand curve, we conclude that consumers would be willing and able to purchase 35,000 pairs of jeans when the price is $22.50 (and all other variables stay the same). Notice that the line is downward sloping, which reflects the law of demand, and that all other factors that influence demand are held constant at each point on the line.

law of demand As the price of a good rises (falls) and all other things remain constant, the quantity demanded of the good falls (rises).  

market demand curve A curve indicating the total quantity of a good all consumers are willing and able to purchase at each possible price, holding the prices of related goods, income, advertising, and other variables constant.

Table 2–1 The Demand Schedule for Jeans in a Small Foreign Market

Price of Jeans

Quantity of Jeans Sold

Average Consumer Income

Advertising Expenditure

Average Price of Shirts

$0 80,000 $25,000 $50,000 $20

5 70,000 25,000 50,000 20

10 60,000 25,000 50,000 20

15 50,000 25,000 50,000 20

20 40,000 25,000 50,000 20

25 30,000 25,000 50,000 20

30 20,000 25,000 50,000 20

35 10,000 25,000 50,000 20

40 0 25,000 50,000 20

Figure 2–1 The Demand Curve

0

Price ($)

Quantity (thousands per year)10 20 30 40 50 60 70 80

5

10

15

20

25

30

35

40

D

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Demand Shifters Economists recognize that variables other than the price of a good influence demand. For example, the number of pairs of jeans individuals are willing and financially able to buy also depends on the price of shirts, consumer income, advertising expenditures, and so on. Variables other than the price of a good that influence demand are known as demand shifters.

When we graph the demand curve for good X, we hold everything but the price of X constant. A representative demand curve is given by D0 in Figure 2–2. The movement along a demand curve, such as the movement from A to B, is called a change in quantity demanded. Whenever advertising, income, or the price of related goods changes, it leads to a change in demand; the position of the entire demand curve shifts. A rightward shift in the demand curve is called an increase in demand, since more of the good is demanded at each price. A leftward shift in the demand curve is called a decrease in demand.

Now that we understand the general distinction between a shift in a demand curve and a movement along a demand curve, it is useful to explain how five demand shifters—consumer income, prices of related goods, advertising and consumer tastes, population, and consumer expectations—affect demand.

Income Because income affects the ability of consumers to purchase a good, changes in income affect how much consumers will buy at any price. In graphical terms, a change in income shifts the entire demand curve. Whether an increase in income shifts the demand curve to the right or to the left depends on the nature of consumer consumption patterns. Accordingly, economists distinguish between two types of goods: normal and inferior goods.

A good whose demand increases (shifts to the right) when consumer incomes rise is called a normal good. Normal goods may include goods such as steak, airline travel, and designer jeans: As income goes up, consumers typically buy more of these goods at any given price. Conversely, when consumers suffer a decline in income, the demand for a normal good will decrease (shift to the left).

change in quantity demanded Changes in the price of a good lead to a change in the quantity demanded of that good. This corresponds to a movement along a given demand curve.

change in demand Changes in variables other than the price of a good, such as income or the price of another good, lead to a change in demand. This corresponds to a shift of the entire demand curve.

normal good A good for which an increase (decrease) in income leads to an increase (decrease) in the demand for that good.

Figure 2–2 Changes in Demand

0

Price

Quantity

D1

A

B

D0

D2

Decrease in

demand

Increase in

demand

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During a recent recession, Japan saw many business fail- ures. Even businesses that traditionally do well during eco- nomic downturns, such as the beer brewing industry, were hit hard. Analysts blame the downturn in the beer market on two factors: (1) Japanese incomes (GDP) declined signifi- cantly as a result of the recession and (2) Japan’s govern- ment imposed a beer tax in an effort to raise revenue.

As a result of these events, top Japanese breweries such as Kirin Brewery Company, Ltd., and Sapporo Breweries Ltd. expe- rienced a sharp decline in domestic beer sales. Meanwhile, their competitor—Asahi Breweries—touted double-digit growth and increased its market share. Asahi attributes its growth in sales to its superior sales network and strong mar- keting campaign for its best-selling beer, Asahi Super Dry.

While part of Asahi’s growth and success is attributable to the company’s sales force and marketing activities— both create greater consumer awareness—this does not fully explain why Asahi has done especially well during the recent Asian recession. One possibility is that Asahi beer is an inferior good. This does not mean that Asahi beer is “skunky” or of low quality; indeed, its Super Dry is the beer of choice for many Japanese beer drinkers. The term inferior good simply means that when Japanese incomes decline due to a recession, the demand for Asahi beer increases.

Sources: Annual Reports for Asahi Breweries Ltd., Sapporo Breweries Ltd., and Kirin Brewery Company, Ltd.

INSIDE BUSINESS 2–1

Asahi Breweries Ltd. and the Asian Recession

Changes in income tend to have profound effects on the demand for durable goods, and these effects are typically amplified in developing countries and rural areas. In 2004, for instance, farmers in India enjoyed higher incomes thanks to the impact on crops of bene- ficial monsoons. As a result, the demand in rural areas of India for tractors and motorcy- cles surged, almost tripling the level of demand in the previous year. By 2009, this surge in demand reversed due to significant reductions in consumer incomes stemming from a global economic recession. The demand for durables in developed countries also declined dramati- cally, and automakers were especially hard hit.

In some instances, an increase in income reduces the demand for a good. Economists refer to such a good as an inferior good. Bologna, bus travel, and “generic” jeans are possible examples of inferior goods. As income goes up, consumers typically consume less of these goods at each price. It is important to point out that by calling such goods inferior, we do not imply that they are of poor quality; we use this term simply to define products that consumers purchase less of when their incomes rise and purchase more of when their incomes fall.

Prices of Related Goods Changes in the prices of related goods generally shift the demand curve for a good. For exam- ple, if the price of a Coke increases, most consumers will begin to substitute Pepsi because the relative price of Coke is higher than before. As more and more consumers substitute Pepsi for Coke, the quantity of Pepsi demanded at each price will tend to increase. In effect, an increase in the price of Coke increases the demand for Pepsi. This is illustrated by a shift in the demand for Pepsi to the right. Goods that interact in this way are known as substitutes.

Many pairs of goods readily come to mind when we think of substitutes: chicken and beef, cars and trucks, raincoats and umbrellas. Such pairs of goods are substitutes for most consumers. However, substitutes need not serve the same function. For example, televisions and patio furniture could be substitutes; as the price of televisions increases, you may choose to purchase additional patio furniture rather than an additional television. Goods are substi- tutes when an increase in the price of one good increases the demand for the other good.

inferior good A good for which an increase (decrease) in income leads to a decrease (increase) in the demand for that good.

substitutes Goods for which an increase (decrease) in the price of one good leads to an increase (decrease) in the demand for the other good.

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Not all goods are substitutes; in fact, an increase in the price of a good such as com- puter software may lead consumers to purchase fewer computers at each price. Goods that interact in this manner are called complements. Beer and pretzels are another example of complementary goods. If the price of beer increased, most beer drinkers would decrease their consumption of pretzels. Notice that when good X is a complement to good Y, a reduction in the price of Y actually increases (shifts to the right) the demand for good X. More of good X is purchased at each price due to the reduction in the price of the complement, good Y.

Advertising and Consumer Tastes Another variable that is held constant when drawing a given demand curve is the level of advertising. An increase in advertising shifts the demand curve to the right, from D1 to D2, as in Figure 2–3. Notice that the impact of advertising on demand can be interpreted in two ways. Under the initial demand curve, D1, consumers would buy 50,000 units of high-style clothing per month when the price is $40. After the advertising, the demand curve shifts to D2, and consumers will now buy 60,000 units of the good when the price is $40. Alternatively, when demand is D1, consumers will pay a price of $40 when 50,000 units are available. Advertising shifts the demand curve to D2, so consumers will pay a higher price—$50—for 50,000 units.

Why does advertising shift demand to the right? Advertising often provides consumers with information about the existence or quality of a product, which in turn induces more consumers to buy the product. These types of advertising messages are known as informative advertising.

Advertising can also influence demand by altering the underlying tastes of consumers. For example, advertising that promotes the latest fad in clothing may increase the demand for a specific fashion item by making consumers perceive it as “the” thing to buy. These types of advertising messages are known as persuasive advertising.

Population The demand for a product is also influenced by changes in the size and composition of the population. Generally, as the population rises, more and more individuals wish to buy a given

complements Goods for which an increase (decrease) in the price of one good leads to a decrease (increase) in the demand for the other good.

Figure 2–3 Advertising and the Demand for Clothing

0

Price of high-style clothing

Quantity of high-style clothing50,000 60,000

$40

D1 D2

$50

Due to an increase in advertising

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product, and this has the effect of shifting the demand curve to the right. Over the twentieth century, the demand curve for food products shifted to the right considerably with the increas- ing population.

It is important to note that changes in the composition of the population can also affect the demand for a product. To the extent that middle-aged consumers desire different types of products than retirees, an increase in the number of consumers in the 30- to 40-year-old age bracket will increase the demand for products like real estate. Similarly, as a greater propor- tion of the population ages, the demand for medical services will tend to increase.

Consumer Expectations Changes in consumer expectations also can change the position of the demand curve for a product. For example, if consumers suddenly expect the price of automobiles to be signifi- cantly higher next year, the demand for automobiles today will increase. In effect, buying a car today is a substitute for buying a car next year. If consumers expect future prices to be higher, they will substitute current purchases for future purchases. This type of consumer behavior often is referred to as stockpiling and generally occurs when products are durable in nature. We often see this behavior for less expensive durables, too; consumers may stockpile laundry detergent in response to temporary sales at grocery stores. The current demand for a perishable product such as bananas generally is not affected by expectations of higher future prices.

Other Factors In concluding our list of demand shifters, we simply note that any variable that affects the will- ingness or ability of consumers to purchase a particular good is a potential demand shifter. Health scares affect the demand for cigarettes. The birth of a baby affects the demand for diapers.

The Demand Function By now you should understand the factors that affect demand and how to use graphs to illus- trate those influences. The final step in our analysis of the demand side of the market is to show that all the factors that influence demand may be summarized in what economists refer to as a demand function.

The demand function for good X describes how much X will be purchased at alternative prices of X and related goods, alternative levels of income, and alternative values of other variables that affect demand. Formally, let Q x

d represent the quantity demanded of good X, Px the price of good X, Py the price of a related good, M income, and H the value of any other variable that affects demand, such as the level of advertising, the size of the population, or consumer expectations. Then the demand function for good X may be written as

Q x d = f ( P x , P y , M, H)

Thus, the demand function explicitly recognizes that the quantity of a good consumed depends on its price and on demand shifters. Different products will have demand functions of different forms. One very simple but useful form is the linear representation of the demand function: Demand is linear if Q x

d is a linear function of prices, income, and other variables that influence demand. The following equation is an example of a linear demand function:

Q x d = α 0 + α x P x + α y P y + α M M + α H H

The αis are fixed numbers that the firm’s research department or an economic consultant typ- ically provides to the manager. (Chapter 3 provides an overview of the statistical techniques used to obtain these numbers.)

demand function A function that describes how much of a good will be purchased at alternative prices of that good and related goods, alternative income levels, and alternative values of other variables affecting demand.

linear demand function A representation of the demand function in which the demand for a given good is a linear function of prices, income levels, and other variables influencing demand.

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By the law of demand, an increase in Px leads to a decrease in the quantity demanded of good X. This means that αx < 0. The sign of αy will be positive or negative depending on whether goods X and Y are substitutes or complements. If αy is a positive number, an increase in the price of good Y will lead to an increase in the consumption of good X; therefore, good X is a substitute for good Y. If αy is a negative number, an increase in the price of good Y will lead to a decrease in the consumption of good X; hence, good X is a complement to good Y. The sign of αM also can be positive or negative depending on whether X is a normal or an inferior good. If αM is a positive number, an increase in income (M) will lead to an increase in the consumption of good X, and good X is a normal good. If αM is a negative number, an increase in income will lead to a decrease in the consumption of good X, and good X is an inferior good.

DEMONSTRATION PROBLEM 2–1

An economic consultant for X Corp. recently provided the firm’s marketing manager with this esti- mate of the demand function for the firm’s product:

Q x d = 12,000 − 3 P x + 4 P y − 1M + 2 A x

where Q x d represents the amount consumed of good X, Px is the price of good X, Py is the price of

good Y, M is income, and Ax represents the amount of advertising spent on good X. Suppose good X sells for $200 per unit, good Y sells for $15 per unit, the company utilizes 2,000 units of advertising, and consumer income is $10,000. How much of good X do consumers purchase? Are goods X and Y substitutes or complements? Is good X a normal or an inferior good?

ANSWER: To find out how much of good X consumers will purchase, we substitute the given values of prices, income, and advertising into the linear demand equation to get

Q x d = 12,000 − 3 (200) + 4 (15) − 1 (10,000) + 2 (2,000)

Adding up the numbers, we find that the total consumption of X is 5,460 units. Since the coeffi- cient of Py in the demand equation is 4 > 0, we know that a $1 increase in the price of good Y will increase the consumption of good X by 4 units. Thus, goods X and Y are substitutes. Since the coeffi- cient of M in the demand equation is −1 < 0, we know that a $1 increase in income will decrease the consumption of good X by 1 unit. Thus, good X is an inferior good.

The information summarized in a demand function can be used to graph a demand curve. Since a demand curve is the relation between price and quantity, a representative demand curve holds everything but price constant. This means one may obtain the formula for a demand curve by inserting given values of the demand shifters into the demand function, but leaving Px in the equation to allow for various values. If we do this for the demand function in Demonstration Problem 2–1 (where Py = $15, M = $10,000, and Ax = 2,000), we get

Q x d = 12,000 − 3 P x + 4 (15) − 1 (10,000) + 2 (2,000)

which simplifies to

Q x d = 6,060 − 3 P x (2−1)

Because we usually graph this relation with the price of the good on the vertical axis, it is useful to represent Equation 2–1 with price on the left-hand side and everything else on the

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right-hand side. This relation is called an inverse demand function. For this example, the inverse demand function is P x = 2,020 −

1 __

3 Q x

d

It reveals how much consumers are willing and able to pay for each additional unit of good X. This demand curve is graphed in Figure 2–4.

Consumer Surplus We now show how a manager can use the demand curve to ascertain the value a consumer or group of consumers receives from a product. The concepts developed in this section are particularly useful in marketing and other disciplines that emphasize strategies such as value pricing and price discrimination.

By the law of demand, the amount a consumer is willing to pay for an additional unit of a good falls as more of the good is consumed. For instance, imagine that the demand curve in Figure 2–5(a) represents your demand for water immediately after participating in a 10K run. Initially, you are willing to pay a very high price—in this case, $5 per liter—for the first drop of water. As you consume more water, the amount you are willing to pay for an additional drop declines from $5.00 to $4.99 and so on as you move down the demand curve. Notice that after you have consumed an entire liter of water, you are willing to pay only $4 per liter for another drop. Once you have enjoyed 2 liters of water, you are willing to pay only $3 per liter for another drop.

Figure 2–4 Graphing the Inverse Demand Function

0

Price

Quantity

P x = 2,020 – Q

x d

6,060

$2,020

1 3

Figure 2–5 Consumer Surplus

Price per liter

Quantity (liters)

Quantity D

1 2 3 4 5

1

0

2

3

4

5

0

Price

D

(a) (b)

Px 0

Consumer surplus

Q 0x

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To find your total value (or benefit) of 2 liters of water, we simply add up the maximum amount you were willing to pay for each of these drops of water between 0 and 2 liters. This amount corresponds to the area underneath the demand curve in Figure 2–5(a) up to the quantity of 2 liters. Since the area of this region is $8, the total value you receive from 2 liters of water is $8.

Fortunately, you don’t have to pay different prices for the different drops of water you consume. Instead, you face a per-unit price of, say, $3 per liter and get to buy as many drops (or even liters) as you want at that price. Given the demand curve in Figure 2–5(a), when the price is $3 you will choose to purchase 2 liters of water. In this case, your total out-of-pocket expense for the 2 liters of water is $6. Since you value 2 liters of water at $8 and only have to pay $6 for it, you are getting $2 in value over and above the amount you have to pay for water. This “extra” value is known as consumer surplus—the value consumers get from a good but do not have to pay for. This concept is important to managers because it tells how much extra money consumers would be willing to pay for a given amount of a purchased product.

More generally, consumer surplus is the area above the price paid for a good but below the demand curve. For instance, the shaded triangle in Figure 2–5(b) illustrates the consumer surplus of a consumer who buys Q x

0 units at a price of P x 0 . To see why, recall that each point

on the demand curve indicates the value to the consumer of another unit of the good. The dif- ference between each price on the demand curve and the price P x

0 paid represents surplus (the value the consumer receives but does not have to pay for). When we add up the “surpluses” received for each unit between 0 and Q x

0 (this sum equals the shaded region), we obtain the consumer surplus associated with purchasing Q x

0 units at a price of P x 0 each.

Managers can use the notion of consumer surplus to determine the total amount consumers would be willing to pay for multiunit packages. While this will be discussed in detail in Chapter 11 where we examine pricing strategies, we illustrate the basic idea in the following problem.

consumer surplus The value consumers get from a good but do not have to pay for.

DEMONSTRATION PROBLEM 2–2

A typical consumer’s demand for the Happy Beverage Company’s product looks like that in Figure 2–5(a). If the firm charges a price of $2 per liter, how much revenue will the firm earn and how much consumer surplus will the typical consumer enjoy? What is the most a consumer would be willing to pay for a bottle containing exactly 3 liters of the firm’s beverage?

ANSWER: At a price of $2 per liter, a typical consumer will purchase 3 liters of the beverage. Thus, the firm’s revenue is $6 and the consumer surplus is $4.50 [the area of the consumer surplus triangle is one-half the base times the height, or .5(3)($5 − $2) = $4.50]. The total value of 3 liters of the firm’s beverage to a typical consumer is thus $6 + $4.50, or $10.50. This is also the maximum amount a consumer would be willing to pay for a bottle containing exactly 3 liters of the firm’s beverage. Expressed differently, if the firm sold the product in 3-liter bottles rather than in smaller units, it could sell each bottle for $10.50 to earn higher revenues and extract all consumer surplus.

SUPPLY

In the previous section we focused on demand, which represents half of the forces that deter- mine the price in a market. The other determinant is market supply. In a competitive market there are many producers, each producing a similar product. The market supply curve sum- marizes the total quantity all producers are willing and able to produce at alternative prices, holding other factors that affect supply constant.

market supply curve A curve indicating the total quantity of a good that all producers in a competitive market would produce at each price, holding input prices, technology, and other variables affecting supply constant.

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While the market supply of a good generally depends on many things, when we graph a sup- ply curve, we hold everything but the price of the good constant. The movement along a supply curve, such as the one from A to B in Figure 2–6, is called a change in quantity supplied. The fact that the market supply curve slopes upward reflects the inverse law of supply: As the price of a good rises (falls) and other things remain constant, the quantity supplied of the good rises (falls). Producers are willing to produce more output when the price is high than when it is low.

Supply Shifters Variables that affect the position of the supply curve are called supply shifters, and they include the prices of inputs, the level of technology, the number of firms in the market, taxes, and producer expectations. Whenever one or more of these variables change, the position of the entire supply curve shifts. Such a shift is known as a change in supply. The shift from S0 to S2 in Figure 2–6 is called an increase in supply since producers sell more output at each given price. The shift from S0 to S1 in Figure 2–6 represents a decrease in supply since pro- ducers sell less of the product at each price.

Input Prices

The supply curve reveals how much producers are willing to produce at alternative prices. As production costs change, the willingness of producers to produce output at a given price changes. In particular, as the price of an input rises, producers are willing to produce less output at each given price. This decrease in supply is depicted as a leftward shift in the supply curve.

Technology or Government Regulations Technological changes and changes in government regulations also can affect the position of the supply curve. Changes that make it possible to produce a given output at a lower cost, such as the ones highlighted in Inside Business 2–2, have the effect of increasing supply. Conversely, natural disasters that destroy existing technology and government regulations, such as emis- sions standards that have an adverse effect on businesses, shift the supply curve to the left.

Number of Firms The number of firms in an industry affects the position of the supply curve. As additional firms enter an industry, more and more output are available at each given price. This is reflected by a rightward shift in the supply curve. Similarly, as firms leave an industry, fewer units are sold at each price, and the supply decreases (shifts to the left).

change in quantity supplied Changes in the price of a good lead to a change in the quantity supplied of that good. This corresponds to a movement along a given supply curve.

change in supply Changes in variables other than the price of a good, such as input prices or technological advances, lead to a change in supply. This corresponds to a shift of the entire supply curve.

Figure 2–6 Changes in Supply

0

A

B

Price

Quantity

S2

S0

S1

Increase in supply

Decrease in supply

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Substitutes in Production Many firms have technologies that are readily adaptable to several different products. For example, automakers can convert a truck assembly plant into a car assembly plant by altering its production facilities. When the price of cars rises, these firms can convert some of their truck assembly lines to car assembly lines to increase the quantity of cars supplied. This has the effect of shifting the truck supply curve to the left.

Taxes The position of the supply curve is also affected by taxes. An excise tax is a tax on each unit of output sold, where the tax revenue is collected from the supplier. For example, suppose the government levies a tax of $.20 per gallon on gasoline. Since each supplier must now pay the government $.20 per gallon for each gallon of gasoline sold, each must receive an additional $.20 per gallon to be willing to supply the same quantity of gasoline as before the tax. An excise tax shifts the supply curve up by the amount of the tax, as in Figure 2–7. Note that at any given price, producers are willing to sell less gasoline after the tax than before. Thus, an excise tax has the effect of decreasing the supply of a good.

Another form of tax often used by a government agency is an ad valorem tax. Ad valorem literally means “according to the value.” An ad valorem tax is a percentage tax; the sales tax is a well-known example. If the price of a good is $1 and a 10 percent ad valorem tax is attached to that good, the price after the tax is $1.10. Because an ad valorem tax is a percentage tax, it will be higher for high-priced items.

In Figure 2–8, S0 represents the supply curve for backpacks before the inception of a 20 percent ad valorem tax. Notice that 1,100 backpacks are offered for sale when the price of a backpack is $10 and 2,450 backpacks are offered when the price is $20.

Once the 20 percent tax is implemented, the price required to produce each unit goes up by 20 percent at any output level. Therefore, price will go up by $2 at a quantity of 1,100 and by $4 at a quantity of 2,450. An ad valorem tax will rotate the supply curve counterclockwise,

Figure 2–7 A Per Unit (Excise) Tax

0

Price of

gasoline

Quantity of

gasoline per week

S0 + t

t = per unit tax of 20

S0

t = 20

$1.00

$1.20 t

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Producer Expectations Producer expectations about future prices also affect the position of the supply curve. In effect, selling a unit of output today and selling a unit of output tomorrow are substitutes in production. If firms suddenly expect prices to be higher in the future and the product is not perishable, producers can hold back output today and sell it later at a higher price. This has the effect of shifting the current supply curve to the left.

Figure 2–8 An Ad Valorem Tax

0

Price of

backpacks

Quantity of

backpacks per week

S1 = 1.20 × S 0

S 0

$10

$20

$24

$12

1,100 2,450

Over the past two decades, presidents from both political par- ties have signed trade agreements and laws that include provi- sions designed to reduce the cost of producing goods at home and abroad. These cost reductions translate into increases in the supply of goods and services available to U.S. consumers.

The North American Free Trade Agreement (NAFTA) between the United States, Canada, and Mexico was signed into law by Bill Clinton and contained provisions to eliminate or phase out tariffs and other barriers in industrial products (such as textiles and apparel) and agricultural products. NAFTA also included provisions designed to reduce barriers to investment in Mexican petrochemicals and financial service sectors.

The Trade Act of 2002 was enacted under George W. Bush and gives the president the ability to negotiate

additional international agreements (subject to an up-or- down vote by Congress).

During his campaign and early in his presidency, Barack Obama pledged to renegotiate NAFTA. However, the deep recession during that time caused him to post- pone that effort. Only time will tell whether the current and future administrations will continue on the course set by Presidents Clinton and Bush.

Sources: “NAFTA Renegotiation Must Wait, Obama Says,” Washington Post, February 20, 2009; Economic Report of the President, Washington, D.C.: U.S. Government Printing Office, February 2007, p. 60; Economic Report of the President, Washington, D.C.: U.S. Government Printing Office, February 2006, p. 153; Economic Report of the President, Washington, D.C.: U.S. Government Printing Office, February 1995, pp. 220−21.

INSIDE BUSINESS 2–2

The Trade Act of 2002, NAFTA, and the Supply Curve

and the new curve will shift farther away from the original curve as the price increases. This explains why S1 is steeper than S0 in Figure 2–8.

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The Supply Function You should now understand the difference between supply and quantity supplied and recog- nize the factors that influence the position of the supply curve. The final step in our analysis of supply is to show that all the factors that influence the supply of a good can be summarized in a supply function.

The supply function of a good describes how much of the good will be produced at alter- native prices of the good, alternative prices of inputs, and alternative values of other variables that affect supply. Formally, let Q x

s represent the quantity supplied of a good, Px the price of the good, W the price of an input (such as the wage rate on labor), Pr the price of technolog- ically related goods, and H the value of some other variable that affects supply (such as the existing technology, the number of firms in the market, taxes, or producer expectations). Then the supply function for good X may be written as

Q x s = f ( P x , P r , W, H )

Thus, the supply function explicitly recognizes that the quantity produced in a market depends not only on the price of the good but also on all the factors that are potential supply shifters. While there are many different functional forms for different types of products, a particularly useful representation of a supply function is the linear relationship. Supply is linear if Q x

s is a linear function of the variables that influence supply. The following equation is representative of a linear supply function:

Q x s = β 0 + β x P x + β r P r + β w W + β H H

The coefficients (the βis) represent given numbers that have been estimated by the firm’s research department or an economic consultant.

supply function A function that describes how much of a good will be produced at alternative prices of that good, alternative input prices, and alternative values of other variables affecting supply.

linear supply function A representation of the supply function in which the supply of a given good is a linear function of prices and other variables affecting supply.

DEMONSTRATION PROBLEM 2–3

Your research department estimates that the supply function for high definition televisions (HDTVs) is given by

Q x s = 2,000 + 3 P x − 4 P t − P w

where Px is the price of HDTVs, Pt represents the price of a tablet, and Pw is the price of an input used to make HDTVs. Suppose HDTVs are sold for $400 per unit, tablets are sold for $250 per unit, and the price of an input is $1,400. How many HDTVs are produced?

ANSWER: To find out how many television sets are produced, we insert the given values of prices into the supply function to get

Q x s = 2,000 + 3 ( 400 ) − 4 ( 250 ) − 1 ( 1, 400 )

Adding up the numbers, we find that the total quantity of HDTVs produced is 800.

The information summarized in a supply function can be used to graph a supply curve. Since a supply curve is the relationship between price and quantity, a representative sup- ply curve holds everything but price constant. This means one may obtain the formula for a supply curve by inserting given values of the supply shifters into the supply function, but

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leaving Px in the equation to allow for various values. If we do this for the supply function in Demonstration Problem 2–3 (where Pt = $250 and Pw = 1,400), we get

Q x s = 2,000 + 3 P x − 4 ( 250 ) − 1 ( 1,400 )

which simplifies to Q x

s = 3 P x − 400 (2−2)

Since we usually graph this relation with the price of the good on the vertical axis, it is useful to represent Equation 2–2 with price on the left-hand side and everything else on the right-hand side. This is known as an inverse supply function. For this example, the inverse supply function is

P x = 400

____ 3 +

1 __

3 Q x

s

which is the equation for the supply curve graphed in Figure 2–9. This curve reveals how much producers must receive to be willing to produce each additional unit of good X.

Producer Surplus Just as consumers want price to be as low as possible, producers want price to be as high as possible. The supply curve reveals the amount producers will be willing to produce at a given price. Alternatively, it indicates the price firms would have to receive to be willing to produce an additional unit of a good. For example, the supply curve in Figure 2–9 indicates that a total of 800 units will be produced when the price is $400. Alternatively, if 800 units are produced, producers will have to receive $400 to be induced to produce another unit of the good.

Producer surplus is the producer analogue to consumer surplus. It is the amount of money producers receive in excess of the amount necessary to induce them to produce the good. More specifically, note that producers are willing to sell each unit of output below 800 units at a price less than $400. But if the price is $400, producers receive an amount equal to $400 for each unit of output below 800, even though they would be willing to sell those indi- vidual units for a lower price.

Geometrically, producer surplus is the area above the supply curve but below the mar- ket price of the good. Thus, the shaded area in Figure 2–9 represents the surplus producers receive by selling 800 units at a price of $400—an amount above what would be required to produce each unit of the good. The shaded area, ABC, is the producer surplus when the price is $400. Mathematically, this area is one-half of 800 times $266.67, or $106,668.

producer surplus The amount producers receive in excess of the amount necessary to induce them to produce the good.

Figure 2–9 Producer Surplus

0

Price

Quantity

$400

100 200 300 400 500 600

S

$400 3

700 800

A B

Producer surplus

900

P x = 400 + 1

3 3

C

Q x s

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Producer surplus can be a powerful tool for managers. For instance, suppose the manager of a major fast-food restaurant currently purchases 10,000 pounds of ground beef each week from a supplier at a price of $1.25 per pound. The producer surplus the meat supplier earns by selling 10,000 pounds at $1.25 per pound tells the restaurant manager the dollar amount that the supplier is receiving over and above what it would be willing to accept for meat. In other words, the meat supplier’s producer surplus is the maximum amount the restaurant could save in meat costs by bargaining with the supplier over a package deal for 10,000 pounds of meat. Chapters 6 and 10 will provide details about how managers can negotiate such a bargain.

MARKET EQUILIBRIUM

The equilibrium price in a competitive market is determined by the interactions of all buyers and sellers in the market. The concepts of market supply and market demand make this notion of interaction more precise: The price of a good in a competitive market is determined by the interaction of market supply and market demand for the good.

Since we will focus on the market for a single good, it is convenient to drop subscripts at this point and let P denote the price of this good and Q the quantity of the good. Figure 2–10 depicts the market supply and demand curves for such a good. To see how the competitive price is determined, let the price of the good be PL. This price corresponds to point B on the market demand curve; consumers wish to purchase Q1 units of the good. Similarly, the price of PL corresponds to point A on the market supply curve; producers are willing to produce only Q0 units at this price. Thus, when the price is PL, there is a shortage of the good; that is, there is not enough of the good to satisfy all consumers willing to purchase it at that price.

In situations where a shortage exists, there is a natural tendency for the price to rise; consumers unable to buy the good may offer producers a higher price in an attempt to get the product. As the price rises from PL to P e in Figure 2–10, producers have an incentive to expand output from Q0 to Qe. Similarly, as the price rises, consumers are willing to purchase less of the good. When the price rises to P e, the quantity demanded is Qe. At this price, just enough of the good is produced to satisfy all consumers willing and able to purchase at that price; quantity demanded equals quantity supplied.

Figure 2–10 Market Equilibrium

0

Price

Quantity Q0

D

Qe Q1

A B

F G

S

PL

Pe

PH

Surplus

Shortage

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Suppose the price is at a higher level—say, PH. This price corresponds to point F on the market demand curve, indicating that consumers wish to purchase Q0 units of the good. The price PH corresponds to point G on the market supply curve; producers are willing to produce Q1 units at this price. Thus, when the price is PH, there is a surplus of the good; firms are producing more than they can sell at a price of PH.

Whenever a surplus exists, there is a natural tendency for the price to fall to equate quan- tity supplied with quantity demanded; producers unable to sell their products may ask for a lower price in an attempt to reduce their unsold inventories. As the price falls from PH to P e, producers have an incentive to reduce quantity supplied to Qe. Similarly, as the price falls, consumers are willing to purchase more of the good. When the price falls to P e, the quantity demanded is Qe; quantity demanded equals quantity supplied.

Thus, the interaction of supply and demand ultimately determines a competitive price, P e, such that there is neither a shortage nor a surplus of the good. This price is called the equi- librium price and the corresponding quantity, Qe, is called the equilibrium quantity for the competitive market. Once this price and quantity are realized, the market forces of supply and demand are balanced; there is no tendency for prices either to rise or to fall.

For a recent college graduation, each graduating student was directed to pick up three free tickets any time between April 9 and April 20. After April 20, remaining tickets were given to those desiring additional tickets, on a first-come, first-served basis. Once the free tickets were fully dis- tributed, any trades between ticket holders and ticket demanders were left to market forces—which led to a very unpopular equilibrium price.

With several concurrent events competing for students’ attention during this time, many students did not claim their three free tickets by the deadline. As graduation approached, students who did not claim their tickets were willing to pay large sums of money to purchase tickets for

visiting family members and friends. Since the demand for tickets was great and only a limited number of tickets were available, some sellers were asking as much as $400 for a ticket!

Several students expressed outrage over the high prices. However, the high prices are merely a symptom of the high value many students placed on graduation tickets coupled with the limited supply. Had graduating seniors without tickets better forecasted this market outcome, they would have picked up their free tickets on time.

Source: “$400? Ticket Scalpers Cash in on IU Kelley’s Commencement,” The Herald-Times, May 3, 2012.

INSIDE BUSINESS 2–3

Unpopular Equilibrium Prices

P R I N C I P L E

Competitive Market Equilibrium Equilibrium in a competitive market is determined by the intersection of the market demand and supply curves. The equilibrium price is the price that equates quantity demanded with quantity sup- plied. Mathematically, if Qd(P) and Qs(P) represent the quantity demanded and supplied when the price is P, the equilibrium price, P e, is the price such that

Q d ( P e ) = Q s ( P e )

The equilibrium quantity is simply Qd(Pe ) or, equivalently, Qs(P e).

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DEMONSTRATION PROBLEM 2–4

According to an article in China Daily, China recently accelerated its plan to privatize tens of thou- sands of state-owned firms. Imagine that you are an aide to a senator on the Foreign Relations Committee of the U.S. Senate, and you have been asked to help the committee determine the price and quantity that will prevail when competitive forces are allowed to equilibrate the market. The best estimates of the market demand and supply for the good (in U.S. dollar equivalent prices) are given by Qd = 10 − 2P and Qs = 2 + 2P, respectively. Determine the competitive equilibrium price and quantity.

ANSWER: Competitive equilibrium is determined by the intersection of the market demand and supply curves. Mathematically, this simply means that Qd = Qs. Equating demand and supply yields

10 − 2P = 2 + 2P

or

8 = 4P

Solving this equation for P yields the equilibrium price Pe = 2. To determine the equilibrium quan- tity, we simply plug this price into either the demand or the supply function (since, in equilibrium, quantity supplied equals quantity demanded). For example, using the supply function, we find that

Q e = 2 + 2 ( 2 ) = 6

PRICE RESTRICTIONS AND MARKET EQUILIBRIUM

The previous section showed how prices and quantities are determined in a free market. In some instances, government places limits on how much prices are allowed to rise or fall, and these restrictions can affect the market equilibrium. In this section, we examine the impact of price ceilings and price floors on market allocations.

Price Ceilings One basic implication of the economic doctrine of scarcity is that there are not enough goods to satisfy the desires of all consumers at a price of zero. As a consequence, some method must be used to determine who gets to consume goods and who does not. People who do not get to consume goods are essentially discriminated against. One way to determine who gets a good and who does not is to allocate the goods based on hair color: If you have red hair, you get the good; if you don’t have red hair, you don’t get the good.

The price system uses price to determine who gets a good and who does not. The price system allocates goods to consumers who are willing and able to pay the most for the goods. If the competitive equilibrium price of a pair of jeans is $40, consumers willing and able to pay $40 will purchase the good; consumers unwilling or unable to pay that much for a pair of jeans will not buy the good.

It is important to keep in mind that it is not the price system that is “unfair” if one cannot afford to pay the market price for a good; rather, it is unfair that we live in a world of scarcity. Any method of allocating goods will seem unfair to someone because there are not enough resources to satisfy everyone’s wants. For example, if jeans were allocated to people on the

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basis of hair color instead of the price system, you would think this allocation rule was unfair unless you were born with the “right” hair color.

Often individuals who are discriminated against by the price system attempt to persuade the government to intervene in the market by requiring producers to sell the good at a lower price. This is only natural, for if we were unable to own a house because we had the wrong hair color, we most certainly would attempt to get the government to pass a law allowing peo- ple with our hair color to own a house. But then there would be too few houses to go around, and some other means would have to be used to allocate houses to people.

Suppose that, for whatever reason, the government views the equilibrium price of P e in Figure 2–11 as “too high” and passes a law prohibiting firms from charging prices above P c. Such a price is called a price ceiling.

Do not be confused by the fact that the price ceiling is below the initial equilibrium price; the term ceiling refers to that price being the highest permissible price in the market. It does not refer to a price set above the equilibrium price. In fact, if a ceiling were imposed above the equilibrium price, it would be ineffective; the equilibrium price would be below the max- imum legal price.

Given the regulated price of Pc, quantity demanded exceeds quantity supplied by the distance from A to B in Figure 2–11; there is a shortage of Qd − Qs units. The reason for the shortage is twofold. First, producers are willing to produce less at the lower price, so the available quantity is reduced from Qe to Qs. Second, consumers wish to purchase more at the lower price; thus, quantity demanded increases from Qe to Qd. The result is that there is not enough of the good to satisfy all consumers willing and able to purchase it at the price ceiling.

How, then, are the goods to be allocated now that it is no longer legal to ration them on the basis of price? In most instances, goods are rationed on the basis of “first come, first served.” As a consequence, price ceilings typically result in long lines such as those created in the 1970s due to price ceilings on gasoline. Thus, price ceilings discriminate against people who have a high opportunity cost of time and do not like to wait in lines. If a consumer has to wait in line two hours to buy 10 gallons of gasoline and his or her time is worth $5 per hour, it costs the consumer 2 × $5 = $10 to wait in line. Since 10 gallons of gasoline are purchased, this amounts to spending $1 per gallon waiting in line to purchase the good.

price ceiling The maximum legal price that can be charged in a market.

Figure 2–11 A Price Ceiling

0

Price

Quantity Qs

D

Qe Qd

A B

F

S

Pc

Pe

PF

Lost social welfare due

to a price ceiling

Ceiling

Shortage

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This basic idea can be depicted graphically. Under the price ceiling of Pc, only Qs units of the good are available. Since this quantity corresponds to point F on the demand curve in Figure 2–11, we see that consumers are willing to pay PF for another unit of the good. By law, however, they cannot pay the firm more than Pc. The difference PF − Pc reflects the price per unit consumers are willing to pay by waiting in line. The full economic price paid by a con- sumer (PF) is thus the amount paid to the firm (Pc) plus the implicit amount paid by waiting in line (PF − Pc). The latter price is paid not in dollars but through opportunity cost and thus is termed the nonpecuniary price.

P F

Full economic

price

=

P c

Dollar price

+

( P F − P c )

Nonpecuniary

price

As Figure 2–11 shows, PF is greater than the initial equilibrium price, P e. When opportunity costs are taken into account, the full economic price paid for a good is actually higher after the ceiling is imposed.

Since price ceilings reduce the quantity available in the market, such regulations reduce social welfare even if they do not result in long lines. The dollar value of the lost social wel- fare is given by the shaded triangle in Figure 2–11. Intuitively, each point on the demand curve represents the amount consumers would be willing to pay for an additional unit, while each point on the supply curve indicates the amount producers would have to receive to induce them to sell an additional unit. The vertical difference between the demand and supply curves at each quantity therefore represents the change in social welfare (consumer value less relevant production costs) associated with each incremental unit of output. Summing these vertical differences for all units between Qe and Qs yields the shaded triangle in Figure 2–11 and thus represents the total dollar value of the lost social welfare due to a price ceiling. The triangle in Figure 2–11 is sometimes called “deadweight loss.”

full economic price The dollar amount paid to a firm under a price ceiling, plus the nonpecuniary price.

DEMONSTRATION PROBLEM 2–5

Based on your answer to the Senate Foreign Relations Committee (Demonstration Problem 2–4), one of the senators raises a concern that the free market price might be too high for the typical Chinese citizen to pay. Accordingly, she asks you to explain what would happen if the Chinese government privatized the market but then set a price ceiling at the Chinese equivalent of $1.50. How do you answer? Assume that the market demand and supply curves (in U.S. dollar equivalent prices) are still given by

Q d = 10 − 2P and  Q s = 2 + 2P

ANSWER: Since the price ceiling is below the equilibrium price of $2, a shortage will result. More specifically, when the price ceiling is $1.50, quantity demanded is

Q d = 10 − 2 (1.50) = 7

and quantity supplied is

Q s = 2 + 2 ( 1.50 ) = 5 Thus, there is a shortage of 7 − 5 = 2 units.

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To determine the full economic price, we simply determine the maximum price consumers are will- ing to pay for the five units produced. To do this, we first set quantity equal to 5 in the demand formula:

5 = 10 − 2 P F

or

2 P F = 5

Next, we solve this equation for PF to obtain the full economic price, PF = $2.50. Thus, consum- ers pay a full economic price of $2.50 per unit; $1.50 of this price is in money and $1 represents the nonpecuniary price of the good. Lastly, we can solve for the deadweight loss generated by the price ceiling. This is equal to (PF − PC)(Qe − Qs) = (2.50 − 1.50)(6 − 5) = 1.

Based on the preceding analysis, one may wonder why the government would ever impose price ceilings. One answer might be that politicians do not understand the basics of supply and demand. This probably is not the answer, however.

The answer lies in who benefits from and who is harmed by ceilings. When lines develop due to a shortage caused by a price ceiling, people with high opportunity costs are hurt, while people with low opportunity costs may actually benefit. For example, if you have nothing better to do than wait in line, you will benefit from the lower dollar price; your nonpecuniary price is close to zero. On the other hand, if you have a high opportunity cost of time because your time is valuable to you, you are made worse off by the ceiling. If a particular politician’s constituents tend to have a lower-than-average opportunity cost, that politician naturally will attempt to invoke a price ceiling.

Federal, state, and local authorities around the world are often persuaded to enact laws that restrict the prices that businesses can legally charge their customers. Many states in the United States have usury laws—price ceilings on inter- est rates—that restrict the rate that banks and other lenders can legally charge their customers. In 2005, Poland passed the Anti-Usury Act, which limited the consumer interest rate to quadruple the security rate of the National Bank of Poland; violators of the Act can face a fine or up to two years of imprisonment. Thailand allowed gasoline prices to be deter- mined by market forces during the 1990s, but its Commerce Ministry imposed a price ceiling in an attempt to hold down the rapidly rising gasoline prices during the early 2000s.

All but five states in the United States have enacted min- imum wage legislation—that is, a price floor on the hourly rate a business can legally pay its employees. These restric- tions are in addition to the minimum wage set by the federal government, and as of 2012, state minimum wages were

higher than the federal minimum wage in 18 states. The effect of these minimum wages is similar to that shown in Figure 2–12. However, since governments do not hire work- ers who are unable to find employment at the artificially high wage, the “surplus” of labor translates into unem- ployment. Every Canadian province and territory also have enacted minimum wage laws. In addition, Ontario, British Columbia, and Quebec have established floor prices (called “minimum retail prices”) on beer to keep prices artificially high in an attempt to discourage alcohol consumption and to protect Canadian brewers from inexpensive U.S. brands.

Sources: “Oil Sales: Ceiling Set on Retail Margin,” The Nation, June 15, 2002; “An Oil Shock of Our Own Making,” The Nation, May 20, 2004; “Italian Usury Laws: Mercy Strain’d,” The Economist, November 23, 2000; “Democrats Look to Keep Minimum Wage on Table,” The Wall Street Journal, June 20, 2006; “Beer Price War Punishes Mom-and-Pop Shops,” The Gazette, November 4, 2005; “EU Lawmakers Pass Credit Directive,” Krakow Post, May 15, 2012; and U.S. Department of Labor, www.dol.gov/ whd/minwage/america.htm, accessed May 15, 2012.

INSIDE BUSINESS 2–4

Price Ceilings and Price Floors around the Globe

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Sometimes when shortages are created by a ceiling, goods are not allocated on the basis of lines. Producers may discriminate against consumers on the basis of other factors, including whether or not consumers are regular customers. During the gasoline shortage of the 1970s, many gas stations sold gas only to customers who regularly used the stations. In California during the late 1990s, price ceilings were imposed on the fees that banks charged nondeposi- tors for using their automatic teller machines (ATMs). The banks responded by refusing to let nondepositors use their ATM machines. In other situations, such as ceilings on loan interest rates, banks may allocate money only to consumers who are relatively well-to-do.

The key point is that in the presence of a shortage created by a ceiling, managers must use some method other than price to allocate the goods. Depending on which method is used, some consumers will benefit and others will be worse off.

Price Floors In contrast to the case of a price ceiling, sometimes the equilibrium competitive price may be considered too low for sellers. In these instances, individuals may lobby for the government to legislate a minimum legal price for a good. Such a price is called a price floor. Perhaps the best-known price floor is the minimum wage, the lowest legal wage that can be paid to workers.

If the equilibrium price is above the price floor, the price floor has no effect on the market. But if the price floor is set above the competitive equilibrium level, such as Pf in Figure 2–12, there is an effect. Specifically, when the price floor is set at Pf, quantity supplied is Qs and quantity demanded is Qd. In this instance, more is produced than consumers are willing to purchase at that price, and a surplus develops. In the context of the labor market, there are more people looking for work than there are jobs to go around at that wage, and unemployment results. In the context of a product market, the surplus translates into unsold inventories. In a free market, price would fall to alleviate the unemployment or excess inven- tories, but the price floor prevents this mechanism from working. Buyers end up paying a higher price and purchasing fewer units.

When price floors are above the equilibrium price, there will be consumers with willingness- to-pay that is more than production costs but is less than the price floor. These consumers will be unable to purchase when the price floor is in place, which results in a loss of social welfare. The dollar value of the lost social welfare is given by the blue triangle in Figure 2–12. Similar to

price floor The minimum legal price that can be charged in a market.

Figure 2–12 A Price Floor

0

Price

Quantity Qd

D

Qe Qs

F G S

Pe

Pf

Surplus

Floor

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the case of a price ceiling, the lost social welfare is the vertical difference between the demand and supply curve for all units between Qd and Qe. The difference is that the constraint on units purchased for a price floor comes from constrained quantity demanded—in response to a price floor that is higher than P e—rather than constrained quantity supplied—in response to a price ceiling that is lower than P e. The area of the blue triangle in Figure 2–12 is deadweight loss.

When a price floor is a minimum wage, the deadweight loss that results is fully captured by the blue triangle in Figure 2–12. However, when the price floor applies to a product, the deadweight loss can be even greater. How much additional deadweight loss there is depends on what happens to the unsold inventories. One possibility is that the government purchases and discards the surplus. This is the case with price floors on many agricultural products, such as cheese. This type of price floor, where the government purchases the surplus, is called a price support. Revisiting Figure 2–12, the quantity of unsold products is given by the dis- tance from G to F, and this surplus is the amount of product the government purchases at the price floor. The total cost to the government then is Pf(Qs – Qd). If the government discards the surplus it purchases, this results in additional deadweight loss, as indicated by the red trap- ezoid. This additional deadweight loss is the cost of producing the product that was discarded. Again, if producers of cheese receiving the price support, this additional deadweight loss is the cost of producing the cheese that the government purchased and discarded.

DEMONSTRATION PROBLEM 2–6

One of the members of the Senate Foreign Relations Committee has studied your analysis of Chinese privatization (Demonstration Problems 2–4 and 2-5) but is worried that the free-market price might be too low to enable producers to earn a fair rate of return on their investment. He asks you to explain what would happen if the Chinese government privatized the market but agreed to purchase (and discard) unsold units of the good at a floor price of $3.50. What do you tell the senator? Assume that the market demand and supply curves (in U.S. dollar equivalent prices) are still given by

Q d = 10 − 2P and  Q s = 2 + 2P

ANSWER: Since the price floor is above the equilibrium price of $2, the floor results in a surplus. More specif- ically, when the price is $3.50, quantity demanded is

Q d = 10 − 2 (3.50) = 3

and quantity supplied is

Q s = 2 + 2 ( 3.50 ) = 9

Thus, there is a surplus of 9 − 3 = 6 units. Consumers pay a higher price ($3.50), and producers have unsold inventories of 6 units. However, the Chinese government must purchase the amount con- sumers are unwilling to purchase at the price of $3.50. Therefore, the cost to the Chinese government of buying the surplus of 6 units is $3.50 × 6 = $21.

Lastly, the deadweight loss is comprised of the two shaded regions illustrated in Figure 2–12. The first part, corresponding to the blue triangle, is (3.50 – 0.50)(6 – 3) = 9. Note that the figure of 0.50 in this formula is the price at which producers will supply 3 units (which is the quantity demanded at the price floor). The second part of the deadweight loss, corresponding to the red trapezoid, is $21 – (1/2)(3.50 – 0.50)(6) = 12. Here, we calculate the area of the trapezoid by taking the govern- ment expenditure ($21) and subtracting the portion of that expenditure that adds to producer surplus (i.e., the area below the price floor and above the supply curve for the surplus units).

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COMPARATIVE STATICS

You now understand how equilibrium is determined in a competitive market and how gov- ernment policies such as price ceilings and price floors affect the market. Next, we show how managers can use supply and demand to analyze the impact of changes in market condi- tions on the competitive equilibrium price and quantity. The study of the movement from one equilibrium to another is known as comparative static analysis. Throughout this analysis, we assume that no legal restraints, such as price ceilings or floors, are in effect and that the price system is free to work to allocate goods among consumers.

Changes in Demand Suppose that The Wall Street Journal reports that consumer incomes are expected to rise by about 2.5 percent over the next year, and the number of individuals over 25 years of age will reach an all-time high by the end of the year. We can use our supply and demand apparatus to examine how these changes in market conditions will affect car rental agencies like Avis, Hertz, and National. It seems reasonable to presume that rental cars are normal goods: A rise in consumer incomes will most likely increase the demand for rental cars. The increased num- ber of consumers aged 25 and older will also increase demand since at many locations those who rent cars must be at least 25 years old.

We illustrate the ultimate effect of this increase in the demand for rental cars in Figure 2–13. The initial equilibrium in the market for rental cars is at point A, where demand curve D0 intersects the market supply curve S. The changes reported in The Wall Street Journal suggest that the demand for rental cars will increase over the next year, from D0 to some curve like D1. The equilibrium moves to point B, where car rental companies rent more cars and charge a higher price than before the demand increase.

The reason for the rise in rental car prices is as follows: The growing number of consum- ers aged 25 or older, coupled with the rise in consumer incomes, increases the demand for rental cars. At the old price of $45 per day, there are only 100,000 cars available. This is less than the 108,000 cars that customers want to rent at that price. Car rental companies thus find

Figure 2–13 Effect of a Change in Demand for Rental Cars

0

Price

Quantity (thousands

rented per day)

D0

100 104 108

B

S

$45

$49

D1

A

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it in their interest to raise their prices and to increase their quantity supplied of rental cars until ultimately enough cars are available at the new equilibrium price of $49 to exactly equal the quantity demanded at this higher price.

DEMONSTRATION PROBLEM 2–7

The manager of a fleet of cars currently rents them out at the market price of $49 per day, with rent- ers paying for their own gasoline and oil. In a front-page newspaper article, the manager learns that economists expect gasoline prices to rise dramatically over the next year due to increased tensions in the Middle East. What should she expect to happen to the price of the cars her company rents?

ANSWER: Since gasoline and rental cars are complements, the increase in gasoline prices will decrease the demand for rental cars. To see the impact on the market price and quantity of rental cars, let D1 in Figure 2–13 represent the initial demand for rental cars, so that the initial equilibrium is at point B. An increase in the price of gasoline will shift the demand curve for rental cars to the left (to D0), resulting in a new equilibrium at point A. Thus, she should expect the price of rental cars to fall.

In today’s global economy, the number of firms in the market critically depends on the entry and exit decisions of foreign firms. Recently, several Chinese automakers— including the country’s biggest domestic brand, Chery Automobile Co.—announced ambitious plans to expand abroad. Chery already exports to 70 developing coun- tries in Asia, the Middle East, and Latin America, and is eyeing further expansion into more developed markets.

Entry by Chery and other Chinese manufacturers into a developed market such as the U.S. automobile market would shift the supply curve to the right. Other things equal, this will negatively impact the bottom lines of firms that currently sell in these markets: The increase in supply will reduce the equilibrium prices of automobiles and the profits of existing U.S. automakers.

Source: “Chinese Automakers Aim for Global Expansion,” Manufacturing. net, April 23, 2010.

INSIDE BUSINESS 2–5

Globalization and the Supply of Automobiles

Changes in Supply We can also use our supply and demand framework to predict how changes in one or more supply shifters will affect the equilibrium price and quantity of goods or services. For instance, consider a bill before Congress that would require all employers, small and large alike, to provide health care to their workers. How would this bill affect the prices charged for goods at retailing outlets?

This health care mandate would increase the cost to retailers and other firms of hiring work- ers. Many retailers rely on semiskilled workers who earn relatively low wages, and the cost of providing health insurance to these workers is large relative to their annual wage earnings. While firms might lower wages to some extent to offset the mandated health insurance costs paid, the net effect would be to raise the total cost to the firm of hiring workers. These higher labor costs, in turn, would decrease the supply of retail goods. The final result of the legislation would be to increase the prices charged by retailing outlets and to reduce the quantity of goods sold there.

We can see this more clearly in Figure 2–14. The market is initially in equilibrium at point A, where demand curve D intersects the market supply curve, S0. Higher input prices decrease

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supply from S0 to S1, and the new competitive equilibrium moves to point B. In this instance, the market price rises from P0 to P1, and the equilibrium quantity decreases from Q0 to Q1.

Simultaneous Shifts in Supply and Demand Managers in both the private and public sectors sometimes encounter events that lead to simul- taneous shifts in both demand and supply. A tragic example occurred at the end of the last cen- tury when an earthquake hit Kobe, Japan. The earthquake did considerable damage to Japan’s sake wine industry, and the nation’s supply of sake wine decreased as a result. Unfortunately, the stress caused by the earthquake led many to increase their demand for sake and other alcoholic beverages. We can use the tools of this chapter to examine how these simultaneous changes in supply and demand affected the equilibrium price and quantity of sake.

Figure 2–14 Effect of a Change in Supply

0

Price

Quantity

D

Q1 Q0

S1

P0

P1 B

S0

A

The website for the ninth edition, www.mhhe.com/baye9e, contains a file named SupplyandDemandSolver.xls. With a few clicks of a mouse, you can use this tool to determine equilib- rium in the linear supply and demand model under different scenarios by accessing different tabs in the file. You can also use this program to see how equilibrium prices and quantities change through “real-time” comparative static exercises.

Additionally, this tool permits you to calculate both producer and consumer surplus and investigate how their magnitudes change when demand and supply parameters change. You can also use it to examine the quantitative impact of price regulations, such as price ceilings and price floors, and the resulting lost social welfare (or deadweight

loss) associated with prices that are regulated at levels above or below the equilibrium price.

It is important to stress that this tool is not a substitute for being able to perform these tasks without the aid of the tool. But the tool will help you visualize how different demand and supply parameters lead to different quantita- tive effects. Just as important, you can create a never-end- ing number of practice problems and solve them by hand, and then use this tool to check your answers. For Connect users, the algorithmic versions of the end-of-chapter prob- lems will allow you to solve many versions of these types of equilibrium problems with immediate feedback on your performance.

INSIDE BUSINESS 2–6

Using a Spreadsheet to Calculate Equilibrium in the Supply and Demand Model

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Figure 2–15 A Simultaneous Increase in Demand and Decrease in Supply Raises the Equilibrium Price

0

Price

Quantity Q2 Q0

S2

P1

P2 C

S1

B

P0

Q1

A

S0

D1

D0

In Figure 2–15, the market is initially in equilibrium at point A, where demand curve D0 intersects market supply curve S0. Since the earthquake led to a simultaneous decrease in supply and increase in demand for sake, suppose supply decreases from S0 to S1 and demand increases from D0 to D1. In this instance, a new competitive equilibrium occurs at point B; the price of sake increases from P0 to P1, and the quantity consumed increases from Q0 to Q1.

As the curves are drawn in Figure 2–15, the effect of the decrease in supply and increase in demand was to increase both the price and the quantity. But what if, instead of shifting from S0 to S1, the supply curve shifted much farther to the left to S2 so that it intersected the new demand curve at point C instead of B? In this instance, price would still be higher than the initial equilibrium price, P0. But the resulting quantity would be lower than the initial equilib- rium (point C implies a lower quantity than point A). Thus, we have seen that when demand increases and supply decreases, the market price rises, but the market quantity may rise or fall depending on the relative magnitude of the shifts.

When using supply and demand analysis to predict the effects of simultaneous changes in demand and supply, you must be careful that the predictions are not artifacts of how far you have shifted the curves. As shown in Table 2–2, simultaneous changes in demand and supply generally lead to ambiguities regarding whether the equilibrium price or quantity will rise or fall. A valuable exercise is to draw various simultaneous shifts in supply and demand to verify the results summarized in Table 2–2.

Table 2–2 Equilibrium Price and Quantity: The Impact of Simultaneous Shifts in Demand and Supply

Nature of the Change Increase in Demand Decrease in Demand

Increase in Supply Price: Ambiguous Price: Decreases

  Quantity: Increases Quantity: Ambiguous

Decrease in Supply Price: Increases Price: Ambiguous

  Quantity: Ambiguous Quantity: Decreases

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Figure 2–16 Rising Chip Prices Decrease the Supply of PCs

DEMONSTRATION PROBLEM 2–8

Suppose you are the manager of a chain of computer stores. For obvious reasons you have been closely following developments in the computer industry, and you have just learned that Congress has passed a two-pronged program designed to further enhance the U.S. computer industry’s position in the global economy. The legislation provides increased funding for computer education in primary and secondary schools, as well as tax breaks for firms that develop computer software. As a result of this legislation, what do you predict will happen to the equilibrium price and quantity of software?

ANSWER: The equilibrium quantity certainly will increase, but the market price may rise, remain the same, or fall, depending on the relative changes in demand and supply. To see this, note that the increased funding for computer education at primary and secondary schools will lead to an increase in the demand for computer software since it is a normal good. The reduction in taxes on software manu- facturers will lead to an increase in the supply of software. You should draw a figure to verify that if the rightward shift in supply is small compared to the rightward shift in demand, both the equilib- rium price and quantity will increase. If supply increases by the same amount as demand, there will be no change in the price, but the equilibrium quantity will rise. Finally, if supply increases more than the increase in demand, the resulting equilibrium will entail a lower price and a greater quantity. In all cases, the equilibrium quantity increases. But the effect on the market price depends on the relative magnitudes of the increases in demand and supply.

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

ANSWERING THE headLINE Now that we have developed a formal apparatus for understanding how markets work, we will return to the story that opened this chapter.

Sam recognized that a cut in chip production will ultimately lead to higher chip prices. Since chips are a key input in the production of PCs, an increase in the price of chips would in turn lead to a decrease in the market supply of PCs, as indicated by the change in supply from S0 to S1 in Figure 2–16. Notice that total quantity of PCs sold in the market falls as the equilibrium moves from point A to point B. In light of this anticipated decline in PC sales, Sam and Jane discussed the wisdom of going ahead with their plan to double PC Solutions’ workforce at this time.

Price of PCs

Quantity of PCs

S1

S0

B

A

D

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SUMMARY

This chapter provided an overview of supply and demand and the interaction of these forces. We covered applica- tions of demand, supply, price ceilings, price floors, and comparative statics. By reading this chapter and work- ing through the demonstration problems presented, you should have a basic understanding of how to analyze the workings of a competitive market.

The model of supply and demand is just a starting point for this book. Throughout the remainder of the book, we assume you have a thorough understanding of the concepts presented in this chapter. In the next chapter, we will present the concepts of elasticity and show how to use them in making managerial decisions. We will also present some additional quantitative tools to help managers make better decisions.

KEY TERMS AND CONCEPTS

ad valorem tax change in demand change in quantity demanded change in quantity supplied change in supply comparative static analysis complements consumer expectations consumer surplus decrease in demand decrease in supply demand demand function demand shifters equilibrium price

equilibrium quantity excise tax full economic price increase in demand increase in supply inferior good informative advertising inverse demand function inverse supply function law of demand law of supply linear demand function linear supply function market demand curve market supply curve

nonpecuniary price normal good persuasive advertising price ceiling price floor price support producer expectations producer surplus shortage stockpiling substitutes supply supply function supply shifters surplus

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. The X-Corporation produces a good (called X) that is a normal good. Its competitor, Y-Corp., makes a substitute good that it markets under the name Y. Good Y is an inferior good. (LO1) a. How will the demand for good X change if consumer incomes decrease? b. How will the demand for good Y change if consumer incomes increase? c. How will the demand for good X change if the price of good Y increases? d. Is good Y a lower-quality product than good X? Explain.

2. Good X is produced in a competitive market using input A. Explain what would happen to the supply of good X in each of the following situations: (LO1, LO4) a. The price of input A decreases. b. An excise tax of $3 is imposed on good X. c. An ad valorem tax of 7 percent is imposed on good X. d. A technological change reduces the cost of producing additional units of good X.

3. Suppose the supply function for product X is given by Q x s = − 30 + 2 P x − 4 P z . (LO1)

a. How much of product X is produced when Px = $600 and Pz = $60? b. How much of product X is produced when Px = $80 and Pz = $60? c. Suppose Pz = $60. Determine the supply function and inverse supply function for

good X. Graph the inverse supply function. 4. The demand for good X is given by

Q x d = 6,000 − 1 __

2 P x − P y + 9 P z +

1 __

10 M

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Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000. (LO1) a. Indicate whether goods Y and Z are substitutes or complements for good X. b. Is X an inferior or a normal good? c. How many units of good X will be purchased when Px = $5,230? d. Determine the demand function and inverse demand function for good X. Graph the

demand curve for good X. 5. The demand curve for product X is given by Q x

d = 300 − 2 P x . (LO2) a. Find the inverse demand curve. b. How much consumer surplus do consumers receive when Px = $45? c. How much consumer surplus do consumers receive when Px = $30? d. In general, what happens to the level of consumer surplus as the price of a good falls?

6. Suppose demand and supply are given by Qd = 60 − P and Qs = P − 20. (LO3, LO4) a. What are the equilibrium quantity and price in this market? b. Determine the quantity demanded, the quantity supplied, and the magnitude of the

surplus if a price floor of $50 is imposed in this market. c. Determine the quantity demanded, the quantity supplied, and the magnitude of the

shortage if a price ceiling of $32 is imposed in this market. Also, determine the full economic price paid by consumers.

7. Suppose demand and supply are given by: (LO3, LO4)

Q x d = 14 − 1 __

2 P x and Q x s =

1 __

4 P x − 1

a. Determine the equilibrium price and quantity. Show the equilibrium graphically. b. Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium

price and quantity. c. How much tax revenue does the government earn with the $12 tax?

8. Use the accompanying graph to answer these questions. (LO2, LO3, LO4) a. Suppose demand is D and supply is S0. If a price ceiling of $6 is imposed, what are

the resulting shortage and full economic price? b. Suppose demand is D and supply is S0. If a price support of $12 is imposed, what is the

resulting surplus? What is the cost to the government of purchasing any and all unsold units? c. Suppose demand is D and supply is S0 so that the equilibrium price is $10. If an

excise tax of $6 is imposed on this product, what happens to the equilibrium price paid by consumers? The price received by producers? The number of units sold?

d. Calculate the level of consumer and producer surplus when demand and supply are given by D and S0 respectively.

e. Suppose demand is D and supply is S0. Would a price ceiling of $2 benefit any consum- ers? Explain.

0 1 2 3 4 5 6

Price of X ($)

Quantity of Good X

20

18

16

14

12

10

8

6

4

2

0

S1 S 0

D

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PROBLEMS AND APPLICATIONS

11. You are the manager of a midsized company that assembles personal computers. You purchase most components—such as random access memory (RAM)—in a competitive market. Based on your marketing research, consumers earning over $80,000 purchase 1.5 times more RAM than consumers with lower incomes. One morning, you pick up a copy of The Wall Street Journal and read an article indicating that input components for RAM are expected to rise in price, forcing manufacturers to produce RAM at a higher unit cost. Based on this information, what can you expect to happen to the price you pay for random access memory? Would your answer change if, in addition to this change in RAM input prices, the article indicated that consumer incomes are expected to fall over the next two years as the economy dips into recession? Explain. (LO1, LO3, LO5)

12. You are the manager of a firm that produces and markets a generic type of soft drink in a competitive market. In addition to the large number of generic products in your mar- ket, you also compete against major brands such as Coca-Cola and Pepsi. Suppose that, due to the successful lobbying efforts of sugar producers in the United States, Congress is going to levy a $0.50 per pound tariff on all imported raw sugar—the primary input for your product. In addition, Coke and Pepsi plan to launch an aggressive advertising campaign designed to persuade consumers that their branded products are superior to generic soft drinks. How will these events impact the equilibrium price and quantity of generic soft drinks? (LO1, LO3, LO5)

13. Some have argued that higher cigarette prices do not deter smoking. While there are many arguments both for and against this view, some find the following argument to be the most persuasive of all: “The laws of supply and demand indicate that higher prices are ineffective in reducing smoking. In particular, higher cigarette prices will reduce the demand for cigarettes. This reduction in demand will push the equilibrium price back down to its original level. Since the equilibrium price will remain unchanged, smokers will consume the same number of cigarettes.” Do you agree or disagree with this view? Explain. (LO1, LO3, LO5)

14. You are the manager of an organization in America that distributes blood to hospitals in all 50 states and the District of Columbia. A recent report indicates that nearly 50 Americans contract HIV each year through blood transfusions. Although every pint of blood donated in the United States undergoes a battery of nine different tests, existing screening methods can detect only the antibodies produced by the body’s immune system—not foreign agents in the blood. Since it takes weeks or even months for these antibodies to build up in the blood, newly infected HIV donors can pass along the virus through blood that has passed existing screening tests. Happily, researchers have developed a series of new tests aimed at detecting and removing infections from donated blood before it is used in transfusions. The obvious benefit of these tests is the reduced incidence of infection through blood transfusions. The report indicates that the current price of decontaminated blood is $60

9. The supply curve for product X is given by Q x s = −520 + 20 P x . (LO2)

a. Find the inverse supply curve. b. How much surplus do producers receive when Qx = 400? When Qx = 1,200?

10. Consider a market where supply and demand are given by Q x s = −16 + P x and Q x

d = 92 − 2 P x . Suppose the government imposes a price floor of $40 and agrees to purchase and discard any and all units consumers do not buy at the floor price of $40 per unit. (LO3, LO4, LO5) a. Determine the cost to the government of buying firms’ unsold units. b. Compute the lost social welfare (deadweight loss) that stems from the $40 price floor.

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per pint. However, if the new screening methods are adopted, the demand and supply for decontaminated blood will change to Qd = 210 − 1.5P and Qs = 2.5P − 150. What price do you expect to prevail if the new screening methods are adopted? How many units of blood will be used in the United States? What is the level of consumer and producer sur- plus? Illustrate your findings in a graph. (LO2, LO3)

15. As a result of increased tensions in the Middle East, oil production is down by 1.21 mil- lion barrels per day—a 5 percent reduction in the world’s supply of crude oil. Explain the likely impact of this event on the market for gasoline and the market for small cars. (LO1, LO3, LO5)

16. You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, tele- com taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for tele- communication services is given by Qd = 300 − 4P and the market supply (including taxes) is Qs = 3P − 120 (both in millions), where P is the monthly price of telecommu- nication services. The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of Qs = 3.2P − 120. How much money per unit would a typical consumer save each month as a result of the pro- posed legislation? (LO2, LO3)

17. G.R. Dry Foods Distributors specializes in the wholesale distribution of dry goods, such as rice and dry beans. The firm’s manager is concerned about an article he read in this morning’s Wall Street Journal indicating that the incomes of individuals in the lowest income bracket are expected to increase by 10 percent over the next year. While the manager is pleased to see this group of individuals doing well, he is concerned about the impact this will have on G.R. Dry Foods. What do you think is likely to happen to the price of the products G.R. Dry Foods sells? Why? (LO1, LO3, LO5)

18. From California to New York, legislative bodies across the United States are consid- ering eliminating or reducing the surcharges that banks impose on noncustomers, who make $12 million in withdrawals from other banks’ ATM machines. On average, non- customers earn a wage of $24 per hour and pay ATM fees of $3.00 per transaction. It is estimated that banks would be willing to maintain services for 5 million transactions at $1.25 per transaction, while noncustomers would attempt to conduct 19 million trans- actions at that price. Estimates suggest that, for every 1 million gap between the desired and available transactions, a typical consumer will have to spend an extra minute trav- eling to another machine to withdraw cash. Based on this information, use a graph to carefully illustrate the impact of legislation that would place a $1.25 cap on the fees banks can charge for noncustomer transactions. (LO3, LO4)

19. Rapel Valley in Chile is renowned for its ability to produce high-quality wine at a frac- tion of the cost of many other vineyards around the world. Rapel Valley produces over 20 million bottles of wine annually, of which 5 million are exported to the United States. Each bottle entering the United States is subjected to a $0.50 per bottle excise tax, which generates about $2.5 million in tax revenues. Strong La Niña weather patterns have caused unusually cold temperatures, devastating many of the wine producers in that region of Chile. How will La Niña affect the price of Chilean wine? Assuming La Niña does not impact the California wine-producing region, how will La Niña impact the market for Californian wines? (LO1, LO3, LO5)

20. Viking InterWorks is one of many manufacturers that supplies memory products to original equipment manufacturers (OEMs) of desktop systems. The CEO recently read

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an article in a trade publication that reported the projected demand for desktop sys- tems to be Q desktop

d = 1,600 − 2 P desktop + .6M (in millions of units), where Pdesktop is the price of a desktop system and M is consumer income. The same article reported that the incomes of the desktop systems’ primary consumer demographic would increase 4.2 percent this year to $61,300 and that the selling price of a desktop would decrease to $980, both of which the CEO viewed favorably for Viking. In a related article, the CEO read that the upcoming year’s projected demand for 512 MB desktop memory modules is Q memory

d = 11,200 − 100 P memory − 2 P desktop (in thousands of units), where Pmemory is the market price for a 512 MB memory module and Pdesktop is the selling price of a desktop system. The report also indicated that five new, small start-ups entered the 512 MB memory module market, bringing the total number of competitors to 100 firms. Furthermore, suppose that Viking’s CEO commissioned an industrywide study to examine the industry capacity for 512 MB memory modules. The results indicate that when the industry is operating at maximum efficiency, this competitive industry supplies modules according to the following function: Q memory

S = 1,000 + 25 P memory + N (in thousands), where Pmemory is the price of a 512 MB memory module and N is the number of memory module manufacturers in the market. Viking’s CEO provides you, the production manager, with this information and requests a report containing the mar- ket price for memory modules and the number of units to manufacture in the upcoming year based on the assumption that all firms producing 512 MB modules supply an equal share to the market. How would your report change if the price of desktops were $1,080? What does this indicate about the relationship between memory modules and desktop systems? (LO1, LO3)

21. Seventy-two percent of the members of the United Food and Commercial Workers Local 655 voted to strike against Stop ’n Shop in the St. Louis area. In fear of similar union responses, two of Stop ’n Shop’s larger rivals in the St. Louis market—Dierberg’s and Schnuck’s—decided to lock out their union employees. The actions of these supermar- kets, not surprisingly, caused Local 655 union members to picket and boycott each of the supermarkets’ locations. While the manager of Mid Towne IGA—one of many smaller competing grocers—viewed the strike as unfortunate for both sides, he was quick to point out that the strike provided an opportunity for his store to increase market share. To take advantage of the strike, the manager of Mid Towne IGA increased newspaper advertising by pointing out that Mid Towne employed Local 655 union members and that it operated under a different contract than “other” grocers in the area. Use a graph to describe the expected impact of advertising on Mid Towne IGA (how the equilibrium price and quantity change). Identify the type of advertising in which Mid Towne IGA engaged. Do you believe the impact of advertising will be permanent? Explain. (LO1, LO3, LO5)

22. Florida, like several other states, has passed a law that prohibits “price gouging” imme- diately before, during, or after the declaration of a state of emergency. Price gouging is defined as “selling necessary commodities such as food, gas, ice, oil, and lumber at a price that grossly exceeds the average selling price for the 30 days prior to the emer- gency.” Many consumers attempt to stock up on emergency supplies, such as bottled water, immediately before and after a hurricane or other natural disaster hits an area. Also, many supply shipments to retailers are interrupted during a natural disaster. Assuming that the law is strictly enforced, what are the economic effects of the price gouging statute? Explain carefully. (LO1, LO3, LO5)

23. In a recent speech, the governor of your state announced: “One of the biggest causes of juvenile delinquency in this state is the high rate of unemployment among 16 to 19 year olds. The low wages offered by employers in the state have given fewer teenagers the incentive to find summer employment. Instead of working all summer, the way we used

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SELECTED READINGS

Ault, Richard W.; Jackson, John D.; and Saba, Richard P., “The Effect of Long-Term Rent Control on Tenant Mobility.” Journal of Urban Economics 35(2), March 1994, pp. 140–58.

Espana, Juan R., “Impact of the North American Free Trade Agreement (NAFTA) on U.S.–Mexican Trade and Investment Flows.” Business Economics 28(3), July 1993, pp. 41–47.

Friedman, Milton, Capitalism and Freedom. Chicago: University of Chicago Press, 1962.

Katz, Lawrence F., and Murphy, Kevin M., “Changes in Relative Wages, 1963–1987: Supply and Demand Factors.” Quarterly Journal of Economics 107(1), February 1992, pp. 35–78.

Olson, Josephine E., and Frieze, Irene Hanson, “Job Interruptions and Part-Time Work: Their Effect on MBAs’ Income.” Industrial Relations 28(3), Fall 1989, pp. 373–86.

O’Neill, June, and Polachek, Solomon, “Why the Gender Gap in Wages Narrowed in the 1980s.” Journal of Labor Economics 11(1), January 1993, pp. 205–28.

Simon, Herbert A., “Organizations and Markets.” Journal of Economic Perspectives 5(2), Spring 1991, pp. 25–44.

Smith, Vernon L., “An Experimental Study of Competitive Market Behavior.” Journal of Political Economy 70(2), April 1962, pp. 111–39.

Williamson, Oliver, The Economic Institutions of Capitalism. New York: Free Press, 1985.

to, today’s teenagers slack off and cause trouble. To address this problem, I propose to raise the state’s minimum wage by $1.50 per hour. This will give teens the proper incen- tive to go out and find meaningful employment when they are not in school.” Evaluate the governor’s plan to reduce juvenile delinquency. (LO3, LO4, LO5)

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64

3 LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Apply various elasticities of demand as a quantitative tool to forecast changes in revenues, prices, and/or units sold.

LO2 Illustrate the relationship between the elasticity of demand and total revenues.

LO3 Discuss three factors that influence whether the demand for a given prod- uct is relatively elastic or inelastic.

LO4 Explain the relationship between marginal revenue and the own price elas- ticity of demand.

LO5 Show how to determine elasticities from linear and log-linear demand functions.

LO6 Explain how regression analysis may be used to estimate demand func- tions, and how to interpret and use the output of a regression.

Quantitative Demand Analysis

headLINE Walmart Hoping for Another Big Holiday Showing In October of every year, Walmart’s national sales director knows the calls are coming for his holiday forecasts. This year, the firm’s holiday performance is especially important, after disappointing sales to date. 

While the director has no problem expressing his hope for strong holiday sales, investors and reporters—as well as local managers—are seeking a prediction that has evidence to back it. Consequently, he turns to his analytics department, which has been collecting wide swaths of data for Walmart over many years across the 381 metropolitan statis- tical areas (MSAs) in the United States. Some variables of particular interest include holi- day sales, average prices, and consumer confidence. Using these data, the analysts arrive at the following equation, designed to predict HolidaySales (measured as revenues):

ln ( HolidaySales ) = 25.8 − 0.8 ln ( Price ) + 0.9 ln ( ConsumerConfidence )

The director notes that most MSAs saw a decrease in consumer confidence of approx- imately 4 percent. Based on this information, does the evidence support optimism for holi- day sales if prices remain unchanged? Could a change in price help to bolster revenues?

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INTRODUCTION

In Chapter 2 we saw that the demand for a firm’s product ( Q x d ) depends on its price (Px), the prices of substitutes or complements (Py), consumer incomes (M), and other variables (H) such as advertising, the size of the population, or consumer expectations:

Q x d = f ( P x , P y , M, H )

Until now, our analysis of the impact of changes in prices and income on consumer demand has been qualitative rather than quantitative; that is, we focused on the “big picture” to iden- tify only the directions of the changes and said little about their magnitude.

While seeing the big picture is an important first step to sound managerial decisions, the suc- cessful manager is also adept at providing “detailed” quantitative answers to questions like these:

∙ How much do we have to cut our price to achieve 3.2 percent sales growth? ∙ If we cut prices by 6.5 percent, how many more units will we sell? Do we have suf-

ficient inventories on hand to accommodate this increase in sales? If not, do we have enough personnel to increase production? How much will our revenues and cash flows change as a result of this price cut?

∙ How much will our sales change if rivals cut their prices by 2 percent or a recession hits and household incomes decline by 2.5 percent?

The first half of this chapter shows how a manager can use elasticities of demand as a quan- titative forecasting tool to answer these and hundreds of other questions asked each day by managers in charge of pricing decisions, inventory management, yield (revenue) manage- ment, production decisions, strategic (competitor) analysis, and other operations including human resource management.

The second half of the chapter describes regression analysis, which is the primary method economists use to estimate the parameters of demand functions. The primary focus is on how a manager can use managerial economics to evaluate information available in the library or provided by the firm’s research department. Accordingly, we will explain how to interpret regression results and how managers can use regression tools contained in spreadsheet pro- grams like Excel to actually estimate simple demand relationships.

THE ELASTICITY CONCEPT

Suppose some variable, such as the price of a product, increased by 10 percent. What would happen to the quantity demanded of the good? Based on the analysis in Chapter 2 and the law of demand, we know that the quantity demanded would fall. It would be useful for a manager to know whether the quantity demanded would fall by 5 percent, 10 percent, or some other amount.

The primary tool used to determine the magnitude of such a change is elasticity analysis. Indeed, the most important concept introduced in this chapter is elasticity. Elasticity is a very general concept. An elasticity measures the responsiveness of one variable to changes in another variable. For example, the elasticity of your grade with respect to studying, denoted EG, S, is the percentage change in your grade (%ΔG) that will result from a given percentage change in the time you spend studying (%ΔS). In other words,

E G, S = %ΔG

_____ %ΔS

elasticity A measure of the responsiveness of one variable to changes in another variable; the percentage change in one variable that arises due to a given percentage change in another variable.

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Since %ΔG = ΔG/G and %ΔS = ΔS/S, we may also write this as EG, S = (ΔG/ΔS) × (S/G). Notice that ΔG/ΔS represents the slope of the functional relation between G and S; it tells the change in G that results from a given change in S. By multiplying this by S/G, we convert each of these changes into percentages, which means that the elasticity measure does not depend on the units in which we measure the variables G and S.

A C A L C U L U S A L T E R N A T I V E If the variable G depends on S according to the functional relationship G = f(S), the elasticity of G with respect to S may be found using calculus:

E G, S = dG

___ dS

S __

G

Two aspects of an elasticity are important: (1) whether it is positive or negative and (2) whether it is greater than 1 or less than 1 in absolute value. The sign of the elasticity deter- mines the relationship between G and S. If the elasticity is positive, an increase in S leads to an increase in G. If the elasticity is negative, an increase in S leads to a decrease in G.

Whether the absolute value of the elasticity is greater or less than 1 determines how responsive G is to changes in S. If the absolute value of the elasticity is greater than 1, the numerator is larger than the denominator in the elasticity formula, and we know that a small percentage change in S will lead to a relatively large percentage change in G. If the absolute value of the elasticity is less than 1, the numerator is smaller than the denominator in the elas- ticity formula. In this instance, a given percentage change in S will lead to a relatively small percentage change in G. It is useful to keep these points in mind as we define some specific elasticities.

OWN PRICE ELASTICITY OF DEMAND

We begin with a very important elasticity concept: the own price elasticity of demand, which measures the responsiveness of quantity demanded to a change in price. Later in this section we will see that managers can use this measure to determine the quantitative impact of price hikes or cuts on the firm’s sales and revenues. The own price elasticity of demand for good X, denoted EQx, Px, is defined as

E Q x , P x = %Δ Q x

d ______

%Δ P x

If the own price elasticity of demand for a product is −2, for instance, we know that a 10 percent increase in the product’s price leads to a 20 percent decline in the quantity demanded of the good since −20%/10% = −2.

A C A L C U L U S A L T E R N A T I V E The own price elasticity of demand for a good with a demand function Q x

d = f( P x , P y , M, H ) may be found using calculus:

E Q x , P x = ∂ Q x

d ____

∂ P x

P x ___ Q x

Recall that two aspects of an elasticity are important: (1) its sign and (2) whether it is greater or less than 1 in absolute value. By the law of demand, there is an inverse relation

own price elasticity of demand A measure of the responsiveness of the quantity demanded of a good to a change in the price of that good; the percentage change in quantity demanded divided by the percentage change in the price of the good.

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between price and quantity demanded; thus, the own price elasticity of demand is a negative number. The absolute value of the own price elasticity of demand can be greater or less than 1 depending on several factors that we will discuss next. However, it is useful to introduce some terminology to aid in this discussion.

First, demand is said to be elastic if the absolute value of the own price elasticity is greater than 1:

| E Q x , P x | > 1 Second, demand is said to be inelastic if the absolute value of the own price elasticity is

less than 1:

| E Q x , P x | < 1 Finally, demand is said to be unitary elastic if the absolute value of the own price elas-

ticity is equal to 1:

| E Q x , P x | = 1 Conceptually, the quantity consumed of a good is relatively responsive to a change in the price

of the good when demand is elastic and relatively unresponsive to changes in price when demand is inelastic. This means that price increases will reduce consumption very little when demand is inelastic. However, when demand is elastic, a price increase will reduce consumption considerably.

Elasticity and Total Revenue Table 3–1 shows the hypothetical prices and quantities demanded of software, the own price elasticity, and the total revenue (TR = PxQx) for the linear demand function, Q x

d = 80 − 2 P x . Notice that the absolute value of the own price elasticity gets larger as price increases. In par- ticular, the slope of this linear demand function is constant ( Δ Q x d /Δ P x = −2 ) , which implies that E Q x , P x = ( Δ Q x

d /Δ P x ) ( P x / Q x ) increases in absolute value as Px increases. Thus, the own price elasticity of demand varies along a linear demand curve.

elastic demand Demand is elastic if the absolute value of the own price elasticity is greater than 1.

inelastic demand Demand is inelastic if the absolute value of the own price elasticity is less than 1.

unitary elastic demand Demand is unitary elastic if the absolute value of the own price elasticity is equal to 1.

Table 3–1 Total Revenue and Elasticity ( Q x

d = 80 − 2 P x )

Price of Software

(Px)

Quantity of Software Sold

(Qx)

Own Price Elasticity

(EQx, Px  )

Total Revenue

(Px Qx)

A $ 0 80    0.00 $    0

B 5 70 −0.14   350 C 10 60 −0.33   600 D 15 50 −0.60   750 E 20 40 −1.00   800 F 25 30 −1.67   750 G 30 20 −3.00   600 H   35 10 −7.00   350 I   40   0     −∞       0

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When the absolute value of the own price elasticity is less than 1 (points A through D in Table 3–1), an increase in price increases total revenue. For example, an increase in price from $5 to $10 per unit increases total revenue by $250. Notice that for these two prices, the corresponding elasticity of demand is less than 1 in absolute value.

When the absolute value of the own price elasticity is greater than 1 (points F through I in Table 3–1), an increase in price leads to a reduction in total revenue. For example, when the price increases from $25 (where the own price elasticity is −1.67) to $30 (where the own price elasticity is −3), we see that total revenue decreases by $150. The price–quantity combi- nation that maximizes total revenue in Table 3–1 is at point E, where the own price elasticity equals −1.

The demand curve corresponding to the data in Table 3–1 is presented in the top panel of Figure 3–1, while the total revenue associated with each price–quantity combination on the demand curve is graphed in the lower panel. As we move up the demand curve from point A to point I, demand becomes increasingly elastic. At point E, where demand is unitary elas- tic, total revenue is maximized. At points to the northwest of E, demand is elastic and total revenue decreases as price increases. At points to the southeast of E, demand is inelastic and total revenue increases when price increases. This relationship among the changes in price, elasticity, and total revenue is called the total revenue test.

Figure 3–1 Demand, Elasticity, and Total Revenue

0

Total revenue

$

Quantity 10 20 30 40 50 60 70 80

350

0

Price

Quantity

Elastic

A

10 20 30 40 50 60 70 80

5 10 15 20 25 30 35 40

B C

D E

F G

H I

Demand

Inelastic

Unitary elastic

90

600

750 800

Total revenue

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Businesses around the globe use the total revenue test to help manage cash flows. For instance, Dell recently faced a dilemma regarding its pricing strategy for computers: Should it increase prices to boost cash flow or adopt a “cut price and make it up in volume” strategy? Based on a careful analysis of its demand, the company decided to adopt the latter strategy and reduced prices in order to increase revenues.

To see why, suppose the research department of a computer company estimates that the own price elasticity of demand for a particular desktop computer is −1.7. If the company cuts prices by 5 percent, will computer sales increase enough to increase overall revenues? We can answer this question by setting −1.7 = EQx, Px and −5 = %ΔPx in the formula for the own price elasticity of demand:

−1.7 = %Δ Q x

d ______

−5

Solving this equation for %Δ Q x d yields %Δ Q x

d = 8.5 . In other words, the quantity of computers sold will rise by 8.5 percent if prices are reduced by 5 percent. Since the percentage increase in quantity demanded is greater than the percentage decline in prices ( | EQx, Px | > 1), the price cut will actually raise the firm’s sales revenues. Expressed differently, since demand is elastic, a price cut results in a greater than proportional increase in sales and thus increases the firm’s total revenues.

In extreme cases the demand for a good may be perfectly elastic or perfectly inelastic. Demand is perfectly elastic if the own price elasticity of demand is infinite in absolute value. Demand is perfectly inelastic if the own price elasticity of demand is zero.

When demand is perfectly elastic, a manager who raises price even slightly will find that none of the good is purchased. In this instance the demand curve is horizontal, as illustrated in Figure 3–2(a). Producers of generic (unbranded) products, such as aspirin, may face a demand

perfectly elastic demand Demand is perfectly elastic if the own price elasticity is infinite in absolute value. In this case the demand curve is horizontal.

perfectly inelastic demand Demand is perfectly inelastic if the own price elasticity is zero. In this case the demand curve is vertical.

P R I N C I P L E

Total Revenue Test If demand is elastic, an increase (decrease) in price will lead to a decrease (increase) in total reve- nue. If demand is inelastic, an increase (decrease) in price will lead to an increase (decrease) in total revenue. Finally, total revenue is maximized at the point where demand is unitary elastic.

Figure 3–2 Perfectly Elastic and Inelastic Demand

0

D

Perfectly Inelastic

(b)

0

Price Price

Quantity Quantity

D

Perfectly Elastic

(a)

E Q

x , P

x = – ∞ E

Q x , P

x = 0

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curve that is perfectly elastic; a small increase in price may induce their customers to stop buying their product, in favor of a competing generic version of the product. In contrast, when demand is perfectly inelastic, consumers do not respond at all to changes in price. In this case the demand curve is vertical, as shown in Figure 3–2(b). Many perceive products and services in the health care industry (such as life-saving drugs) to have demand curves that are perfectly inelastic. While many have highly inelastic demand curves, they generally are not perfectly inelastic (see Inside Business 3–2 for a more thorough discussion).

Usually, demand is neither perfectly elastic nor perfectly inelastic. In these instances knowledge of the particular value of an elasticity can be useful for a manager. Large firms,

While in many instances managers can obtain estimates of elasticities from the library or the firm’s research staff, sometimes managers are confronted with situations where elasticity estimates are not readily available. Fortunately, all is not lost in these instances thanks to a concept called the arc elasticity of demand.

To be specific, suppose a manager has data that show when the price of some good was P1, consumers purchased Q1 units of the good, and when the price changed to P2, Q2 units were purchased. Other things equal, these data can be used to approximate the own price elasticity of demand for the good by using the arc elasticity formula:

E Arc = Δ Q d

____ ΔP

× Average P

__________ Average Q

In the formula, the average Q is (Q1 + Q2)/2 and the average P is (P1 + P2)/2.

In order to illustrate how this formula can be used to compute an elasticity based on real-world data, we can analyze data on sales and price for existing single-fam- ily homes in the United States. According to the National Association of Realtors, the median sales price for such homes in October was $160,800, and at this price 343,000 homes were sold. Thus, P1 = $160,800 and Q1 = 343,000 represent one point on the demand curve—the price and quantity of existing single-family homes in October.

Similarly, P2 = $164,000 and Q2 = 335,000 represent the price and quantity of existing single-family homes one month later. Interest rates and income—the two primary determinants of the demand for housing—were roughly constant between October and November. Thus, it is rea- sonable to assume that demand was stable (did not shift)

over this one-month period, and that this price–quantity pair represents another point on the demand curve for single-family homes in the United States.

Based on these two points on the demand curve, we may approximate the own price elasticity of demand for existing single-family homes in the United States by using the arc elasticity formula:

E   Arc = (Q1 − Q2)(P1 + P2)/2 __________________ (P1 − P2)(Q1 + Q 2)/2

= 343,000 − 335,000

___________________ 160,800 − 164,000

× (160,800 + 164,000)/2

_____________________ (343,000 + 335,000)/2

= −1.2 The own price elasticity of demand is greater than 1 in

absolute value, so by the total revenue test we know that the increase in housing prices over the period resulted in lower total expenditures on housing. We might also spec- ulate that the incomes of real estate agents fell over this period due to the lower real estate commissions generated by these reduced expenditures on housing.

It is important to point out that the arc elasticity technique described here only approximates the true elasticity of demand for housing. The accuracy of the approximation depends cru- cially on the assumption that the demand curve did not shift between October and November. If the demand for single- family housing in the United States shifted over the period, due to unusually good househunting weather, for instance, then the true elasticity of demand will differ from our approximation.

SOURCE: www.realtor.org/topics/existing-home-sales/data

INSIDE BUSINESS 3–1

Calculating and Using the Arc Elasticity: An Application to the Housing Market

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the government, and universities commonly hire economists or statisticians to estimate the demand for products. The manager’s job is to know how to interpret and use such estimates.

Factors Affecting the Own Price Elasticity Now that you understand what the own price elasticity is and how it can be used to assess the impact of price changes on sales volume and revenues, we will discuss three factors that affect the magnitude of the own price elasticity of a good: available substitutes, time, and expenditure share.

Available Substitutes One key determinant of the elasticity of demand for a good is the number of close substitutes for that good. Intuitively, the more substitutes available for the good, the more elastic the demand for it. In these circumstances, a price increase leads consumers to substitute toward another product, thus reducing considerably the quantity demanded of the good. When there are few close substitutes for a good, demand tends to be relatively inelastic. This is because consumers cannot readily switch to a close substitute when the price increases.

A key implication of the effect of the number of close substitutes on the elasticity of demand is that the demand for broadly defined commodities tends to be more inelastic than the demand for specific commodities. For example, the demand for food (a broad commodity) is more inelastic than the demand for beef. Short of starvation, there are no close substitutes for food, and thus the quantity demanded of food is much less sensitive to price changes than is a particular type of food, such as beef. When the price of beef increases, consumers can substitute toward other types of food, including chicken, pork, and fish. Thus, the demand for beef is more elastic than the demand for food.

Table 3–2 shows some own price elasticities from market studies in the United States. These studies reveal that broader categories of goods indeed have more inelastic demand than more specifically defined categories. The own price elasticity of food is slightly inelastic, whereas the elasticity of cereal, a more specific type of food, is elastic. We would expect this outcome because there are many substitutes for cereal, but no substitutes exist for food. Table 3–2 also reveals that the demand for women’s clothing is more elastic than the demand for clothing in general (a broader category).

Table 3–2 Selected Own Price Elasticities

Market Own Price Elasticity

Transportation −0.6 Motor vehicles −1.4 Motorcycles and bicycles −2.3 Food −0.7 Cereal −1.5 Clothing −0.9 Women’s clothing −1.2

Sources: M. R. Baye, D. W. Jansen, and J. W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992), pp. 1087–96; W. S. Commanor and T. A. Wilson, Advertising and Market Power (Cambridge, MA: Harvard University Press, 1974).

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Finally, consider the reported estimates of the own price elasticities for motorcycles and bicycles, motor vehicles, and transportation. Transportation is the most broadly defined group, followed by motor vehicles and then motorcycles and bicycles. Therefore, we would expect the demand for motorcycles and bicycles to be more elastic than the demand for motor vehicles and the demand for motor vehicles to be more elastic than the demand for trans- portation. The numbers in Table 3–2 are consistent with these expectations; market studies support the statement that demand is more elastic when there are more close substitutes for a product.

Time Demand tends to be more inelastic in the short term than in the long term. The more time con- sumers have to react to a price change, the more elastic the demand for the good. Conceptually, time allows the consumer to seek out available substitutes. For example, if a consumer has 30 minutes to catch a flight, he or she is much less sensitive to the price charged for a taxi ride to the airport than would be the case if the flight were several hours later. Given enough time, the consumer can seek alternative modes of transportation such as a bus, a friend’s car, or even on foot. But in the short term, the consumer does not have time to seek out the available substitutes, and the demand for taxi rides is more inelastic.

Table 3–3 presents short-term and long-term own price elasticities for transportation, food, alcohol and tobacco, recreation, and clothing. Notice that all the short-term elasticities are less (in absolute value) than the corresponding long-term elasticities. In the short term, all the own price elasticities are less than 1 in absolute value, with the exception of the own price elasticity for recreation. The absolute values of the long-term own price elasticities are all greater than 1, except for alcohol and tobacco.

Expenditure Share Goods that comprise a relatively small share of consumers’ budgets tend to be more inelastic than goods for which consumers spend a sizable portion of their incomes. In the extreme case, where a consumer spends her or his entire budget on a good, the consumer must decrease consumption when the price rises. In essence, there is nothing to give up but the good itself. When a good comprises only a small portion of the budget, the consumer can reduce the con- sumption of other goods when the price of the good increases. For example, most consumers spend very little on salt; a small increase in the price of salt would reduce quantity demanded very little since salt constitutes a small fraction of consumers’ total budgets.

Table 3–3 Selected Short- and Long-Term Own Price Elasticities

Market Short-Term Own Price Elasticity

Long-Term Own Price Elasticity

Transportation −0.6 −1.9 Food −0.7 −2.3 Alcohol and tobacco −0.3 −0.9 Recreation −1.1 −3.5 Clothing −0.9 −2.9

Source: M. R. Baye, D. W. Jansen, and J. W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992), pp. 1087–96.

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Would you expect the own price elasticity of demand for food to be more or less elastic than that for transportation? Since food is a much greater necessity than transportation (after all, you cannot live without food), you might expect the demand for food to be more inelastic than the demand for transportation. However, Table 3–3 reveals that the demand for transpor- tation is more inelastic (in both the short and long term) than the demand for food. How can this be true?

The answer lies in the percentage of income Americans spend on food and transportation. The average U.S. consumer spends almost four times as much on food as on transportation. Even though food is more “important” in a biological sense than transportation, the demand for food tends to be more elastic because a much larger proportion of people’s budgets is spent on food.

Marginal Revenue and the Own Price Elasticity of Demand We learned in Chapter 1 that marginal revenue (MR) is the change in total revenue due to a change in output, and that to maximize profits a firm should produce where marginal reve- nue equals marginal cost. We will explore profit-maximizing output and pricing decisions in detail later in this book, but it is useful at this point to show how a firm’s marginal revenue is linked to the own price elasticity of demand for the firm’s product.

The line labeled MR in Figure 3–3 is the marginal revenue associated with each price– output pair on the demand curve. Notice that for a linear demand curve, the marginal revenue schedule lies exactly halfway between the demand curve and the vertical axis. Furthermore, marginal revenue is less than the price for each unit sold.

Why is marginal revenue less than the price charged for the good? To induce consumers to purchase more of a good, a firm must lower its price. When the firm charges the same price for each unit sold, this lower price is received not only on the last unit sold, but also on those units that could have been sold at a higher price had the firm not lowered its price. To be concrete, suppose consumers purchase 1 unit of output at a price of $5 per unit, for total expenditures (revenues to producers) of $5 × 1 = $5. Consumers will purchase an additional unit of the good only if the price falls, say from $5 to $4 per unit. Now the firm receives $4 on the first unit sold and $4 on the second unit sold. In effect, the firm loses $1 in revenue

Figure 3–3 Demand and Marginal Revenue

Price

Elastic

Inelastic

Unitary

3

P

MR

6

D

1 6 MR

Quantity

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because the first unit now brings $4 instead of $5. Total revenue rises from $5 to $8 as output is increased by 1 unit, so marginal revenue is $8 − $5 = $3, which is less than price.

Notice in our example that by decreasing price from $5 to $4, quantity demanded increased from 1 unit to 2 units, and total revenues increased from $5 to $8. By the total reve- nue test, this means that demand is elastic over this range. In contrast, had the price reduction increased quantity demanded but decreased total revenues, demand would be inelastic over the range and marginal revenue would be negative. In fact, the more inelastic the demand for a product, the greater the decline in revenue that results from a price cut, despite the increased quantity demanded.

This intuition leads to the following general relationship between marginal revenue and the elasticity of demand:

MR = P [ 1 + E

_____ E

]

This formula, which is formally derived in Chapter 8, simplifies notation by dropping subscripts: P is the price of the good and E is the own price elasticity of demand for the good. Notice that when −∞ < E < −1, demand is elastic, and the formula implies that MR is posi- tive. When E = −1, demand is unitary elastic, and marginal revenue is zero. As we learned in Chapter 1, the point where marginal revenue is zero corresponds to the output at which total revenue is maximized. Finally, when −1 < E < 0, demand is inelastic, and marginal revenue is negative. These general results are consistent with what you saw earlier in Table 3–1 for the case of linear demand.

Many people perceive the demand for prescription drugs and other pharmaceutical products to be perfectly inelas- tic. After all, a patient needing an expensive cardiovascular drug might die in the absence of treatment. Moreover, in many instances the cost of medication is paid by an insur- ance company and not by the patient. These two factors do tend to make the demand for many pharmaceutical prod- ucts relatively inelastic. However, since surgery and lifestyle changes are substitutes for many life-saving drugs, eco- nomic theory predicts that the demand for such products is unlikely to be perfectly inelastic.

The accompanying table summarizes results from two classical studies that confirm this prediction: The demand for pharmaceutical products is inelastic, but not perfectly so. For instance, the own price elasticity of demand for anti-ulcer drugs is –0.7, while the own price elasticity of demand for cardiovascular drugs is slightly more inelastic at –0.4. Consequently, a 10 percent increase in the price of anti-ulcer drugs reduces their use by 7 percent. A 10 percent

increase in the price of cardiovascular drugs results in only a 4 percent reduction in quantity demanded.

The own price elasticities of demand reported here are based on the industry demand for each type of drug. The demand for particular brands within each industry is even more responsive to price changes.

SOURCES: M. Baye, R. Maness, and S. Wiggins, “Demand Systems and the True Subindex of the Cost of Living for Pharmaceuticals,” Applied Economics 29 (1997), pp. 1179–89; and E. Berndt, L. Bui, D. Reiley, and G. Urban, “Information, Marketing, and Pricing in the U.S. Anti-ulcer Drug Market,” American Economic Review 85, no. 2 (May 1995), pp. 100–5.

INSIDE BUSINESS 3–2

Inelastic Demand for Prescription Drugs

Type of Drug Own Price Elasticity

Cardiovascular −0.4 Anti-infective −0.9 Psychotherapeutic −0.3 Anti-ulcer −0.7

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CROSS-PRICE ELASTICITY

Another important elasticity is the cross-price elasticity of demand, which reveals the respon- siveness of the demand for a good to changes in the price of a related good. This elasticity helps managers ascertain how much its demand will rise or fall due to a change in the price of another firm’s product. The cross-price elasticity of demand between goods X and Y, denoted EQx, Py, is mathematically defined as

E Q x , P y = %Δ Q x

d ______

%Δ P y

For instance, if the cross-price elasticity of demand between Corel WordPerfect and Microsoft Word word processing software is 3, a 10 percent hike in the price of Word will increase the demand for WordPerfect by 30 percent since 30%/10% = 3. This increase in demand for WordPerfect occurs because consumers substitute away from Word and toward WordPerfect, due to the price increase.

A C A L C U L U S A L T E R N A T I V E When the demand function is Q x

d = f( P x , P Y , M, H ) , the cross-price elasticity of demand between goods X and Y may be found using calculus:

E Q x , P y = ∂ Q x

d ____

∂ P y

P y ___ Q x

More generally, whenever goods X and Y are substitutes, an increase in the price of Y leads to an increase in the demand for X. Thus, EQx, Py > 0 whenever goods X and Y are substi- tutes. When goods X and Y are complements, an increase in the price of Y leads to a decrease in the demand for X. Thus, EQx, Py < 0 whenever goods X and Y are complements.

Table 3–4 provides some representative cross-price elasticities. For example, clothing and food have a cross-price elasticity of –0.18. This means that if the price of food increases by 10 percent, the demand for clothing will decrease by 1.8 percent; food and clothing are complements. More important, these data provide a quantitative measure of the impact of a change in the price of food on the consumption of clothing.

Based on the data summarized in Table 3–4, are food and recreation complements or sub- stitutes? If the price of recreation increased by 15 percent, what would happen to the demand for food? These questions are embedded in the following problem.

cross-price elasticity A measure of the responsiveness of the demand for a good to changes in the price of a related good; the percentage change in the quantity demanded of one good divided by the percentage change in the price of a related good.

Table 3–4 Selected Cross-Price Elasticities

  Cross-Price Elasticity

Transportation and recreation −0.05 Food and recreation   0.15

Clothing and food −0.18

Source: M. R. Baye, D. W. Jansen, and J. W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992), pp. 1087–96.

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Cross-price elasticities play an important role in the pricing decisions of firms that sell multiple products. Indeed, many fast-food restaurants offer hamburgers for under $1.00 because their managers realize that hamburgers and sodas are complements: When consumers buy a hamburger, a soda typically accompanies the purchase. Thus, by lowering the price of burgers, a restaurant affects its revenues from both burger sales and soda sales. The precise impact on these revenues depends on the own price and cross-price elasticities of demand.

Specifically, we know from the total revenue test that a reduction in the price of ham- burgers will increase (decrease) revenues from hamburger sales when the own price elasticity of demand for hamburgers is elastic (inelastic). In addition, since hamburgers and sodas are complements, reducing the price of hamburgers increases the quantity demanded of sodas, thus increasing soda revenues. The magnitude of the increase in soda revenues will depend on the magnitude of the cross-price elasticity of demand between burgers and soda.

More generally, suppose a firm’s revenues are derived from the sales of two products, X and Y. We may express the firm’s revenues as R = Rx + Ry, where Rx = PxQx denotes revenues from the sale of product X and Ry = PyQy represents revenues from product Y. The impact of a small percentage change in the price of product X (%ΔPx = ΔPx/Px) on the total revenues of the firm is

1

ΔR = [ R x (1 + E Q x , P x ) + R y E Q y , P x ] × %Δ P x

To illustrate how to use this formula, suppose a restaurant earns $4,000 per week in rev- enues from hamburger sales (product X) and $2,000 per week from soda sales (product Y). Thus, Rx = $4,000 and Ry = $2,000. If the own price elasticity of demand for burgers is EQx, Px = −1.5 and the cross-price elasticity of demand between sodas and hamburgers is EQx, Px = −4.0, what would happen to the firm’s total revenues if it reduced the price of hamburgers by 1 percent? Plugging these numbers into the formula reveals

ΔR

=

[ $4,000 ( 1 − 1.5 ) + $2,000 ( − 4.0 ) ] ( − 1% )

= $20 + $80

= $100

1This formula is an approximation for large changes in price.

DEMONSTRATION PROBLEM 3–1

You have just opened a new grocery store. Every item you carry is generic (generic beer, generic bread, generic chicken, etc.). You recently read an article in the Wall Street Journal reporting that the price of recreation is expected to increase by 15 percent. How will this affect your store’s sales of generic food products?

ANSWER: Table 3–4 reveals that the cross-price elasticity of demand for food and recreation is 0.15. If we insert the given information into the formula for the cross-price elasticity, we get

0.15 = %Δ Q x

d ______

15

Solving this equation for %Δ Q x d , we get

%Δ Q x d = 2.25

Thus, food and recreation are substitutes. If the price of recreation increases by 15 percent, you can expect the demand for generic food products to increase by 2.25 percent.

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In other words, lowering the price of hamburgers 1 percent increases total revenues by $100. Notice that $20 of this increase comes from increased burger revenues (the demand for burg- ers is elastic, so the reduction in the price of burgers increases hamburger revenues) and $80 of the increase is from additional soda sales (the demand for soda increases by 4 percent, resulting in additional revenues of $80 from soft drink sales).

INCOME ELASTICITY

Income elasticity is a measure of the responsiveness of consumer demand to changes in income. Mathematically, the income elasticity of demand, denoted EQx, M, is defined as

E Q x , M = %Δ Q x

d ______

%ΔM

A C A L C U L U S A L T E R N A T I V E The income elasticity for a good with a demand function Q x

d = f( P x , P y , M, H ) may be found using calculus:

E Q x , M = ∂ Q x

d ____

∂ M

M ___

Q x

When good X is a normal good, an increase in income leads to an increase in the con- sumption of X. Thus, EQx, M > 0 when X is a normal good. When X is an inferior good, an increase in income leads to a decrease in the consumption of X. Thus, EQx, M < 0 when X is an inferior good.

income elasticity A measure of the responsiveness of the demand for a good to changes in consumer income; the percentage change in quantity demanded divided by the percentage change in income.

At the close of the last century, increases in the price of gas- oline led to decreases in demand for products that are com- plements for gasoline, such as automobiles. The reason was that higher gasoline prices moved consumers to sub- stitute toward public transportation, bicycling, and walking. An econometric study by Patrick McCarthy provides quan- titative information about the impact of fuel costs on the demand for automobiles. One of the more important deter- minants of the demand for automobiles is the fuel operating cost, defined as the cost of fuel per mile driven. The study reveals that for each 1 percent increase in fuel costs, the demand for automobiles will decrease by 0.214 percent. A 10 percent increase in the price of gasoline increases the cost of fuel per mile driven by 10 percent and thus reduces the demand for a given car by 2.14 percent.

What did automakers do during this period to mitigate the negative impact of rising gasoline prices on the demand for new automobiles? They made cars more fuel efficient. The results just summarized imply that for every 10 per- cent increase in fuel efficiency (measured by the increase in miles per gallon), the demand for automobiles increases by 2.14 percent. Auto manufacturers could completely offset the negative impact of higher gasoline prices by increasing the fuel efficiency of new cars by the same percentage as the increase in gasoline prices. In fact, by increasing fuel efficiency by a greater percentage than the increase in gasoline prices, they would actually increase the demand for new automobiles.

SOURCE: Patrick S. McCarthy, “Consumer Demand for Vehicle Safety: An Empirical Study,” Economic Inquiry 28 (July 1990), pp. 530–43.

INSIDE BUSINESS 3–3

Using Cross-Price Elasticities to Improve New Car Sales in the Wake of Increasing Gasoline Prices

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Table 3–5 presents some classic estimates of income elasticities for various products. Consider, for example, the income elasticity for transportation, 1.8. This number gives us two important pieces of information about the relationship between income and the demand for transportation. First, since the income elasticity is positive, we know that consumers increase the amount they spend on transportation when their incomes rise. Transportation thus is a normal good. Second, since the income elasticity for transportation is greater than 1, we know that expenditures on transportation grow more rapidly than income.

The second row of Table 3–5 reveals that food also is a normal good since the income elasticity of food is 0.8. Since the income elasticity is less than 1, an increase in income will increase the expenditure on food by a lower percentage than the percentage increase in income. When income declines, expenditures on food decrease less rapidly than income.

The third row of Table 3–5 presents the income elasticity for nonfed ground beef. Nonfed beef comes from cattle that have not been fed a special diet. Most cattle are fed corn for 90 to 120 days before going to market and thus produce more tender beef than nonfed cattle. The income elasticity for nonfed ground beef is negative; hence, we know that nonfed ground beef is an inferior good. The consumption of nonfed ground beef will decrease by 1.94 percent for every 1 percent rise in consumer income. Therefore, managers of grocery stores should decrease their orders of nonfed ground beef during economic booms and increase their orders during recessions.

DEMONSTRATION PROBLEM 3–2

Your firm’s research department has estimated the income elasticity of demand for nonfed ground beef to be −1.94. You have just read in The Wall Street Journal that due to an upturn in the economy, consumer incomes are expected to rise by 10 percent over the next three years. As a manager of a meat-processing plant, how will this forecast affect your purchases of nonfed cattle?

ANSWER: Set EQx, M = −1.94 and %ΔM = 10 in the formula for the income elasticity of demand to obtain

−1.94 = %Δ Q x

d ______

10

Solving this equation for %Δ Q x d yields −19.4. Since nonfed ground beef has an income elasticity

of −1.94 and consumer income is expected to rise by 10 percent, you can expect to sell 19.4 percent less nonfed ground beef over the next three years. Therefore, you should decrease your purchases of nonfed cattle by 19.4 percent, unless something else changes.

v Table 3–5 Selected Income Elasticities

  Income Elasticity

Transportation 1.80

Food 0.80

Ground beef, nonfed −1.94

SOURCES: M. R. Baye, D. W. Jansen, and J. W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992), pp. 1087–96; G. W. Brester and M. K. Wohlsenant, “Estimating Interrelated Demands for Meats Using New Measures for Ground and Table Cut Beef,” American Journal of Agricultural Economics 73 (November 1991), p. 21.

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OTHER ELASTICITIES

Given the general notion of an elasticity, it is not difficult to conceptualize how the impact of changes in other variables, such as advertising, may be analyzed in elasticity terms. For example, the own advertising elasticity of demand for good X is the ratio of the percentage change in the consumption of X to the percentage change in advertising spent on X. The cross-advertising elasticity between goods X and Y would measure the percentage change in the consumption of X that results from a 1 percent change in advertising directed toward Y.

v Table 3–6 Selected Long-Term Advertising Elasticities

  Advertising Elasticity

Clothing 0.04

Recreation 0.25

SOURCE: M. R. Baye, D. W. Jansen, and J. W. Lee, “Advertising Effects in Complete Demand Systems,” Applied Economics 24 (1992), pp. 1087–96.

Table 3–6 shows estimates of the advertising elasticities for clothing and recreation. Both elasticities are positive and less than 1. The fact that they are positive reveals, as you might expect, that increases in advertising lead to an increase in the demand for the products; that is, if clothing manufacturers increase their advertising, they can expect to sell more clothing at any given price. However, the fact that the advertising elasticity of clothing is 0.04 means that a 10 percent increase in advertising will increase the demand for clothing by only 0.4 percent. As a broad category, clothing is not very advertising elastic.

To illustrate how managers can use estimates such as these, imagine that you have just been hired by the U.S. Department of Commerce to help direct the tourist trade in the United States. Your boss knows you recently took a course in managerial economics and asks you how much she should increase advertising to increase the demand for recreation in the United States by 15 percent.

From Table 3–6, we know that EQx Ax = 0.25. Plugging this and %Δ Q x d = 15 into the gen-

eral formula for the elasticity of Q x d with respect to Ax yields

0.25 = %Δ Q x

d ______

%Δ A x =

15 ______

%Δ A x

Solving this equation for the percentage change in advertising shows that advertising must increase by a hefty 60 percent to increase the demand for recreation by 15 percent.

OBTAINING ELASTICITIES FROM DEMAND FUNCTIONS

Now that you understand what elasticities are and how to use them to make managerial deci- sions, we will examine how to calculate elasticities from demand functions. First, we will consider elasticities based on linear demand functions. Then we will see how to calculate elasticities from particular nonlinear demand functions.

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Elasticities for Linear Demand Functions Given an estimate of a linear demand function, it is quite easy to calculate the various elastic- ities of demand.

Formula: Elasticities for Linear Demand. If the demand function is linear and given by

Q x d = α 0 + α x P x + α y P y + α M M + α H H

the elasticities are

own price elasticity:

E Q x , P x = α x P x ___ Q x

cross-price elasticity: E Q x , P y = α y P y ___ Q x

income elasticity:

E Q x , M = α M M

___ Q x

A C A L C U L U S A L T E R N A T I V E The elasticities for a linear demand curve may be found using calculus. Specifically,

E Q x , P x = ∂ Q x

d ____

∂ P x

P x ___ Q x

= α x P x ___ Q x

and similarly for the cross-price and income elasticities.

Thus, for a linear demand curve, the elasticity of demand with respect to a given variable is simply the coefficient of the variable multiplied by the ratio of the variable to the quantity demanded. For instance, the own price elasticity of demand is simply the coefficient of Px (which is αx in the demand function) multiplied by the ratio of the price of X to the quantity consumed of X.

For a linear demand curve, the value of an elasticity depends on the particular price and quantity at which it is calculated. This means that the own price elasticity is not the same as the slope of the demand curve. In fact, for a linear demand function, demand is elastic at high prices and inelastic at lower prices. To see this, note that when P x = 0, | E Q x , P x | = | α x 0 __ Q x | = 0 < 1 . In other words, for prices near zero, demand is inelastic. On the other hand, when prices rise, Qx decreases and the absolute value of the elasticity increases.

DEMONSTRATION PROBLEM 3–3

The daily demand for Invigorated PED shoes is estimated to be

Q x d = 100 − 3 P x + 4 P y − .01M + 2 A x

where Ax represents the amount of advertising spent on shoes (X), Px is the price of good X, Py is the price of good Y, and M is average income. Suppose good X sells at $25 a pair, good Y sells at $35, the company utilizes 50 units of advertising, and average consumer income is $20,000. Calculate and interpret the own price, cross-price, and income elasticities of demand.

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

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Elasticities for Nonlinear Demand Functions Managers frequently encounter situations where a product’s demand is not a linear function of prices, income, advertising, and other demand shifters. In this section we demonstrate that the tools we developed can easily be adapted to these more complex environments.

Suppose the demand function is not a linear function but instead is given by

Q x d = c P x

β x P y β y M β M H β H

where c is a constant. In this case, the quantity demanded of good X is not a linear function of prices and income but a nonlinear function. If we take the natural logarithm of this equation, we obtain an expression that is linear in the logarithms of the variables:2

ln Q x d = β 0 + β x ln P x + β y ln P y + β M ln M + β H ln H

where β0 = ln(c) and the βi’s are arbitrary real numbers. This relation is called a log-linear demand function.

As in the case of linear demand, the sign of the coefficient of ln Py determines whether goods X and Y are substitutes or complements, whereas the sign of the coefficient of ln M

log-linear demand Demand is log-linear if the logarithm of demand is a linear function of the logarithms of prices, income, and other variables.2 Here, ln denotes the natural logarithm. In some spreadsheets (such as Excel), this function is denoted LN.

ANSWER: To calculate the own price elasticity for linear demand, we use the formula

E Q x , P x = α x P x ___ Q x

Here αx = −3 and Px = 25. The only other information we need to calculate the elasticity is the quan- tity consumed of X. To find Qx, we substitute the given values of prices, income, and advertising into the demand equation to get

Q x d = 100 − 3(25) + 4(35) − .01(20,000) + 2(50) = 65 units

Hence the own price elasticity of demand is given by

E Q x , P x = −3 ( 25

___ 65

) = −1.15

If Invigorated PED raises shoe prices, the percentage decline in the quantity demanded of its shoes will be greater in absolute value than the percentage rise in price. Consequently, demand is elastic: Total revenues will fall if it raises shoe prices.

Similarly, the cross-price elasticity of demand is

E Q x , P y = 4 ( 35

___ 65

) = 2.15

Since this is positive, good Y is a substitute for Invigorated PED shoes. The income elasticity of demand for Invigorated PED’s shoes is

E Q x , M = −0.01 ( 20,000

______ 65

) = −3.08

Invigorated PED’s shoes are inferior goods since this is a negative number.

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determines whether X is a normal or an inferior good. For example, if βy is a positive number, an increase in the price of good Y will lead to an increase in the consumption of good X; in this instance, X and Y are substitutes. If βy is a negative number, an increase in the price of good Y will lead to a decrease in the consumption of good X; in this instance, goods X and Y are com- plements. Similarly, if βM is a positive number, an increase in income leads to an increase in the consumption of good X, and X is a normal good. If βM is a negative number, an increase in income leads to a decrease in the consumption of good X, and X is an inferior good.

Formula: Elasticities for Log-Linear Demand. When the demand function for good X is log-linear and given by

ln Q x d = β 0 + β x ln P x + β y ln P y + β M ln M + β H ln H

the elasticities are

own price elasticity:

E Q x , P x = β x

cross-price elasticity: E Q x , P y = β y income elasticity:

E Q x , M = β M

A C A L C U L U S A L T E R N A T I V E The elasticity formulas for log-linear demand may also be derived using calculus. Taking the antilogarithm of the equation for log-linear demand gives

Q x d = c P x

β x P y β y M β M H β H

where c is a constant. Using the calculus formula for an elasticity yields

E Q x . P x = ∂ Q x

d ____

∂ P x (

P x ___ Q x

) = β x c P x β x −1 P y

β y M β M H β H (

P x ______________

c P x β x P y

β y M β M H β H )

= β x

and similarly for the cross-price and income elasticities.

Notice that when demand is log-linear, the elasticity with respect to a given variable is simply the coefficient of the corresponding logarithm. The own price elasticity of demand is the coefficient of ln (Px), and, in fact, the coefficient of any other logarithm on the right-hand side of the log-linear demand relation tells us the elasticity of demand with respect to that demand shifter. Since all of these coefficients are constants, none of the elasticities depend on the value of variables like prices, income, or advertising.

Table 3–7 shows the results of a statistical study that found the demand for retail gasoline to be log-linear. Since this is a log-linear demand relation, we know that the coefficients may be interpreted as elasticities.

v Table 3–7 The Log-Linear Demand for Retail Gasoline in the United States

SOURCE: Adapted from J. Hughes, C. Knittel, and D. Sperling, “Evidence of a Shift in the Short-Run Price Elasticity of Gasoline Demand,” The Energy Journal 29, no. 1 (2008), pp. 93–114.

ln(QG) = −1.697 − 0.042 ln(PG) + 0.53 ln(Y  ) QG = per capita consumption of gasoline in gallons PG = real retail price of gasoline Y = real per capita disposable income

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The study summarized in Table 3–7 focused on the price elasticity of demand for gasoline for the early 2000s. The coefficient of the logarithm of price is –0.042. This shows that the demand for gasoline is highly inelastic and downward sloping. Furthermore, an increase of 10 percent in the price of retail gasoline will decrease the quantity of retail gasoline demanded by only 0.4 percent, and therefore would raise the revenues of retail gasoline stations. The coefficient of the logarithm of income is 0.53, indicating that retail gasoline is a normal good. A 10 percent increase in consumers’ per capita income would result in a 5.3 percent increase in retail gasoline demand.

As a final check of your ability to utilize elasticities, try to work the following problem.

DEMONSTRATION PROBLEM 3–4

An analyst for a major apparel company estimates that the demand for its raincoats is given by

ln Q x d = 10 − 1.2 ln P x + 3 ln R − 2 ln A y

where R denotes the daily amount of rainfall and Ay represents the level of advertising on good Y. What would be the impact on demand of a 10 percent increase in the daily amount of rainfall? What would be the impact of a 10 percent reduction in the amount of advertising directed toward good Y? Can you think of a good that might be good Y in this example?

ANSWER: We know that for log-linear demand functions, the coefficient of the logarithm of a variable gives the elasticity of demand with respect to that variable. Thus, the elasticity of demand for raincoats with respect to rainfall is

E Q x , R = β R = 3

Furthermore,

E Q x , R = β R = %Δ Q x

d ______

%ΔR

Hence,

3 = %Δ Q x

d ______

10

Solving this equation yields %Δ Q x d = 30 . In other words, the 10 percent increase in rainfall will lead

to a 30 percent increase in the demand for raincoats. To examine the impact on the demand for raincoats of a 10 percent reduction in advertising spent

on good Y, again note that for log-linear demand functions, each coefficient gives the elasticity of demand with respect to that variable. Thus, the elasticity of demand for raincoats with respect to advertising directed toward good Y is

E Q x ,  A y = β A y = −2

Furthermore,

E Q x ,  A y = β A y = %Δ Q x

d ______

%Δ A y

Hence,

−2 = %Δ Q x

d ______

−10

Solving this equation yields %Δ Q x d = 20 . In other words, the 10 percent reduction in advertising

directed toward good Y leads to a 20 percent increase in the demand for raincoats. Perhaps good Y is umbrellas, for one would expect the demand for raincoats to increase whenever fewer umbrella advertisements are made.

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REGRESSION ANALYSIS

The preceding analysis assumes the manager knows the demand for the firm’s product. We pointed out several studies that provide explicit estimates of demand elasticities and func- tional forms for demand functions. As a manager, you may obtain estimates of demand and elasticity from published studies available in the library or from a consultant hired to estimate the demand function based on the specifics of your product. Or you might enter data into a spreadsheet program and click the regression toolbar to obtain an estimated demand function, along with some regression diagnostics. Regardless of how the manager obtains the estimates, it is useful to have a general understanding of how demand functions are estimated and what the various diagnostic statistics that accompany the reported output mean. This entails knowl- edge of a branch of economics called econometrics.

Econometrics is simply the statistical analysis of economic data. It is far beyond the scope of this book to teach you how to estimate demand functions, but it is possible to convey the basic ideas econometricians use to obtain such information. Your primary job as a manager is to use the information to make decisions similar to the examples provided in previous sections of this chapter.

Let us briefly examine the basic ideas underlying the estimation of the demand for a product. Suppose there is some underlying data on the relation between a dependent variable, Y, and some explanatory variable, X. Suppose that when the values of X and Y are plotted, they appear as points A, B, C, D, E, and F in Figure 3–4. Clearly, the points do not lie on a straight line, or even a smooth curve (try alternative ways of connecting the dots if you are not convinced).

The job of the econometrician is to find a smooth curve or line that does a “good” job of approximating the points. For example, suppose the econometrician believes that, on aver- age, there is a linear relation between Y and X, but there is also some random variation in the relationship. Mathematically, this would imply that the true relationship between Y and X is

Y = a + bX + e

Figure 3–4 The Regression Line

0

Y

X

Aâ

ê A

ê C

ê D

ê E

B

C

E

F

Regression line (slope = b̂ )

D

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where a and b are unknown parameters and e is a random variable (an error term) that has a zero mean. Because the parameters that determine the expected relation between Y and X are unknown, the econometrician must find out the values of the parameters a and b.

Note that for any line drawn through the points, there will be some discrepancy between the actual points and the line. For example, consider the line in Figure 3–4, which does a reasonable job of fitting the data. If a manager used the line to approximate the true relation, there would be some discrepancy between the actual data and the line. For example, points A and D actually lie above the line, while points C and E lie below it. The deviations between the actual points and the line are given by the distance of the dashed lines in Figure 3–4, namely êA, êC, êD, and êE. Since the line represents the expected, or average, relation between Y and X, these deviations are analogous to the deviations from the mean used to calculate the variance of a random variable.

The econometrician uses a regression software package to find the values of a and b that minimize the sum of the squared deviations between the actual points and the line. In essence, the regression line is the line that minimizes the squared deviations between the line (the expected relation) and the actual data points. These values of a and b, which frequently are denoted â and b̂, are called parameter estimates, and the corresponding line is called the least squares regression.

The least squares regression line for the equation

Y = a + bX + e is given by

Y = â  + b̂ X

The parameter estimates â and b̂  represent the values of a and b that result in the smallest sum of squared errors between a line and the actual data.

Spreadsheet software packages, such as Excel, make it easy to use regression analysis to estimate demand functions. To illustrate, suppose a television manufacturer has data on the price and quantity of TVs sold last month at 10 outlets in Pittsburgh. Here we use price and quantity as our explanatory and dependent variables, respectively. When the data are entered into a spread- sheet, it looks like the first 11 rows in Table 3–8. A few clicks of the mouse, and the spreadsheet calculates the average price and quantity reported in row 12. Furthermore, clicking the regres- sion toolbar produces the regression output reported in rows 16 through 33. Cell 32-B shows that the intercept of the estimated demand function for TVs is 1631.47, and cell 33-B shows that the estimated coefficient of price is –2.60. Thus, the linear demand function for TVs that minimizes the sum of squared errors between the actual data points and the line through the points is

Q = 1631.47 − 2.60P

Notice that the spreadsheet program also produces detailed information about the regres- sion and the estimated coefficients as a by-product of the regression. As we discuss next, these statistics enable the manager to test for the statistical significance of the estimated coef- ficients and to assess the performance of the overall regression.

Evaluating the Statistical Significance of Estimated Coefficients Rows 30 through 33 of the regression output in Table 3–8 provide information about the precision with which the parameters of the demand function are estimated. The coefficients reported in cells 32-B and 33-B are merely the parameter estimates—estimates of the true, unknown coefficients. Given different data generated from the same true demand relation,

least squares regression The line that minimizes the sum of squared deviations between the line and the actual data points.

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different estimates of the true coefficients would be obtained. The standard error of each esti- mated coefficient is a measure of how much each estimated coefficient would vary in regres- sions based on the same underlying true demand relation, but with different observations. The smaller the standard error of an estimated coefficient, the smaller the variation in the estimate given data from different outlets (different samples of data).

Given a set of standard, but somewhat technical, assumptions about the regression model, data sampling, and means of the errors, the least squares estimates are unbiased estimators of the true demand parameters. If, in addition, the ei’s are independently and identically distrib- uted normal random variables (in short, iid normal random variables) with constant variance, the reported standard errors of the estimated coefficients can be used to construct confidence intervals and to perform significance tests. These techniques are discussed next.

Confidence Intervals Given a parameter estimate, its standard error, and the necessary technical assumptions men- tioned previously, the firm manager can construct upper and lower bounds on the true value of

Table 3–8 Using a Spreadsheet to Perform a Regression

A B C D E F G 1 Observation Quantity Price 2   1 180 475 3   2 590 400 4   3 430 450 5   4 250 550 6   5 275 575 7   6 720 375 8   7 660 375 9   8 490 450

10   9 700 400 11   10 210 500 12   Average 450.50  455.00 13   14   15   16   Regression Statistics 17   18   Multiple R 0.87  19   R-Square 0.75  20   Adjusted R-Square 0.72  21   Standard Error 112.22  22   Observations 10.00  23   24   Analysis of Variance 25   df Sum of Squares Mean Square F Significance F 26   Regression 1.00  301470.89  301470.89 23.94 0.0012 27   Residual 8.00  100751.61  12593.95 28   Total 9.00  402222.50  29   30   Coefficients Standard Error t-Statistic P-Value Lower 95% Upper 95% 31   32   Intercept 1631.47 243.97 6.69 0.0002   1068.87 2194.07  33   Price −2.60 0.53 −4.89 0.0012   −3.82 −1.37 

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The t-Statistic The t-statistic of a parameter estimate is the ratio of the value of the parameter estimate to its standard error. For example, if the parameter estimates are â and b̂ and the corresponding standard errors are σâ and σb̂, the t-statistic for â is

tâ = â

__ σâ

and the t-statistic for b̂  is

tb̂ = b __

σb̂

When the t-statistic for a parameter estimate is large in absolute value, then you can be confident that the true parameter is not zero. The reason for this is that when the absolute value of the t-statistic is large, the standard error of the parameter estimate is small relative to the absolute value of the parameter estimate. Thus, one can be more confident that, given a different sample of data drawn from the true model, the new parameter estimate will be in the same ballpark.

A useful rule of thumb is that if the absolute value of a t-statistic is greater than or equal to 2, then the corresponding parameter estimate is statistically different from zero. Regression packages report P-values, which are a much more precise measure of statistical significance. For instance, in cell 33-E of Table 3–8 we see that the P-value for the estimated coefficient of price is .0012. This means that there is only a 12 in 10,000 chance that we’d get an estimate at least as big as –2.60 in absolute value if the true coefficient of price is actually 0. Notice that the lower the P-value for an estimated coefficient, the more confident you are in the estimate.

Usually, P-values of .05 or lower are considered low enough for a researcher to be con- fident that the estimated coefficient is statistically significant. If the P-value is .05, we say that the estimated coefficient is statistically significant at the 5 percent level. Notice that the P-value reported in Table 3–8 for the coefficient of price implies that it is statistically signifi- cant at the .12 percent level: The estimated coefficient is highly significant.

t-statistic The ratio of the value of a parameter estimate to the standard error of the parameter estimate.

the estimated coefficient by constructing a 95 percent confidence interval. A useful rule of thumb is presented in the following principle, but fortunately regression packages compute pre- cise confidence intervals for each coefficient estimated in a regression. For instance, cells 33-F and 33-G in Table 3–8 indicate that the upper and lower bounds of the 95 percent confidence interval for the coefficient of price are −3.82 and −1.37. The parameter estimate for the price coefficient, −2.60, lies in the middle of these bounds. Thus, we know that the best estimate of the price coefficient is −2.60, and we are 95 percent confident that the true value lies between −3.82 and −1.37.

P R I N C I P L E

Rule of Thumb for a 95 Percent Confidence Interval If the parameter estimates of a regression equation are â and b̂ , the 95 percent confidence intervals for the true values of a and b can be approximated by

â ± 2σâ

and

b̂ ± 2 σb̂

where σâ and σb̂ are the standard errors of â and b̂ , respectively.

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Evaluating the Overall Fit of the Regression Line In addition to evaluating the statistical significance of one or more coefficients, one can also measure the precision with which the overall regression line fits the data. Two yard- sticks frequently used to measure the overall fit of the regression line—the R-square and the F-statistic—are discussed next.

The R-Square Rows 18 through 20 of Table 3–8 provide diagnostics that indicate how well the regression line explains the sample of observations of the dependent variable (in the example, quantity is the dependent variable and price is the explanatory variable). The R-square (also called the coefficient of determination) tells the fraction of the total variation in the dependent variable that is explained by the regression. It is computed as the ratio of the sum of squared errors from the regression (SSRegression) to the total sum of squared errors (SSTotal):

R 2 = Explained Variation

_________________ Total Variation

= S S Regression _________

S S Total

For instance, in cell 26-C of Table 3–8 we see that the sum of squared errors from the regression is 301470.89, while cell 28-C reveals that the total sum of squared errors is 402222.50. Thus, the R-square is .75 (= 301470.89/402222.50). This means that the esti- mated demand equation (the regression line) explains 75 percent of the total variation in TV sales across the sample of 10 outlets. Most spreadsheet regression packages automatically calculate the R-square, as seen in cell 19-B of Table 3–8.3

The value of an R-square ranges from 0 to 1:

0 ≤ R 2 ≤ 1

The closer the R-square is to 1, the “better” the overall fit of the estimated regression equation to the actual data. Unfortunately, there is no simple cutoff that can be used to determine whether an R-square is close enough to 1 to indicate a “good” fit. With time series data, R-squares are often in excess of .9; with cross-sectional data, R-squares below .2 are not uncommon. Thus, a major drawback of the R-square is that it is a subjective measure of goodness of fit.

Another problem with the R-square is that it cannot decrease when additional explanatory variables are included in the regression. Thus, if we included income, advertising, and other explanatory variables in our regression, but held other things constant, we would almost surely get a higher R-square. Eventually, when the number of estimated coefficients increased to the number of observations, we would end up with an R-square of 1. Sometimes, the R-square is very close to 1 merely because the number of observations is small relative to the number of estimated parameters. This situation is undesirable from a statistical viewpoint because it can provide a very misleading indicator of the goodness of fit of the regression line. For this reason, many research- ers use the adjusted R-square reported in cell 20-B of Table 3–8 as a measure of goodness of fit.

3 The square root of the R-square, called the Multiple R, is also reported by most spreadsheet regression programs. It is given in cell 18-B of Table 3-8.

P R I N C I P L E Rule of Thumb for Using t-Statistics When the absolute value of the t-statistic is greater than 2, the manager can be 95 percent confident that the true value of the underlying parameter in the regression is not zero.

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The adjusted R-square is given by

̄ R 2 = 1 − (1 − R 2 ) ( n − 1 )

_____ ( n − k )

where n is the total number of observations and k is the number of estimated coefficients. In performing a regression, the number of parameters to be estimated cannot exceed the num- ber of observations. The difference (n − k) represents the residual degrees of freedom after conducting the regression. Notice that the adjusted R-square “penalizes” the researcher for performing a regression with only a few degrees of freedom (that is, estimating numerous coefficients from relatively few observations). In fact, the penalty can be so high that, in some instances, the adjusted R-square is actually negative.

In our example, cell 22-B in Table 3–8 shows us that n = 10. Cells 32-B and 33-B indicate that we estimated 2 parameters, so k = 2. With 8 residual degrees of freedom, the adjusted R-square of our regression is 1 − (1 − .75)(9/8) = .72. This number is reported in cell 20-B. For these data, there is little difference between the R-square and the adjusted R-square, so it does not appear that the “high” R- square is a result of an excessive number of estimated coefficients relative to the sample size.

The F-Statistic While the R-square and adjusted R-square of a regression both provide a gauge of the overall fit of a regression, we note that there is no universal rule for determining how “high” they must be to indicate a good fit. An alternative measure of goodness of fit, called the F-statistic, does not suffer from this shortcoming. The F-statistic provides a measure of the total varia- tion explained by the regression relative to the total unexplained variation. The greater the F-statistic, the better the overall fit of the regression line through the actual data. In our exam- ple, the F-statistic is reported as 23.94 in cell 26-E of Table 3–8.

The primary advantage of the F-statistic stems from the fact that its statistical properties are known. Thus, one can objectively determine the statistical significance of any reported F value. The significance value for our regression, .0012, is reported in cell 26-F of Table 3–8. This low number means that there is only a .12 percent chance that the estimated regression model fit the data purely by accident.

As with P-values, the lower the significance value of the F-statistic, the more confident you can be of the overall fit of the regression equation. Regressions that have F-statistics with significance values of 5 percent or less are generally considered significant. Based on the significance value reported in cell 26-F of Table 3–8, our regression is significant at the .12 percent level. The regression is therefore highly significant.

Regression for Nonlinear Functions and Multiple Regression The techniques described to estimate a linear demand function with a single explanatory vari- able can also be used to estimate nonlinear demand functions. These same tools can be used to estimate demand functions in which the quantity demanded depends on several explanatory variables, such as prices, income, advertising, and so on. These issues are discussed next.

Regression for Nonlinear Functions Sometimes, a plot of the data will reveal nonlinearities in the data, as seen in Figure 3–5. Here, it appears that price and quantity are not linearly related: The demand function is a curve. The log-linear demand curve we examined earlier in this chapter has such a curved shape.

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To estimate a log-linear demand function, the econometrician takes the natural logarithm of prices and quantities before executing the regression routine that minimizes the sum of squared errors (e):

ln Q = β 0 + β p ln P + e

In other words, by using a spreadsheet to compute Q′ = ln Q and P′ = ln P, this demand spec- ification can be viewed equivalently as

Q ′ = β 0 + β p P ′ + e

which is linear in Q′ and P′. Therefore, one can use procedures identical to those described earlier and regress the transformed Q′ on P′ to obtain parameter estimates. Recall that the resulting parameter estimate for βP in this case is the own price elasticity of demand since this is a log-linear demand function.

Figure 3–5 Log-Linear Regression Line

0

Price

Quantity

DEMONSTRATION PROBLEM 3–5

During the 31 days this past March, an online ticket agent offered varying price discounts on Broadway tickets in order to gather information needed to estimate the demand for its tickets. A file named Demo_3_5. xls is available at www.mhhe.com/baye9e. If you open this file and view the tab labeled Data, you will find information about the quantity of Broadway tickets the company sold at various prices in March. Use these data to estimate a log-linear demand function. Use an equation to summarize your findings.

ANSWER: The first step is to transform the price and quantity data into natural logarithms, using the relevant spreadsheet command. You can see how to do this step by viewing the tab labeled Transformed in the Demo_3_5.xls file. The second step is to perform a linear regression on the transformed data. These regression results are displayed in the Results tab of the file. The final step is to summarize the regression results in a demand equation. In this case, the estimates in the Results tab imply the following log-linear demand function:

ln Q d = 8.44 − 1.58 ln P

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Multiple Regression In general, the demand for a good will depend not only on the good’s price, but also on demand shifters. Regression techniques can also be used to perform multiple regressions— regressions of a dependent variable on multiple explanatory variables. For the case of a linear demand relation, one might specify the demand function as

Q x d = α 0 + α x P x + α y P y + α M M + α H H + e

where the α’s are the parameters to be estimated; Py, M, and H are demand shifters; and e is the random error term that has a zero mean. Alternatively, a log-linear specification might be appropriate if the quantity demanded is not linearly related to the explanatory variables:

ln Q x d = β 0 + β x ln P x + β y ln P y + β M ln M + β H ln H + e

Provided the number of observations is greater than the number of parameters to be esti- mated, one can use standard regression packages included in spreadsheet programs to find the values of the parameters that minimize the sum of squared errors of the regression. The R-square, F-statistic, t-statistic, and confidence intervals for multiple regressions have the same use and interpretations described earlier for the case of a simple regression with one explanatory variable. Demonstration Problem 3-6 illustrates this fact.

Written in this manner, the logarithm of quantity demanded is a linear function of the logarithm of price, and the company’s elasticity of demand for tickets is −1.58. Alternatively, one can express the actual quantity demanded as a nonlinear function of price by taking the exponential of both sides of the equation:

exp[ln Q d ]

=

exp[8.44 ] exp [ − 1.58 ln P ]

Q d = exp  [8.44] P −1.58

   Q d   =  4629 P −1.58

DEMONSTRATION PROBLEM 3–6

FCI owns 10 apartment buildings in a college town, which it rents exclusively to students. Each apartment building contains 100 rental units, but the owner is having cash flow problems due to an average vacancy rate of nearly 50 percent. The apartments in each building have comparable floor plans, but some buildings are closer to campus than others. The owner of FCI has data from last year on the number of apartments rented, the rental price (in dollars), and the amount spent on advertising (in hundreds of dollars) at each of the 10 apartments. These data, along with the distance (in miles) from each apartment building to campus, are presented in rows 1 through 11 of Table 3–9. The owner regressed the quantity demanded of apartments on price, advertising, and distance. The results of the regression are reported in rows 16 through 35 of Table 3–9. What is the estimated demand function for FCI’s rental units? If FCI raised rents at one complex by $100, what would you expect to happen to the number of units rented? If FCI raised rents at an average apartment building, what would happen to FCI’s total revenues? What inferences should be drawn from this analysis?

ANSWER: Letting P, A, and D represent price, advertising, and distance from campus, the estimated coeffi- cients imply the following demand for rental units at an apartment building:

Q x d = 135.15 − 0.14P + 0.54A − 5.78D

Since the coefficient of price is −0.14, a $100 increase in price reduces the quantity demanded at an apartment building by 14 units. The own price elasticity of demand for FCI’s rental units, calcu- lated at the average price and quantity, is (−.14)(420/53.10) = −1.11. Since demand is elastic, raising

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A B C D E F G

1   Observation Quantity Price Advertising Distance 2   1 28 250 11 12 3   2 69 400 24 6 4   3 43 450 15 5 5   4 32 550 31 7 6   5 42 575 34 4 7   6 72 375 22 2 8   7 66 375 12 5 9   8 49 450 24 7

10   9 70 400 22 4 11   10 60 375 10 5 12   Average 53.10 420.00 20.50 5.70 13   14   15   16   Regression Statistics 17   18   Multiple R 0.89 19   R-Square 0.79 20   Adjusted R-Square 0.69 21   Standard Error 9.18 22   Observations 10.00 23   24   Analysis of Variance 25   df Sum of Squares Mean Square F Significance F 26   Regression 3.00 1920.99 640.33 7.59 0.0182 27   Residual 6.00 505.91 84.32 28   Total 9.00 2426.90 29   30   Coefficients Standard Error t-Statistic P-Value Lower 95% Upper 95% 31   32   Intercept 135.15  20.65 6.54 0.0006   84.61 185.68 33   Price −0.14  0.06 −2.41 0.0500   −0.29 0.00 34   Advertising 0.54  0.64 0.85 0.4296   −1.02 2.09 35   Distance −5.78  1.26 −4.61 0.0037   −8.86 −2.71

Table 3–9 Input and Output from a Multiple Regression

the rent at an average apartment building would decrease not only the number of units rented, but total revenues as well.

The R-square of .79 indicates that the regression explains 79 percent of the variation in the quan- tity of apartments rented across the 10 buildings. The F-statistic suggests that the regression is sig- nificant at the 1.82 percent level, so the manager can be reasonably confident that the good fit of the equation is not due to chance. Notice that all the estimated parameters are statistically significant at the 5 percent level, except for the coefficient of advertising. Thus, it does not appear that advertising has a statistically significant effect on the demand for the rental units.

Distance from campus appears to be a very significant determinant of the demand for apartments. The t-statistic for this coefficient is in excess of 4 in absolute value, and the P-value is .37 percent. Based on the lower and upper bounds of its confidence interval, the owner can be 95 percent confident that for every mile an apartment is away from campus, FCI loses between 2.71 and 8.86 renters.

Since FCI can’t relocate its apartments closer to campus, and advertising does not have a statis- tically significant impact on units rented, it would appear that all FCI can do to reduce its cash flow problems is to lower rents at those apartment buildings where demand is elastic.

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A Caveat You now know how to interpret the output of a regression and how to use the output to sum- marize the demand for a product in a simple equation. Demand functions are not fictitious textbook constructs—they are equations that managers may actually obtain by using appropri- ate econometric techniques and data.

It is important to stress, however, that econometrics is a specialized field of economics that takes years of study to master. For the same reason it would not be prudent for you to perform LASIK eye surgery after merely reading a section called “The Eye” in your biology textbook, prudent managers rely on the expertise of “specialists” (economic experts or con- sultants) to obtain demand estimates. Unless you invest in the coursework required to master a host of econometric issues that are beyond the scope of any managerial economics textbook or spreadsheet program (e.g., endogeneity, sample selection, heteroskedasticity, autocorrelation,

Thanks to the Internet, consumers can let their mouse do the shopping instead of paying bus fares or filling their cars with gasoline to visit brick-and-mortar stores. How responsive are the demands of online shoppers to the prices charged by online retailers? Recently, economists working at the Haas School of Business at Berkeley, Cambridge University, and the Kelley School of Business at Indiana University used regression tech- niques and online data from Europe to answer this question.

The economists estimated demand functions for a variety of different brands and models of personal digital assistants (PDAs) sold by different online retailers at the leading European shopping site, Kelkoo.com. This site per- mits shoppers in Europe to purchase a wide array of prod- ucts online, ranging from electronic gadgets to vacuum cleaners and washing machines. While Kelkoo.com may not be familiar to shoppers on the American side of the pond, its parent company—Yahoo!—is a household name worldwide.

The accompanying table summarizes the authors’ econometric estimates of the elasticity of demand facing

firms selling six different models of PDAs. Notice that an online retailer selling the IPAQ 1940 faces the most elastic demand (−14.7), while a firm selling the Clie SJ22 faces the least elastic demand (−3.3). Depending on the brand and model, an online retailer that reduced price by 10 percent would enjoy a 33 to 147 percent increase in online sales. The t-statistics all exceed 2 in absolute value, which indi- cates that the estimates are statistically significant at the 5 percent level.

SOURCE: Michael R. Baye, J. Rupert J. Gatti, Paul Kattuman, and John Morgan, “Clicks, Discontinuities, and Firm Demand Online,” Journal of Economics and Management Strategy 18, no. 4 (2009), pp. 935–75.

INSIDE BUSINESS 3–4

Shopping Online in Europe: Elasticities of Demand for Personal Digital Assistants Based on Regression Techniques

Brand/Model Elasticity t-statistic

HP Compaq IPAQ 1940 −14.7 −20.39 HP Compaq IPAQ 2210 −11.7 −10.54 Palm Tungsten T2   −6.1 −11.90 Palm Zire 71 −11.1 −11.47 Sony Clié NX73V   −5.9 −10.82 Sony Clié SJ22   −3.3    −8.65

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and unobserved effects), it is probably best for you to use your econometric knowledge pri- marily as a tool for communicating with (and interpreting the output provided by) econometric specialists.

ANSWERING THE headLINE At the beginning of the chapter, we asked whether Walmart should expect a good hol- iday season absent a price change and whether a price change could improve sales (measured as revenues). Recall that the firm’s analysts provided the following regression results, linking sales to prices and consumer confidence:

ln ( HolidaySales ) = 25.8 − 0.8 ln ( Price ) + 0.9 ln ( ConsumerConfidence )

Since this is a log-linear equation, the coefficients are elasticities. In particular, the coeffi- cient of ln(ConsumerConfidence) (0.9) tells us the percentage change in holiday sales (HS) resulting from each 1 percent change in consumer confidence. Consequently, when con- sumer confidence decreases by 4 percent, this means 0.9 = %ΔHS/(–4), or %ΔHS = –3.6. In other words, the director should expect holiday sales to be 3.6 percent lower in MSAs where consumer confidence has declined by 4 percent, and so should not be particularly optimistic about holiday sales this year. The results indicate the director could mitigate the sales decrease by lowering price. For example, the director could recommend a 3 percent price reduction across the board, which, according to the regression, will result in a 2.4 percent increase in holiday sales (–0.8 = %ΔHS/(–3), or %ΔHS = 2.4). However, the director should be sure not to lose sight of any effects a price change would have on profits, as opposed to sales.

In addition to the usual caveat that it should be left to experts to obtain these revenues estimates, note also that the director is not working with a demand curve to make these decisions. Since it is revenues and not quantity as the dependent variable, the sign of the coefficient on price tells us whether demand is elastic or inelastic. In this case, the nega- tive coefficient on price—indicating revenues fall with a price increase—implies an elastic demand curve.

SUMMARY

In this chapter we covered quantitative aspects of demand analysis, including the own price elasticity, income elas- ticity, and cross-price elasticity of demand. We examined functional forms for demand functions, including linear and log-linear specifications, and discussed the regression pro- cedures used to estimate demand relationships. Armed with these tools, a manager can predict not only the direction of changes in demand but how far demand will move when one of the determinants of demand changes. Knowing the con- cepts of elasticity and the use of t-statistics and confidence intervals is extremely important when making decisions about how much inventory to hold, how many employees to schedule, and how many units of a product to produce when different determinants of demand change.

In this chapter, we saw that increasing price does not always increase revenues. If the absolute value of own price elasticity is greater than 1, an increase in price will decrease total revenue. We also covered the magnitude of changes caused by a change in the price of a substitute or a complement.

Finally, we introduced the concepts of regression and confidence intervals. By utilizing the elasticities based on an estimated demand function and constructing a confi- dence interval, a manager can be 95 percent certain about the amount by which demand will move when a variable like income or advertising changes.

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KEY TERMS AND CONCEPTS

adjusted R-square arc elasticity of demand coefficient of determination confidence interval cross-advertising elasticity cross-price elasticity econometrics elastic demand elasticity F-statistic iid normal assumption

income elasticity inelastic demand least squares regression log-linear demand multiple regression own advertising elasticity own price elasticity of demand P-value parameter estimates perfectly elastic demand perfectly inelastic demand

R-square regression analysis regression line residual degrees of freedom standard error sum of squared errors t-statistic total revenue test unitary elastic demand

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. Answer the following questions based on the accompanying diagram. (LO1, LO2, LO4)

Price ($)

3 4

20 18 16 14 12 10 8 6 4 2 0

1 20 5 6

D Quantity

a. How much would the firm’s revenue change if it lowered the price from $12 to $10? Is demand elastic or inelastic in this range?

b. How much would the firm’s revenue change if it lowered the price from $4 to $2? Is demand elastic or inelastic in this range?

c. What price maximizes the firm’s total revenues? What is the elasticity of demand at this point on the demand curve?

2. The demand curve for a product is given by Q x d = 1,200 − 3 P x − 0.1 P z where Pz =

$300. (LO1, LO4, LO5) a. What is the own price elasticity of demand when Px = $140? Is demand elastic or

inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price below $140?

b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240?

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?

3. Suppose the demand function for a firm’s product is given by

ln Q x d = 7 − 1.5 ln P x + 2 ln P y − 0.5 ln M + ln A

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where

P x = $15,

P y = $6, M = $40,000, and

A = $350

(LO1, LO5) a. Determine the own price elasticity of demand, and state whether demand is elastic,

inelastic, or unitary elastic. b. Determine the cross-price elasticity of demand between good X and good Y, and

state whether these two goods are substitutes or complements. c. Determine the income elasticity of demand, and state whether good X is a normal or

inferior good. d. Determine the own advertising elasticity of demand.

4. Suppose the own price elasticity of demand for good X is –3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is –4. Determine how much the consumption of this good will change if: (LO1) a. The price of good X decreases by 5 percent. b. The price of good Y increases by 8 percent. c. Advertising decreases by 4 percent. d. Income increases by 4 percent.

5. Suppose the cross-price elasticity of demand between goods X and Y is 4. How much would the price of good Y have to change in order to increase the consumption of good X by 20 percent? (LO1)

6. You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is −1.5 and the cross-price elasticity of demand between products Y and X is −1.8. How much will your firm’s total revenues (revenues from both products) change if you increase the price of good X by 2 percent? (LO1, LO2)

7. A quant jock from your firm used a linear demand specification to estimate the demand for its product and sent you a hard copy of the results. Unfortunately, some entries are missing because the toner was low in her printer. Use the information presented below to find the missing values labeled ‘1’ through ‘7’ (round your answers to the nearest hundredth). Then, answer the accompanying questions. (LO6)

SUMMARY OUTPUT            

              Regression Statistics             Multiple R 0.38           R-Square ‘1’           Adjusted R-Square ‘2’           Standard Error 20.77           Observations 150                         Analysis of Variance            

  Degrees of Freedom Sum of Squares Mean Square F Significance F  

Regression 2 ‘3’ 5199.43 12.05 0.00   Residual 147 63,408.62 431.35       Total ‘4’ 73,807.49                      

  Coefficients Standard Error t-Statistic P-Value Lower 95% Upper 95% Intercept 58.87 ‘5’ 3.84 0.00 28.59 89.15 Price of X −1.64 0.85 ‘6’ 0.06 −3.31 0.04 Income ‘7’ 0.24 4.64 0.00 0.63 1.56

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a. Based on these estimates, write an equation that summarizes the demand for the firm’s product.

b. Which regression coefficients are statistically significant at the 5 percent level? c. Comment on how well the regression line fits the data.

8. Suppose the true inverse demand relation for good X is Q x d = a + b P x + cM + e , and

you estimated the parameters to be â = 22, b̂ = −1.8,  σâ = 2.5 , and σb̂ = 0.7 . Find the approximate 95 percent confidence interval for the true values of a and b. (LO6)

9. The demand function for good X is Q x d = a + b P x + cM + e , where Px is the price of

good X and M is income. Least squares regression reveals that â = 8.27 , b̂ = −2.14 , ĉ = 0.36 , σâ = 5.32 , σb̂ = 0.41 , and σĉ = 0.22 . The R-squared is 0.35. (LO6) a. Compute the t-statistic for each of the estimated coefficients. b. Determine which (if any) of the estimated coefficients are statistically different

from zero. c. Explain, in plain words, what the R-square in this regression indicates.

10. The demand function for good X is ln Q x d = a + b ln Px + c ln M + e, where Px is the

price of good X and M is income. Least squares regression reveals that â = 7.42, b̂ = −2.18, and   ĉ  = 0.34. (LO5, LO6) a. If M = 55,000 and Px = 4.39, compute the own price elasticity of demand based on

these estimates. Determine whether demand is elastic or inelastic. b. If M = 55,000 and Px = 4.39, compute the income elasticity of demand based on

these estimates. Determine whether X is a normal or inferior good.

PROBLEMS AND APPLICATIONS

11. Revenue at a major smartphone manufacturer was $2.3 billion for the nine months end- ing March 2, up 85 percent over revenues for the same period last year. Management attributes the increase in revenues to a 108 percent increase in shipments, despite a 21 percent drop in the average blended selling price of its line of phones. Given this information, is it surprising that the company’s revenue increased when it decreased the average selling price of its phones? Explain. (LO1, LO4)

12. You are the manager of a firm that sells a leading brand of alkaline batteries. A file named Q12.xls with data on the demand for your product is available online at www.mhhe.com/baye9e. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world. Use this information to perform a log-linear regression, and then determine the likely impact of a 3 percent decline in global income on the overall demand for your product. (LO1, LO5, LO6)

13. For the first time in two years, Big G (the cereal division of General Mills) raised cereal prices by 4 percent. If, as a result of this price increase, the volume of all cereal sold by Big G dropped by 5 percent, what can you infer about the own price elasticity of demand for Big G cereal? Can you predict whether revenues on sales of its Lucky Charms brand increased or decreased? Explain. (LO1, LO3)

14. If Starbucks’s marketing department estimates the income elasticity of demand for its coffee to be 2.6, how will the prospect of an economic boom (expected to increase consumers’ incomes by 6 percent over the next year) impact the quantity of coffee Starbucks expects to sell? (LO1)

15. You are a division manager at Toyota. If your marketing department estimates that the semiannual demand for the Highlander is Q = 150,000 – 1.5P, what price should you charge in order to maximize revenues from sales of the Highlander? (LO1, LO2, LO4, LO5)

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16. You are a manager in charge of monitoring cash flow at a major publisher. Paper books comprise 40 percent of your revenues, which grow about 2 percent annually. You recently received a preliminary report that suggests the growth rate in ebook reading has leveled off and that the cross-price elasticity of demand between paper books and ebooks is –0.3. In 2016, your company earned about $600 million from sales of ebooks and about $400 million from sales of paper books. If the own price elasticity of demand for paper books is –2, how will a 4 percent decrease in the price of paper books affect your overall revenues from both paper book and ebook sales? (LO1, LO2)

17. As newly appointed “Energy Czar,” your goal is to reduce the total demand for resi- dential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by $1, (b) a subsidy that would effectively reduce the price of natural gas by $3, or (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by $4. To assist you in your decision, an econo- mist in your office has estimated the demand for residential heating fuel using a linear demand specification. The regression results are presented as follows. Based on this information, which proposal would you favor? Explain. (LO6)

A B C D E F G 1   SUMMARY OUTPUT 2   3   Regression Statistics 4   Multiple R   0.76 5   R-Square   0.57 6   Adjusted R-Square   0.49 7   Standard Error 47.13 8   Observations 25 9  

10   Analysis of Variance

11   Degrees of Freedom Sum of Squares Mean Square F Significance F  

12   Regression 4 60936.56 15234.14 6.86 .03 13   Residual 20 44431.27 2221.56 14   Total 24 105367.84 15   16   Coefficients Standard Error t-Statistic P-Value Lower 95% Upper 95%   17   Intercept 136.96 43.46 3.15 0.01 50.60 223.32 18   Price of Residential Heating Fuel –91.69 29.09 –3.15 0.01 –149.49 –33.89 19   Price of Natural Gas 43.88 9.17 4.79 0.00 25.66 62.10 20   Price of Electricity –11.92 8.35 –1.43 0.17 –28.51 4.67 21   Income –0.050 0.3500 –0.14 0.90 – 0.75 0.65

18. As the owner of Barney’s Broilers—a fast-food chain—you see an increase in the demand for broiled chicken as consumers become more health conscious and reduce their consump- tion of beef and fried foods. As a result, you believe it is necessary to purchase another oven to meet the increased demand. To finance the oven you go to the bank seeking a loan. The loan officer tells you that your revenues of $750,000 are insufficient to support additional debt. To qualify for the loan, Barney’s Broilers’s revenue would need to be $50,000 higher. In developing a strategy to generate the additional revenue, you collect data on the price (in cents) per pound you charge customers and the related quantity of chicken consumed per year in pounds. This information is contained in the file called Q18.xls available online at www.mhhe.com/baye9e. Use these data and a log-linear demand specification to obtain least squares estimates of the demand for broiled chicken. Write an equation that summa- rizes the demand for broiled chicken, and then determine the percentage price increase or decrease that is needed in order to boost revenues by $50,000. (LO1, LO4, LO5, LO6)

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19. Suppose the Kalamazoo Brewing Company (KBC) currently sells its microbrews in a seven-state area: Illinois, Indiana, Michigan, Minnesota, Mississippi, Ohio, and Wisconsin. The company’s marketing department has collected data from its distrib- utors in each state. These data consist of the quantity and price (per case) of micro- brews sold in each state, as well as the average income (in thousands of dollars) of consumers living in various regions of each state. The data for each state are available online at www.mhhe.com/baye9e under the filename Q19.xls, where there are mul- tiple tabs at the bottom of the spreadsheet, each referring to one of the seven states selling the Kalamazoo Brewing Company’s microbrews. Assuming that the under- lying demand relation is a linear function of price and income, use your spreadsheet program to obtain least squares estimates of the state’s demand for KBC microbrews. Print the regression output and provide an economic interpretation of the regression results. (LO6)

20. With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on from the famous “Got Milk” ad slogan in favor of a new one, “Milk Life.” The new tagline emphasizes milk’s nutritional benefits, including its protein content. MPEP began collecting data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars) for the period following the launch of the new campaign. These data, in forms to estimate both a linear model and log-linear model, are available online at www.mhhe.com/baye9e in a file named Q20.xls. Use these data to perform two regressions: a linear regression and a log-linear regression. Compare and contrast the regression output of the two models. Comment on which model does a better job fitting the data. Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use the best-fitting regression model to estimate the weekly quantity of milk consumed after this advertising increase. (LO6)

21. Suppose that News Corp., which controls the United States’ largest satellite-to-TV broadcaster, is contemplating launching a Spaceway satellite that could provide high- speed Internet service. Prior to launching the Spaceway satellite, suppose that News Corp. used least squares to estimate the regression line of demand for satellite Internet services. The best-fitting results indicate that demand is Q sat

d = 152.5 − .8 P sat + 1.2 P DSL + .5 P cable (in thousands), where Psat is the price of satellite Internet service, PDSL is the price of DSL Internet service, and Pcable is the price of high-speed cable Internet service. Suppose that after the FCC’s ruling the price of DSL, PDSL, is $25 per month and the monthly price of high-speed cable Internet, Pcable, is $50. Furthermore, News Corp. has identified that its monthly revenues need to be at least $15 million to cover its monthly costs. If News Corp. set its monthly subscription price for satellite Internet service at $55, would its revenue be sufficiently high to cover its cost? Is it possible for News Corp. to cover its cost given the current demand function? Justify your answer. (LO1, LO2, LO4, LO5)

22. Recently, Verizon Wireless ran a pricing trial in order to estimate the elasticity of demand for its services. The manager selected three states that were representative of its entire service area and increased prices by 5 percent to customers in those areas. One week later, the number of customers enrolled in Verizon’s cellular plans declined 4 percent in those states, while enrollments in states where prices were not increased remained flat. The manager used this information to estimate the own price elasticity of demand and, based on her findings, immediately increased prices in all market areas by 5 percent in an attempt to boost the company’s 2012 annual revenues. One year later, the manager was perplexed because Verizon’s 2012 annual revenues were 10 percent lower than those in 2011—the price increase apparently led to a reduction in the company’s revenues. Did the manager make an error? Explain. (LO1, LO3, LO4)

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100

23. The owner of a small chain of gasoline stations in a large Midwestern town read an arti- cle in a trade publication stating that the own price elasticity of demand for gasoline in the United States is –0.2. Because of this highly inelastic demand in the United States, he is thinking about raising prices to increase revenues and profits. Do you recommend this strategy based on the information he has obtained? Explain. (LO1, LO3, LO4)

SELECTED READINGS

Chiles, Ted W., Jr., and Sollars, David L., “Estimating Cigarette Tax Revenue.” Journal of Economics and Finance 17(3), Fall 1993, pp. 1–15.

Crandall, R., “Import Quotas and the Automobile Industry: The Cost of Protectionism.” Brookings Review 2(4), Summer 1984, pp. 8–16.

Houthakker, H., and Taylor, L., Consumer Demand in the United States: Analyses and Projections, 2nd ed. Cambridge, MA: Harvard University Press, 1970.

Maxwell, Nan L., and Lopus, Jane S., “The Lake Wobegon Effect in Student Self-Reported Data.” American Economic Review 84(2), May 1994, pp. 201–205.

Pratt, Robert W., Jr., “Forecasting New Product Sales from Likelihood of Purchase Ratings: Commentary.” Marketing Science 5(4), Fall 1986, pp. 387–88.

Sawtelle, Barbara A., “Income Elasticities of Household Expenditures: A U.S. Cross Section Perspective.” Applied Economics 25(5), May 1993, pp. 635–44.

Stano, Miron, and Hotelling, Harold, “Regression Analysis in Litigation: Some Overlooked Considerations.” Journal of Legal Economics 1(3), December 1991, pp. 68–78.

Williams, Harold R., and Mount, Randall I., “OECD Gasoline Demand Elasticities: An Analysis of Consumer Behavior with Implications for U.S. Energy Policy.” Journal of Behavioral Economics 16(1), Spring 1987, pp. 69–79.

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101

headLINE Packaging Firm Uses Overtime Pay to Overcome Labor Shortage Boxes Ltd. produces corrugated paper containers at a small plant in Sunrise Beach, Texas. Sunrise Beach is a retirement community with an aging population, and over the past decade the size of its working population has shrunk. In 2016, this labor shortage hampered Boxes Ltd.’s ability to hire enough workers to meet its growing demand and production targets. This is despite the fact that it pays $16 per hour—almost 30 percent more than the local average—to its workers.

Last year, Boxes Ltd. hired a new manager who instituted an overtime wage plan at the firm. Under her plan, workers earn $16 per hour for the first eight hours worked each day, and $24 per hour for each hour worked in a day in excess of eight hours. This plan eliminated the firm’s problems, as the firm’s production levels and profits are up by 20 percent this year.

Why did the new manager institute the overtime plan instead of simply raising the wage rate in an attempt to attract more workers to the firm?

The Theory of Individual Behavior

4 LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Explain four basic properties of a consumer’s preference ordering and their ramifications for a consumer’s indifference curves.

LO2 Illustrate how changes in prices and income impact an individual’s opportunities.

LO3 Illustrate a consumer’s equilibrium choice and how it changes in response to changes in prices and income.

LO4 Separate the impact of a price change into substitution and income effects.

LO5 Show how to derive an individual’s demand curve from indifference curve analysis and market demand from a group of individuals’ demands.

LO6 Illustrate how “buy one, get one free” deals and gift certificates impact a consumer’s purchase decisions.

LO7 Apply the income–leisure choice framework to illustrate the opportunities, incentives, and choices of workers and managers.

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INTRODUCTION

This chapter develops tools that help a manager understand the behavior of individuals, such as consumers and workers, and the impact of alternative incentives on their decisions. This is not as simple as you might think. Human beings use complicated thought processes to make decisions, and the human brain is capable of processing vast quantities of information. At this very moment your heart is pumping blood throughout your body, your lungs are providing oxygen and expelling carbon dioxide, and your eyes are scanning this page while your brain processes the information on it. The human brain can do what even supercomput- ers and sophisticated “artificial intelligence” technology are incapable of doing.

Despite the complexities of human thought processes, managers need a model that explains how individuals behave in the marketplace and in the work environment. Of course, attempts to model individual behavior cannot capture the full range of real-world behavior. Life would be simpler for managers of firms if the behavior of individuals were not so com- plicated. On the other hand, the rewards for being a manager of a firm would be much lower. If you achieve an understanding of individual behavior, you will gain a marketable skill that will help you succeed in the business world.

Our model of behavior will necessarily be an abstraction of the way individuals really make decisions. We must begin with a simple model that focuses on essentials instead of dwelling on behavioral features that would do little to enhance our understanding. Keep these thoughts in mind as we begin our study of an economic model of consumer behavior.

CONSUMER BEHAVIOR

Now that you recognize that any theory about individual behavior must be an abstraction of reality, we may begin to develop a model to help us understand how consumers will respond to the alternative choices that confront them. A consumer is an individual who purchases goods and services from firms for the purpose of consumption. As a manager of a firm, you are interested not only in who consumes the good but in who purchases it. A six-month-old baby consumes goods but is not responsible for purchase decisions. If you are employed by a manufacturer of baby food, it is the parent’s behavior you must understand, not the baby’s.

In characterizing consumer behavior, there are two important but distinct factors to con- sider: consumer opportunities and consumer preferences. Consumer opportunities represent the possible goods and services consumers can afford to consume. Consumer preferences determine which of these goods will be consumed. The distinction is very important: While I can afford (and thus have the opportunity to consume) one pound of beef liver each week, my preferences are such that I would be unlikely to choose to consume beef liver at all. Keeping this distinction in mind, let us begin by modeling consumer preferences.

In today’s global economy literally millions of goods are offered for sale. However, to focus on the essential aspects of individual behavior and to keep things manageable, we will assume that only two goods exist in the economy. This assumption is made purely to sim- plify our analysis: All of the conclusions that we draw from this two-good setting remain valid when there are many goods. We will let X represent the quantity of one good and Y the quantity of the other good. By using this notation to represent the two goods, we have a very general model in the sense that X and Y can be any two goods rather than restricted to, say, beef and pork.

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Assume a consumer is able to order his or her preferences for alternative bundles or combinations of goods from best to worst. We will let ≻ denote this ordering and write A ≻ B whenever the consumer prefers bundle A to bundle B. If the consumer views the two bundles as equally satisfying, we will say she or he is indifferent between bundles A and B and use A ∼ B as shorthand notation. If A ≻ B, then, if given a choice between bundle A and bundle B, the consumer will choose bundle A. If A ∼ B, the consumer, given a choice between bundle A and bundle B, will not care which bundle he or she gets. The preference ordering is assumed to satisfy four basic properties: completeness, more is better, diminish- ing marginal rate of substitution, and transitivity. Let us examine these properties and their implications in more detail.

Property 4–1: Completeness. For any two bundles—say, A and B—either A ≻ B, B ≻ A, or A ∼ B.

By assuming that preferences are complete, we assume the consumer is capable of expressing a preference for, or indifference among, all bundles. If preferences were not complete, there might be cases where a consumer would claim not to know whether he or she preferred bundle A to B, preferred B to A, or was indifferent between the two bundles. If the consumer cannot express her or his own preference for or indifference among goods, the manager can hardly predict that individual’s consumption patterns with reasonable accuracy.

Property 4–2: More Is Better. If bundle A has at least as much of every good as bundle B and more of some good, bundle A is preferred to bundle B.

If more is better, the consumer views the products under consideration as “goods” instead of “bads.” Graphically, this implies that as we move in the northeast direction in Figure 4–1, we move to bundles that the consumer views as being better than bundles to the southwest. For example, in Figure 4–1 bundle A is preferred to bundle D because it has the same amount of good X and more of good Y. Bundle C is also preferred to bundle D because it has more of both goods. Similarly, bundle B is preferred to bundle D.

Figure 4–1 The Indifference Curve

Y

X

A

B

C

I D

0 1 2 3 4 5 6

1

2

3

4

5

6

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While the assumption that more is better provides important information about consumer preferences, it does not help us determine a consumer’s preference for all possible bundles. For example, note in Figure 4–1 that the “more is better” property does not reveal whether bundle B is preferred to bundle A or bundle A is preferred to bundle B. To be able to make such comparisons, we will need to make some additional assumptions.

An indifference curve defines the combinations of goods X and Y that give the consumer the same level of satisfaction; that is, the consumer is indifferent between any combination of goods along an indifference curve. A typical indifference curve is depicted in Figure 4–1. By definition, all combinations of X and Y located on the indifference curve provide the consumer with the same level of satisfaction. For example, if you asked the consumer, “Which would you prefer—bundle A, bundle B, or bundle C?” the consumer would reply, “I don’t care” because bundles A, B, and C all lie on the same indifference curve. In other words, the consumer is indifferent among the three bundles.

The shape of the indifference curve depends on the consumer’s preferences. Different consumers generally will have indifference curves of different shapes. One important way to summarize information about a consumer’s preferences is in terms of the marginal rate of substitution. The marginal rate of substitution (MRS) is the absolute value of the slope of an indifference curve. The marginal rate of substitution between two goods is the rate at which a consumer is willing to substitute one good for the other and still maintain the same level of satisfaction.

The concept of the marginal rate of substitution is actually quite simple. In Figure 4–1, the consumer is indifferent between bundles A and B. In moving from A to B, the consumer gains 1 unit of good X. To remain on the same indifference curve, she or he gives up 2 units of good Y. Thus, in moving from point A to point B, the marginal rate of substitution between goods X and Y is 2.

The careful reader will note that the marginal rate of substitution associated with moving from A to B in Figure 4–1 differs from the rate at which the consumer is willing to substitute between the two goods in moving from B to C. In particular, in moving from B to C, the consumer gains 1 unit of good X. But now he or she is willing to give up only 1 unit of good Y to get the additional unit of X. The reason is that this indifference curve satisfies the property of the diminishing marginal rate of substitution.

Property 4–3: Diminishing Marginal Rate of Substitution. As a consumer obtains more of good X, the amount of good Y he or she is willing to give up to obtain another unit of good X decreases.

This assumption implies that indifference curves are convex from the origin; that is, they look like the indifference curve in Figure 4–1. To see how the locations of various indiffer- ence curves can be used to illustrate different levels of consumer satisfaction, we must make an additional assumption: that preferences are transitive.

Property 4–4: Transitivity. For any three bundles, A, B, and C, if A ≻ B and B ≻ C, then A ≻ C. Similarly, if A ∼ B and B ∼ C, then A ∼ C.

The assumption of transitive preferences, together with the more-is-better assumption, implies that indifference curves do not intersect one another. It also eliminates the possibility that the consumer is caught in a perpetual cycle in which she or he never makes a choice.

To see this, suppose Billy’s preferences are such that he prefers jelly beans to licorice, licorice to chocolate, and chocolate to jelly beans. He asks the clerk to fill a bag with jelly

indifference curve A curve that defines the combinations of two goods that give a consumer the same level of satisfaction.

marginal rate of substitution (MRS) The rate at which a consumer is willing to substitute one good for another good and still maintain the same level of satisfaction.

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Have you ever wondered why some individuals choose to undertake risky prospects, such as skydiving and investing in risky financial assets, while others choose safer activi- ties? Indifference curve analysis provides an answer to this question.

The accompanying figures plot three potential invest- ment options (represented by points A, B, and C), each with different expected returns and risks. Option A is the safest investment, but it offers the lowest return (2.94 percent); option B is of medium safety, with a moderate return (4.49 percent); and fund C is the least safe, but it carries the high- est potential return (6.00 percent).

Investors view safety and the level of the return on an investment as “goods”; investments with higher returns and higher levels of safety are preferred to investments with lower returns and lower levels of safety. Investors are willing to substitute between the level of return and the level of safety. Given the three options, from an investor’s

viewpoint, there is a trade-off between a higher reward (return) and the level of safety of the investment.

The relatively steep indifference curves drawn in panel (a) describe an investor who has a high marginal rate of sub- stitution between return and safety; she or he must receive a large return to be induced to give up a small amount of safety. The relatively flat indifference curves drawn in panel (b) indicate an investor with a low marginal rate of substi- tution between return and safety. This individual is willing to give up a lot of safety to get a slightly higher return. An investor with indifference curves such as those in panel (a) finds investment option A most attractive, because it is associated with the highest indifference curve. In contrast, an investor with indifference curves such as those in panel (b) achieves the highest indifference curve with investment option C. Both types of investors are rational, but one inves- tor is willing to give up some additional financial return for more safety.

INSIDE BUSINESS 4–1

Indifference Curves and Risk Preferences

0

Return

(a): Safety Chooser

Safety Low Medium

2.94

4.49

6.00 C

High

B

A

(b): Risk Chooser

0

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Safety Low Medium

2.94

4.49

6.00 C

High

B

A

beans because he prefers jelly beans to licorice. When the clerk hands him a bagful of jelly beans, Billy tells her he likes chocolate even more than jelly beans. When the clerk hands him a bagful of chocolate, he tells her he likes licorice even more than chocolate. When the clerk hands him a bagful of licorice, Billy tells her he likes jelly beans even more than licorice. The clerk puts back the licorice and hands Billy a bagful of jelly beans. Now Billy is right back where he started! He is unable to choose the “best” kind of candy because his prefer- ences for kinds of candy are not transitive.

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The implications of these four properties are conveniently summarized in Figure 4–2, which depicts three indifference curves. Every bundle on indifference curve III is preferred to those on curve II, and every bundle on indifference curve II is preferred to those on curve I. The three indifference curves are convex and do not cross. Curves farther from the origin imply higher levels of satisfaction than curves closer to the origin.

CONSTRAINTS

In making decisions, individuals face constraints. There are legal constraints, time constraints, physical constraints, and, of course, budget constraints. To maintain our focus on the essen- tials of managerial economics without delving into issues beyond the scope of this course, we will examine the role prices and income play in constraining consumer behavior.

The Budget Constraint Simply stated, the budget constraint restricts consumer behavior by forcing the consumer to select a bundle of goods that is affordable. If a consumer has only $30 in his or her pocket when reaching the checkout line in the supermarket, the total value of the goods the consumer presents to the cashier cannot exceed $30.

To demonstrate how the presence of a budget constraint restricts the consumer’s choice, we need some additional shorthand notation. Let M represent the consumer’s income, which can be any amount. By using M instead of a particular value of income, we gain generality in that the theory is valid for a consumer with any income level. We will let Px and Py represent the prices of goods X and Y, respectively. Given this notation, the opportunity set (also called the budget set) may be expressed mathematically as

Px X + Py Y ≤ M

In words, the budget set defines the combinations of goods X and Y that are affordable for the consumer: The consumer’s expenditures on good X, plus her or his expenditures on good Y, do not exceed the consumer’s income. Note that if the consumer spends his or her entire income on the two goods, this equation holds with equality. This relation is called the budget line:

Px X + Py Y = M

In other words, the budget line defines all the combinations of goods X and Y that exactly exhaust the consumer’s income.

budget set The bundles of goods a consumer can afford.

budget line The bundles of goods that exhaust a consumer’s income.

Figure 4–2 A Family of Indifference Curves

Y

X 0

I II

III

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It is useful to manipulate the equation for the budget line to obtain an alternative expres- sion for the budget constraint in slope-intercept form. If we multiply both sides of the budget line by 1/Py , we get

Px

___ Py

 X + Y =  M

___ Py

Solving for Y yields

Y =  M

___ Py

 −  Px

___ Py

 X

Note that Y is a linear function of X with a vertical intercept of M/Py and a slope of −Px /Py . The consumer’s budget constraint is graphed in Figure 4–3. The shaded area represents

the consumer’s budget set, or opportunity set. In particular, any combination of goods X and Y within the shaded area, such as point G, represents an affordable combination of X and Y. Any point above the shaded area, such as point H, represents a bundle of goods that is unaffordable.

The upper boundary of the budget set in Figure 4–3 is the budget line. If a consumer spent her or his entire income on good X, the expenditures on good X would exactly equal the consumer’s income:

Px X = M

By manipulating this equation, we see that the maximum affordable quantity of good X consumed is

X =  M

___ P x

This is why the horizontal intercept of the budget line is

M

___ P x

Figure 4–3 The Budget Set

0

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X

H

Y = – X

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M P

y

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P y

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Similarly, if the consumer spent his or her entire income on good Y, expenditures on Y would exactly equal income:

Py Y = M

Consequently, the maximum quantity of good Y that is affordable is

Y =  M

___ P y

The slope of the budget line is given by −Px /Py and represents the market rate of substitution between goods X and Y. To obtain a better understanding of the market rate of substitution between goods X and Y, consider Figure 4–4, which presents a budget line for a consumer who has $10 in income and faces a price of $1 for good X and a price of $2 for good Y. If we substitute these values of Px , Py , and M into the formula for the budget line, we observe that the vertical intercept of the budget line (the maximum amount of good Y that is affordable) is M/Py = 10/2 = 5. The horizontal intercept is M/Px = 10/1 = 10 and represents the maximum amount of good X that can be purchased. The slope of the budget line is −Px /Py = −(1/2).

The reason the slope of the budget line represents the market rate of substitution between the two goods is as follows: Suppose a consumer purchased bundle A in Figure 4–4, which represents the situation where the consumer purchases 3 units of good Y and 4 units of good X. If the consumer purchased bundle B instead of bundle A, she would gain one addi- tional unit of good Y. But to afford this, she must give up 2 units (4 − 2 = 2) of good X. For every unit of good Y the consumer purchases, she must give up 2 units of good X in order to be able to afford the additional unit of good Y. Thus the market rate of substitution is ΔY/ΔX = (4 − 3)/(2 − 4) = −1/2, which is the slope of the budget line.

Changes in Income The consumer’s opportunity set depends on market prices and the consumer’s income. As these parameters change, so will the consumer’s opportunities. Let us now examine the effects on the opportunity set of changes in income by assuming prices remain constant.

market rate of substitution The rate at which one good may be traded for another in the market; slope of the budget line.

Figure 4–4 The Budget Line

0

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Budget line

B

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2 4

A

10 X

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In today’s economy, many consumers choose to make purchases using credit cards rather than cash. How does access to a credit card affect a consumer’s budget constraint? A key aspect of credit cards is that they allow us to consume today and pay later. We can capture this feature of credit cards within our framework by considering a consumer’s decision about purchasing a product, e.g., music downloads, at different points in time.

Let X be music downloads today (period 1) and Y be music downloads one period later (period 2). For simplicity, let the price of a music download in both periods be $1. Suppose in period 1 Kate is considering purchasing some music down- loads but has no more cash on hand. However, she has access to $100 of credit on her credit card, which she must pay off in period 2. The interest rate on her card is 25 percent. Since, regardless of her purchase timing, she does not make any payments until period 2, we can construct her budget line in terms of income and prices in period 2. The price of a music download in period 2 is $1; however, the price of a music down- load in period 1 will cost her $1.25 in period 2 money since she must borrow the $1 price at an interest rate of 25 percent.

From the preceding discussion, Kate’s budget line in terms of period 2 money has the following features: M = $125, Px = $1.25, and Py = $1. This budget line is illustrated in the accompanying figure. The slope of −1.25 represents the amount of music downloads she must give up from period 2 to buy one more in period 1.

INSIDE BUSINESS 4–2

The Budget Constraints and Credit Cards

Y

X

125

100

Budget line (Slope = −1.25)

0

Suppose the consumer’s initial income in Figure 4–5 is M 0. What happens if M 0 increases to M1 while prices remain unchanged? Recall that the slope of the budget line is given by −Px /Py . Under the assumption that prices remain unchanged, the increase in income will not affect the slope of the budget line.

However, the vertical and horizontal intercepts of the budget line both increase as the consumer’s income increases because more of each good can be purchased at the higher

0

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Increase in income

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M1

P y

M1

P x

M0

P y

M 0

P x

M2

P y

M 2

P x

M 2< M 0< M1

Decrease in income

Figure 4–5 Changes in Income Shrink or Expand Opportunities

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income. Thus, when income increases from M 0 to M 1, the budget line shifts to the right in a parallel fashion. This reflects an increase in the consumer’s opportunity set because more goods are affordable after the increase in income than before. Similarly, if income decreases to M 2 from M 0, the budget line shifts toward the origin and the slope of the budget line remains unchanged.

Changes in Prices Now suppose the consumer’s income remains fixed at M, but the price of good X decreases to P x

1  <  P x 0 . Furthermore, suppose the price of good Y remains unchanged. Since the slope of the

budget line is given by −Px /Py , the reduction in the price of good X changes the slope, making it flatter than before. Since the maximum amount of good Y that can be purchased is M/Py , a reduction in the price of good X does not change the Y intercept of the budget line. But the maximum amount of good X that can be purchased at the lower price (the X intercept of the budget line) is M/ P x

1 , which is greater than M/ P x 0 . Thus, the ultimate effect of a reduction in

the price of good X is to rotate the budget line counterclockwise, as in Figure 4–6. Similarly, an increase in the price of good X leads to a clockwise rotation of the budget line, as the next demonstration problem indicates.

Figure 4–6 A Decrease in the Price of Good X

0

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Initial budget line

X

M

M M

New budget lineP y

>

Px 0

Px 0 Px

1

Px 1

DEMONSTRATION PROBLEM 4–1

A consumer has initial income of $100 and faces prices of Px = $1 and Py = $5. Graph the budget line, and show how it changes when the price of good X increases to P x

1  = $5 .

ANSWER: Initially, if the consumer spends his entire income on good X, he can purchase M/Px = 100/1 = 100 units of X. This is the horizontal intercept of the initial budget line in Figure 4–7. If the consumer spends his entire income on good Y, he can purchase M/Py = 100/5 = 20 units of Y. This is the vertical intercept of the initial budget line. The slope of the initial budget line is −Px /Py = −1/5.

When the price of good X increases to 5, the maximum amount of X the consumer can purchase is reduced to M/Px = 100/5 = 20 units of X. This is the horizontal intercept of the new budget line in Figure 4–7. If the consumer spends his entire income on good Y, he can purchase M/Py = 100/5 = 20 units of Y. Thus, the vertical intercept of the budget line remains unchanged; the slope changes to − P x

1 /P y = −5/5 = −1 .

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CONSUMER EQUILIBRIUM

The objective of the consumer is to choose the consumption bundle that maximizes his or her utility, or satisfaction. If there was no scarcity, the more-is-better property would imply that the consumer would want to consume bundles that contained infinite amounts of goods. However, one implication of scarcity is that the consumer must select a bundle that lies inside the budget set, that is, an affordable bundle. Let us combine our theory of consumer preferences with our analysis of constraints to see how the consumer goes about selecting the best affordable bundle.

Consider a bundle such as A in Figure 4–8. This combination of goods X and Y lies on the budget line, so the cost of bundle A completely exhausts the consumer’s income. Given the income and prices corresponding to the budget line, can the consumer do better—that is, can the consumer achieve a higher indifference curve? Clearly, if the consumer consumed bundle B instead of bundle A, she or he would be better off since the indifference curve through B lies above the one through A. Moreover, bundle B lies on the budget line and thus is affordable. In short, it is inefficient for the consumer to consume bundle A because bundle B both is affordable and yields a higher level of well-being.

Is bundle B optimal? The answer is no. Bundle B exhausts the consumer’s budget, but there is another affordable bundle that is even better: bundle C. Note that there are bundles, such as D, that the consumer prefers more than bundle C, but those bundles are not affordable. Thus, we say bun- dle C represents the consumer’s equilibrium choice. The term equilibrium refers to the fact that the consumer has no incentive to change to a different affordable bundle once this point is reached.

0

Y

Initial budget line

X

20

20 100

New budget line

Figure 4–7 An Increase in the Price of Good X

Figure 4–8 Consumer Equilibrium

Y

X 0

A

B C

D

Consumer equilibrium

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An important property of consumer equilibrium is that at the equilibrium consumption bundle, the slope of the indifference curve is equal to the slope of the budget line. Recalling that the absolute value of the slope of the indifference curve is called the marginal rate of substitution and the slope of the budget line is given by −Px /Py , we see that at a point of consumer equilibrium,

MRS =  P x ___ P y

If this condition did not hold, the personal rate at which the consumer is willing to sub- stitute between goods X and Y would differ from the market rate at which he or she is able to substitute between the goods. For example, at point A in Figure 4–8, the slope of the indiffer- ence curve is steeper than the slope of the budget line. This means the consumer is willing to give up more of good Y to get an additional unit of good X than she or he actually has to give up, based on market prices. Consequently, it is in the consumer’s interest to consume less of good Y and more of good X. This substitution continues until ultimately the consumer is at a point such as C in Figure 4–8, where the MRS is equal to the ratio of prices.

COMPARATIVE STATICS

Price Changes and Consumer Behavior A change in the price of a good will lead to a change in the equilibrium consumption bundle. To see this, recall that a reduction in the price of good X leads to a counterclockwise rotation of the budget line. Thus, if the consumer initially is at equilibrium at point A in Figure 4–9, when the price of good X falls to P x

1 , his or her opportunity set expands. Given this new opportunity set, the consumer can achieve a higher level of satisfaction. This is illustrated as a movement to the new equilibrium point, B, in Figure 4–9.

Precisely where the new equilibrium point lies along the new budget line after a price change depends on consumer preferences. Accordingly, it is useful to recall the definitions of substitutes and complements that were introduced in Chapter 2.

consumer equilibrium The equilibrium consumption bundle is the affordable bundle that yields the greatest satisfaction to the consumer.

Figure 4–9 Change in Consumer Equilibrium Due to a Decrease in the Price of Good X (Note that good Y is a substitute for X.)

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First, goods X and Y are called substitutes if an increase (decrease) in the price of X leads to an increase (decrease) in the consumption of Y. Most consumers would view Coke and Pepsi as substitutes. If the price of Pepsi increased, most people would tend to consume more Coke. If goods X and Y are substitutes, a reduction in the price of X would lead the consumer to move from point A in Figure 4–9 to a point such as B, where less of Y is consumed than at point A.

Second, goods X and Y are called complements if an increase (decrease) in the price of good X leads to a decrease (increase) in the consumption of good Y. Beer and pretzels are an example of complementary goods. If the price of beer increased, most beer drinkers would decrease their consumption of pretzels. When goods X and Y are complements, a reduction in the price of X would lead the consumer to move from point A in Figure 4–10 to a point such as B, where more of Y is consumed than before.

One of the more important decisions a manager must make is how much inventory to have on hand. Too little inventory means an insufficient quantity of products to meet the demand of consumers, in which case your cus- tomers may defect to another store. The opportunity cost of inventory is the forgone interest that could be earned on the money tied up in inventory, storage costs, and so on. In performing inventory management, an effective manager recognizes the relationship that exists among products in the store and the impact of a change in the price of one product on the required inventories of other products. For example, a decline in the price of video game consoles not only increases the quantity demanded of game consoles, but also increases the demand for video games, which are complementary goods. This result has obvious implications for inventory management.

A more subtle aspect of a reduction in the price of a product is its impact on the demand for, and optimal inven- tories of, substitute goods. If a retailer sells many products, and some of the products are substitutes, a reduction in the price of one product will lead to a reduction in the retail- er’s sales of these substitute goods. For instance, when the price of Xbox One game consoles is reduced, the con- sumption of Xbox One consoles increases as a direct con- sequence of the price reduction. However, note that the consumption of substitutes like PlayStation4 game consoles will decrease as a result of the reduction in the price of Xbox One game consoles. If the manager does not account for the impact of a price reduction on the consumption of substitute goods, he or she is likely to face a buildup of inventories of PlayStation4 consoles when the price of Xbox One game consoles decreases.

INSIDE BUSINESS 4–3

Price Changes and Inventory Management for Multiproduct Firms

Figure 4–10 When the Price of Good X Falls, the Consumption of Complementary Good Y Rises

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From a managerial perspective, the key thing to note is that changes in prices affect the market rate at which a consumer can substitute among various goods. Therefore, changes in prices will change the behavior of consumers. Price changes might occur because of updated pricing strategies within your own firm. Or they might arise because of price changes made by rivals or firms in other industries. Ultimately, price changes alter consumer incentives to buy different goods, thereby changing the mix of goods they purchase in equilibrium. The primary advantage of indifference curve analysis is that it allows a manager to see how price changes affect the mix of goods that consumers purchase in equilibrium. As we will see below, indifference curve analysis also allows us to see how changes in income affect the mix of goods consumers purchase.

Income Changes and Consumer Behavior A change in income also will lead to a change in the consumption patterns of consumers. The reason is that changes in income either expand or contract the consumer’s budget constraint, and the consumer therefore finds it optimal to choose a new equilibrium bundle. For example, assume the consumer initially is at equilibrium at point A in Figure 4–11. Now suppose the consumer’s income increases to M 1 so that his or her budget line shifts out. Clearly the consumer can now achieve a higher level of satisfaction than before. This par- ticular consumer finds it in her or his interest to choose bundle B in Figure 4–11, where the indifference curve through point B is tangent to the new budget line.

As in the case of a price change, the exact location of the new equilibrium point will depend on consumer preferences. Let us now review our definitions of normal and inferior goods.

Recall that good X is a normal good if an increase (decrease) in income leads to an increase (decrease) in the consumption of good X. Normal goods include goods such as steak, airline travel, and designer jeans. As income goes up, consumers typically buy more of these goods. Note in Figure 4–11 that the consumption of both goods X and Y increased due to the increase in consumer income. Thus, the consumer views X and Y as normal goods.

Recall that good X is an inferior good if an increase (decrease) in income leads to a decrease (increase) in the consumption of good X. Bologna, bus travel, and generic jeans are examples of inferior goods. As income goes up, consumers typically consume less of these goods and services. It is important to repeat that by calling the goods inferior, we do not imply that they are of poor quality; it is simply a term used to define products consumers purchase less of when their incomes rise.

Figure 4–11 An Increase in Income Increases the Consumption of Normal Goods

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Figure 4–12 depicts the effect of an increase in income for the case when good X is an inferior good. When income increases, the consumer moves from point A to point B to maximize his or her satisfaction given the higher income. Since at point B the consumer consumes more of good Y than at point A, we know that good Y is a normal good. However, note that at point B less of good X is consumed than at point A, so we know this consumer views X as an inferior good.

An important consideration in running a firm is the impact of changes in prices on the demand for the firm’s product. Suppose you are the manager of a firm that sells a product that is a normal good and are considering expanding your product line to include another good. There are several things you may wish to consider in making your decision. Since your product is a normal good, you will sell more of it when the economy is booming (consumer incomes are high) than when times are tough (incomes are low). Your product is a cyclical product, that is, sales vary directly with the economy. This information may be useful to you when considering alternative products to include in your store. If you expand your offerings to include more normal goods, you will continue to have an operation that sells more during an economic boom than during a recession. But if you include in your operation some inferior goods, the demand for these products will increase during bad eco- nomic times (when incomes are low) and perhaps offset the

decline in demand for normal goods. This is not to say that the optimal mix of products involves a 50–50 mix of normal and inferior goods; indeed, the optimal mix will depend on your own risk preference. The analysis does suggest that running a gourmet food store will likely involve a higher level of risk than running a supermarket. In particular, gourmet shops sell almost exclusively normal goods, while supermarkets have a more “balanced portfolio” of normal and inferior goods. This explains why, during recessions, many gourmet shops go out of business while supermar- kets do not.

It is also useful to know the magnitude of the income effect when designing a marketing campaign. If the product is a normal good, it is most likely in the firm’s interest to target advertising campaigns toward individuals with higher incomes. These factors should be considered when deter- mining which magazines, television shows, and websites are the best outlets for advertising messages.

INSIDE BUSINESS 4–4

Income Effects and the Business Cycle

Figure 4–12 An Increase in Income Decreases the Equilibrium Consumption of Good X—An Inferior Good

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Substitution and Income Effects We can combine our analysis of price and income changes to gain a better understanding of the effect of a price change on consumer behavior. Suppose a consumer initially is in equilibrium at point A in Figure 4–13, along the budget line connecting points F and G. Suppose the price of good X increases so that the budget line rotates clockwise and becomes the budget line connecting points F and H. There are two things to notice about this change. First, since the budget set is smaller due to the price increase, the consumer will be worse off after the price increase. A lower “real income” will be achieved, as a lower indifference curve is all that can be reached after the price increase. Second, the increase in the price of good X leads to a budget line with a steeper slope, reflecting a higher market rate of substitution between the two goods. These two factors lead the consumer to move from the initial consumer equilibrium (point A) to a new equilibrium (point C) in Figure 4–13.

It is useful to isolate the two effects of a price change to see how each effect individually alters consumer choice. In particular, ignore for the moment the fact that the price increase leads to a lower indifference curve. Suppose that after the price increase, the consumer is given enough income to achieve the budget line connecting points J and I in Figure 4–13. This budget line has the same slope as budget line FH, but it implies a higher income than budget line FH. Given this budget line, the consumer will achieve equilibrium at point B, where less of good X is consumed than in the initial situation, point A. The movement from A to B is called the substitution effect; it reflects how a consumer will react to a different market rate of substitution. The substitution effect is the difference X 0 − X m in Figure 4–13. Importantly, the movement from A to B leaves the consumer on the same indifference curve, so the reduction in the consumption of good X implied by that movement reflects the higher market rate of substitution, not the reduced “real income,” of the consumer.

The consumer does not actually face budget line JI when the price increases but instead faces budget line FH. Let us now take back the income we gave to the consumer to compen- sate for the price increase. When this income is taken back, the budget line shifts from JI to FH. This shift in the budget line reflects only a reduction in income; the slopes of budget

substitution effect The movement along a given indifference curve that results from a change in the relative prices of goods, holding real income constant.

Figure 4–13 An Increase in the Price of Good X Leads to a Substitution Effect (A to B) and an Income Effect (B to C)

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lines JI and FH are identical. Thus, the movement from B to C is called the income effect. The income effect is the difference X m − X 1 in Figure 4–13; it reflects the fact that when price increases, the consumer’s “real income” falls. Since good X is a normal good in Figure 4–13, the reduction in income leads to a further reduction in the consumption of X.

The total effect of a price increase thus is composed of substitution and income effects. The substitution effect reflects a movement along an indifference curve, thus isolating the effect of a relative price change on consumption. The income effect results from a parallel shift in the budget line; thus, it isolates the effect of reduced “real income” on consumption and is represented by the movement from B to C. The total effect of a price increase, which is what we observe in the marketplace, is the movement from A to C. The total effect of a change in consumer behavior results not only from the effect of a higher relative price of good X (the movement from A to B) but also from the reduced real income of the consumer (the movement from B to C).

APPLICATIONS OF INDIFFERENCE CURVE ANALYSIS

Choices by Consumers Buy One, Get One Free A very popular sales technique at pizza restaurants is to offer the following deal:

Buy one large pizza, get one large pizza free (limit one free pizza per customer).

It is tempting to conclude that this is simply a 50 percent reduction in the price of pizza so that the budget line rotates as it does for any price decrease. This conclusion is invalid, however. A price reduction decreases the price of each unit purchased. The “buy one, get one” pizza deal reduces only the price of the second unit purchased (in fact, it reduces the price of the second large pizza to zero). The offer does not change the price of units below one pizza and above two pizzas.

The “buy one, get one free” marketing scheme is quite easy to analyze in our framework. In Figure 4–14, a consumer initially faces a budget line connecting points A and B and is in equilibrium at point C. Point C represents one-half of a large pizza (say, a small pizza), so the consumer decides it is best to buy a small pizza instead of a large one. Point D represents the

income effect The movement from one indifference curve to another that results from the change in real income caused by a price change.

Figure 4–14 A Buy One, Get One Free Pizza Deal

Other goods

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point at which she buys one large pizza, but, as we can see, the consumer prefers bundle C to bundle D since it lies on a higher indifference curve.

When the consumer is offered the “buy one, get one free” deal, her budget line becomes ADEF. The reason is as follows: If she buys less than one large pizza, she gets no deal, and her budget line to the left of one pizza remains as it was, namely AD. But if she buys one large pizza, she gets a second one free. In this instance, the budget line becomes DEF as soon as she buys one pizza. In other words, the price of pizza is zero for units between one and two large pizzas. This implies that the budget line for pizzas is horizontal between one and two units (recall that the slope of the budget line is −Px /Py , and for these units Px is zero). If the consumer wants to consume more than two large pizzas, she must buy them at regular prices. But note that if she spent all of her income on pizza, she could buy one more than she could before (since one of the pizzas is free). Thus, for pizzas in excess of two units, the budget constraint is the line connecting points E and F. After the deal is offered, the opportunity set increases. In fact, bundle E is now an affordable bundle. Moreover, it is clear that bundle E is preferred to bundle C, and the consumer’s optimal choice is to consume bundle E, as in Figure 4–14. The sales technique has induced the consumer to purchase more pizza than she would have otherwise.

Cash Gifts, In-Kind Gifts, and Gift Certificates Along with death and taxes, lines in refund departments after Christmas appear to be an unpleasant but necessary aspect of life. To understand why, and to be able to pose a potential solution to the problem, consider the following story.

One Christmas morning, a consumer named Sam is in equilibrium, consuming bundle A as in Figure 4–15. He opens a package and, to his surprise, it contains a $10 fruitcake (good X). He smiles and tells Aunt Sarah that he always wanted a fruitcake. Graphically, when Sam receives the gift, his opportunity set expands to include point B in Figure 4–15. Bundle B is just like bundle A except that it has one more fruitcake (good X) than bundle A. Given this new opportunity set, Sam moves to the higher indifference curve through point B after receiving the gift.

Figure 4–15 A Cash Gift Yields Higher Utility Than an In-Kind Gift

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While Sam likes fruitcake and is better off after receiving it, the gift is not what he would have purchased had Aunt Sarah given him the cash she spent on the fruitcake. For concreteness, suppose the cost of the fruitcake was $10. Had Sam been given $10 in cash, his budget line would have shifted out, parallel to the old budget line but through point B, as in Figure  4–15. To see why, note that when Sam gets additional income, prices are not changed, so the slope of the budget line is unchanged. Note also that if Sam used the money to buy one more fruitcake, he would exactly exhaust his income. Thus, the budget line after the cash gift must go through point B—and, given the cash gift, Sam would achieve a higher level of satisfaction at point C compared to the gift of a fruitcake (point B).

Thus, a cash gift generally is preferred to an in-kind gift of equal value, unless the in-kind gift is exactly what the consumer would have purchased personally. This explains why refund departments are so busy after the Christmas holidays; individuals exchange gifts for cash so that they can purchase bundles they prefer.

One way stores attempt to reduce the number of gifts returned is to sell gift certificates. To see why, suppose Sam received a gift certificate, good for $10 worth of merchandise at store X, which sells good X, instead of the $10 fruitcake. Further, suppose the certificate is not good at store Y, which sells good Y. By receiving a gift certificate, Sam cannot purchase any more of good Y than he could before he received the certificate. But if he spends all his income on good Y, he can purchase $10 worth of good X since he has a certificate worth $10 at store X. And if he spends all his income on good X, he can purchase $10 more than he could before because of the gift certificate. In effect, the gift certificate is like money that is good only at store X.

Graphically, the effect of receiving a gift certificate at store X is depicted in Figure 4–16. The straight black line is the budget line before Sam receives the gift certificate. When he receives the $10 gift certificate, the budget constraint becomes the kinked blue line. In effect, the gift certificate allows the consumer up to $10 worth of good X without spending a dime of his own money.

The effect of gift certificates on consumer behavior depends, among other things, on whether good X is a normal or inferior good. To examine what happens to behavior when a consumer receives a gift certificate, let us suppose a consumer initially is in equilibrium at point A in Figure 4–16, spending $10 on good X. What happens if the consumer is given a $10 gift certificate good only for items in store X? If both X and Y are normal goods, the consumer

Figure 4–16 A Gift Certificate Valid at Store X

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will desire to spend more on both goods as income increases. Thus, if both goods are normal goods, the consumer moves from A to C in Figure 4–16. In this instance, the con- sumer reacts to the gift certificate just as she or he would have reacted to a cash gift of equal value.

DEMONSTRATION PROBLEM 4–2

How would the analysis of gift certificates just presented change if good X were an inferior good?

ANSWER: In this instance, a gift of $10 in cash would result in a movement from point A in Figure 4–17 to a point like D since X is an inferior good. However, when a $10 gift certificate is received, bundle D is not affordable, and the best the consumer can do is consume bundle E. In other words, had the consumer been given cash, his or her budget line would have extended up along the dotted line, and point D would have been an affordable bundle. If given cash, the consumer would have purchased less of good X than she or he did with the gift certificate. Also, note that the consumer would have achieved a higher indifference curve with the cash than that achieved with the gift certificate. (Conceptual and Computational Question 4 appearing at the end of this chapter asks you whether a gift certificate always leads to a lower indifference curve and higher sales than a cash gift when the good is inferior.)

Figure 4–17 Here, a Cash Gift Yields Higher Utility Than a Gift Certificate of Equal Dollar Value

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This analysis reveals two important benefits to a firm that sells gift certificates. First, as a manager you can reduce the strain on your refund department by offering gift certificates to customers looking for gifts. This is true for both normal and inferior goods. Second, if you sell an inferior good, offering to sell gift certificates to those looking for gifts may result in a greater quantity sold than if customers resorted to giving cash gifts. (This assumes you do not permit individuals to redeem gift certificates for cash.)

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Choices by Workers and Managers Until now, our analysis of indifference curves has focused on the decisions of consumers of goods and services. Managers and workers also are individuals and therefore have preferences among the alternatives that confront them. In this section, we will see that the indifference curve analysis developed earlier for consumers can easily be modified to analyze the behavior of managers and other individuals employed by firms. In Chapter 6 we will show how these insights into the behavior of workers and managers can be used to construct efficient employ- ment contracts.

A Simplified Model of Income–Leisure Choice Most workers view both leisure and income as goods and substitute between them at a diminishing rate along an indifference curve. Thus, a typical worker’s indifference curve has the usual shape in Figure 4–18, where we measure the quantity of leisure consumed by an employee on the horizontal axis and worker income on the vertical axis. Note that while workers enjoy leisure, they also enjoy income.

To induce workers to give up leisure, firms must compensate them. Suppose a firm offers to pay a worker $10 for each hour of leisure the worker gives up (i.e., spends working). In this instance, opportunities confronting the worker or manager are given by the straight line in Figure 4–18. If the worker chooses to work 24-hour days, he or she consumes no leisure but earns $10 × 24 = $240 per day, which is the vertical intercept of the line. If the worker chooses not to work, he or she consumes 24 hours of leisure but earns no income. This is the horizontal intercept of the line in Figure 4–18.

Worker behavior thus may be examined in much the same way we analyzed consumer behavior. The worker attempts to achieve a higher indifference curve until he or she achieves one that is tangent to the opportunity set at point E in Figure 4–18. In this instance, the worker consumes 16 hours of leisure and works 8 hours to earn a total of $80 per day.

Figure 4–18 Labor–Leisure Choice

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1 William J. Baumol, Business Behavior, Value, and Growth, rev. ed. (New York: Harcourt, Brace and World, 1967).

DEMONSTRATION PROBLEM 4–3

Suppose a worker is offered a wage of $5 per hour, plus a fixed payment of $40. What is the equation for the worker’s opportunity set in a given 24-hour day? What are the maximum total earnings the worker can earn in a day? The minimum? What is the price to the worker of consuming an additional hour of leisure?

ANSWER: The total earnings (E) of a worker who consumes L hours of leisure in a 24-hour day is given by

E = $40 + $5(24 − L)

so the combinations of earnings (E) and leisure (L) satisfy

E = $160 − $5L

Thus, the most a worker can earn in a 24-hour day is $160 (by consuming no leisure); the least that can be earned is $40 (by not working at all). The price of a unit of leisure is $5 since the oppor- tunity cost of an hour of leisure is one hour of work.

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

The Decisions of Managers A classic argument by William Baumol1 states that many managers derive satisfaction from the underlying output and profits of their firms. According to Baumol, higher profits and sales lead to a larger firm, and larger firms provide more “perks” like spacious offices, executive health clubs, corporate jets, and the like.

Gift-givers are resorting to gift certificates in record droves. A recent survey showed that about 80 percent of Christmas shoppers plan to give gift certificates. The total dollar value of these certificates amounts to a staggering $32 billion. Why are gift certificates such a popular medium of gift-giving?

An economist offered one explanation. Based on data from a group of college students, the researcher esti- mated that between 10 and 30 percent of the monetary value of the typical in-kind gift is “lost.” This loss stems from the discrepancy between the amount actually paid for the gift and how much the recipient values it. These data from the real world indicate that it is indeed difficult to pick a gift that exactly matches that recipient’s prefer- ences. For this reason, in-kind gifts create a “deadweight

loss” that averages 10 to 30 percent of the amount spent on gifts.

As the text shows, one way of avoiding this deadweight loss is to give cash rather than an in-kind gift. Unfortunately, this creates a different type of loss when there is a stigma associated with giving cash: The gift is “discounted” because the recipient feels that little thought went into it. Gift certificates are a happy medium. Ideally, they are able to eliminate both the stigma associated with cash gifts and the deadweight loss that stems from giving a gift that doesn’t exactly match the recipient’s preferences.

SOURCES: “Harried Shoppers Turn to Gift Certificates,” New York Times, January 4, 1997; J. Waldfogel, “The Deadweight Loss of Christmas,” American Economic Review 83, no. 5 (December 1993), pp. 1328–36; Statistics from National Retail Federation Gift Card survey, November 2014.

INSIDE BUSINESS 4–5

The “Deadweight Loss” of In-Kind Gifts

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Suppose a manager’s preferences are such that she or he views the “profits” and the “output” of the firm to be “goods” so that more of each is preferred to less. We are not suggest- ing that it is optimal for you, as a manager, to have these types of preferences, but there may be instances in which your preferences are so aligned. In many sales jobs, for example, individuals receive a bonus depending on the overall profitability of the firm. But the salesperson’s ability to receive reimbursement for certain business-related expenses may depend on that individu- al’s total output (e.g., number of cars sold). Additionally, perks such as a company plane, car, and so forth may be allocated to individuals based on the firm’s output and profitability. In all of these scenarios, managerial preferences depend on the firm’s output as well as profits.

Panels (a), (b), and (c) of Figure 4–19 show the relation between profits and the output of a firm on the curve labeled “firm’s profits.” This curve goes from the origin through points C, A, and B and represents the profits of the firm as a function of output. When the firm sells no output, profits are zero. As the firm expands output, profits increase, reach a maximum at Qm , and then begin to decline until, at point Q0, they are again zero.

Given this relationship between output and profits, a manager who views output and prof- its as “goods” (the Baumol hypothesis) has indifference curves like those in Figure 4–19(a). She attempts to achieve higher and higher indifference curves until she eventually reaches equilibrium at point A. Note that this level of output, Qu , is greater than the profit-maximizing level of output, Qm . Thus, when the manager views both profits and output as “goods,” she produces more than the profit-maximizing level of output.

In contrast, when the manager’s preferences depend solely on output, the indifference curves look like those in Figure 4–19(b), which are vertical straight lines. One example of this situation occurs when the owner of a car dealership pays the manager based solely on the number of cars sold (the manager gets nothing if the company goes bankrupt). Since the manager does not care about profits, his or her indifference curves are vertical lines, and satisfaction increases as the lines move farther to the right. A manager with such preferences will attempt to obtain the indifference curves farther and farther to the right until indifference curve I2 is reached. Point B represents equilibrium for this manager, where Q0 units of output are produced. Again, in this instance the manager produces more than the profit-maximizing level of output.

Finally, suppose the manager cares solely about the profits of the firm. In this instance, the manager’s indifference curves are horizontal straight lines as shown in Figure 4–19(c). The manager maximizes satisfaction at point C, where the indifference curve I2 is as high as possible given the opportunity set. In this instance, profits are greater and output is lower than in the other two cases.

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Figure 4–19 A Manager’s Preferences Might Depend on: (a) prof- its and output, (b) output only, or (c) profits only

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Figure 4–20 Deriving an Individual’s Demand Curve

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An important issue for the firm’s owners is to induce managers to care solely about profits so that the result is the maximization of the underlying value of the firm, as in Figure 4–19(c). We will examine this issue in more detail in Chapter 6.

THE RELATIONSHIP BETWEEN INDIFFERENCE CURVE ANALYSIS AND DEMAND CURVES

We have seen how the consumption patterns of an individual consumer depend on variables that include the prices of substitute goods, the prices of complementary goods, tastes (i.e., the shape of indifference curves), and income. The indifference curve approach developed in this chapter, in fact, is the basis for the demand functions we studied in Chapters 2 and 3. We conclude by examining the link between indifference curve analysis and demand curves.

Individual Demand To see where the demand curve for a normal good comes from, consider Figure 4–20(a). The consumer initially is in equilibrium at point A, where income is fixed at M and prices are P x

0 and Py . But when the price of good X falls to the lower level, indicated by P x 1 , the opportu-

nity set expands and the consumer reaches a new equilibrium at point B. The important thing to notice is that the only change that caused the consumer to move from A to B was a change in the price of good X; income and the price of good Y are held constant in the diagram.

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When the price of good X is P x 0 , the consumer consumes X0 units of good X; when the price

falls to P x 1 , the consumption of X increases to X1.

This relationship between the price of good X and the quantity consumed of good X is graphed in Figure 4–20(b) and is the individual consumer’s demand curve for good X. This consumer’s demand curve for good X indicates that, holding other things constant, when the price of good X is P 0, the consumer will purchase X0 units of X; when the price of good X is P x

1 , the consumer will purchase X1 units of X.

Market Demand You will usually, in your role as a manager, be interested in determining the total demand by all consumers for your firm’s product. This information is summarized in the market demand curve. The market demand curve is the horizontal summation of individual demand curves and indicates the total quantity all consumers in the market would purchase at each possible price.

This concept is illustrated graphically in Figures 4–21(a) and 4-21(b). The curves DA and DB represent the individual demand curves of two hypothetical consumers, Ms. A and Mr. B, respectively. When the price is $60, Ms. A buys 0 units and Mr. B buys 0 units. Thus, at the market level, 0 units are sold when the price is $60, and this is one point on the market demand curve [labeled DM in Figure 4–21(b)]. When the price is $40, Ms. A buys 10 units (point A) and Mr. B buys 20 units (point B). Thus, at the market level [Figure 4–21(b)], 30 units are sold when the price is $40, and this is another point (point A + B) on the market demand curve. When the price of good X is zero, Ms. A buys 30 units and Mr. B buys 60  units; thus, at the market level, 90 units are sold when the price is $0. If we repeat the analysis for all prices between $0 and $60, we get the curve labeled DM in Figure 4–21(b).

Thus, the demand curves we studied in Chapters 2 and 3 are based on indifference curve analysis.

Figure 4–21 Deriving the Market Demand Curve

0

Price

20

40

$60

A B

D A

D B

10 6030

(a) Individual demand curves

Price

20

A B

D M

A + B

10 9030

(b) Market demand curve Quantity Total market

quantity demanded

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ANSWERING THE headLINE The question posed at the beginning of the chapter asked why Boxes Ltd. paid a higher overtime wage only on hours in excess of eight hours per day instead of offering workers a higher wage for every hour worked during a given day.

Figure 4–22 presents the analysis of income–leisure choice for a hypothetical worker. When the wage is $16 per hour, the worker’s opportunity set is given by line DF. If the worker consumed no leisure, his earnings would be $16 × 24 = $384. However, given a $16 wage, this worker maximizes satisfaction at point A, where he consumes 16 hours of leisure (works 8 hours per day) to earn $128 in wage income.

With overtime pay of $24 for each hour worked in excess of 8 hours, the oppor- tunity set becomes EAF. The reason is simple. If the worker works 8 hours or less, he does not earn overtime pay, and this part of his budget line (AF) remains the same. But if he consumes less than 16 hours of leisure, he gets $24 instead of $16 for these hours worked, so the budget line is steeper (EA). When no leisure is consumed (point E), the first 8 hours given up generate $16 × 8 = $128 in earnings, while the last 16 hours of leisure given up generate $24 × 16 = $384 in earnings. Thus, point E on the overtime budget line corresponds to earnings of $128 + $384 = $512. Given the overtime option, this worker maximizes satisfaction at point B, where he works 13 hours to earn $248. Overtime pay increases the amount of work from 8 hours to 13 hours.

Why doesn’t the firm simply increase the wage to $24 instead of initiating the more com- plicated overtime system? If this worker were paid a wage of $24 for every hour worked, his budget line would be HF. This worker would obtain a higher indifference curve at point C, where 12 hours of leisure are consumed (12 hours of work). When leisure is a normal good, the $24 wage yields fewer hours of work from each worker than does the overtime system. In addition, labor costs are lower with overtime pay (point B) than a $24 wage (point C).

To summarize, we have shown that the manager could get workers who view leisure as a normal good to work longer hours with overtime pay than she could by simply offering a higher wage on all hours worked.

Unlike most private companies, government-run agen- cies and nonprofit organizations generally are not concerned with maximizing profits; instead they have other objectives, often output maximization. This is largely the case with public health centers, which seek to provide health care to as many citizens as possible. However, the employees at public health centers may not share the government’s preference regarding out- put production.

Recently in Rwanda, the country’s public health centers suffered several years of poor performance. In response, the Rwandan Ministry of Health along with HealthNet International decided to change their support strategy for

Rwandan public health centers. Specifically, in addition to their salaries, employees were compensated via output- based bonuses. In short, as more services were provided, employees received more money.

This output-oriented incentive scheme helped to align employees’ preferences with those of the government. In fact, the productivity of the public health centers that expe- rienced this change in payment scheme showed productiv- ity increases exceeding 50 percent!

SOURCE: B. Meesen, J. P. Kashala, and L. Musango, “Output-Based Payment to Boost Staff Productivity in Public Health Centres: Contracting in Kabutare District, Rwanda,” Bulletin of the World Health Organization 85 (2007), pp. 108–15.

INSIDE BUSINESS 4–6

Public Health Centers and Output-Oriented Incentives

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SUMMARY

In this chapter, we provided a basic model of individ- ual behavior that enables the manager to understand the impact of various managerial decisions on the actions of consumers and workers.

After reading and working through the demonstration problems in this chapter, you should understand what a budget constraint is and how it changes when prices or income changes. You should also understand that when there is a change in the price of a good, consumers change their behavior because there is a change in the ratio of prices (which leads to a substitution effect) and a change in real income (which leads to the income effect). The model of consumer behavior also articulates the assumptions underlying the demand curve.

In equilibrium, consumers adjust their purchasing behavior so that the ratio of prices they pay just equals their marginal rate of substitution. This information, along

with observations of consumer behavior, helps a manager determine when to use a “buy one, get one free” pricing strategy instead of a half-price offer. During holiday sea- sons, the same manager will have a sound basis for deter- mining whether offering gift certificates is a wise strategy.

Effective managers also use the theory of consumer behavior to direct the behavior of employees. In this chapter, we examined the benefits to the firm of paying overtime wages; additional issues will be discussed in Chapter 6.

In conclusion, remember that the models of individ- ual behavior developed in this chapter are basic tools for analyzing the behavior of your customers and employees. By taking the time to become familiar with the models and working through the demonstration and end-of- chapter problems, you will be better equipped to make decisions that will maximize the value of your firm.

KEY TERMS AND CONCEPTS

budget constraint budget line budget set “buy one, get one free” deals completeness consumer equilibrium

diminishing marginal rate of substitution

gift certificates income effect indifference curve marginal rate of substitution (MRS)

market rate of substitution more is better substitution effect transitivity

Figure 4–22 An Overtime Wage Increases Hours Worked

0

Earnings ($)

Leisure

576

248

E

16 24 8 hours of work

512

384

288

128

1211

F

A

C B

H

D

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128

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. A consumer has $300 to spend on goods X and Y. The market prices of these two goods are Px = $15 and Py = $5. (LO2) a. What is the market rate of substitution between goods X and Y? b. Illustrate the consumer’s opportunity set in a carefully labeled diagram. c. Show how the consumer’s opportunity set changes if income increases by $300.

How does the $300 increase in income alter the market rate of substitution between goods X and Y?

2. A consumer is in equilibrium at point A in the accompanying figure. The price of good X is $5. (LO2, LO3) a. What is the price of good Y? b. What is the consumer’s income? c. At point A, how many units of good X does the consumer purchase? d. Suppose the budget line changes so that the consumer achieves a new equilibrium

at point B. What change in the economic environment led to this new equilibrium? Is the consumer better off or worse off as a result of the price change?

Product Y

Product X 20

45

40

35

30

25

20

15

10

5

0

A

B

3. A consumer must divide $600 between the consumption of product X and product Y. The relevant market prices are Px = $10 and Py = $40. (LO2) a. Write the equation for the consumer’s budget line. b. Illustrate the consumer’s opportunity set in a carefully labeled diagram. c. Show how the consumer’s opportunity set changes when the price of good X

increases to $20. How does this change alter the market rate of substitution between goods X and Y?

4. In the answer to Demonstration Problem 4–2 in the text, we showed a situation in which a gift certificate leads a consumer to purchase a greater quantity of an inferior good than he or she would consume if given a cash gift of equal value. Is this always the case? Explain. (LO6)

5. Provide an intuitive explanation for why a “buy one, get one free” deal is not the same as a “half-price” sale. (LO6)

6. In the following figure, a consumer is initially in equilibrium at point C. The consum- er’s income is $400, and the budget line through point C is given by $400 = $100X +

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$200Y. When the consumer is given a $100 gift certificate that is good only at store X, she moves to a new equilibrium at point D. (LO1, LO3, LO6) a. Determine the prices of goods X and Y. b. How many units of product Y could be purchased at point A? c. How many units of product X could be purchased at point E? d. How many units of product X could be purchased at point B? e. How many units of product X could be purchased at point F? f. Based on this consumer’s preferences, rank bundles A, B, C, and D in order from

most preferred to least preferred. g. Is product X a normal or an inferior good?

Product Y

Product X E F

BA

C D

I2 I1

7. A consumer must spend all of her income on two goods (X and Y). In each of the following scenarios, indicate whether the equilibrium consumption of goods X and Y will increase or decrease. Assume good X is a normal good and good Y is an inferior good. (LO3) a. Income doubles. b. Income quadruples and all prices double. c. Income and all prices quadruple. d. Income is halved and all prices double.

8. Determine which, if any, of Properties 4–1 through 4–4 are violated by the indifference curves shown in the following diagram. (LO1)

Product Y

Product X

U3

U2

U1

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9. A consumer’s budget set for two goods (X and Y) is 600 ≥ 3X + 6Y. (LO2) a. Illustrate the budget set in a diagram. b. Does the budget set change if the prices of both goods double and the consumer’s

income also doubles? Explain. c. Given the equation for the budget set, can you determine the prices of the two

goods? The consumer’s income? Explain. 10. A worker views leisure and income as “goods” and has an opportunity to work at an

hourly wage of $15 per hour. (LO7) a. Illustrate the worker’s opportunity set in a given 24-hour period. b. Suppose the worker is always willing to give up $11 of income for each hour of

leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?

PROBLEMS AND APPLICATIONS

11. It is common for supermarkets to carry both generic (store-label) and brand-name (pro- ducer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a con- stant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute four pounds of a generic store-brand sugar for two pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of sub- stitution between store-brand and producer-brand sugar? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound? (LO1, LO2, LO3)

12. The U.S. government spends over $74 billion on its Supplemental Nutrition Assistance Program (SNAP) to provide millions of Americans with the means to purchase food. Beneficiaries use an Electronic Benefits Transfer (EBT) card to transfer their govern- ment benefits from a federal account to a retailer account. The funds on an EBT card cannot be sold for cash or used to purchase nonfood items. The average SNAP benefit is about $284 per month. Suppose that, in the absence of SNAP, the average consumer must divide $600 in monthly income between food and “all other goods” such that the following budget constraint holds: $600 = $12A + $4F, where A is the quantity of “all other goods” and F is the quantity of food purchased. Using the vertical axis for “all other goods,” draw the consumer’s budget line in the absence of SNAP. What is the market rate of substitution between food and “all other goods”? On the same graph, show how SNAP alters the average consumer’s budget line. Would this consumer bene- fit from illegally exchanging SNAP benefits for cash? Explain. (LO2, LO6)

13. A recent newspaper circular advertised the following special on tires: “Buy three, get the fourth tire for free—limit one free tire per customer.” If a consumer has $360 to spend on tires and other goods and each tire usually sells for $40, how does this deal impact the consumer’s opportunity set? (LO6)

14. During the past major recession, upscale hotels in the United States recently cut their prices by 25 percent in an effort to bolster dwindling occupancy rates among business travelers. A survey performed by a major research organization indicated that businesses were becoming wary of bad economic conditions and began resorting to electronic media, such as the Internet and the telephone, to transact business. Assume a compa- ny’s budget permits it to spend $6,000 per month on either business travel or electronic

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media to transact business. Graphically illustrate how a 25 percent decline in the price of business travel would impact this company’s budget set if the price of business travel was initially $1,200 per trip and the price of electronic media was $600 per hour. Suppose that, after the price of business travel drops, the company issues a report indi- cating that its marginal rate of substitution between electronic media and business travel is −1. Is the company allocating resources efficiently? Explain. (LO1, LO2, LO3)

15. Consider an employee who does not receive employer-based health insurance and must divide her $1,000 per week in after-tax income between health insurance and “other goods.” Draw this worker’s opportunity set if the price of health insurance is $200 per week and the price of “other goods” is $100 per week. On the same graph, illustrate how the opportunity set would change if the employer agreed to give this employee $200 worth of health insurance per week (under current tax laws, this form of com- pensation is nontaxable). Would this employee be better or worse off if, instead of the health insurance, the employer gave her a $200 per week raise that was taxable at a rate of 25 percent? Explain. (LO6)

16. An internal study at Mimeo Corporation—a manufacturer of low-end photocopiers— revealed that each of its workers assembles three photocopiers per hour and is paid $6 for each assembled copier. Although the company does not have the resources needed to supervise the workers, a full-time inspector verifies the quality of each unit produced before a worker is paid for his or her output. You have been asked by your superior to evaluate a new proposal designed to cut costs. Under the plan, workers would be paid a fixed wage of $16 per hour. Would you favor the plan? Explain. (LO7)

17. The Einstein Bagel Corp. offers a frequent buyer program whereby a consumer receives a stamp each time she purchases one dozen bagels for $6. After a consumer accrues 10 stamps, she receives one dozen bagels free. This offer is an unlimited offer, valid throughout the year. The manager knows her products are normal goods. Given this information, construct the budget set for a consumer who has $200 to spend on bagels and other goods throughout the year. Does Einstein’s frequent buyer program have the same effect on the consumption of its bagels that would occur if it simply lowered the price of one dozen bagels by 3 percent? Explain. (LO6)

18. The average 15-year-old purchases 100 song downloads from iTunes and buys 20 cheese pizzas in a typical year. If cheese pizzas are inferior goods, would the average 15-year- old be indifferent between receiving a $50 gift certificate for iTunes and $50 in cash? Explain. (LO6)

19. A common marketing tactic among many liquor stores is to offer their clientele quan- tity (or volume) discounts. For instance, the second-leading brand of wine exported from Chile sells in the United States for $15 per bottle if the consumer purchases up to eight bottles. The price of each additional bottle is only $8. If a consumer has $200 to divide between purchasing this brand of wine and other goods, graphically illustrate how this marketing tactic affects the consumer’s budget set if the price of other goods is $1. Assuming a consumer has standard indifference curves (i.e., resembling those in Figure 4–2), will she ever purchase exactly eight bottles of wine? Explain. (LO6)

20. Suppose that a CEO’s goal is to increase profitability and output from her company by bolstering its sales force and that it is known that profits as a function of output are π = 40q − 2q2 (in millions of U.S. dollars). Graph the company’s profit function. Compare and contrast output and profits using the following compensation schemes based on the assumption that sales managers view output and profits as “goods”: (a) the company compensates sales managers solely based on output, (b) the company com- pensates sales managers solely based on profits, and (c) the company compensates sales managers based on a combination of output and profits. (LO7)

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21. Suppose that the owner of Boyer Construction is feeling the pinch of increased pre- miums associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)

22. Over the past decade, holiday gift cards have become increasingly popular at online retail- ers. Not long ago, online shoppers had to really hunt at most e-retailers’ sites to purchase a gift certificate, but today it is easier to purchase gift cards online than at traditional retail outlets. Do you think online gift cards are merely a fad? Explain carefully. (LO6)

23. Recently, an Internet service provider (ISP) in the United Kingdom implemented a “no-strings U.S.-style flat-rate plan” whereby its commercial subscribers can send and receive unlimited volume (measured in gigabytes) up to a cap of 10,000 gigabytes (per month) via their broadband Internet service for a flat monthly fee of £399.99. Under the old “metered plan,” Alistair Willoughby Cook sent and received a grand total of 3,500 gigabytes over his broadband connection and paid £399.99 in usage fees in a typical 30-day month. If all customers are exactly like Alistair, what is the impact of the flat- rate plan on consumer welfare and the company’s profits? Explain. (LO2, LO3)

24. A large Coca-Cola vendor recently hired some economic analysts to assess the effect of a price increase in its 16-ounce bottles from $1.00 to $2.00. The analysts determined that, on average, the vendor’s customers spend about $15.00 on soda (Coke and all other brands) each week, and the average price for other 16-ounce soda bottles is $1.00. The analysts also utilized some focus groups to determine the preferences of the vendor’s customers. They used this analysis to build the following graph:

Bottles of Other Soda

Bottles of Coke

Budget line with price of $1.00

Budget line with price of $2.00

X0X1

Suppose X0 = 9 and X1 = 7. Should the vendor expect to sell 7, more than 7, or less than 7 bottles of Coke after raising the price to $2.00 if Coke is a normal good? (LO4)

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25. When trying to assess differences in her customers, Claire—the owner of Claire’s Rose Boutique—noticed a difference between the typical demand of her female versus her male customers. In particular, she found her female customers to be more price sensitive in general. After conducting some sales analysis, she determined that her female cus- tomers have the following demand curve for roses: Q F = 24 − 2P. Here, Q F is the quan- tity of roses demanded by a female customer and P is the price charged per rose. She determined that her male customers have the following demand curve for roses: Q M = 27 − P. Here, Q M is the quantity of roses demanded by a male customer. If two unaffili- ated customers walk into her boutique, one male and one female, determine the demand curve for these two customers combined (i.e., what is their aggregate demand?). (LO5)

SELECTED READINGS

Battalio, Raymond C.; Kagel, John H.; and Kogut, Carl A., “Experimental Confirmation of the Existence of a Giffen Good.” American Economic Review 81(4), September 1991, pp. 961–70.

Baumol, William J., Business Behavior, Value and Growth. New York: Macmillan, 1959.

Davis, J., “Transitivity of Preferences.” Behavioral Science, Fall 1958, pp. 26–33.

Evans, William N., and Viscusi, W. Kip, “Income Effects and the Value of Health.” Journal of Human Resources 28(3), Summer 1993, pp. 497–518.

Gilad, Benjamin; Kaish, Stanley; and Loeb, Peter D., “Cognitive Dissonance and Utility Maximization:

A General Framework.” Journal of Economic Behavior and Organization 8(1), March 1987, pp. 61–73.

Lancaster, Kelvin, Consumer Demand: A New Approach. New York: Columbia University Press, 1971.

MacKrimmon, Kenneth, and Toda, Maseo, “The Experimental Determination of Indifference Curves.” Review of Economic Studies 37, October 1969, pp. 433–51.

Smart, Denise T., and Martin, Charles L., “Manufacturer Responsiveness to Consumer Correspondence: An Empirical Investigation of Consumer Perceptions.” Journal of Consumer Affairs 26(1), Summer 1992, pp. 104–28.

APPENDIX

A CALCULUS APPROACH TO INDIVIDUAL BEHAVIOR

THE UTILITY FUNCTION

Suppose the preferences of a consumer are represented by a utility function U(X, Y). Let A = (XA, YA) be the bun- dle with XA units of good X and YA units of good Y, and let B = (XB, YB) be a different bundle of the two goods. If bundle A is preferred to bundle B, then U(A) > U(B); the consumer receives a higher utility level from bundle A than from bundle B. Similarly, if U(B) > U(A), the con- sumer views bundle B as “better” than bundle A. Finally, if U(A) = U(B), the consumer views the two bundles to be equally satisfying; she or he is indifferent between bun- dles A and B.

UTILITY MAXIMIZATION

Given prices of Px and Py and a level of income M, the consumer attempts to maximize utility subject to the bud- get constraint. Formally, this problem can be solved by forming the Lagrangian:

ℒ ≡ U(X, Y ) + λ(M − Px X − Py Y )

where λ is the Lagrange multiplier. The first-order condi- tions for this problem are

∂ℒ

____ ∂X

 =  ∂U

___ ∂X

 − λ Px = 0 (A-1)

∂ℒ

____ ∂Y

 =  ∂U

___ ∂Y

 − λ Py = 0 (A-2)

∂ℒ

____ ∂λ

 = M − Px X − Py Y = 0

Equations (A-1) and (A-2) imply that

∂U/∂X

______ ∂U/∂Y

 =  Px

___ Py

(A-3)

or, in economic terms, the ratio of the marginal utilities equals the ratio of prices.

THE MARGINAL RATE OF SUBSTITUTION

Along an indifference curve, utility is constant:

U(X, Y) = constant

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Taking the total derivative of this relation yields

∂U

___ ∂X

 dX +  ∂U

___ ∂Y

 dY = 0

Solving for dY/dX along an indifference curve yields

dY ___ dX

| utility constant  = −  ∂U/∂X

_______ ∂U/∂Y

Thus, the slope of an indifference curve is

− ∂U/∂X

_______ ∂U/∂Y

The absolute value of the slope of an indifference curve is the marginal rate of substitution (MRS). Thus,

MRS =  ∂U/∂X

______ ∂U/∂Y

(A-4)

THE MRS = PX /PY RULE Substitution of Equation (A-4) into Equation (A-3) reveals that to maximize utility, a consumer equates

MRS =  P x ___ P y

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headLINE Boeing Loses the Battle but Wins the War After nearly eight weeks, Boeing and its International Association of Machinists and Aerospace Workers Union (IAM) reached an agreement that ended a strike involving 27,000 workers. The strike followed several days of “last minute,” around-the-clock talks that began when management and union negotiators failed to reach an agreement over compensation and job protection issues.

As a result of the agreement, IAM workers won benefits in areas that include health care, pensions, wages, and job security for 2,900 workers in inventory management and delivery categories. Boeing also agreed to retrain workers who are laid off or displaced. Despite these concessions, a spokesman for Boeing was quoted as saying that the

The Production Process and Costs

5 LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Explain alternative ways of measuring the productivity of inputs and the role of the manager in the production process.

LO2 Calculate input demand and the cost-minimizing combination of inputs and use isoquant analysis to illustrate optimal input substitution.

LO3 Calculate a cost function from a production function and explain how eco- nomic costs differ from accounting costs.

LO4 Explain the difference between and the economic relevance of fixed costs, sunk costs, variable costs, and marginal costs.

LO5 Calculate average and marginal costs from algebraic or tabular cost data and illustrate the relationship between average and marginal costs.

LO6 Distinguish between short-run and long-run production decisions and illus- trate their impact on costs and economies of scale.

LO7 Conclude whether a multiple-output production process exhibits economies of scope or cost complementarities and explain their significance for mana- gerial decisions.

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agreement “gives us the flexibility we need to run the company.” The four-year agree- ment allows Boeing to retain critical subcontracting provisions it won in past struggles with the union.

Commenting on all this, one analysis concluded that “the union probably won the battle and Boeing probably wins the war.” Can you explain what this analyst means?

SOURCES: C. Isidore, “Union Strikes Boeing,” CNNMoney.com, September 6, 2008; S. Freeman, “Boeing Contract Offers Pay Raise, Job Protections,” The Washington Post, October 29, 2008.

INTRODUCTION

Companies as well as nonprofit organizations are in the business of producing goods or providing services, and their successful operation requires managers to optimally choose the quantity and types of inputs to use in the production process. The successful opera- tion of a consulting business, for instance, requires getting the right quantity and mix of employees and optimally substituting among these and other inputs as wages and other input prices change.

This chapter provides the economic foundations needed to succeed in managerial posi- tions such as production and pricing management. The concepts of production and costs pre- sented are also important in their own right, as they serve as the basic building blocks for business areas that include human resources, operations, managerial accounting, and strategic management.

THE PRODUCTION FUNCTION

We will begin by describing the technology available for producing output. Technology sum- marizes the feasible means of converting raw inputs, such as steel, labor, and machinery, into an output such as an automobile. The technology effectively summarizes engineering know- how. Managerial decisions, such as those concerning expenditures on research and devel- opment, can affect the available technology. In this chapter, we will see how a manager can exploit an existing technology to its greatest potential. In subsequent chapters, we will analyze the decision to improve a technology.

To begin our analysis, let us consider a production process that utilizes two inputs, cap- ital and labor, to produce output. We will let K denote the quantity of capital, L the quantity of labor, and Q the level of output produced in the production process. Although we call the inputs capital and labor, the general ideas presented here are valid for any two inputs. However, most production processes involve machines of some sort (referred to by econ- omists as capital) and people (labor), and this terminology will serve to solidify the basic ideas.

The technology available for converting capital and labor into output is summarized in the production function. The production function is an engineering relation that defines the maximum amount of output that can be produced with a given set of inputs. Mathematically, the production function is denoted as

Q = F(K, L)

that is, the maximum amount of output that can be produced with K units of capital and L units of labor.

production function A function that defines the maximum amount of output that can be produced with a given set of inputs.

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Short-Run versus Long-Run Decisions As a manager, your job is to use the available production function efficiently; this means that you must determine how much of each input to use to produce output. In the short run, some factors of production are fixed, and this limits your choices in making input decisions. For example, it takes several years for automakers to develop and build new assembly lines for producing hybrids. The level of capital is generally fixed in the short run. However, in the short run automakers can adjust their use of inputs such as labor and steel; such inputs are called variable factors of production.

The short run is defined as the time frame in which there are fixed factors of production. To illustrate, suppose capital and labor are the only two inputs in production and that the level of capital is fixed in the short run. In this case, the only short-run input decision to be made by a manager is how much labor to utilize. The short-run production function is essentially only a function of labor since capital is fixed rather than variable. If K* is the fixed level of capital, the short-run production function may be written as

Q = f (L) = F(K*, L)

Columns 1, 2, and 4 in Table 5–1 give values of the components of a short-run produc- tion function where capital is fixed at K* = 2. For this production function, 5 units of labor are needed to produce 1,100 units of output. Given the available technology and the fixed level of capital, if the manager wishes to produce 1,952 units of output, 8 units of labor must be utilized. In the short run, more labor is needed to produce more output because increasing capital is not possible.

fixed factors of production The inputs a manager cannot adjust in the short run.

variable factors of production The inputs a manager can adjust to alter production.

Table 5–1 The Production Function

(1) (2) (3) (4) (5) (6)

K* L ΔL Q ΔQ

____ ΔL

= M P L Q

__ L

= A P L

Fixed Input

(Capital)

Variable Input

(Labor)

Change in

Labor

Output Marginal Product of Labor

Average Product of Labor

[Given] [Given] [Δ(2)] [Given] [Δ(4)/Δ(2)] [(4)/(2)]

2 0 — 0 — —

2 1 1 76 76 76

2 2 1 248 172 124

2 3 1 492 244 164

2 4 1 784 292 196

2 5 1 1,100 316 220

2 6 1 1,416 316 236

2 7 1 1,708 292 244

2 8 1 1,952 244 244

2 9 1 2,124 172 236

2 10 1 2,200 76 220

2 11 1 2,156 −44 196

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The long run is defined as the horizon over which the manager can adjust all factors of production. If it takes a company three years to acquire additional capital machines, the long run for its management is three years, and the short run is less than three years.

Measures of Productivity An important component of managerial decision making is the determination of the produc- tivity of inputs used in the production process. As we will see, these measures are useful for evaluating the effectiveness of a production process and for making input decisions that max- imize profits. The three most important measures of productivity are total product, average product, and marginal product.

Total Product Total product (TP) is simply the maximum level of output that can be produced with a given amount of inputs. For example, the total product of the production process described in Table 5–1 when 5 units of labor are employed is 1,100. Since the production function defines the maximum amount of output that can be produced with a given level of inputs, this is the amount that would be produced if the 5 units of labor put forth maximal effort. Of course, if workers did not put forth maximal effort, output would be lower. Five workers who drink coffee all day cannot produce any output, at least given this production function.

Average Product In many instances, managerial decision makers are interested in the average productivity of an input. For example, a manager may wish to know, on average, how much each worker contrib- utes to the total output of the firm. This information is summarized in the economic concept of average product. The average product (AP) of an input is defined as total product divided by the quantity used of the input. In particular, the average product of labor (APL) is

APL = Q

__ L

and the average product of capital (APK) is

A P K = Q

__ K

Thus, average product is a measure of the output produced per unit of input. In Table 5–1, for example, five workers can produce 1,100 units of output; this amounts to 220 units of output per worker.

Marginal Product The marginal product (MP) of an input is the change in total output attributable to the last unit of an input. The marginal product of capital (MPK) therefore is the change in total output divided by the change in capital:

M P K = ΔQ

____ ΔK

The marginal product of labor (MPL) is the change in total output divided by the change in labor:

M P L = ΔQ

____ ΔL

total product (TP) The maximum level of output that can be produced with a given amount of inputs.

average product (AP) A measure of the output produced per unit of input.

marginal product (MP) The change in total output attributable to the last unit of an input.

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For example, in Table 5–1 the second unit of labor increases output by 172 units, so the mar- ginal product of the second unit of labor is 172.

Table 5–1 illustrates an important characteristic of the marginal product of an input. Notice that as the units of labor are increased from 0 to 5 in column 2, the marginal product of labor increases in column 5. This helps explain why assembly lines are used in so many production processes: By using several workers, each performing potentially different tasks, a manager can avoid inefficiencies associated with stopping one task and starting another. But note in Table 5–1 that after 5 units of labor, the marginal product of each additional unit of labor declines and eventually becomes negative. A negative marginal product means that the last unit of the input actually reduced the total product. This is consistent with common sense. If a manager continued to expand the number of workers on an assembly line, he or she would eventually reach a point where workers were packed like sardines along the line, getting in one another’s way and resulting in less output than before.

Figure 5–1 shows graphically the relationship among total product, marginal product, and average product. The first thing to notice about the curves is that total product increases and its slope gets steeper as we move from point A to point E along the total product curve. As the use of labor increases between points A and E, the slope of the total product curve increases (becomes steeper); thus, marginal product increases as we move from point a to point e. The range over which marginal product increases is known as the range of increasing marginal returns.

In Figure 5–1, we see that marginal product reaches its maximum at point e, where 5 units of labor are employed. As the usage of labor increases from the 5th through the 10th units, total output increases, but at a decreasing rate. This is why marginal product declines between 5 and 10 units of labor but is still positive. The range over which marginal product is positive but declining is known as the range of decreasing or diminishing marginal returns to the variable input.

In Figure 5–1, marginal product becomes negative when more than 10 units of labor are employed. After a point, using additional units of input actually reduces total product, which is what it means for marginal product to be negative. The range over which marginal product is negative is known as the range of negative marginal returns.

increasing marginal returns Range of input usage over which marginal product increases.

decreasing (diminishing) marginal returns Range of input usage over which marginal product declines.

negative marginal returns Range of input usage over which marginal product is negative.

Figure 5–1 Increasing, Decreasing, and Negative Marginal Returns

0

Total product, average product, marginal product

Variable input

(labor)1 2 3 4 5 6 7 8

Increasing marginal

returns to

labor

Decreasing marginal

returns to

labor

Negative marginal

returns to

labor

9 10 11

A B

C

D

E

G

F

H I J K

e

Total product

(TP )

APL

MPL

a

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In studying for an exam, you have very likely experienced various phases of marginal returns. The first few hours spent studying increase your grade much more than the last few hours. For example, suppose you will make a 0 if you do not study but will make a 75 if you study 10 hours. The marginal product of the first 10 hours thus is 75 points. If it takes 20 hours of studying to score 100 on the exam, the marginal product of the second 10 hours is only 25 points. Thus, the marginal improvement in your grade diminishes as you spend additional hours studying. If you have ever pulled an “all-nighter” and ended up sleeping through an exam or performing poorly due to a lack of sleep, you studied in the range of negative marginal returns. Clearly, neither students nor firms should ever employ resources in this range.

The Role of the Manager in the Production Process The manager’s role in guiding the production process described earlier is twofold: (1) to ensure that the firm operates on the production function and (2) to ensure that the firm uses the correct level of inputs. These two aspects ensure that the firm operates at the right point on the production function. These two aspects of production efficiency are discussed next.

Produce on the Production Function The first managerial role is relatively simple to explain, but it is one of the most difficult for a manager to perform. The production function describes the maximum possible output that can be produced with given inputs. For the case of labor, this means that workers must be putting forth maximal effort. To ensure that workers are in fact working at full potential, the manager must institute an incentive structure that induces them to put forth the desired level of effort. For example, the manager of a restaurant must institute an incentive scheme that ensures that food servers do a good job waiting on tables. Most restaurants pay workers low wages but allow them to collect tips, which effectively provides the workers with an incentive to perform well on the job. More generally, many firms institute profit-sharing plans to provide workers with an incentive to produce on the production function. A more detailed discussion of this role of the manager is presented in Chapter 6.

Use the Right Level of Inputs The second role of the manager is to ensure that the firm operates at the right point on the pro- duction function. For a restaurant manager, this means hiring the “correct” number of servers. To see how this may be accomplished, let us assume that the output produced by a firm can be sold in a market at a price of $3. Furthermore, assume each unit of labor costs $400. How many units of labor should the manager hire to maximize profits? To answer this question, we must first determine the benefit of hiring an additional worker. Each worker increases the firm’s output by his or her marginal product, and this increase in output can be sold in the market at a price of $3. Thus, the benefit to the firm from each unit of labor is $3 × MPL. This number is called the value marginal product of labor. The value marginal product of

value marginal product The value of the output produced by the last unit of an input.

P R I N C I P L E

Phases of Marginal Returns As the usage of an input increases, marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns).

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an input thus is the value of the output produced by the last unit of that input. For example, if each unit of output can be sold at a price of P, the value marginal product of labor is VM P L = P × M P L and the value marginal product of capital is VM P K = P × M P K

In our example, the cost to the firm of an additional unit of labor is $400. As Table 5–2 shows, the first unit of labor generates VMPL = $228 and the VMPL of the second unit is $516. If the manager were to look only at the first unit of labor and its corresponding VMPL, no labor would be hired. However, careful inspection of the table shows that the second worker will add $116 in value above her or his cost. If the first worker is not hired, the second will not be hired.

In fact, each worker between the second and the ninth produces additional output whose value exceeds the cost of hiring the worker. It is profitable to hire units of labor so long as the VMPL is greater than $400. Notice that the VMPL of the 10th unit of labor is $228, which is less than the cost of the 10th unit of labor. It would not pay for the firm to hire this unit of labor because the cost of hiring it would exceed the benefits. The same is true for additional units of labor. Thus, given the data in Table 5–2, the manager should hire nine workers to maximize profits.

Table 5–2 The Value Marginal Product of Labor

(1) (2) (3) (4) (5)

L P ΔQ

___ ΔL

= M P L VMPL = P × MPL W

Variable Input

(Labor) [Given]

Price of

Output [Given]

Marginal Product of Labor

[Column 5 of Table 5-1]

Value Marginal Product of

Labor [(2) × (3)]

Unit Cost of

Labor [Given]

0 $3 — — $400

1 3 76 $228 400

2 3 172 516 400

3 3 244 732 400

4 3 292 876 400

5 3 316 948 400

6 3 316 948 400

7 3 292 876 400

8 3 244 732 400

9 3 172 516 400

10 3 76 228 400

11 3 −44 −132 400

P R I N C I P L E

Profit-Maximizing Input Usage To maximize profits, a manager should use inputs at levels at which the marginal benefit equals the marginal cost. More specifically, when the cost of each additional unit of labor is w, the manager should continue to employ labor up to the point where VMPL = w in the range of diminishing marginal product.

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The profit-maximizing input usage rule defines the demand for an input by a profit- maximizing firm. For example, in Figure 5–2 the value marginal product of labor is graphed as a function of the quantity of labor utilized. When the wage rate is w0, the profit-maximizing quantity of labor is that quantity such that VMPL = w

0 in the range of diminishing marginal returns. In the figure, we see that the profit-maximizing quantity of labor is L0 units.

The downward-sloping portion of the VMPL curve defines demand for labor by a prof- it-maximizing firm; it shows the relationship between the wage rate and the amount of labor a firm will want to hire at that rate. We know the demand for an input slopes downward because of the law of diminishing marginal returns, which states that the marginal product of an additional unit of an input will at some point be lower than the marginal product of the

law of diminishing marginal returns States that the marginal product of an additional unit of an input will at some point be lower than the marginal product of the previous unit.

In this chapter, we simply assume that the manager knows the underlying technology available for producing goods. How do managers acquire information about technology? A study by Richard Levin suggests there are seven principal methods.

INDEPENDENT R&D The most important means of acquiring product and pro- cess innovations is independent research and development (R&D). This essentially involves engineers employed by the firm who devise new production processes or products.

LICENSING TECHNOLOGY The firm that was originally responsible for developing the technology and thus owns the rights to the technology often sells the production function to another firm for a licensing fee. The fee may be fixed, in which case the cost of acquiring the technology is a fixed cost of production. The fee may involve payments based on how much output is produced. In this instance, the cost of the technology is a variable cost of production.

PUBLICATIONS OR TECHNICAL MEETINGS Trade publications and meetings provide a forum for the dissemination of information about production processes.

REVERSE ENGINEERING As the term suggests, this involves working backward: taking a product produced by a competitor and devising a method of producing a similar product. The typical result is a product that differs slightly from the existing product and

involves a slightly different production function from that used by the original developer.

HIRING EMPLOYEES OF INNOVATING FIRMS Former employees of other firms often have information about the production process.

PATENT DISCLOSURES A patent gives the holder the exclusive rights to an inven- tion for a specified period of time—17 to 20 years in most countries. However, to obtain a patent an inventor must file detailed information about the invention, which becomes public information. Virtually anyone can look at the infor- mation filed, including competitors. In many instances, this information can enable a competitor to “clone” the product in a way that does not infringe on the patent. Interestingly, while a patent is pending, this information is not publicly available. For this reason, stretching out the time in which a patent is pending often provides more protection for an inventor than actually acquiring the patent.

CONVERSATIONS WITH EMPLOYEES OF INNOVATING FIRMS Despite the obvious benefits of keeping trade secrets “secret,” employees inadvertently relay information about the production process to competitors. This is especially common in industries where firms are concentrated in the same geographic region and employees from different firms intermingle in nonbusiness settings.

SOURCE: Richard C. Levin, “Appropriability, R&D Spending, and Technological Performance,” American Economic Review 78 (May 1988), pp. 424–28.

INSIDE BUSINESS 5–1

Where Does Technology Come From?

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Figure 5–2   The Demand for Labor

0

$

L L0

w0 Profit-

maximizing point

VMP L

Demand for labor

previous unit. Since the marginal product of an input declines as more of that input is used, the value of the marginal product also declines as more of the input is used. Since the demand for an input is the value marginal product of the input in the range of diminishing marginal returns, the demand for an input slopes downward. In effect, each additional unit of an input adds less profits than the previous unit. Profit-maximizing firms thus are willing to pay less for each additional unit of an input.

Algebraic Forms of Production Functions Up until now, we have relied on tables and graphs to illustrate the concepts underlying pro- duction. The underlying notion of a production function can be expressed mathematically, and in fact it is possible to use statistical techniques like those discussed in Chapter 3 to estimate a particular functional form for a production function. In this section, we highlight some more commonly encountered algebraic forms of production functions. We begin with the most sim- ple production function: a linear function of the inputs.

The linear production function is

Q = F ( K, L ) = aK + bL

where a and b are constants. With a linear production function, inputs are perfect substitutes. There is a perfect linear relationship between all the inputs and total output. For instance, sup- pose it takes workers at a plant four hours to produce what a machine can make in one hour. In this case the production function is linear with a = 4 and b = 1:

Q = F ( K, L ) = 4K + L

This is the mathematical way of stating that capital is always 4 times as productive as labor. Furthermore, since F(5,2) = 4(5) + 1(2) = 22, we know that 5 units of capital and 2 units of labor will produce 22 units of output.

The Leontief production function is given by

Q = F ( K, L ) = min  { aK, bL }

where a and b are constants. The Leontief production function is also called the fixed- proportions production function because it implies that inputs are used in fixed proportions. To see this, suppose the production function for a word processing firm is Leontief, with a = b = 1; think of K as the number of keyboards and L as the number of keyboarders. The production function then implies that one keyboarder and one keyboard can produce one paper per hour, two keyboarders and two keyboards can produce two papers per hour, and so forth. But how many papers can one keyboarder and five keyboards produce per hour? The answer is only one paper. Additional keyboards are useful only to the extent that additional

linear production function A production function that assumes a perfect linear relationship between all inputs and total output.

Leontief production function A production function that assumes that inputs are used in fixed proportions.

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keyboarders are available to use them. In other words, keyboards and keyboarders must be used in the fixed proportion of one keyboarder for every keyboard.

DEMONSTRATION PROBLEM 5–1

The engineers at Morris Industries obtained the following estimate of the firm’s production function:

Q = F ( K, L ) = min  { 3K, 4L }

How much output is produced when 2 units of labor and 5 units of capital are employed?

ANSWER: We simply calculate F(5, 2). But F(5, 2) = min{3(5), 4(2)} = min{15, 8}. Since the minimum of the numbers “15” and “8” is 8, we know that 5 units of capital and 2 units of labor produce 8 units of output.

A production function that lies between the extremes of the linear production func- tion and the Leontief production function is the Cobb-Douglas production function. The Cobb-Douglas production function is given by

Q = F(K, L) = K aLb

where a and b are constants. Unlike in the case of the linear production function, the relationship between output and

inputs is not linear. Unlike in the Leontief production function, inputs need not be used in fixed proportions. The Cobb-Douglas production function assumes some degree of substitut- ability between the inputs, albeit not perfect substitutability.

Algebraic Measures of Productivity Given an algebraic form of a production function, we may calculate various measures of pro- ductivity. For example, we learned that the average product of an input is the output produced divided by the number of units used of the input. This concept can easily be extended to pro- duction processes that use more than one input.

To be concrete, suppose a consultant provides you with the following estimate of your firm’s Cobb-Douglas production function:

Q = F(K, L) = K 1/2 L 1/2

What is the average product of labor when 4 units of labor and 9 units of capital are employed? Since F(9,4) = 91/241/2 = (3)(2) = 6, we know that 9 units of capital and 4 units of labor pro- duce 6 units of output. Thus, the average product of 4 units of labor is APL = 6/4 = 1.5 units.

Notice that when output is produced with both capital and labor, the average product of labor will depend not only on how many units of labor are used but also on how much capital is used. Since total output (Q) is affected by the levels of both inputs, the corresponding measure of the average product depends on both capital and labor. Likewise, the average product of capital depends not only on the level of capital but also on the level of labor used to produce Q.

Recall that the marginal product of an input is the change in output that results from a given change in the input. When the production function is linear, the marginal product of an input has a very simple representation, as the following formula reveals.

Cobb-Douglas production function A production function that assumes some degree of substitutability among inputs.

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Formula: Marginal Product for a Linear Production Function. If the production func- tion is linear and given by

Q = F(K, L) = aK + bL

then

M P K = a

and

M P L = b

A C A L C U L U S A L T E R N A T I V E The marginal product of an input is the derivative of the production function with respect to the input. Thus, the marginal product of labor is

M P L = ∂ Q

___ ∂ L

and the marginal product of capital is

M P K = ∂ Q

___ ∂ K

For the case of the linear production function Q = aK + bL,

M P K = ∂ Q

___ ∂ K

= a and M P L = ∂ Q

___ ∂ L

= b

Thus, for a linear production function, the marginal product of an input is simply the coefficient of the input in the production function. This implies that the marginal prod- uct of an input is independent of the quantity of the input used whenever the production function is linear; linear production functions do not obey the law of diminishing marginal product.

In contrast to the linear case, the marginal product of an input for a Cobb-Douglas production function does depend on the amount of the input used, as the following formula reveals.

Formula: Marginal Product for a Cobb-Douglas Production Function. If the produc- tion function is Cobb-Douglas and given by

Q = F(K, L) = K a L b

then

M P L = b K a L b−1

and

M P K = a K a−1 L b

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A C A L C U L U S A L T E R N A T I V E The marginal product of an input is the derivative of the production function with respect to the input. Taking the derivative of the Cobb-Douglas production function yields

M P K = ∂ Q

___ ∂ K

= a K a −1 L b

and

M P L = ∂ Q

___ ∂ L

=  b K a L b −1

which correspond to the equations in the previous formula.

Recall that the profit-maximizing use of an input occurs at the point where the value marginal product of an input equals the price of the input. As the next problem illustrates, we can apply the same principle to algebraic functional forms of production functions to attain the profit-maximizing use of an input.

DEMONSTRATION PROBLEM 5–2

A firm produces output that can be sold at a price of $10. The production function is given by

Q = F(K, L) = K 1/2 L 1/2

If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?

ANSWER: We simply set the value marginal product of labor equal to the wage rate and solve for L. Since the production function is Cobb-Douglas, we know that MPL = bK

aLb −1. Here a = 1/2, b = 1/2, and K = 1. Hence, MPL = .5L

1/2 −1. Now, since P = $10, we know that VMPL = P × MPL = 5L −1/2 =

5/ √ __

L . Setting this equal to the wage, which is $2, we get 5/ √ __

L = 2. If we square both sides of this equation, we get 25/L = 4. Thus, the profit-maximizing quantity of labor is L = 25/4 = 6.25 units.

Isoquants Our next task is to examine the optimal choice of capital and labor in the long run, when both inputs are free to vary. In the presence of multiple variables of production, various com- binations of inputs enable the manager to produce the same level of output. For example, an automobile assembly line can produce 1,000 cars per hour by using 10 workers and one robot. It can also produce 1,000 cars by using only two workers and three robots. To minimize the costs of producing 1,000 cars, the manager must determine the efficient combination of inputs to use to produce them. The basic tool for understanding how alternative inputs can be used to produce output is an isoquant. An isoquant defines the combinations of inputs (K and L) that yield the producer the same level of output; that is, any combination of capital and labor along an isoquant produces the same level of output.

Figure 5–3 depicts a typical set of isoquants. Because input bundles A and B both lie on the same isoquant, each will produce the same level of output, namely, Q0 units. Input mix A implies a more capital-intensive plant than does input mix B. As more of both inputs are used,

isoquant Defines the combinations of inputs that yield the same level of output.

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a higher isoquant is obtained. Thus, as we move in the northeast direction in the figure, each new isoquant is associated with higher and higher levels of output.

Notice that the isoquants in Figure 5–3 are convex. The reason isoquants are typically drawn with a convex shape is that inputs such as capital and labor typically are not perfectly substitutable. In Figure 5–3, for example, if we start at point A and begin substituting labor for capital, it takes increasing amounts of labor to replace each unit of capital that is taken away. The rate at which labor and capital can substitute for each other is called the marginal rate of technical substitution (MRTS). The MRTS of capital and labor is the absolute value of the slope of the isoquant and is simply the ratio of the marginal products:

MRT S KL = M P L _____ M P K

Different production functions will imply different marginal rates of technical substi- tution. For example, the linear production function implies isoquants that are linear, as in Figure 5–4(a). This is because the inputs are perfect substitutes for each other and the rate at which the producer can substitute between the inputs is independent of the level of input usage. Specifically, for the linear production function Q = aK + bL, the marginal rate of technical substitution is b/a since MPL = b and MPK = a. This is independent of the level of inputs utilized.

The Leontief production function, on the other hand, implies isoquants that are L shaped, as in Figure 5–4(b). In this case, inputs must be used in fixed proportions; the manager cannot substitute between capital and labor and maintain the same level of output. For the Leontief production function there is no MRTS because there is no substitution among inputs along

marginal rate of technical substitution (MRTS) The rate at which a producer can substitute between two inputs and maintain the same level of output.

Figure 5–3 A Family of Isoquants

K

L 0

Q0 = 100 units of output Q1 = 200 units of output

Q2 = 300 units of output

Substituting

labor for capital

Incre asing

outp ut

A

B

Figure 5–4 Linear and Leontief Isoquants

0

K

L Q0

Q1 Q2

0

K

L

Q0

Q1

Q2

(a) Linear (b) Leontief

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an isoquant. For most production relations, the isoquants lie somewhere between the perfect- substitute and fixed-proportions cases. In these instances, the inputs are substitutable for one another, but not perfectly, and the rate at which a manager can substitute among inputs will change along an isoquant. For instance, by moving from point A to point B in Figure 5–5, the manager substitutes 1 unit of capital for 1 unit of labor and still produces 100 units of output. But in moving from point C to point D, the manager would have to substitute 3 units of cap- ital for 1 unit of labor to produce 100 units of output. Thus, the production function satisfies the law of diminishing marginal rate of technical substitution: As a producer uses less of an input, increasingly more of the other input must be employed to produce the same level of output. It can be shown that the Cobb-Douglas production function implies isoquants that have a diminishing marginal rate of technical substitution. Whenever an isoquant exhibits a diminishing marginal rate of technical substitution, the corresponding isoquants are convex from the origin; that is, they look like the isoquants in Figure 5–5.

Isocosts Isoquants describe the combinations of inputs that produce a given level of output. Notice that different combinations of capital and labor end up costing the firm the same amount. The combinations of inputs that will cost the firm the same amount comprise an isocost line.

The relation for an isocost line is graphed in Figure 5–6. To understand this concept, suppose the firm spends exactly $C on inputs. Then the cost of labor plus the cost of capital exactly equals $C:

wL + rK = C (5–1)

where w is the wage rate (the price of labor) and r is the rental rate (the price of capital). This equation represents the formula for an isocost line.

We may obtain a more convenient expression for the slope and intercept of an isocost line as follows. We multiply both sides of Equation 5–1 by 1/r and get

w

__ r  L + K =

C __

r  

or

K = C

__ r  − 

w __

r  L

law of diminishing marginal rate of technical substitution A property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output.

isocost line A line that represents the combinations of inputs that will cost the producer the same amount of money.

Figure 5–5 The Marginal Rate of Technical Substitution

0

K

ΔK = 3

ΔK = 1

ΔL = −1 ΔL = −1

A

1

4

4

2 7 81 3 5 6 L

2

3

5

6

7

8

9

Q0 = 100

B

C

D

1

1

1

3 ΔK ΔL

Slope = = − = – MRTSKL 3 1

ΔK ΔL

Slope = = − = – MRTSKL 1 1

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Thus, along an isocost line, K is a linear function of L with a vertical intercept of C/r and a slope of −w /r.

Note that if the producer wishes to use more of both inputs, more money must be spent. Thus, isocosts associated with higher costs lie above those with lower costs. When input prices are constant, the isocost lines will be parallel to one another. Figure 5–7(a) illustrates the isocost lines for cost levels C 0 and C1, where C 0 < C1.

Similarly, changes in input prices affect the position of the isocost line. An increase in the price of labor makes the isocost curve steeper, while an increase in the price of capital makes it flatter. For instance, Figure 5–7(b) reveals that the isocost line rotates clockwise when the wage rate increases from w0 to w1.

P R I N C I P L E Changes in Isocosts For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slopes of isocost lines.

Figure 5–6 Isocosts

0

K

L

C r

C w

K = – LC r

w r

Figure 5-7 Changes in Isocosts

0 L

Combinations of inputs costing C0 (less expensive input bundles)

Combinations of inputs costing C1 (more expensive input bundles)

0 L

K

C1

r

K

C r

C0

r

C0

w C1

w

(a) (b)

Due to increase in wage rate

(w1 > w0)

C

w1 C

w 0

Cost Minimization The isocosts and isoquants just defined may be used to determine the input usage that min- imizes production costs. If there were no scarcity, the producer would not care about pro- duction costs. But because scarcity is an economic reality, producers are interested in cost minimization—that is, producing output at the lowest possible cost. After all, to maximize

cost minimization Producing output at the lowest possible cost.

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profits, the firm must first produce its output in the least-cost manner. Even not-for-profit organizations can achieve their objectives by providing a given level of service at the lowest possible cost. Let us piece together the tools developed thus far to see how to choose the opti- mal mix of capital and labor.

Consider an input bundle such as that at point A in Figure 5–8. This combination of L and K lies on the isoquant labeled Q0 and thus produces Q0 units of output. It also lies on the isocost line through point A. Thus, if the producer uses input mix A, he or she will produce Q0 units of output at a total cost of C1. Is this the cost-minimizing way to produce the given level of output? Clearly not, for by using input mix B instead of A, the producer could produce the same amount of output at a lower cost, namely C2. In short, it is inefficient for the producer to use input mix A because input mix B produces the same output and lies on a lower isocost line.

At the cost-minimizing input mix, the slope of the isoquant is equal to the slope of the isocost line. Recalling that the absolute value of the slope of the isoquant reflects the marginal rate of technical substitution and that the slope of the isocost line is given by −w /r, we see that at the cost-minimizing input mix,

MRTSKL = w /r

If this condition did not hold, the technical rate at which the producer could substitute between L and K would differ from the market rate at which she or he could substitute between the inputs. For example, at point A in Figure 5–8, the slope of the isoquant is steeper than the slope of the isocost line. Consequently, capital is “too expensive”; the producer finds it in his or her interest to use less capital and more labor to produce the given level of output. This substitution continues until ultimately the producer is at a point such as B, where the MRTS is equal to the ratio of input prices. The condition for the cost-minimizing use of inputs also can be stated in terms of marginal products.

To see why this condition must hold to be able to minimize the cost of producing a given level of output, suppose MPL/w > MPK /r. Then, on a last-dollar-spent basis, labor is a better deal than capital, and the firm should use less capital and more labor to minimize costs. In particular, if the firm reduced its expenditures on capital by $1, it could produce the same level of output if it increased its expenditures on labor by less than $1. Thus, by substituting away from capital and toward labor, the firm could reduce its costs while producing the same level of output. This substitution clearly would continue until the marginal product per dollar spent on capital exactly equaled the marginal product per dollar spent on labor.

Figure 5–8 Input Mix B Minimizes the Cost of Producing 100 Units of Output

0

K

L C2

C2

C1

B

C1

A

Q0 = 100 units of output

r

r

w w

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DEMONSTRATION PROBLEM 5–3

Terry’s Lawn Service rents five small push mowers and two large riding mowers to cut the lawns of neighborhood households. The marginal product of a small push mower is 3 lawns per day, and the marginal product of a large riding mower is 6 lawns per day. The rental price of a small push mower is $10 per day, whereas the rental price of a large riding mower is $25 per day. Is Terry’s Lawn Service utilizing small push mowers and large riding mowers in a cost-minimizing manner?

ANSWER: Let MPS be the marginal product of a small push mower and MPL be the marginal product of a large riding mower. If we let PS and PL be the rental prices of a small push mower and large riding mower, respectively, cost minimization requires that

M P S ____ P S

= M P L _____ P L

Substituting in the appropriate values, we see that

3 ___

10 =

M P S ____ P S

> M P L _____ P L

= 6 ___

25

Thus, the marginal product per dollar spent on small push mowers exceeds the marginal product per dollar spent on large riding mowers. Riding mowers are twice as productive as push mowers, but more than twice as expensive. The firm clearly is not minimizing costs and thus should use fewer riding mowers and more push mowers.

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

P R I N C I P L E

Cost-Minimizing Input Rule To minimize the cost of producing a given level of output, the marginal product per dollar spent should be equal for all inputs:

M P L ____

w =

M P K ____ r

Equivalently, to minimize the cost of production, a firm should employ inputs such that the marginal rate of technical substitution is equal to the ratio of input prices:

M P L _____ M P K

= w

__ r

Optimal Input Substitution A change in the price of an input will lead to a change in the cost-minimizing input bundle. To see this, suppose the initial isocost line in Figure 5–9 is FG and the producer is cost- minimizing at input mix A, producing Q0 units of output. Now suppose that the wage rate increases so that if the firm spent the same amount on inputs, its isocost line would rotate clockwise to FH in Figure 5–9. Clearly, if the firm spends the amount it spent prior to the increase in the wage rate, it cannot produce the same level of output.

Given the new slope of the isocost line, which reflects a higher relative price of labor, the cost-minimizing way to maintain the output implied by the initial isoquant is at point B, where isocost line IJ is tangent to the isoquant. Due to the increase in the price of labor relative to

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capital, the producer substitutes away from labor and toward capital and adopts a more capi- tal-intensive mode of production. This suggests the following important result:

P R I N C I P L E Optimal Input Substitution To minimize the cost of producing a given level of output, the firm should use less of an input and more of other inputs when that input’s price rises.

Figure 5–9 Substituting Capital for Labor, Due to Increase in the Wage Rate

0

K

L

K2

F

K1

L1L2

Isoquant

I

G

Initial point of cost minimization

B

A

Q0

New cost-minimizing point due to higher wage

H J

Figure 5–10 shows the isocost line (AB) and isoquant for a firm that produces rugs using computers and labor. The initial point of cost minimization is at point M, where the manager has chosen to use 40 units of capital (computers) and 80 units of labor when the wage rate is w = $20 and the rental rate of computers (capital) is r 0 = $20. This implies that at point M, total costs are C 0 = ($20 × 40) + ($20 × 80) = $2,400. Notice also at point M that the MRTS equals the ratio of the wage to the rental rate.

Now assume that due to a decrease in the supply of silicon chips, the rental rate of capital increases to r1 = $40. What will the manager do to minimize costs? Since the price of cap- ital has increased, the isocost line will rotate counterclockwise from AB to DB. To produce the same amount of output, the manager will have to spend more than C 0 = $2,400. The additional expenditures will shift the isocost line out to EF in Figure 5–10. The new point of cost minimization is at point N, where the firm now employs more labor (120 units) and less capital (10 units) to minimize the production costs of rugs. Costs are now C1 = ($40 × 10) + ($20 × 120) = $2,800, which are higher than C0.

THE COST FUNCTION

For given input prices, different isoquants will entail different production costs, even allowing for optimal substitution between capital and labor. Each isoquant corresponds to a different level of output, and the isocost line tangent to higher isoquants will imply higher costs of production, even assuming the firm uses the cost-minimizing input mix. Since the cost of production increases as higher isoquants are reached, it is useful to let C(Q) denote the cost

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Figure 5–10 Substituting Labor for Computers, Due to Higher Computer Prices

0

Computers (K)

M

Labor (L)

C0

r0 = = $2,400

$20 120

80 C0

w = = $2,400

$20 120

B F

40

10

C0

r1 = = $2,400

$40 60

C1

r1 = = $2,800

$40 70 E

D

N

A

Q0

Initial input mix

New input mix due to higher

computer prices

C1

w = = $2,800

$20 140

to the firm of producing isoquant Q in the cost-minimizing fashion. The function C is called the cost function.

The cost function is extremely valuable because, as we will see in later chapters, it pro- vides essential information a manager needs to determine the profit-maximizing level of output. In addition, the cost function summarizes information about the production process. The cost function thus reduces the amount of information the manager has to process to make optimal output decisions.

Short-Run Costs Recall that the short run is defined as the period over which the amounts of some inputs are fixed. In the short run, the manager is free to alter the use of variable inputs but is “stuck” with existing levels of fixed inputs. Because inputs are costly whether fixed or variable, the total cost of producing output in the short run consists of (1) the cost of fixed inputs and (2) the cost of variable inputs. These two components of short-run total cost are called fixed costs and variable costs, respectively. Fixed costs, denoted FC, are costs that do not vary with output. Fixed costs include the costs of fixed inputs used in production. Variable costs, denoted VC(Q), are costs that change when output is changed. Variable costs include the costs of inputs that vary with output.

Since all costs fall into one category or the other, the sum of fixed and variable costs is the firm’s short-run cost function. In the presence of fixed factors of production, the short-run cost function summarizes the minimum possible cost of producing each level of output when variable factors are being used in the cost-minimizing way.

total cost Sum of fixed and variable costs.

fixed costs Costs that do not change with changes in output; include the costs of fixed inputs used in production.

variable costs Costs that change with changes in output; include the costs of inputs that vary with output.

short-run cost function A function that defines the minimum possible cost of producing each output level when variable factors are employed in the cost- minimizing fashion.

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Government regulations often have unintended conse- quences. In 2010, President Obama signed into law the Affordable Care Act, which marked a significant overhaul of the American health care system. The new law introduced many new regulations, several of which proved highly controversial. One notably controversial new regulation is the employer mandate, which requires every American business with 50 or more full-time employees to “offer affordable health coverage that provides a minimum level of coverage to their full-time employees (and their depen- dents).” If firms do not comply with the mandate, they must pay a fee of $2,000 per employee for every employee beyond the first 30.

Opponents of the mandate argue it will have a detri- mental effect on low-wage workers, presumably one of the groups the law is intended to assist. To see why, con- sider a company that hires computer programmers and administrative assistants. Suppose the annual wage bill of a computer programmer is $80,000 and that of an admin- istrative assistant is $40,000. Next, suppose the employer mandate forces businesses to offer additional benefits of $4,000 to its employees. Without the employer mandate, the relative price of an administrative assistant to a com- puter programmer is $40,000/$80,000 = .5. But when the cost of the additional benefits is added in, the relative price of an administrative assistant increases to a little over .52 of

that of a computer programmer. Isoquant and isocost analy- ses suggest that firms should substitute away from the now higher-priced administrative assistants to minimize costs.

Seem far-fetched? Economists Frank Scott, Mark Berger, and Dan Black examined the relationship between health care costs and employment of low-wage workers. They found that industries that offered more generous health care plans employed significantly fewer bookkeepers, key- punch operators, receptionists, secretaries, clerk-typists, janitors, and food service workers than did industries with lower health care costs. Moreover, industries with higher levels of fringe benefits hired more part-time workers than did industries with lower fringe-benefit levels since the government does not require firms to offer pension, health care, and many other fringe benefits to part-time workers.

Lastly, note that firms that choose not to comply with the mandate and instead pay the penalty still have an incentive to substitute away from administrative assistants, as the rel- ative price of an administrative assistant is a little over .51.

SOURCES: Frank Scott, Mark Berger, and Dan Black, “Effects of Fringe Benefits on Labor Market Segmentation,” Industrial and Labor Relations Review 42 (January 1989), pp. 216–29; https://www.irs.gov/Affordable- Care-Act/Employers/Questions-and-Answers-on-Employer-Shared- Responsibility-Provisions-Under-the-Affordable-Care-Act, accessed October 2015.

INSIDE BUSINESS 5–2

The Affordable Care Act, Employer Mandate, and Input Substitution

Table 5–3 illustrates the costs of producing with the technology used in Table 5–1. Notice that the first three columns comprise a short-run production function because they summarize the maximum amount of output that can be produced with two units of the fixed factor (capital) and alternative units of the variable factor (labor). Assuming capital costs $1,000 per unit and labor costs $400 per unit, we can calculate the fixed and variable costs of production, which are summarized in columns 4 and 5 of Table 5–3. Notice that irrespective of the amount of output produced, the cost of the capital equipment is $1,000 × 2 = $2,000. Thus, every entry in col- umn 4 contains this number, illustrating the principle that fixed costs do not vary with output.

To produce more output, more of the variable factor must be employed. For example, to produce 1,100 units of output, 5 units of labor are needed; to produce 1,708 units of output, 7 units of labor are required. Since labor is the only variable input in this simple example, the variable cost of producing 1,100 units of output is the cost of 5 units of labor, or $400 × 5 = $2,000. Similarly, the variable cost of producing 1,708 units of output is $400 × 7 = $2,800. Total costs, summarized in the last column of Table 5–3, are simply the sum of fixed costs (column 4) and variable costs (column 5) at each level of output.

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Table 5–3 The Cost Function

(1) (2) (3) (4) (5) (6)

K L Q FC VC TC

Fixed Input

[Given]

Variable Input

[Given]

Output

[Given]

Fixed Cost

[$1,000 × (1)]

Variable Cost

[$400 × (2)]

Total Cost

[(4) + (5)]

2 0 0 $2,000 $0 $2,000

2 1 76 2,000 400 2,400

2 2 248 2,000 800 2,800

2 3 492 2,000 1,200 3,200

2 4 784 2,000 1,600 3,600

2 5 1,100 2,000 2,000 4,000

2 6 1,416 2,000 2,400 4,400

2 7 1,708 2,000 2,800 4,800

2 8 1,952 2,000 3,200 5,200

2 9 2,124 2,000 3,600 5,600

2 10 2,200 2,000 4,000 6,000

Figure 5–11 illustrates graphically the relations among total costs (TC), variable costs (VC), and fixed costs (FC). Because fixed costs do not change with output, they are constant for all out- put levels and must be paid even if zero units of output are produced. Variable costs, on the other hand, are zero if no output is produced but increase as output increases above zero. Total cost is the sum of fixed costs and variable costs. Thus, the distance between the TC and VC curves in Figure 5–11 is simply fixed costs. Note that the curves look closer together as they get steeper; however, this is due to the fact that, with a fixed vertical difference in the curves, the horizontal difference will get smaller as the curves get steeper, making them look closer on that dimension.

Figure 5–11 The Relationship among Costs

0

Total costs, variable

costs, and fixed

costs

Q

FC FC FC

FC

FC FC

FC

TC = VC + FC

VC

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Average and Marginal Costs One common misconception about costs is that large firms have lower costs than smaller firms because they produce larger quantities of output. One fundamental implication of scar- city is that to produce more output, more must be spent. What individuals most likely have in mind when they consider the advantages of producing large quantities of output is that the overhead is spread out over a larger level of output. This idea is intricately related to the eco- nomic concept of average fixed cost. Average fixed cost (AFC) is defined as fixed costs (FC) divided by the number of units of output:

AFC = FC

___ Q

Since fixed costs do not vary with output, as more and more output is produced, the fixed costs are allocated over a greater quantity of output. As a consequence, average fixed costs decline continuously as output is expanded. This principle is revealed in column 5 of Table  5–4, where we see that average fixed costs decline as total output increases.

Average variable cost provides a measure of variable costs on a per-unit basis. Average variable cost (AVC) is defined as variable cost (VC) divided by the number of units of output:

AVC = VC ( Q )

______ Q

Column 6 of Table 5–4 provides the average variable cost for the production function in our example. Notice that as output increases, average variable cost initially declines, reaches a minimum between 1,708 and 1,952 units of output, and then begins to increase.

average fixed cost (AFC) Fixed costs divided by the number of units of output.

average variable cost (AVC) Variable costs divided by the number of units of output.

Table 5–4 Derivation of Average Costs

(1) (2) (3) (4) (5) (6) (7)

Q FC VC TC AFC AVC ATC

Output Fixed Cost

Variable Cost

Total Cost

Average Fixed Cost

Average Variable

Cost

Average Total Cost

[Given] [Given] [Given] [(2) + (3)] [(2)/(1)] [(3)/(1)] [(4)/(1)]

0 $2,000 $    0 $2,000 — — —

76 2,000 400 2,400 $26.32 $5.26 $31.58

248 2,000 800 2,800 8.06 3.23 11.29

492 2,000 1,200 3,200 4.07 2.44 6.50

784 2,000 1,600 3,600 2.55 2.04 4.59

1,100 2,000 2,000 4,000 1.82 1.82 3.64

1,416 2,000 2,400 4,400 1.41 1.69 3.11

1,708 2,000 2,800 4,800 1.17 1.64 2.81

1,952 2,000 3,200 5,200 1.02 1.64 2.66

2,124 2,000 3,600 5,600 0.94 1.69 2.64

2,200 2,000 4,000 6,000 0.91 1.82 2.73

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Average total cost is analogous to average variable cost, except that it provides a mea- sure of total costs on a per-unit basis. Average total cost (ATC) is defined as total cost (TC) divided by the number of units of output:

ATC = C ( Q )

_____ Q

Column 7 of Table 5–4 provides the average total cost of various outputs in our example. Notice that average total cost declines as output expands to 2,124 units and then begins to rise. Furthermore, note that average total cost is the sum of average fixed costs and average variable costs (the sum of columns 5 and 6) in Table 5–4.

The most important cost concept is marginal (or incremental) cost. Conceptually, marginal cost (MC) is the cost of producing an additional unit of output, that is, the change in cost attributable to the last unit of output:

MC = ΔC

____ ΔQ

To understand this important concept, consider Table 5–5, which summarizes the short-run cost function with which we have been working. Marginal cost, depicted in col- umn 7, is calculated as the change in costs arising from a given change in output. For example, increasing output from 248 to 492 units (ΔQ = 244) increases costs from 2,800 to 3,200 (ΔC = $400). Thus, the marginal cost of increasing output to 492 units is ΔC/ΔQ = 400/244 = $1.64.

When only one input is variable, the marginal cost is the price of that input divided by its marginal product. Remember that marginal product increases initially, reaches a maxi- mum, and then decreases. Since marginal cost is the reciprocal of marginal product times the input’s price, it decreases as marginal product increases and increases when marginal product is decreasing.

average total cost (ATC) Total cost divided by the number of units of output.

marginal (incremental) cost (MC) The change in total costs arising from a change in the managerial control variable Q.

Table 5–5 Derivation of Marginal Costs

(1) (2) (3) (4) (5) (6) (7)

Q ΔQ VC ΔVC TC ΔTC MC [Given] [Δ(1)] [Given] [Δ(3)] [Given] [Δ(5)] [(6)/(2) or (4)/2)]

0 — 0 — 2,000 — —

76 76 400 400 2,400 400 400/76 = 5.26 248 172 800 400 2,800 400 400/172 = 2.33 492 244 1,200 400 3,200 400 400/244 = 1.64 784 292 1,600 400 3,600 400 400/292 = 1.37

1,100 316 2,000 400 4,000 400 400/316 = 1.27 1,416 316 2,400 400 4,400 400 400/316 = 1.27 1,708 292 2,800 400 4,800 400 400/292 = 1.37 1,952 244 3,200 400 5,200 400 400/244 = 1.64 2,124 172 3,600 400 5,600 400 400/172 = 2.33 2,200 76 4,000 400 6,000 400 400/76 = 5.26

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Relations among Costs Figure 5–12 graphically depicts average total, average variable, average fixed, and marginal costs under the assumption that output is infinitely divisible (the firm is not restricted to pro- ducing only the outputs listed in Tables 5–4 and 5–5 but can produce any outputs). The shapes of the curves indicate the relation between the marginal and average costs presented in those tables. These relations among the cost curves, also depicted in Figure 5–12, are very import- ant. The first thing to notice is that the marginal cost curve intersects the ATC and AVC curves at their minimum points. This implies that when marginal cost is below an average cost curve, average cost is declining, and when marginal cost is above average cost, average cost is rising.

There is a simple explanation for this relationship among the various cost curves. Again consider your grade in this course. If your grade on an exam is below your average grade, the new grade lowers your average grade. If the grade you score on an exam is above your average grade, the new grade increases your average. In essence, the new grade is the marginal con- tribution to your total grade. When the marginal is above the average, the average increases; when the marginal is below the average, the average decreases. The same principle applies to marginal and average costs, and this is why the curves in Figure 5–12 look the way they do.

The second thing to notice in Figure 5–12 is that the ATC and AVC curves get closer together as output increases. This is because the only difference in ATC and AVC is AFC. To see why, note that total costs consist of variable costs and fixed costs:

C ( Q ) = VC ( Q )  + FC

If we divide both sides of this equation by total output (Q), we get

C ( Q )

_____ Q

= VC ( Q )

______ Q

 +  FC

___ Q

But C(Q)/Q = ATC, VC(Q)/Q = AVC, and FC/Q = AFC. Thus,

ATC = AVC + AFC

The difference between average total costs and average variable costs is ATC − AVC = AFC. Since average fixed costs decline as output is expanded, as in Figure 5–12, this difference between average total and average variable costs diminishes as fixed costs are spread over increasing levels of output.

Figure 5–12 The Relationship among Average and Marginal Costs

ATC

AVC

MC

Minimum of

ATC

Minimum of

AVC

$

Q AFC

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Fixed and Sunk Costs We now make an important distinction between fixed costs and sunk costs. Recall that a fixed cost is a cost that does not change when output changes. A related concept, called sunk cost, is a cost that is lost forever once it has been paid. To be concrete, imagine that you are the manager of a coal company and have just paid $10,000 to lease a railcar for one month. This expense reflects a fixed cost to your firm—the cost is $10,000 regardless of whether you use the railcar to transport 10 tons or 10,000 tons of coal. How much of this $10,000 is a sunk cost depends on the terms of your lease. If the lease does not permit you to recoup any of the $10,000 once it has been paid, the entire $10,000 is a sunk cost—you have already incurred the cost and there is nothing you can do to change it. If the lease states that you will be refunded $6,000 in the event you do not need the railcar, then only $4,000 of the $10,000 in fixed costs is a sunk cost. Sunk costs are thus the amount of these fixed costs that cannot be recouped.

Since sunk costs are lost forever once they have been paid, they are irrelevant to decision making. To illustrate, suppose you paid a nonrefundable amount of $10,000 to lease a rail- car for one month, but immediately after signing the lease, you realize that you do not need it—the demand for coal is significantly lower than you expected. A farmer approaches you and offers to sublease the railcar from you for $2,000. If the terms of your lease permit you to sublease the railcar, should you accept the farmer’s offer?

You might reason that the answer is no; after all, your firm would appear to lose $8,000 by subleasing a $10,000 railcar for a measly $2,000. This reasoning is wrong. Your lease pay- ment is nonrefundable, which means that the $10,000 is an unavoidable cost that has already been lost. Since there is nothing you can do to eliminate this $10,000 cost, the only relevant issue is whether you can do something to enhance your inflow of cash. In this case your opti- mal decision is to sublease the railcar because doing so provides you with $2,000 in revenues that you would not get otherwise. Notice that, while sunk costs are irrelevant in making your decision, they do affect your calculation of total profits. If you do not sublease the railcar, you lose $10,000; if you sublease it, you lose only $8,000.

sunk cost A cost that is forever lost after it has been paid.

DEMONSTRATION PROBLEM 5–4

ACME Coal paid $5,000 to lease a railcar from the Reading Railroad. Under the terms of the lease, $1,000 of this payment is refundable if the railcar is returned within two days of signing the lease.

1. Upon signing the lease and paying $5,000, how large are ACME’s fixed costs? Its sunk costs? 2. One day after signing the lease, ACME realizes that it has no use for the railcar. A farmer

has a bumper crop of corn and has offered to sublease the railcar from ACME at a price of $4,500. Should ACME accept the farmer’s offer?

ANSWER: 1. ACME’s fixed costs are $5,000. For the first two days, its sunk costs are $4,000 (this is the

amount that cannot be recouped). After two days, the entire $5,000 becomes a sunk cost. 2. Yes, ACME should sublease the railcar. Note that ACME’s total loss is $500 if it accepts

the farmer’s offer. If it does not, its losses will equal $4,000 (assuming it returns the railcar by the end of the next business day).

P R I N C I P L E Irrelevance of Sunk Costs A decision maker should ignore sunk costs to maximize profits or minimize losses.

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Algebraic Forms of Cost Functions In practice, cost functions may take many forms, but the cubic cost function is frequently encountered and closely approximates any cost function. The cubic cost function is given by

C(Q) = f + aQ + b Q 2  + c Q 3

where a, b, c, and f are constants. Note that f represents fixed costs. Given an algebraic form of the cubic cost function, we may directly calculate the mar-

ginal cost function.

Formula: Marginal Cost for Cubic Costs. For a cubic cost function,

C(Q) = f + aQ + b Q 2  + c Q 3

the marginal cost function is

MC(Q) = a + 2bQ + 3c Q 2

A C A L C U L U S A L T E R N A T I V E Marginal cost is simply the derivative of the cost function with respect to output:

MC(Q) = dC

___ dQ

For example, the derivative of the cubic cost function with respect to Q is

dC

___ dQ

= a + 2bQ + 3c Q 2

which is the equation for marginal cost given in the formula.

cubic cost function Costs are a cubic function of output; provides a reasonable approximation to virtually any cost function.

DEMONSTRATION PROBLEM 5–5

The cost function for Managerial Enterprises is given by C(Q) = 20 + 3Q2. Determine the marginal cost, average fixed cost, average variable cost, and average total cost when Q = 10.

ANSWER: Using the formula for marginal cost (here a = c = 0), we know that MC = 6Q. Thus, the marginal cost when Q = 10 is $60.

To find the various average costs, we must first calculate total costs. The total cost of producing 10 units of output is

C(10) = 20 + 3(10 ) 2 = $320

Fixed costs are those costs that do not vary with output; thus fixed costs are $20. Variable costs are the costs that vary with output, namely VC(Q) = 3Q2. Thus, VC(10) = 3(10)2 = $300. It follows that the average fixed cost of producing 10 units is $2, the average variable cost is $30, and the average total cost is $32.

Long-Run Costs In the long run, all costs are variable because the manager is free to adjust the levels of all inputs. In Figure 5–13, the short-run average cost curve ATC0 is drawn under the assumption that there are some fixed factors of production. The average total cost of producing output level

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Q0, given the fixed factors of production, is ATC0(Q0). In the short run, if the firm increases output to Q1, it cannot adjust the fixed factors, and thus average costs rise to ATC0(Q1). In the long run, however, the firm can adjust the fixed factors. Let ATC1 be the average cost curve after the firm adjusts the fixed factors in the optimal manner. Now the firm can produce Q1 with average cost curve ATC1. If the firm produced Q1 with average cost curve ATC0, its aver- age costs would be ATC0(Q1). By adjusting the fixed factors in a way that optimizes the scale of operation, the firm economizes in production and can produce Q1 units of output at a lower average cost, ATC1(Q1). Notice that the curve labeled ATC1 is itself a short-run average cost curve, based on the new levels of fixed inputs that have been selected to minimize the cost of producing Q1. If the firm wishes to further expand output—say, to Q2—it would follow curve ATC1 in the short run to ATC1(Q2) until it again changed its fixed factors to incur lower aver- age costs of producing Q2 units of output, namely ATC2(Q2).

The long-run average cost curve, denoted LRAC in Figure 5–13, defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of all variables of production (both fixed and variable factors). The long-run average cost curve is the lower envelope of all the short-run average cost curves. This means that the long-run aver- age cost curve lies below every point on the short-run average cost curves, except that it equals each short-run average cost curve at the points where the short-run curve uses fixed factors optimally. In essence, we may think of each short-run average cost curve in Figure 5–13 as the average cost of producing in a plant of fixed size. Different short-run average cost curves are associated with different plant sizes. In the long run, the firm’s manager is free to choose the optimal plant size for producing the desired level of output, and this determines the long-run average cost of producing that output level.

Economies of Scale Notice that the long-run average cost curve in Figure 5–14(a) is U shaped. This implies that initially an expansion of output allows the firm to produce at lower long-run average cost, as is shown for outputs between 0 and Q*. This condition is known as economies of scale. When there are economies of scale, increasing the size of the operation decreases the minimum average cost. After a point, such as Q* in Figure 5–14(a), further increases in out- put lead to an increase in average costs. This condition is known as diseconomies of scale.

long-run average cost curve A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production.

economies of scale Exist whenever long-run average costs decline as output increases.

diseconomies of scale Exist whenever long-run average costs increase as output increases.

Figure 5–13 Optimal Plant Size and Long-Run Average Cost

0

$

Output

ATC0(Q1)

Q1

ATC1(Q2)

ATC2(Q1) ATC0(Q0)

Q0 Q2

ATC2(Q2)

ATC1(Q1)

ATC1 ATC0

ATC2

LRAC

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While serving in the U.S. Army, Marc Nerlove conceived a research project to model the economic factors that impact the production of electricity. The primary innovation in Nerlove’s model of electricity supply was the way it was rooted in the theory of production and costs. His approach was the first to empirically utilize the “dual” approach to production and costs—that is, to exploit the fact that a cost function summarizes all of the information contained in a production function, and vice versa.

Two primary findings emerged from Nerlove’s empirical analysis. First, substantial economies of scale existed at the firm level in the market for electricity in the 1950s. The degree of the scale economies, however, varies inversely with output and is considerably lower than previously esti- mated for individual plant facilities. This was especially true for large firms. Second, though the size of an electricity company’s operations impacted its economies of scale, it did not impact its marginal rate of substitution between fac- tors of production.

Advances in the theory of duality between produc- tion and costs led Christensen and Greene to distinguish between scale economies and cost reductions that stem

from technological change. Their analysis suggests that technological change explains a large portion of the reductions in electricity costs that occurred between 1955 and 1970.

Today, these pioneering techniques—as well as more advanced econometric approaches—are used to estimate the production and cost functions needed to guide manage- rial decisions in industries ranging from electricity to health care, as more recent work by economists Michael Maloney and James Thornton shows. There are some spreadsheet files and data available via McGraw-Hill Connect that give you an opportunity to use the econometric techniques introduced in Chapter 3 to estimate production and cost functions.

SOURCES: M. Nerlove, “Returns to Scale in Electricity Supply,” Measurement in Economics, ed. C. Christ et al. (Palo Alto, CA: Stanford University Press, 1963), pp. 167–98; L. R. Christensen and W. H. Greene, “Economies of Scale in U.S. Electric Power Generation,” Journal of Political Economy  84 (1976), pp. 655–76; M. Maloney, “Economies and Diseconomies: Estimating Electricity Cost Functions,” Review of Industrial Organization  19 (2001), pp. 165–80; J. Thornton, “Estimating a Health Production Function for the US: Some New Evidence,” Applied Economics 34 (2002), pp. 59–62.

INSIDE BUSINESS 5–3

Estimating Production Functions, Cost Functions, and Returns to Scale

Figure 5–14 Scale Economies

0 Q

0

$

Q Q*

Economies of scale

Diseconomies of scale

LRAC

ATC 1 ATC 2 ATC 3

LRAC

$

(a) Economies and diseconomies of scale (b) Constant returns to scale

Sometimes the technology in an industry allows a firm to produce different levels of output at the same minimum average cost, as in Figure 5–14(b). This condition is called constant returns to scale.

A Reminder: Economic Costs versus Accounting Costs In concluding this section, it is important to recall the difference between economic costs and accounting costs. Accounting costs are the costs most often associated with the costs

constant returns to scale Exist when long-run average costs remain constant as output is increased.

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of producing. For example, accounting costs include direct payments to labor and capital to produce output. Accounting costs are the costs that appear on the income statements of firms.

These costs are not the only costs of producing a good, however. The firm could use the same resources to produce some other good. By choosing to produce one good, produc- ers give up the opportunity for producing some other good. Thus, the costs of production include not only the accounting costs but also the opportunities forgone by producing a given product.

MULTIPLE-OUTPUT COST FUNCTIONS

Until now, our analysis of the production process has focused on situations where the firm produces a single output. There are also numerous examples of firms that produce multiple outputs. Toyota produces cars, trucks, and SUVs (and many varieties of each); Dell produces many different types of computers and printers. While our analysis for the case of a firm that produces a single output also applies to a multiproduct firm, the latter raises some additional issues. This section will highlight these concepts.

In this section, we will assume that the cost function for a multiproduct firm is given by C(Q1,  Q2), where Q1 is the number of units produced of product 1 and Q2 is the num- ber of units produced of product 2. The multiproduct cost function thus defines the cost of producing Q1 units of product 1 and Q2 units of product 2 assuming all inputs are used efficiently.

Notice that the multiproduct cost function has the same basic interpretation as a sin- gle-output cost function. Unlike with a single-product cost function, however, the costs of production depend on how much of each type of output is produced. This gives rise to what economists call economies of scope and cost complementarities, discussed next.

multiproduct cost function A function that defines the cost of producing given levels of two or more types of outputs assuming all inputs are used efficiently.

In industries with economies of scale, firms that produce greater levels of output produce at lower average costs and thus gain a potential competitive advantage over rivals. Recently, two international businesses pursued such strate- gies to enhance their bottom line.

Japan’s Matsushita Plasma Display Panel Company, Ltd., invested $835 million to build the world’s largest plant for producing plasma display panels. The factory—a joint venture between Panasonic and Toray Industries—had the capacity to produce 250,000 panels per month by the late 2000s. This strategy was implemented in response to rising global demand for plasma display panels, and a desire on the part of the company to gain a competitive advantage over rivals in this increasingly competitive industry.

An automaker in India—Maruti Udyog Ltd.—produced tangible evidence that economies of scale are important in business decisions. It enjoyed a 271 percent increase in net profits in the mid-2000s, thanks to its ability to exploit these economies. The increase was spawned by a 30 percent increase in sales volume that permitted the firm to spread its sizable fixed costs over greater output. Importantly, the company’s reduction in average costs due to economies of scale was more than enough to offset the higher costs stemming from increases in the price of steel.

SOURCES: “Matsushita Plans Big Expansion of PDP Manufacturing,” IDG News Service, May 19, 2004; “MUL Gains from Cost-Saving Measures,” Sify India, May 18, 2004.

INSIDE BUSINESS 5–4

International Companies Exploit Economies of Scale

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Economies of Scope Economies of scope exist when the total cost of producing Q1 and Q2 together is less than the total cost of producing Q1 and Q2 separately, that is, when

C( Q 1 , 0) + C(0,  Q 2 ) > C( Q 1 ,  Q 2 )

In a restaurant, for example, to produce given quantities of steak and chicken dinners, it gen- erally is cheaper to produce both products in the same restaurant than to have two restaurants, one that sells only chicken and one that sells only steak. The reason is, of course, that produc- ing the dinners separately would require duplication of many common factors of production, such as ovens, refrigerators, tables, the building, and so forth.

Cost Complementarity Cost complementarities exist in a multiproduct cost function when the marginal cost of pro- ducing one output is reduced when the output of another product is increased. Let C(Q1, Q2) be the cost function for a multiproduct firm, and let MC1(Q1, Q2) be the marginal cost of pro- ducing the first output. The cost function exhibits cost complementarity if

ΔM C 1 ( Q 1 ,  Q 2 ) _____________

Δ Q 2 < 0

that is, if an increase in the output of product 2 decreases the marginal cost of producing product 1. An example of cost complementarity is the production of doughnuts and doughnut holes.

The firm can make these products separately or jointly. But the cost of making additional doughnut holes is lower when workers roll out the dough, punch the holes, and fry both the doughnuts and the holes instead of making the holes separately.

The concepts of economies of scope and cost complementarity can also be examined within the context of an algebraic functional form for a multiproduct cost function. For exam- ple, suppose the multiproduct cost function is quadratic:

C( Q 1 ,  Q 2 ) = f + a Q 1 Q 2  + ( Q 1 ) 2  + ( Q 2 )

2

For this cost function,

M C 1 = a Q 2  + 2 Q 1

Notice that when a < 0, an increase in Q2 reduces the marginal cost of producing product 1. Thus, if a < 0, this cost function exhibits cost complementarity. If a > 0, there are no cost complementarities.

Formula: Quadratic Multiproduct Cost Function. The multiproduct cost function

C( Q 1 ,  Q 2 ) = f + a Q 1 Q 2  + ( Q 1 ) 2  + ( Q 2 )

2

has corresponding marginal cost functions,

M C 1 ( Q 1 ,  Q 2 ) = a Q 2  + 2 Q 1

and

M C 2 ( Q 1 ,  Q 2 ) = a Q 1  + 2 Q 2 To examine whether economies of scope exist for a quadratic multiproduct cost function,

recall that there are economies of scope if

economies of scope Exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms.

cost complementarities Exist when the marginal cost of producing one output is reduced when the output of another product is increased.

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C( Q 1 , 0) + C(0,  Q 2 ) > C( Q 1 ,  Q 2 )

or, rearranging,

C( Q 1 , 0) + C(0,  Q 2 ) − C( Q 1 ,  Q 2 ) > 0

This condition may be rewritten as

f + ( Q 1 ) 2  + f + ( Q 2 )

2  − [ f + a Q 1 Q 2  + ( Q 1 ) 2  + ( Q 2 )

2 ] > 0

which may be simplified to

f − a Q 1 Q 2 > 0

Thus, economies of scope are realized in producing output levels Q1 and Q2 if f > aQ1Q2.

Summary of the Properties of the Quadratic Multiproduct Cost Function. The mul- tiproduct cost function C(Q1, Q2) = f + aQ1Q2 + (Q1)

2 + (Q2) 2

1. Exhibits cost complementarity whenever a < 0. 2. Exhibits economies of scope whenever f − aQ1Q2 > 0.

DEMONSTRATION PROBLEM 5–6

Suppose the cost function of firm A, which produces two goods, is given by

C = 100 − .5 Q 1 Q 2  + ( Q 1 ) 2  + ( Q 2 )

2

The firm wishes to produce 5 units of good 1 and 4 units of good 2.

1. Do cost complementarities exist? Do economies of scope exist? 2. Firm A is considering selling the subsidiary that produces good 2 to firm B, in which case

it will produce only good 1. What will happen to firm A’s costs if it continues to produce 5 units of good 1?

ANSWER: 1. For this cost function, a = −1/2 < 0, so indeed there are cost complementarities. To check

for economies of scope, we must determine whether f − aQ1Q2 > 0. This is clearly true since a < 0 in this problem. Thus, economies of scope exist in producing 5 units of good 1 and 4 units of good 2.

2. To determine what will happen to firm A’s costs if it sells the subsidiary that produces good 2 to firm B, we must calculate costs under the alternative scenarios. By selling the subsidiary, firm A will reduce its production of good 2 from 4 to 0 units; since there are cost complementarities, this will increase the marginal cost of producing good 1. Notice that the total costs to firm A of producing the 5 units of good 1 fall from

C ( 5, 4 ) = 100 − 10 + 25 + 16 = 131

to

C ( 5, 0 ) = 100 + 25 = 125

But the costs to firm B of producing 4 units of good 2 will be

C ( 0, 4 ) = 100 + 16 = 116

Firm A’s costs will fall by only $6 when it stops producing good 2, and the costs to firm B of pro- ducing 4 units of good 2 will be $116. The combined costs to the two firms of producing the output originally produced by a single firm will be $110 more than the cost of producing by a single firm.

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The preceding problem illustrates some important aspects of mergers and sales of subsid- iaries. First, when there are economies of scope, two firms producing distinct outputs could merge into a single firm and enjoy a reduction in costs. Second, selling off an unprofitable subsidiary could lead to only minor reductions in costs. In effect, when economies of scope exist, it is difficult to “allocate costs” across product lines.

ANSWERING THE headLINE In the opening headline, the phrase “wins the battle” refers to the short-run impli- cations of the agreement between Boeing and the IAM, while “wins the war” refers to the agreement’s long-run implications. The analyst recognizes that the agree- ment benefited union workers in the short run, but the agreement also increased Boeing’s long-term value by giving it the flexibility to substitute away from more costly unionized inputs.

More specifically, Boeing’s new union contract provided a number of “short-term” provisions (health and pension benefits, higher wages, and job security for some of the union’s more senior workers) that were costly to Boeing but beneficial to the union. In the long run, however, the higher labor costs associated with the agreement provide Boeing with an incentive to substitute away from more expensive union labor, and the agreement provides Boeing the flexibility to do so. For instance, the subcontracting provisions Boeing won in the agreement may, in the long run, permit the company to substitute away from its costly and heavily unionized Pacific Northwest inputs toward assembly facilities in less costly areas. In short, the analyst concluded that the long-run flexibility imbedded in the agreement translates into cost-reducing substitution possibili- ties for Boeing that generate long-run benefits that probably more than offset the short-run costs.

SUMMARY

In this chapter, we introduced the production and cost func- tions, which summarize important information about con- verting inputs into outputs sold by a firm. For firms that use several inputs to produce output, isocosts and isoquants pro- vide a convenient way to determine the optimal input mix.

We broke down the cost function into average total cost, average fixed cost, average variable cost, and marginal cost. These concepts help build a foundation for under- standing the profit-maximizing input and output decisions that will be covered in greater detail in later chapters.

Given a desired level of output, isoquants and iso- costs provide the information needed to determine the

cost- minimizing level of inputs. The cost-minimizing level of inputs is determined by the point at which the ratio of input prices equals the ratio of marginal products for the various inputs.

Finally, we showed how economies of scale, econo- mies of scope, and cost complementarities influence the level and mix of outputs produced by single- and mul- tiproduct firms. In the next chapter we will look at the acquisition of inputs. We will see how managers can use spot markets, contracts, or vertical integration to effi- ciently obtain the inputs needed to produce their desired mix of outputs.

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167

KEY TERMS AND CONCEPTS

average fixed cost (AFC) average product (AP) average total cost (ATC) average variable cost (AVC) capital Cobb-Douglas production

function constant returns to scale cost complementarity cost function cost minimization cubic cost function decreasing (or diminishing)

marginal returns diseconomies of scale economies of scale economies of scope

fixed costs fixed factors of production increasing marginal returns isocost line isoquant labor law of diminishing marginal rate of

technical substitution law of diminishing marginal

returns Leontief (or fixed-proportions)

production function linear production function long run long-run average cost curve marginal (incremental)

cost (MC)

marginal product (MP) marginal rate of technical

substitution (MRTS) multiproduct cost function negative marginal returns optimal input substitution patent production function profit-maximizing input usage short run short-run cost function sunk costs total cost total product (TP) value marginal product variable costs variable factors of production

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. A firm can manufacture a product according to the production function (LO1, LO2, LO5, LO6)

Q = F(K, L) = K 3/4 L 1/4

a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 256 units of labor?

b. Find an expression for the marginal product of labor, MPL, when the amount of capi- tal is fixed at 81 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.

c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at $50 per unit of labor, how many units of labor should the firm hire in order to maximize profits?

2. A firm’s product sells for $4 per unit in a highly competitive market. The firm pro- duces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a contract for 20 hours of labor services). Complete the following table and use that information to answer these questions. (LO1, LO2, LO5, LO6) a. Identify the fixed and variable inputs. b. What are the firm’s fixed costs? c. What is the variable cost of producing 475 units of output? d. How many units of the variable input should be used to maximize profits? e. What are the maximum profits this firm can earn? f. Over what range of the variable input usage do increasing marginal returns exist? g. Over what range of the variable input usage do decreasing marginal returns exist? h. Over what range of input usage do negative marginal returns exist?

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168

K L Q MPK APK APL VMPK

0  20 0 

1  20 50 

2  20 150 

3  20 300 

4  20 400 

5  20 450 

6  20 475 

7  20 475 

8  20 450 

9  20 400 

10  20 300 

11  20 150 

3. Explain the difference between the law of diminishing marginal returns and the law of diminishing marginal rate of technical substitution. (LO2, LO5)

4. An economist estimated that the cost function of a single-product firm is

C(Q) = 100 + 20Q + 15 Q 2  + 10 Q 3

Based on this information, determine: (LO4, LO5) a. The fixed cost of producing 10 units of output. b. The variable cost of producing 10 units of output. c. The total cost of producing 10 units of output. d. The average fixed cost of producing 10 units of output. e. The average variable cost of producing 10 units of output. f. The average total cost of producing 10 units of output. g. The marginal cost when Q = 10.

5. A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $8 per hour. If the mar- ginal product of labor is 60 units of output per hour and the marginal product of capital is 45 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process? (LO2)

6. A firm’s fixed costs for 0 units of output and its average total cost of producing different output levels are summarized in the following table. Complete the table to find the fixed cost, variable cost, total cost, average fixed cost, average variable cost, and marginal cost at all relevant levels of output. (LO5, LO6)

Q FC VC TC AFC AVC ATC MC

    0   $15,000 –

100   300

200   200

300   175

400   225

500   325

600   400

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169

7. A multiproduct firm’s cost function was recently estimated as (LO7)

C( Q 1 ,  Q 2 ) = 90 − 0.5 Q 1 Q 2  + 0.4 Q 1 2  + 0.3 Q 2

2

a. Are there economies of scope in producing 10 units of product 1 and 10 units of product 2?

b. Are there cost complementarities in producing products 1 and 2? c. Suppose the division selling product 2 is floundering and another company has made

an offer to buy the exclusive rights to produce product 2. How would the sale of the rights to produce product 2 change the firm’s marginal cost of producing product 1?

8. Explain the difference between fixed costs, sunk costs, and variable costs. Provide an example that illustrates that these costs are, in general, different. (LO4)

9. A firm produces output according to a production function Q = F(K, L) = min {4K, 8L}. (LO1, LO2) a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is

the cost-minimizing input mix for producing 8 units of output? c. How does your answer to part b change if the wage rate decreases to $20 per hour

but the rental rate on capital remains at $20 per hour? 10. A firm produces output according to the production function Q = F(K, L) = 4K + 8L.

(LO1, LO2) a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is

the cost-minimizing input mix for producing 32 units of output? c. How does your answer to part b change if the wage rate decreases to $20 per hour

but the rental rate on capital remains at $20 per hour?

PROBLEMS AND APPLICATIONS

11. In an effort to stop the migration of many of the automobile manufacturing facilities from the Detroit area, Detroit’s city council is considering passing a statute that would give investment tax credits to auto manufacturers. Effectively, this would reduce auto manufacturers’ costs of using capital and high-tech equipment in their production pro- cesses. On the evening of the vote, local union officials voiced serious objections to this statute. Outline the basis of the argument most likely used by union officials. (Hint: Consider the impact that the statute would have on auto manufacturers’ cap- ital-to-labor ratio.) As a representative for one of the automakers, how would you counter the union officials’ argument? (LO1, LO2)

12. You were recently hired to replace the manager of the Roller Division at a major conveyor- manufacturing firm, despite the manager’s strong external sales record. Roller manu- facturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company’s production information, you learn that labor is paid $12 per hour and the last worker hired produced 80 rollers per hour. The company rents roller cutters and crimping machines for $15 per hour, and the marginal product of capital is 110 rollers per hour. What do you think the previous manager could have done to keep his job? (LO1, LO2)

13. You are a manager for Herman Miller, a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to esti- mate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is

Q = 2(K ) 1/2 (L ) 1/2

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where K represents capital equipment and L is labor. Your company has already spent a total of $8,000 on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. If workers at the firm are paid a competitive wage of $120 per day and chairs can be sold for $400 each, what is your profit-maximizing level of output and labor usage? What is your maximum profit? (LO1, LO2)

14. Recently, the Boeing Commercial Airline Group (BCAG) recorded orders for more than 15,000 jetliners and delivered more than 13,000 airplanes. To maintain its output volume, this Boeing division combines efforts of capital and more than 90,000 workers. Suppose the European company Airbus enjoys a similar production technology and produces a similar number of aircraft but that labor costs (including fringe benefits) are higher in Europe than in the United States. Would you expect workers at Airbus to have the same marginal product as workers at Boeing? Explain carefully. (LO1, LO2)

15. You are a manager at Glass Inc.—a mirror and window supplier. Recently, you con- ducted a study of the production process for your single-side encapsulated window. The results from the study are summarized in the following table, and are based on the eight units of capital currently available at your plant. Each unit of labor costs $60, each unit of capital is $20, and your encapsulated windows sell for $12 each. Given this informa- tion, optimize your human resource and production decisions. Do you anticipate earning a profit or a loss? Explain carefully. (LO1, LO2, LO3)

Labor Output

0   0

1 10

2 30

3 60

4 80

5 90

6 95

7 95

8 90

9 80

10   60

11   30

16. A Nike women’s-only store in California offers women’s running, training, and sports- wear products and also contains an in-store fitness studio for group and personal fitness training sessions. The store consistently earns profits in excess of $500,000 per year and is located on prime real estate in the center of town. The store owner pays $15,000 per month in rent for the building. A real estate agent approached the owner and informed her that she could add $8,000 per month to her firm’s profits by renting out the portion of her store that she uses as a fitness studio. While the prospect of acquiring this rental income was enticing, the owner believed the use of that space as a fitness studio was an important contributor to her store’s profits. What is the opportunity cost of continuing to operate the fitness studio within the store? (LO3)

17. A local restaurateur who had been running a profitable business for many years recently purchased a three-way liquor license. This license gives the owner the legal right to sell beer, wine, and spirits in her restaurant. The cost of obtaining the three-way license was about $90,000 since only 300 such licenses are issued by the state. While the license is transferable, only $75,000 is refundable if the owner chooses not to use the license. After selling alcoholic beverages for about one year, the restaurateur came to

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the realization that she was losing dinner customers and that her profitable restaurant was turning into a noisy, unprofitable bar. Subsequently, she spent about $8,000 placing advertisements in various newspapers and restaurant magazines across the state offer- ing to sell the license for $80,000. After a long wait, she finally received one offer to purchase her license for $77,000. What is your opinion of the restaurateur’s decisions? Would you recommend that she accept the $77,000 offer? (LO4)

18. In the wake of the energy crisis in California in 2000 and 2001, many electricity gener- ating facilities across the nation periodically reassess their projections of future demand and capacity for electricity in their respective markets. As a manager at Florida Power & Light Company, you are in charge of determining the optimal size of two electricity generating facilities. The accompanying figure illustrates the short-run average total cost curves associated with different facility sizes. Demand projections indicate that 6 million kilowatts must be produced at your South Florida facility and 2 million kilowatts must be produced at your facility in the Panhandle. Determine the optimal facility size (S, M, or L) for these two regions, and indicate whether there will be economies of scale, disecono- mies of scale, or constant returns to scale if the facilities are built optimally. (LO6)

Average Total Cost for Various Plant Sizes

0

$10

9

8

7

6

5

4

3

2

1

0 Kilowatts per hour

(millions)

ATC S

ATC L

1 2 3 4 5 6 7 8

ATC M

19. The A-1 Corporation supplies airplane manufacturers with preformed sheet metal panels that are used on the exterior of aircraft. Manufacturing these panels requires only five sheet metal–forming machines, which cost $500 each, and workers. These workers can be hired on an as-needed basis in the labor market at $9,000 each. Given the simplicity of the manu- facturing process, the preformed sheet metal panel market is highly competitive. Therefore, the market price for one of A-1’s panels is $80. Based on the production data in the accom- panying table, how many workers should A-1 hire to maximize its profits? (LO1, LO2)

Sheet Metal–Forming Machines Workers

Number of Panels Produced

5 0        0

5 1    600

5 2 1,000

5 3 1,290

5 4 1,480

5 5 1,600

5 6 1,680

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20. According to The Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labor and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of tech- nical substitution is 0.12 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,800. In the study of its production pro- cess and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.8 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is ¥1,200,000. Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output. To minimize costs Mitsubishi should hire capital and labor until the marginal rate of technical substitution reaches what propor- tion? (LO1, LO2)

21. Hyundai Heavy Industries Co. is one of Korea’s largest industrial producers. According to an article in BusinessWeek Online, the company not only is the world’s largest shipbuilder but also manufactures other industrial goods ranging from construction equipment and marine engines to building power plants and oil refineries worldwide. Despite being a major industrial force in Korea, several of the company’s divisions are unprofitable, or “bleeding red ink” in the words of the article. Indeed, last year the power plant and oil refineries building division recorded a $105 million loss, or 19 per- cent of its sales. Hyundai Heavy Industries recently hired a new CEO who is charged with the mission of bringing the unprofitable divisions back to profitability. According to BusinessWeek, Hyundai’s profit-driven CEO has provided division heads with the following ultimatum: “. . . hive off money-losing businesses and deliver profits within a year—or else resign.” Suppose you are the head of the marine engine division and that it has been unprofitable for 7 of the last 10 years. While you build and sell in the competitive marine engines industry, your primary customer is Hyundai’s profitable ship- building division. This tight relationship is due, in large part, to the technical spec- ifications of building ships around engines. Suppose that in your end-of-year report to the CEO you must disclose that while your division reduced costs by 10 percent, it still remains unprofitable. Make an argument to the CEO explaining why your division should not be shut down. What conditions must hold for your argument to withstand the CEO’s criticism? (LO7)

22. In the aftermath of a hurricane, an entrepreneur took a one-month leave of absence (without pay) from her $5,000-per-month job in order to operate a kiosk that sold fresh drinking water. During the month she operated this venture, the entrepreneur paid the government $2,500 in kiosk rent and purchased water from a local wholesaler at a price of $1.34 per gallon. Write an equation that summarizes the cost function for her opera- tion, as well as equations that summarize the marginal, average variable, average fixed, and average total costs of selling fresh drinking water at the kiosk. If consumers were willing to pay $2.25 to purchase each gallon of fresh drinking water, how many units did she have to sell in order to turn a profit? Explain carefully. (LO1, LO3)

23. You are the manager of a large but privately held online retailer that currently uses 17 unskilled workers and 6 semiskilled workers at its warehouse to box and ship the prod- ucts it sells online. Your company pays its unskilled workers the minimum wage but pays the semiskilled workers $12.75 per hour. Thanks to government legislation, the minimum wage in your state will increase from $10.25 per hour to $10.75 per hour on July 24, 2017. Discuss the implications of this legislation for your company’s operations and in particular the implications for your optimal mix of inputs and long-run invest- ment decisions. (LO1, LO2, LO6)

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SELECTED READINGS

Anderson, Evan E., and Chen, Yu Min, “Implicit Prices and Economies of Scale of Secondary Memory: The Case of Disk Drives.” Managerial and Decision Economics 12(3), June 1991, pp. 241–48.

Carlsson, Bo; Audretsch, David B.; and Acs, Zoltan J., “Flexible Technology and Plant Size: U.S. Manufacturing and Metalworking Industries.” International Journal of Industrial Organization 12(3), 1994, pp. 359–72.

Eaton, C., “The Geometry of Supply, Demand, and Competitive Market Structure with Economies of Scope.” American Economic Review 81, September 1991, pp. 901–11.

Ferrier, Gary D., and Lovell, C. A. Knox, “Measuring Cost Efficiency in Banking: Econometric and Linear Programming Evidence.” Journal of Econometrics 46(12), October–November 1990, pp. 229–45.

Gold, B., “Changing Perspectives on Size, Scale, and Returns: An Interpretive Survey.” Journal of Economic Literature 19(1), March 1981, pp. 5–33.

Gropper, Daniel M., “An Empirical Investigation of Changes in Scale Economies for the Commercial Banking Firm, 1979–1986.” Journal of Money, Credit, and Banking 23(4), November 1991, pp. 718–27.

Kohn, Robert E., and Levin, Stanford L., “Complementarity and Anticomplementarity with the Same Pair of Inputs.” Journal of Economic Education 25(1), Winter 1994, pp. 67–73.

Mills, D., “Capacity Expansion and the Size of Plants.” RAND Journal of Economics 21, Winter 1990, pp. 555–66.

APPENDIX

THE CALCULUS OF PRODUCTION AND COSTS

THE PROFIT-MAXIMIZING USAGE OF INPUTS

In this section we use calculus to show that the profit- maximizing level of an input is the level at which the value marginal product of the input equals the input’s price. Let P denote the price of the output, Q, which is produced with the production function F(K, L). The profits of the firm are

π = PQ − wL − rK

PQ is the revenue of the firm, and wL and rK are labor costs and capital costs, respectively. Since Q = F(K,  L), the objective of the manager is to choose K and L so as to maximize

 π = PF ( K, L )  − wL − rK

The first-order condition for maximizing this function requires that we set the first derivatives equal to zero:

∂ π

___ ∂ K

= P  ∂ F ( K, L )

________ ∂ K

 − r = 0

and

∂ π

___ ∂ L

= P  ∂ F ( K, L )

________ ∂ L

 − w = 0

But since

∂ F ( K, L ) /∂ L = M P L

and

∂ F ( K, L ) /∂ K = M P K

this implies that to maximize profits, P × MPL = w and P × MPK = r; that is, each input must be used up to the point where its value marginal product equals its price.

THE SLOPE OF AN ISOQUANT

In this section, we use calculus to show that the slope of an isoquant is the negative of the ratio of the marginal products of two inputs.

Let the production function be Q = F(K, L). If we take the total derivative of this relation, we have

dQ = ∂ F ( K, L )

________ ∂ K

 dK +  ∂ F ( K, L )

________ ∂ L

 dL

Since output does not change along an isoquant, then dQ = 0. Thus,

0 = ∂ F ( K, L )

________ ∂ K

 dK +  ∂ F ( K, L )

________ ∂ L

 dL

Solving this relation for dK/dL yields

dK

___ dL

= − ∂ F ( K, L ) /∂ L

___________ ∂ F ( K, L ) /∂ K

Since

∂ F ( K, L ) /∂ L = M P L

and

∂ F ( K, L ) /∂ K = M P K

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we have shown that the slope of an isoquant (dK/dL) is

dK

___ dL

= − M P L _____ M P K

THE OPTIMAL MIX OF INPUTS

In this section, we use calculus to show that to minimize the cost of production, the manager chooses inputs such that the slope of the isocost line equals the MRTS.

To choose K and L so as to minimize

wL + rK subject to F ( K, L ) = Q we form the Lagrangian

H = wL + rK + μ [ Q − F ( K, L ) ] where μ is the Lagrange multiplier. The first-order condi- tions for a minimum are

∂ H

___ ∂ L

= w − μ  ∂ F ( K, L )

________ ∂ L

= 0 (A–1)

∂ H

___ ∂ K

= r − μ  ∂ F ( K, L )

________ ∂ K

= 0 (A–2)

and

∂ H

___ ∂ μ

= Q − F(K, L) = 0

Taking the ratio of Equations (A–1) and (A–2) gives us

w

__ r =

∂ F ( K, L ) /∂ L ___________

∂ F ( K, L ) /∂ K

which is w

__ r =

M P L _____ M P K

= MRTS

THE RELATION BETWEEN AVERAGE AND MARGINAL COSTS

Finally, we will use calculus to show that the relation between average and marginal costs in the diagrams in this chapter is indeed correct. If C(Q) is the cost function (the analysis that follows is valid for both variable and total costs, so we do not distinguish between them here), average cost is AC(Q) = C(Q)/Q. The change in average cost due to a change in output is simply the derivative of average cost with respect to output. Taking the derivative of AC(Q) with respect to Q and using the quotient rule, we see that

dAC ( Q )

_______ dQ

= Q ( dC/dQ )  − C ( Q )

_______________ Q 2

= 1 __

Q [MC ( Q )  − AC ( Q ) ]

since dC(Q)/dQ = MC(Q). Thus, when MC(Q) < AC(Q), average cost declines as output increases. When MC(Q) > AC(Q), average cost rises as output increases. Finally, when MC(Q) = AC(Q), average cost is at its minimum.

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headLINE Google Buys Motorola Mobility to Vertically Integrate In a bold move, Google purchased Motorola Mobility—the recently spun-off cellular arm of Motorola—for $12.5 billion. This move marks an attempt by Google to vertically inte- grate into the smartphone hardware market. Industry experts note that the purchase will allow Google to build prototypes and advanced hardware devices that will help to point its software business partners in the direction Google wants to go. Google is banking on the increased coordination between its software and Motorola’s hardware and the reduc- tion in risks associated with vertical integration outweighing the costs.

If you were a decision maker at Google, would you have recommended vertical integration?

SOURCES: “Google Looks for Vertical Integration,” New York Times Online, August 15, 2011; “Google Buys Motorola Mobility . . . And So Begins the Dark Ages,” Forbes Online, August 22, 2011.

The Organization of the Firm 6

LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Discuss the economic trade-offs associated with obtaining inputs through spot exchange, contract, or vertical integration.

LO2 Identify four types of specialized investments, and explain how each can lead to costly bargaining, underinvestment, and/or a “hold-up problem.”

LO3 Explain the optimal manner of procuring different types of inputs.

LO4 Describe the principal–agent problem as it relates to owners and managers.

LO5 Discuss three forces that owners can use to discipline managers.

LO6 Describe the principal–agent problem as it relates to managers and workers.

LO7 Discuss four tools the manager can use to mitigate incentive problems in the workplace.

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INTRODUCTION

In Chapter 5 we saw how a manager can select the mix of inputs that minimizes the cost of production. However, our analysis in that chapter left unresolved two important questions. First, what is the optimal way to acquire this efficient mix of inputs? Second, how can the owners of a firm ensure that workers put forth the maximum effort consistent with their capa- bilities? In this chapter, we address these two issues.1

Figure 6–1 illustrates why it is important to resolve these two questions. The cost func- tion defines the minimum possible cost of producing each level of output. Point A corre- sponds to the situation where a firm has costs in excess of the minimum costs necessary to produce a given level of output. At point A, 10 units of output are being produced for a total cost of $100. Notice that this cost is greater than $80, which is the minimum cost necessary to produce 10 units of output. Even if the firm has the right mix of inputs, if it did not obtain them efficiently or if workers are not expending the maximum effort consistent with their capabilities, the firm’s costs will be higher than the minimum possible costs.

In this chapter we consider techniques a firm can use to ensure that it is operating on the cost function (point B in Figure 6–1) and not above it (point A). We begin by discussing three methods managers can use to obtain inputs needed in production: spot exchange, contracts, and vertical integration. To minimize costs, a firm must not only use all inputs efficiently (the MRTSKL = w/r rule discussed in Chapter 5); it must use the least-cost method of obtaining the inputs. We will explain when it is optimal to acquire inputs (1) via spot exchange, (2) by writing contracts with input suppliers, or (3) by producing the inputs within the firm (verti- cal integration). Thus, the first part of this chapter provides managers with the information needed to acquire a given set of inputs in the optimal manner.

The second part of the chapter examines how a firm can ensure that labor inputs, includ- ing both managers and workers, put forth the maximum effort consistent with their capa- bilities. This is an important consideration because conflicts of interest often arise among

1Other questions that remain include how much output to produce and how to price the product. These important questions will be answered in the remaining chapters of this book.

Figure 6–1 Producing at Minimum Cost

0

Costs

Output 10

A

B$80

$100

Minimum cost function

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workers, managers, and the firm’s owners. For example, the manager may wish to spend the firm’s resources on plush office carpeting or corporate jets, while the owners prefer that the funds be invested to increase profits, which accrue to them by virtue of their status as own- ers. Or workers may wish to spend most of their day gossiping in the lunchroom instead of working. When employees and owners have conflicting interests, a principal–agent problem is said to exist. We will see how manager and worker compensation plans can be constructed to ensure that all employees put forth their highest levels of effort.

METHODS OF PROCURING INPUTS

A manager can use several approaches to obtain the inputs needed to produce a final product. Consider the manager of a car rental company. One input needed to produce output (rental cars) is automobile servicing (tune-ups, oil changes, lube jobs, and the like). The manager has three options: (1) simply take the cars to a firm that services automobiles and pay the market price for the services; (2) sign a contract with a firm that services automobiles and, when service is needed, pay the price negotiated in the contract for that particular service; or (3) create within the firm a division that services automobiles. Each of these methods of servicing automobiles generally will imply different cost functions for producing car rental services. The manager’s job is to choose the method that minimizes costs. Before we examine how to determine the best method of acquiring a given type of input, it is useful to provide a broad overview of these three methods of acquiring inputs.

Purchase the Inputs Using Spot Exchange One method of acquiring inputs is to use spot exchange. Spot exchange occurs when the buyer and seller of an input meet, exchange, and then go their separate ways. If the manager of a car rental company simply takes a car to one of many firms that provide automobile ser- vicing and pays for the services, the manager has used spot exchange to obtain automobile servicing. With the spot exchange, buyers and sellers essentially are “anonymous”; the parties may make an exchange without even knowing each other’s names, and there is no formal (legal) relationship between buyer and seller.

A key advantage of acquiring inputs with spot exchange is that the firm gets to specialize in doing what it does best: converting the inputs into output. The input manufacturer special- izes in what it does best: producing inputs. Spot exchange often is used when inputs are “stan- dardized.” In that case, one simply purchases the desired input from one of many suppliers that will sell the input.

Acquire Inputs Under a Contract A contract is a legal document that creates an extended relationship between a particular buyer and seller of an input. It specifies the terms under which they agree to exchange over a given time horizon, say, three years. For example, the manager of a car rental firm might choose to formalize her relationship with a particular firm that services automobiles by signing a contract. Such a contract specifies the range of services covered, the price of each service, and the hours during which the cars will be serviced. As long as the service require- ments for the automobiles are understood beforehand, the parties can address all the import- ant issues in the written contract. However, if the number of services needed during the term of the contract is very large, or if some types of unanticipated breakdowns occur, the contract

spot exchange An informal relationship between a buyer and seller in which neither party is obligated to adhere to specific terms for exchange.

contract A formal relationship between a buyer and seller that obligates the buyer and seller to exchange at terms specified in a legal document.

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may be incomplete. A contract is incomplete if, for example, a car needs a new transmission and the contract does not specify the price at which the servicing firm will provide this ser- vice. Of course, this opens the door to a dispute between the two parties regarding the price of the service needed but not spelled out in the contract.

By acquiring inputs with contracts, the purchasing firm enjoys the benefits of special- izing in what it does best because the other firm actually produces the inputs the purchasing firm needs. Contracts also allow the purchasing firm a greater ability to purchase “nonstan- dard” inputs for which there may not be many suppliers. This method of obtaining inputs works well when it is relatively easy to write a contract that describes the characteristics of the inputs needed. One key disadvantage of contracts is that they are costly to write; it takes time, and often legal fees, to draw up a contract that specifies precisely the obligations of both parties. Also, it can be extremely difficult to cover all the contingencies that could occur in the future. Thus, in complex contracting environments, contracts will necessarily be incomplete.

Produce the Inputs Internally Finally, a manager may choose to produce the inputs needed for production within the firm. In this situation the manager of the car rental company dispenses with outside service firms entirely. She sets up a facility to service the automobile fleet with her own employees as service personnel. The firm thus bypasses the service market completely and does the work itself. When a firm shuns other suppliers and chooses to produce an input internally, it has engaged in vertical integration.

With vertical integration, however, a firm loses the gains in specialization it would realize were the inputs purchased from an independent supplier. Moreover, the firm now has to manage the production of inputs as well as the production of the final product produced with those inputs. This leads to the bureaucratic costs associated with a larger organization. On the other hand, by producing the inputs it needs internally, the firm no longer has to rely on other firms to provide the desired inputs. This allows the firm to utilize highly “non- standard” inputs, even those for which writing a contract with an outside supplier would be difficult.

vertical integration A situation where a firm produces the inputs required to make its final product.

DEMONSTRATION PROBLEM 6–1

Determine whether the following transactions involve spot exchange, a contract, or vertical integration:

1. Clone 1 PC is legally obligated to purchase 300 computer chips each year for the next three years from AMI. The price paid in the first year is $200 per chip, and the price rises during the second and third years by the same percentage by which the wholesale price index rises during those years.

2. Clone 2 PC purchased 300 computer chips from a firm that ran an advertisement in the back of a computer magazine.

3. Clone 3 PC manufactures its own motherboards and computer chips for its personal computers.

ANSWER: 1. Clone 1 PC is using a contract to purchase its computer chips. 2. Clone 2 PC used spot exchange to acquire its chips. 3. Clone 3 PC uses vertical integration to obtain its chips and motherboards.

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TRANSACTION COSTS

When a firm acquires an input, it may incur costs in excess of the actual amount paid to the input supplier. These costs are known as transaction costs and play a crucial role in deter- mining optimal input procurement.

The transaction costs of acquiring an input are the costs of locating a seller of the input, negotiating a price at which the input will be purchased, and putting the input to use. Transaction costs include:

1. The cost of searching for a supplier willing to sell a given input. 2. The costs of negotiating a price at which the input will be purchased. These costs

may be in terms of the opportunity cost of time, legal fees, and so forth. 3. Other investments and expenditures required to facilitate exchange.

Many transaction costs are obvious. For example, if an input supplier charges a price of $10 per unit but requires you to furnish your own trucks and drivers to pick up the input, the transaction costs to your firm include the cost of the trucks and the personnel needed to “deliver” the input to your plant. Clearly, the relevant price of the input to your firm includes not only the $10 per unit but also the transaction costs of getting the input to your plant.

Some important transaction costs, however, are less obvious. To understand these “hid- den” transaction costs, we must distinguish between transaction costs that are specific to a particular trading relationship and those that are general in nature. The key to this distinction is the notion of a specialized investment. A specialized investment is simply an investment in a particular exchange that cannot be recovered in another trading relationship. For example, suppose that to ascertain the quality of bolts, it is necessary to spend $100 on a machine that tests the bolts’ strength. If the machine is useful only for testing a particular manufacturer’s bolts and the investment in the machine is a sunk (and therefore nonrecoverable) cost, it is a specialized investment. In contrast, if the machine can be resold at its purchase price or used to test the quality of bolts produced by other firms, it does not represent a specialized investment.

When specialized investments are required to facilitate an exchange, the resulting rela- tionship between the parties is known as a relationship-specific exchange. The distinguish- ing feature of relationship-specific exchange is that the two parties are “tied together” because of the specific investments made to facilitate exchange between them. As we will see, this feature often creates transaction costs due to the sunk nature of the specific investments.

Types of Specialized Investments Before we examine how specialized investments affect transaction costs and the optimal method of acquiring inputs, it is important to recognize that specialized investments occur in many forms. Common examples of different types of specialized investments are provided next.

Site Specificity Site specificity occurs when the buyer and the seller of an input must locate their plants close to each other to be able to engage in exchange. For example, electric power plants often locate close to a particular coal mine to minimize the transportation costs of obtaining coal; the output (electricity) is less expensive to ship than the input (coal). The cost of building the two plants close to each other represents a specialized investment that would have little value if the parties were not involved in exchange.

transaction costs Costs associated with acquiring an input that are in excess of the amount paid to the input supplier.

specialized investment An expenditure that must be made to allow two parties to exchange but has little or no value in any alternative use.

relationship-specific exchange A type of exchange that occurs when the parties to a transaction have made specialized investments.

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Physical-Asset Specificity Physical-asset specificity refers to a situation where the capital equipment needed to produce an input is designed to meet the needs of a particular buyer and cannot be readily adapted to produce inputs needed by other buyers. For example, if producing a lawn mower engine requires a special machine that is useful only for producing engines for a particular buyer, the machine is a specific physical asset for producing the engines.

Dedicated Assets Dedicated assets are general investments made by a firm that allow it to exchange with a par- ticular buyer. For example, suppose a computer manufacturer opens a new assembly line to enable it to produce enough computers for a large government purchaser. If opening the new assembly line is profitable only if the government actually purchases the firm’s computers, the investment represents a dedicated asset.

Human Capital A fourth type of specialized investment is human capital. In many employment relationships, workers must learn specific skills to work for a particular firm. If these skills are not useful or transferable to other employers, they represent a specialized investment.

Implications of Specialized Investments Now that you have a broad understanding of specialized investments and relationship-specific exchange, we will consider how the presence of specialized investments can affect the trans- action costs of acquiring inputs. Specialized investments increase transaction costs because they lead to (1) costly bargaining, (2) underinvestment, and (3) opportunism.

Costly Bargaining In situations where transaction costs are low and the desired input is of uniform quality and sold by many firms, the price of the input is determined by the forces of supply and demand. When specialized investments are not required to facilitate exchange, very little time is expended negotiating a price. The scenario differs, however, if specialized investments are required to obtain the input.

Specialized investments imply that only a few parties are prepared for a trading relation- ship. There is no other supplier capable of providing the desired input at a moment’s notice; obtaining the input the buyer needs requires making a specialized investment before the input becomes available. Consequently, there generally is no “market price” for the input; the two par- ties in the relationship-specific exchange bargain with each other over a price at which the input will be bought and sold. The bargaining process generally is costly, as each side employs negoti- ators to obtain a more favorable price. The parties may also behave strategically to enhance their bargaining positions. For example, the buyer may refuse to accept delivery to force the seller to accept a lower price. Ultimatums may be given. The supplier may reduce the quality of the input and the buyer may complain about the input’s quality through company attorneys. All of these factors generate transaction costs as the two firms negotiate a price for the input.

Underinvestment When specialized investments are required to facilitate exchange, the level of the specialized investment often is lower than the optimal level. To see this, suppose the specialized invest- ment is human capital. To work for a particular firm, a worker must first invest his own time in learning how to perform some task. If the worker perceives that he may not work at the

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firm for very long (due to being laid off or accepting another job), he will not invest as heavily in learning the task as he otherwise would. For example, if you plan to transfer to another university at the end of the semester, you will not invest very heavily in learning how to use the library facilities at your present university. The investment in learning about the library facilities is an investment in human capital specific to your present university and will have little value at another university with a completely different library setup.

Similar problems exist with other types of specialized investments. For example, if an input supplier must invest in a specific machine to produce an input used by a particular buyer (physical-asset specificity), the supplier may invest in a cheaper machine that produces an input of inferior quality. This is because the supplier recognizes that the machine will not be useful if the buyer decides to purchase from another firm, in which case the supplier will be “stuck” with an expensive machine it cannot use. Thus, specialized investments may be lower than optimal, resulting in higher transaction costs because the input produced is of inferior quality.

Opportunism and the “Hold-Up Problem” When a specialized investment must be made to acquire an input, the buyer or seller may attempt to capitalize on the “sunk” nature of the investment by engaging in opportunism. To be concrete, suppose the buyer of an input must make a specific investment of $10—say, the cost of verifying the quality of a particular supplier’s input. The manager knows there are many firms willing to sell the input at a price of $100, so she goes to one of them at random and spends $10 inspecting the input. Once she has paid this $10, the supplier attempts to take advantage of the specialized investment and behave in an opportunistic manner: It attempts to “hold up” the manager by asking for a price of $109—$9 more than the price charged by all other suppliers. Since the manager has already spent $10 inspecting this firm’s input, she is better off paying the $109 than spending an additional $10 inspecting another supplier’s input. After all, even if the other supplier did not engage in opportunistic behavior, it would cost the firm $10 + $100 = $110 to inspect and purchase another supplier’s input. This is the “hold-up problem”: Once a firm makes a specialized investment, the other party may attempt to “rob” it of its investment by taking advantage of the investment’s sunk nature. This behav- ior, of course, would make firms reluctant to engage in relationship-specific investments in the first place unless they can structure contracts to mitigate the hold-up problem.

In many instances, both sides in a trading relationship are required to make specialized investments, in which case both parties may engage in opportunism. For example, suppose an automaker needs crankshafts as an input for making engines. The crankshafts are a specialized input designed for use by that particular automobile manufacturer and require an investment by the producer in highly specialized capital equipment to produce them. If the crankshaft manufacturer does not sell the crankshafts to the automaker, the automaker’s investment in continuing production of the engine will be effectively worthless. Similarly, if the automobile manufacturer does not buy the crankshafts, the supplier’s investment in the capital equipment is likely to be wasted as well since the equipment is not designed to serve the needs of other automobile makers. The investments made by both parties have tied them together in a rela- tionship-specific exchange, giving each firm a potential incentive to engage in opportunistic behavior. Once the supplier has invested in the equipment to make crankshafts, the automaker may attempt to capitalize on the sunk nature of the investment by asking for a lower price. On the other hand, once the automaker reaches the stage of production where it must have crank- shafts to finish the cars, the crankshaft supplier may ask for a higher price to capitalize on the sunk investment made by the automaker. The result is that the two parties spend considerable time negotiating over precisely how much will be paid for the crankshafts, thus increasing the transaction costs of acquiring the input.

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An interesting study by Scott Masten, James Meehan, and Edward Snyder not only quantifies the transaction costs of acquiring inputs but points out the high cost to managers of using an inappropriate method to acquire an input.

Based on the procurement decisions of a naval construc- tion firm, the study reveals that transaction costs account for roughly 14 percent of the total costs of ship construction. Thus, transaction costs are an important component of costs; managers must consider them when they make decisions.

What is the cost of not carefully considering transaction costs when deciding which method to use to acquire an input?

The authors of the study report that mistaken integration— that is, producing internally a component that should have been purchased from another firm—increased transaction costs by an average of 70 percent. Subcontracting work that would have been more efficiently performed within the firm, on the other hand, raised transaction costs by almost 300 percent. The potential cost savings to a firm that chooses the best method of acquiring inputs are thus substantial.

SOURCE: Scott Masten, James Meehan, and Edward Snyder, “The Costs of Organization,” Journal of Law, Economics and Organization 7 (Spring 1991), pp. 1–25.

INSIDE BUSINESS 6–1

The Cost of Using an Inefficient Method of Procuring Inputs

OPTIMAL INPUT PROCUREMENT

Now we will examine how the manager should acquire inputs in such a way as to minimize costs. The cost-minimizing method will depend on the extent to which there is relationship- specific exchange.

Spot Exchange The most straightforward way for a firm to obtain inputs for a production process is to use spot exchange. If there are no transaction costs and there are many buyers and sellers in the input mar- ket, the market price (say, p*) is determined by the intersection of the supply and demand curves for the input. The manager can easily obtain the input from a supplier chosen at random by paying a price of p* per unit of input. If any supplier attempted to charge a price greater than p*, the manager could simply decline and purchase the input from another supplier at a price of p*.

Why, then, would a manager ever wish to bear the expense of drafting a contract or have the firm expend resources to integrate vertically and manufacture the inputs itself? The reason is that in the presence of specialized investments, spot exchange does not insulate a buyer from opportunism, and the parties may end up spending considerable time bargaining over the price and incur substantial costs if negotiations break down. These problems will occur each time the buyer attempts to obtain additional units of the input. Also, as we noted earlier, the input purchased may be of inferior quality due to underinvestment in specialized investments needed to facilitate the exchange.

DEMONSTRATION PROBLEM 6–2

Jiffyburger, a fast-food outlet, sells approximately 8,000 quarter-pound hamburgers in a given week. To meet that demand, Jiffyburger needs 2,000 pounds of ground beef delivered to its premises every Monday morning by 8:00 AM sharp.

1. As the manager of a Jiffyburger franchise, what problems would you anticipate if you acquired ground beef using spot exchange?

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2. As the manager of a firm that sells ground beef, what problems would you anticipate if you were to supply meat to Jiffyburger through spot exchange?

ANSWER:

1. While ground beef for hamburgers is a relatively standardized product, the delivery of one ton of meat to a particular store involves specialized investments (in the form of dedicated assets) on the part of both Jiffyburger and the supplier. In particular, Jiffyburger would face a hold-up problem if the supplier showed up at 8:00 AM and threatened not to unload the meat unless Jiffyburger paid it “ransom”; it would be difficult to find another supplier that could supply the desired quantity of meat on such short notice. The supplier may even attempt to unload meat of inferior quality. Thus, Jiffyburger is not protected from opportunism, bargaining, and underin- vestment in quality when it uses spot exchange to acquire such a large quantity of ground beef.

2. By showing up at Jiffyburger at 8:00 AM with one ton of meat, the supplier makes a spe- cific investment in selling to Jiffyburger. Consequently, the supplier also is subject to a potential hold-up problem. Suppose Jiffyburger behaves opportunistically by asking 10 other suppliers to show up with a ton of meat at 8:00 AM too. Since each supplier would rather unload its meat at a low price than let it spoil, Jiffyburger can bargain with the sup- pliers to get a great deal on the meat. In this case, each supplier risks selling meat at a low price, or not at all, since it is not protected from opportunism by using spot exchange.

When the acquisition of an input requires substantial specialized investments, spot exchange is likely to result in high transaction costs due to opportunism, bargaining costs, and underinvestment. Clearly, managers must consider alternatives to spot exchange when inputs require substantial specialized investments.

Contracts Given the prospect of the hold-up problem and a need to bargain over price each time an input is to be purchased, an alternative strategy is to acquire an input from a particular sup- plier under an appropriately structured contract. While a contract often requires substantial up-front expenditures in terms of negotiations, attorneys’ fees, and the like, it offers several advantages. First, a contract can specify prices of the input before the parties make special- ized investments. This feature reduces the magnitude of costly opportunism down the road. For example, if the manager in Demonstration Problem 6–2 had written a contract that speci- fied a price and a quantity of ground beef before the specialized investments were made, they would not have been subject to the hold-up problem. Both parties would have been legally obligated to honor the contracted price and quantity.

Second, by guaranteeing an acceptable price for both parties for an extended time hori- zon, a contract reduces the incentive for either the buyer or the seller to skimp on the special- ized investments required for the exchange. For example, a worker who has a contract that guarantees employment with a particular firm for three years will have a greater incentive to invest in human capital specific to that firm. Similarly, if the firm knows the worker will be around for three years, it will be willing to invest in more training for the worker.

DEMONSTRATION PROBLEM 6–3

In the real world, virtually all purchases involve some type of specialized investment. For instance, by driving to a particular supermarket, you invest time (and gasoline) that is valuable to you only if you purchase groceries at that supermarket. Why, then, don’t consumers sign contracts with super- markets to prevent the supermarkets from engaging in opportunism once they are inside the store?

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ANSWER: The cost of driving to another supermarket if you are “held up” is relatively low: The cashier may be able to extract an extra few cents on a can of beans, but not much more. Thus, when specialized investments involve only small sums of money, the potential cost of being held up is very low com- pared to the cost of writing a contract to protect against such opportunism. It doesn’t make sense to pay an attorney $200 to write a contract that would potentially save you only a few cents. Moreover, when only a small gain can be realized by engaging in opportunistic behavior, the supermarket will likely not find it in its interest to hold up customers. If a supermarket attempts to take advantage of a customer’s minuscule specialized investment, the customer can threaten to tell others not to ever shop at that store. In this instance, the extra few cents extracted from the customer would not be worth the lost future business. In essence, there is an implicit agreement between the two parties— not an agreement that is enforceable in a court of law, but one that is enforceable by consumers’ future actions. Thus, when the gains from opportunistic behavior are small compared to the costs of writing contracts, formal contracts will not emerge. However, when the gains from opportunism are sufficiently large, formal contracts are needed to prevent opportunistic behavior.

Once the decision is made to use a contract to acquire an input, how long should the con- tract last? The “optimal” contract length reflects a fundamental economic trade-off between the marginal costs and marginal benefits of extending the length of a contract. The marginal cost (MC) of extending contract length increases as contracts become longer, as illustrated in Figure 6–2. This is because as a contract gets longer, more time and money must be spent writing into the contract a larger number of increasingly hypothetical contingencies (for example, “If an Ice Age begins, the price will be . . . ”). It may be easy to specify a mutually acceptable price for a contract that is to be executed tomorrow, but with a 10-year agreement it is difficult (and expensive) to write clauses that include contingencies and prices for each year of the contract. Furthermore, the longer the contract, the more locked in the buyer is to a particular seller and the greater the likelihood that some other supplier can provide the input at a lower cost in the future. In other words, the longer the contract, the less flexibility the firm has in choosing an input supplier. For these reasons, the marginal cost of contract length in Figure 6–2 is upward sloping.

The marginal benefit (MB) of extending a contract for another year is the avoided trans- action costs of opportunism and bargaining. These benefits may vary with the length of the contract, but for simplicity we have drawn a flat MB curve in Figure 6–2. The optimal contract length, L*, is the point at which the marginal costs and marginal benefits of longer contracts are equal.

Figure 6–2 Optimal Contract Length

0

$

Contract length

(in years)L*

MC

MB

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The optimal contract length will increase when the level of specialized investment required to facilitate an exchange increases. To see this, note that as specialized investments become more important, the parties face higher transaction costs once the contract expires. Since these costs can be avoided by writing longer contracts, higher levels of specialized investments increase the marginal benefit of writing longer contracts from MB0 to MB1 in Figure 6–3. The result is an increase in the length of the optimal contract from L0 to L1.

The optimal contract length also depends on factors that affect the marginal cost of writ- ing longer contracts. As an input becomes more standardized and the future economic envi- ronment becomes more certain, the marginal cost of writing longer contracts in Figure 6–4 decreases from MC0 to MC1. This decrease in the complexity of the contracting environment leads to longer optimal contracts (from L0 to L1). In contrast, as the input becomes more com- plex and the future economic environment becomes more uncertain, contracts must be made more detailed. This increase in the complexity of the contracting environment increases the marginal cost of writing longer contracts from MC0 to MC2 in Figure 6–4. Optimal contracts, in this case, will be shorter in duration.

As the contract length shortens due to the complexity of the contracting environment, firms must continually write new contracts as existing ones expire. Considerable resources are spent on attorneys’ fees and bargaining over contract terms, and because of the complex contracting environment, it is not efficient to write longer contracts to reduce these costs. Faced with such a prospect, a manager may wish to use yet another method to procure a nec- essary input: have the firm integrate vertically and make the input itself.

Figure 6–3 Specialized Investments and Contract Length

0

$

Contract lengthL0

MC

MB1

Due to greater need for specialized

investments

L1

MB0

Longer contract

Figure 6–4 Contracting Environment and Contract Length

0

$

Contract length

Shorter contract

Longer contract

L2 L0 L1

MC0

Due to less complex contracting

environment MB

Due to more complex contracting

environment

MC1

MC2

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Want to open a McDonald’s or Starbucks as a franchisee? To do so, you’ll need to sign a contract with a franchisor. The contract you sign will spell out details of the relationship, including the royalty, advertising, sales quotas, etc. You will also have to agree on a contract length.

Virtually any franchisee must make some specific invest- ments, including equipment, marketing, employee training, and often off-site training provided by the franchisor. In the text, we explain how, all else equal, franchises requiring relatively more specialized investments will have longer contracts. An alternative theory—sometimes called the näive franchisee view—proposes that relatively powerful franchises will “bully” näive franchisees into short-term contracts, making them more susceptible to hold-up.

Which theory do the data support? Researchers James A. Brickley, Sanjog Misra, and R. Lawrence Van Horn tested these theories using data on contracting by nearly 2,000 franchisors. Their analysis strongly shows that con- tract duration is increasing in physical and human capital investments, which are often firm specific. In contrast, they find no evidence supporting the näive franchisee view, as more experienced franchisors actually tend to offer longer-term contracts compared to newer franchisors.

SOURCE: James A. Brickley, Sanjog Misra, and R. Lawrence Van Horn, “Contract Duration: Evidence from Franchising,” Journal of Law and Economics 49 (April 2006), pp. 173–96.

INSIDE BUSINESS 6–2

What Determines Contract Length in Franchising?

Vertical Integration When specialized investments generate transaction costs (due to opportunism, bargaining costs, or underinvestment), and when the product being purchased is extremely complex or the eco- nomic environment is plagued by uncertainty, complete contracts will be extremely costly or even impossible to write. The only choice left is for the firm to set up a facility to produce the input internally. This process is referred to as vertical integration because it entails the firm moving farther up the production stream toward increasingly basic inputs. For example, most automobile manufacturers make their own fenders from sheet steel and plastics, having vertically integrated up the production stream from automobile assembly to the fabrication of body parts.

The advantage of vertical integration is that the firm “skips the middleman” by pro- ducing its own inputs. This reduces opportunism by uniting previously distinct firms into divisions of a single, integrated firm. While this strategy might seem desirable in general because it mitigates transaction costs by eliminating the market, this approach has some dis- advantages as well. Managers must replace the discipline of the market with an internal reg- ulatory mechanism, a formidable task to anyone familiar with the failure of central planning often encountered in nonmarket economies. In addition, the firm must bear the cost of setting up production facilities for producing a product that, at best, may be tangentially related to the firm’s main line of business; the firm no longer specializes in doing what it does best. Because of these difficulties, vertical integration should be viewed as a last resort, undertaken only when spot exchange or contracts have failed.

The Economic Trade-Off The cost-minimizing method of acquiring an input depends on the characteristics of the input. Whether a manager chooses spot exchange or an alternative method such as a contract or vertical integration depends on the importance of the specialized investments that lead to rela- tionship-specific exchange. The basic questions involved are illustrated in Figure 6–5.

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An interesting account of a firm moving from spot exchange to a long-term contractual relationship and finally to vertical integration is provided by the General Motors–Fisher Body relationship, which has been extensively documented by Benjamin Klein. In the early part of the 20th century, car bodies were primarily open, wooden structures built by craftspeople with fairly general skills. Thus, specialized investments were relatively unimportant, and General Motors bought the bodies for its cars using spot exchange.

As the automobile industry developed, it became appar- ent that closed metal bodies would be a superior method of manufacturing cars. This finding, however, introduced a high degree of physical-asset specificity because it required investment in very specialized machines to stamp out the body parts. To constrain opportunism, General Motors and Fisher Body signed a 10-year contract that set the price of the car bodies and obligated General Motors to purchase all of its closed metal car bodies from Fisher Body.

Initially this agreement worked well enough to permit the parties to make the necessary specialized investments. But as time went on, it became clear that the original agreement

was not nearly complete, leaving numerous opportunities for the parties to engage in opportunism. For example, the pricing formula contained in the contract permitted Fisher Body to receive a 17.6 percent profit on labor and transpor- tation costs. This encouraged Fisher to produce with ineffi- cient labor-intensive technologies in remotely located plants and pass on the costs of inefficiency to General Motors.

In retrospect, it appears that both General Motors and Fisher Body underestimated the difficulty of writing a con- tract to govern their relationship. Rather than spend time and money writing a more detailed contract, the problem was solved in 1926 when General Motors vertically inte- grated by purchasing Fisher Body.

SOURCE: Benjamin Klein, “Vertical Integration as Organizational Ownership: The Fisher Body–General Motors Relationship Revisited,” Journal of Law, Economics and Organization 4 (Spring 1988), pp. 199–213. For an alternative view suggesting that the merger was motivated out of a desire to improve coordination of production and inventories, to assure GM of adequate supplies of auto bodies, and to provide GM with access to the executive talents of the Fisher brothers, see Ramon Casadesus-Masanell and Daniel F. Spulber, “The Fable of Fisher Body,” Journal of Law and Economics 43 (April 2000), pp. 67–104.

INSIDE BUSINESS 6–3

The Evolution of Input Decisions in the Automobile Industry

Figure 6–5 Optimal Procurement of Inputs

Spot exchange

Vertical integration

Contract

Substantial specialized investments relative to contracting costs?

Yes

Yes

Complex contracting environment relative to costs of integration?

No

No

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When the desired input does not involve specialized investments, the firm can use spot exchange to obtain the input without concern for opportunism and bargaining costs. By pur- chasing the input from a supplier, the firm can specialize in doing what it does best rather than spending money writing contracts or engaging in vertical integration.

When substantial specialized investments are required to facilitate exchange, managers should think twice about using spot exchange to purchase inputs. Specialized investments lead to opportunism, bargaining costs, and underinvestment, and these transaction costs of using spot exchange often can be reduced by using some other method to acquire an input. When the contracting environment is simple and the cost of writing a contract is less than the transaction costs associated with spot exchange, it is optimal to acquire the input through a contract. In this case, the optimal contract length is determined by the intersection of the marginal cost and marginal benefits of writing a longer contract, as we illustrated previously in Figure 6–2.

Finally, when substantial specialized investments are required and the desired input has complex characteristics that are difficult to specify in a contract, or when it is very costly to write into the contract all the clauses needed to protect the parties from changes in future conditions, the manager should integrate vertically to minimize the cost of acquiring inputs needed for production—provided the costs of integration are not too high. In this instance, the firm produces the input internally. The firm no longer specializes in doing what it does best, but the elimination of opportunism, bargaining, and underinvestment more than makes up for lack of specialization.

DEMONSTRATION PROBLEM 6–4

Big Bird Air is legally obligated to purchase 50 jet engines from ERUS at the end of two years at a price of $200,000 per engine. Confident that it is protected from opportunism with this contract, Big Bird begins making aircraft bodies designed to fit ERUS’s engines. Due to unforeseen events in the aerospace industry, in the second year of the contract ERUS is on the brink of bankruptcy. It tells Big Bird that unless it increases the engine price to $300,000, it will go bankrupt.

1. What should the manager of Big Bird Air do? 2. How could this problem have been avoided? 3. Did the manager of Big Bird Air use the wrong method of acquiring inputs?

ANSWER:

1. Big Bird is experiencing a hold-up problem because of an incomplete contract; the con- tract did not specify what would happen if ERUS went belly-up. ERUS claims it will go bankrupt if Big Bird does not pay a price of $300,000 for the engines, in which case Big Bird will lose its specialized investment in aircraft bodies. The manager should verify that ERUS is indeed on the brink of bankruptcy. If not, Big Bird can take ERUS to court if ERUS does not honor the contract price. If ERUS is on the verge of bankruptcy, the man- ager should determine how much it would cost to obtain engines from another supplier ver- sus making them within the firm. Once the manager knows the cost of each alternative, Big Bird may wish to bargain with ERUS over how much more it will pay for the engines. This could be risky, however; the lower the price negotiated, the greater the chance ERUS will go bankrupt. New clauses must be put into the contract to protect Big Bird against ERUS’s bankruptcy. The manager should especially guard against attempts by ERUS to reduce the quality of the engines in an attempt to save money. In any event, Big Bird should not spend more money drawing up a new contract and paying for ERUS’s engines than it would cost to obtain them from the best alternative source.

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2. This problem illustrates that when contracts are incomplete, unanticipated events can occur that lead to costly bargaining and opportunism. The problem could have been avoided had Big Bird written clauses into the contract that protected it against ERUS’s going bankrupt. If this was not possible, it could have vertically integrated and produced its own engines.

3. Big Bird’s manager did not necessarily choose the wrong method of acquiring engines. If it was not possible (or would have been extremely costly) to write into the initial contract protection against ERUS’s going bankrupt, and if the costs of vertically integrating would exceed the likely costs of opportunism due to an incomplete contract, the manager made the correct decision at the time. Sometimes bad things happen even when managers make good decisions. If this was not the case, either a more complete contract should have been written or Big Bird should have decided to make its own engines.

MANAGERIAL COMPENSATION AND THE PRINCIPAL–AGENT PROBLEM

You now know the principal factors in selecting the best method of acquiring inputs. Our remaining task in this chapter is to explain how to compensate labor inputs to ensure that they put forth their “best” effort. After completing this section, you will better understand why restaurants rely on tips to compensate employees, why secretaries usually are paid an hourly wage, and even why textbook authors are paid royalties. We will begin, however, by examin- ing managerial compensation.

One characteristic of many large firms is the separation of ownership and control: The own- ers of the firm often are distantly located stockholders, and the firm is run on a day-to-day basis by a manager. The fact that the firm’s owners are not physically present to monitor the manager cre- ates a fundamental incentive problem. Suppose the owners pay the manager a salary of $50,000 per year to manage the firm. Since the owners cannot monitor the manager’s effort, if the firm has lost $1 million by year’s end, they will not know whether the fault lies with the manager or with bad luck. Uncertainty regarding whether low profits are due to low demand or to low effort by the manager makes it difficult for the owners to determine precisely why profits are low. Even if the fault lies with the manager—perhaps he or she never showed up at the plant but instead took an extended fishing trip—the manager can claim it was just a “bad year.” The manager might say, “You should be very glad you hired me as your manager. Had I not worked 18-hour days, your company would have lost twice the amount it did. I was lucky to keep our loss to its current level, but I am confident things will improve next year when our new product line hits the market.” Since the owners are not present at the firm, they will not know the true reason for the low profits.

By creating a firm, an owner enjoys the benefits of reduced transaction costs. But when ownership is separated from control, the principal–agent problem emerges: If the owner is not present to monitor the manager, how can she get the manager to do what is in her best interest?

The essence of the problem is that the manager likes to earn income, but he also likes to consume leisure. Clearly, if the manager spent every waking hour on the job, he would be unable to consume any leisure. But the less time he spends on the job, the more time he has for ball games, fishing trips, and other activities that he values. The job description indicates that the manager is supposed to spend eight hours per day on the job. The important question, from the owner’s point of view, is how much leisure (shirking) the manager will consume while on the job. Shirking may take the form of excessive coffee breaks, long lunch hours, leaving work early, or, in the extreme case, not showing up on the job at all. Note that while the manager enjoys shirking, the owner wants the manager to work hard to enhance profits.

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When the manager is offered a fixed salary of $50,000 and the owner is not physically present at the workplace, he will receive the same $50,000 regardless of whether he works a full eight hours (hence, doesn’t shirk) or spends the entire day at home (shirks eight hours). This situation is illustrated in Table 6–1. From the point of view of the owner, the fixed salary does not give the manager a strong incentive to monitor the other employees, and this has an adverse effect on the firm’s profits. For example, as Table 6–1 shows, if the manager spends the entire day on the job monitoring the other employees (i.e., making sure that they put out maximum effort), shirking is zero and the firm’s profits are $3 million. If the manager spends the entire day shirking, profits are zero. If the manager shirks two hours and thus works six hours, the firm’s profits are $2.8 million. Since the fixed salary of $50,000 provides the man- ager with the same income regardless of his effort level, he has a strong incentive to shirk eight hours. In this case the profits of the firm are zero, but the manager still earns $50,000.

How can the owner of the firm get the manager to spend time monitoring the produc- tion process? You might think if she paid the manager a higher salary, the manager would work harder. But this will not work when the owner cannot observe the manager’s effort; the employment contract is such that there is absolutely no cost to the manager of shirking. Many managers would prefer to earn money without having to work for it, and such a contract allows this manager to do just that.

Suppose the owner of the firm offers the manager the following incentive contract: The manager is to receive 10 percent of profits (gross of managerial compensation) earned by the firm. Table 6–2 summarizes the implications of such a contract. Note that if the manager spends eight hours shirking, profits are zero and the manager earns nothing. But if the man- ager does not shirk at all, the firm earns $3 million in gross profits and the manager receives compensation equal to 10 percent of those profits: $300,000.

Exactly what the manager does under the profit-sharing compensation scheme depends on his preferences for leisure and money. But one thing is clear: If the manager wants to earn income, he cannot shirk the entire day. The manager faces a trade-off: He can consume more leisure on the job, but at a cost of lower compensation. For example, suppose the manager has carefully evaluated the trade-off between leisure on the job and income in Table 6–2 and wishes to earn $250,000. He can achieve this by working five hours instead of shirking all day. What is the impact of the profit-sharing plan on the owner of the firm? The manager has decided to work five hours to earn $250,000 in compensation. The five hours of managerial effort generate

Table 6–1 Managerial Earnings and Firm Profits under a Fixed Salary

Manager’s Earnings Hours Worked

by Manager Hours Shirked

by Manager Profits of Firm

$50,000 8 0 $3,000,000

50,000 7 1 2,950,000

50,000 6 2 2,800,000

50,000 5 3 2,500,000

50,000 4 4 2,000,000

50,000 3 5 1,800,000

50,000 2 6 1,300,000

50,000 1 7 700,000

50,000 0 8 0

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Table 6–2 Managerial Earnings and Firm Profits with Profit Sharing

Hours Worked by Manager

Hours Shirked by Manager

Gross Profits for Firm (π)

Manager’s Share of Profits (.10 × π)

8 0 $3,000,000 $300,000

7 1 2,950,000 295,000

6 2 2,800,000 280,000

5 3 2,500,000 250,000

4 4 2,000,000 200,000

3 5 1,800,000 180,000

2 6 1,300,000 130,000

1 7 700,000 70,000

0 8 0 0

$2.5 million in gross profits for the firm. Thus, by making managerial compensation dependent on performance, the gross profits for the owner rise from zero (under the fixed-salary arrange- ment) to $2.5 million. Note that even after deducting the manager’s compensation, the owner ends up with a hefty $2,500,000 − $250,000 = $2.25 million in profits. The performance bonus has increased not only the manager’s earnings, but also the owner’s net profits.

FORCES THAT DISCIPLINE MANAGERS

Incentive Contracts Typically the chief executive officer of a corporation receives stock options and other bonuses directly related to profits. It may be tempting to argue that a CEO who earns over $1 million per year is receiving excessive compensation. What is important, however, is how the execu- tive earns the $1 million. If the earnings are due largely to a performance bonus, it could be a big mistake to reduce the executive’s compensation. This point is important because the media often imply that it is unfair to heavily reward CEOs of major corporations. Remember, however, that performance-based rewards benefit stockholders as well as CEOs, and reducing such rewards may result in declining profits for the firm.

DEMONSTRATION PROBLEM 6–5

You are attending the annual stockholders’ meeting of PIC Company. A fellow shareholder points out that the manager of PIC earned $100,000 last year, while the manager of a rival firm, CUP Enterprises, earned only $50,000. A motion is made to lower the salary of PIC’s manager. Given only this information, what should you do?

ANSWER: There is not enough information to make an informed decision about the appropriate way to vote; you should ask for additional information. If none is forthcoming, you should move to table the motion until shareholders can obtain additional information about such things as the profits and sales of the two firms, how much of each manager’s earnings is due to profit sharing and performance bonuses, and the like. Explain to the other shareholders that the optimal contract will reward the manager for high profits; if PIC’s manager’s high earnings are due to a huge performance bonus paid

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because of high profits, eliminating the bonus would not be prudent. On the other hand, if CUP’s manager has generated larger profits for that firm than your manager has for PIC, you may wish to adjust your manager’s contract to reflect incentives similar to those of the rival firm or even attempt to hire CUP’s manager to work for PIC.

External Incentives The preceding analysis focused on factors within the firm that provide the manager with an incentive to maximize profits. In addition, forces outside the firm often provide managers with an incentive to maximize profits.

Reputation Managers have increased job mobility when they can demonstrate to other firms that they have the managerial skills needed to maximize profits. It is costly to be an effective manager; many hours must be spent supervising workers and planning production outlays. These costs represent an investment by the manager in a reputation for being an excellent manager. In the long run, this reputation can be sold at a premium in the market for managers, where other firms compete for the right to hire the best managers. Thus, even when the employment con- tract does not explicitly include a performance bonus, a manager may choose to do a good job of running the firm if he or she wishes to work for another firm at some future date.

Takeovers Another external force that provides managers with an incentive to maximize profits is the threat of a takeover. If a manager is not operating the firm in a profit-maximizing manner, investors will attempt to buy the firm and replace management with new managers who will. By installing a better manager, the firm’s profits will rise and the value of the firm’s stock will increase. Thus, one cost to a manager of doing a poor job of running the firm is the increased likelihood of a takeover. To avoid paying this cost, managers will work harder than they oth- erwise would, even if they are paid only a fixed salary.

THE MANAGER–WORKER PRINCIPAL–AGENT PROBLEM

When we introduced the principal–agent problem, the owner of the firm was viewed as hav- ing different objectives from the manager. There is nothing special about the owner–manager relationship that gives rise to the principal–agent problem; indeed, there is a similar problem between the manager and the employees she or he supervises.

To see this, suppose the manager is being paid a fraction of profits and thus has an incen- tive to increase the firm’s profits. The manager cannot be in several places at the same time and thus cannot monitor every worker even if he or she wanted to. The workers, on the other hand, would just as soon gossip and drink coffee as work. How can the manager (the princi- pal) induce the workers (the agents) not to shirk?

Solutions to the Manager–Worker Principal–Agent Problem Profit Sharing One mechanism the manager can use to enhance workers’ efforts is profit sharing—making the workers’ compensation dependent on the underlying profitability of the firm. Offering

profit sharing Mechanism used to enhance workers’ efforts that involves tying compensation to the underlying profitability of the firm.

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workers compensation that is tied to underlying profitability provides an incentive for workers to put forth more effort.

Revenue Sharing Another mechanism for inducing greater effort by workers is revenue sharing—linking com- pensation to the underlying revenues of the firm. Examples of this type of incentive scheme include tips and sales commissions. Food servers usually receive a very low wage, plus tips. Tips are simply a commission paid by the person being served. If the server does a terrible job, the tip is low; if the server does an excellent job, the tip usually is higher. Similarly, car salespeople and insurance agents usually receive a percentage of the sales they generate. The idea behind all these compensation schemes is that it is difficult, if not impossible, for the manager to monitor these people’s efforts, and there is uncertainty regarding what final sales will be. By making these workers’ incomes dependent on their performance, the manager gives workers an incentive to work harder than they otherwise would. By working harder, they benefit both the firm and themselves.

Revenue sharing is particularly effective when worker productivity is related to revenues rather than costs. For example, a restaurant manager can design a contract whereby servers get some fraction of a tip; the tip is presumed to be an increasing function of the servers’ quality (productivity). The manager of a sales firm can provide incentives to employees by paying them a percentage of the sales they generate. In contrast, a retail store that hires a security guard to prevent shoplifting will likely find revenue sharing with the security guard to be ineffective; his productivity is much more strongly related to the store’s costs compared to its revenues.

One problem with revenue-based incentive schemes is that they do not provide an incen- tive for workers to minimize costs. For example, a food server may attempt to collect a big tip by offering the customer larger portions, free drinks, and the like, which will enhance the tip at the expense of the restaurant’s costs.

Piece Rates An alternative compensation method is to pay workers based on a piece rate rather than on a fixed hourly wage. For example, by paying a data entry clerk a fixed amount per word entered into the firm’s database, the payment to the clerk depends on the output produced. To earn more money, the clerk must enter more words into the firm’s database during a given time period.

A potential problem with paying workers based on a piece rate is that effort must be expended in quality control; otherwise, workers may attempt to produce quantity at the expense of quality. One advantage of revenue or profit sharing is that it reduces the incentive to produce low-quality products. Lower quality reduces sales, thus reducing compensation to those receiving revenue- or profit-sharing incentives.

revenue sharing Mechanism used to enhance workers’ efforts that involves linking compensation to the underlying revenues of the firm.

DEMONSTRATION PROBLEM 6–6

Your boss, who just earned an MBA, finished reading Chapter 6 of a noted economics textbook. She asks you why the firm pays its secretaries an hourly wage instead of piece rates or a percentage of the firm’s profits. How do you answer her?

ANSWER: Incentive contracts such as piece rates and profit sharing are designed to solve principal–agent prob- lems when effort is not observable. There is little need to provide “incentive contracts” to secretaries given the presence of bosses in the workplace. In particular, it is very easy to monitor the secretaries’ effort; they usually are within the boss’s eyesight and there are numerous opportunities to observe

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

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the quality of their work (e.g., letters for the boss’s signature). Thus, there is no real separation between the “principal” (the boss) and the “agent” (the secretary); the secretary’s “boss” knows when the secretary “messes up” and can fire him or her if performance is consistently low. In most instances, this provides secretaries with a stronger incentive to work hard than would paying them a fraction of the profits generated by the effort of all employees in the firm.

Paying secretaries piece rates would be an administrative nightmare and involve significant trans- action costs; it would be extremely costly to keep track of all of the pages typed and tasks performed during the course of a week. Piece rates may also encourage secretaries to worry more about the quantity instead of the quality of the work done. All things considered, hourly wages are a reasonable way to compensate most secretaries—provided their bosses are given an incentive to monitor them.

An interesting study by Edward Lazear on the employment practices of the Safelite Glass Corporation documents the importance of properly structuring incentives. The company’s average output per worker increased by almost 50 percent when it changed compensation from an hourly wage to a piece- rate system. Moreover, the average worker’s pay increased by about 10 percent under piece-rate compensation. By more closely aligning the incentives of workers and the firm, both the firm and its employees benefited from the change.

Pay-for-performance contracts are most effective in envi- ronments where a worker’s responsibilities are clearly identi- fied and each worker’s output is objectively measured. They are least effective when the measurement of individual effort is garbled or when it is not possible to write a contract to control important aspects of worker behavior. For instance, the usual benefits of pay-for-performance are mitigated when the pro- duction process requires a team of workers. In this case, work- ers may “shirk” in anticipation of being able to “piggyback” on other employees’ hard work (this behavior is called “free riding” in the economics literature). Likewise, when contracts are incomplete, high-powered contracts may lead to dysfunc- tional behavior. For example, workers may focus exclusively on those aspects of their jobs where performance is rewarded.

For these reasons, the optimality and prevalence of high-powered incentive schemes like piece-rate systems vary across different types of occupations. As the accompanying table shows, piece-rate pay is more common in occupations where output is clearly measurable and quality is relatively unimportant (such as farm labor). It is much less common when quality is important or difficult to objectively measure.

SOURCES: Edward P. Lazear, “Performance Pay and Productivity,” American Economic Review (December 2000), pp. 1346–61; Canice Prendergast, “The Provision of Incentives in Firms,” Journal of Economic Literature (March 1999), pp. 7–63.

INSIDE BUSINESS 6–4

Paying for Performance

The Percentage of Young Workers Paid a Piece Rate in Selected Occupations

Occupation Percentage Paid

a Piece Rate

Farm labor 16.7

Craftsmen 3.6

Clerical 1.3

Managers 0.9

Time Clocks and Spot Checks Many firms use time clocks to assist managers in monitoring workers. However, time clocks are generally not useful in addressing the principal–agent problem. Time clocks essentially are designed to verify when an employee arrives and departs from the job. They do not monitor effort; rather, they simply measure presence at the workplace at the beginning and end of the workday.

A more useful mechanism for monitoring workers is for a manager to engage in spot checks of the workplace. In this case, the manager enters the workplace from time to time to

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monitor workers. Spot checks allow the manager to verify not only that workers are physically present but also that worker effort and the quality of the work are satisfactory.

The advantage of spot checks is that they reduce the cost of monitoring workers. With spot checks, the manager needn’t be in several places at the same time. Because workers do not know when the manager will show up, they will put forth more effort than they would oth- erwise since getting caught “goofing off” may lead to dismissal or a reduction in pay. Thus, to be effective, spot checks need to be random; that is, workers should not be able to predict when the manager will be monitoring the workplace.

A disadvantage of spot checks is that they must occur frequently enough to induce work- ers not to risk getting caught shirking and they must entail some penalty for workers caught shirking. Spot checks work, in effect, through threat. Performance bonuses, on the other hand, work through a promise of reward. These characteristics can have different psychological effects on workers.

ANSWERING THE headLINE Smartphone software and hardware require a great deal of interoperability to work well together. This means that both the software producers and hardware manufacturers often must make substantial specialized investments. Google’s purchase of Motorola Mobility gives it direct control of the specialized hardware investments made by Motorola Mobility, ensuring they will be tailored for Google’s software products and avoiding any risk of hold-up. The high-tech nature of the smartphone market also makes for significant uncertainty about future products and market conditions, resulting in a complex contract- ing environment. Consequently, there is sound economic rationale for vertical integration, but before making such a recommendation you should verify that the expected bene- fits of avoided hold-up problems and quality improvements justify the costs of vertical integration.

SUMMARY

In this chapter, we examined the optimal institutional choice for input procurement and the principal–agent problem as it relates to managerial compensation and worker incentives. The manager must decide which inputs will be purchased from other firms and which inputs the firm will manufacture itself. Spot exchange generally is the most desirable alternative when there are many buy- ers and sellers and low transaction costs. It becomes less attractive when substantial specialized investments gener- ate opportunism, resulting in transaction costs associated with using a market.

When market transaction costs are high, the manager may wish to purchase inputs from a specific supplier using a contract or, alternatively, forgo the market entirely and have the firm set up a subsidiary to produce the required

input internally. In a fairly simple contracting environ- ment, a contract may be the most effective solution. But as the contracting environment becomes more complex and uncertain, internal production through vertical integration becomes an attractive managerial strategy.

The chapter also demonstrated a solution to the principal–agent problem: Rewards must be constructed so as to induce the activities desired of workers. For example, if all a manager wants from a worker is for the worker to show up at the workplace, an hourly wage rate and a time clock form an excellent incentive scheme. If it is desirable to produce a high level of output with very little emphasis on quality, piece-rate pay schemes work well. However, if both quantity and quality of output are concerns, profit sharing is an excellent motivator.

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KEY TERMS AND CONCEPTS

contract dedicated assets human capital incentive contracts opportunism physical-asset specificity

piece-rate system principal–agent problem profit sharing relationship-specific exchange revenue sharing site specificity

specialized investment spot exchange transaction costs vertical integration

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. Discuss the optimal method for procuring inputs that have well-defined and measurable quality specifications and require highly specialized investments. What are the primary advantages and disadvantages of acquiring inputs through this means? Give an example not used in the textbook that uses this method of procurement. (LO1, LO3)

2. Discuss the optimal method for procuring a modest number of standardized inputs that are sold by many firms in the marketplace. What are the primary advantages and disad- vantages of using this method to acquire inputs? Give an example not used in the text- book that uses this method of procurement. (LO1, LO3)

3. Identify whether each of the following transactions involves spot exchange, contract, or vertical integration. (LO1) a. Barnacle, Inc., has a legal obligation to purchase 2 tons of structural steel per week

to manufacture conveyor frames. b. Exxon-Mobil uses the oil extracted from its wells to produce raw polypropylene, a

type of plastic. c. Boat Lifts R Us purchases generic AC motors from a local distributor. d. Kaspar Construction—a home-building contractor—purchases 50 pounds of nails

from the local Home Depot. 4. Explain why automobile manufacturers produce their own engines but purchase mirrors

from independent suppliers. (LO1, LO2) 5. Identify the type of specialized investment that each of the following situations

requires. (LO2) a. You hire an employee to operate a machine that only your company uses. b. An aerosol canning company designs a filling line that can be used only for a partic-

ular firm’s product. c. A company builds a manufacturing facility across the street from its primary buyer.

6. Describe how a manager who derives satisfaction from both income and shirking allocates a 10-hour day between these activities when paid an annual, fixed salary of $100,000. When this same manager is given an annual, fixed salary of $100,000 and 4 percent of the firm’s profits—amounting to $130,000 per year—the manager chooses to work eight hours and shirks for two hours. Explain which of the compensation schemes the manager prefers. (LO4, LO5)

7. Compare the advantages and disadvantages of using spot checks/hidden video cameras in the workplace and pay-for-performance pay schemes as means to influence worker performance. (LO6, LO7)

8. Discuss the impact of the following factors on the optimal method of procuring an input. (LO1, LO3) a. Benefits from specialization. b. Bureaucracy costs.

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c. Opportunism on either side of the transaction. d. Specialized investments. e. Unspecifiable events. f. Bargaining costs.

9. Suppose the marginal benefit of writing a contract is $100, independent of its length. Find the optimal contract length when the marginal cost of writing a contract of length L is: (LO3) a. MC(L) = 30 + 4L. b. MC(L) = 40 + 5L. c. What happens to the optimal contract length when the marginal cost of writing a

contract declines? 10. Suppose the marginal cost of writing a contract of length L is MC(L) = 20 + 5L. Find

the optimal contract length when the marginal benefit of writing a contract is: (LO3) a. MB(L) = 120. b. MB(L) = 180. c. What happens to the optimal contract length when the marginal benefit of writing a

contract increases?

PROBLEMS AND APPLICATIONS

11. During the beginning of the 21st century, the growth in computer sales declined for the first time in almost two decades. As a result, PC makers dramatically reduced their orders of computer chips from Intel and other vendors. Explain why computer manufacturers such as Dell are likely to write relatively short contracts for computer chips. (LO2, LO3)

12. DonutVille caters to its retirement population by selling over 10,000 donuts each week. To produce that many donuts weekly, DonutVille uses 1,000 pounds of flour, which must be delivered by 5:00 AM every Friday morning. How should the manager of DonutVille acquire flour? Explain. (LO1, LO3)

13. The manager of your company’s pension fund is compensated based entirely on fund performance; he earned over $1.2 million last year. As a result, the fund is contemplat- ing a proposal to cap the compensation of fund managers at $100,000. Provide an argu- ment against the proposal. (LO4, LO5)

14. The division of a large office services company that makes high-end copiers recently signed a five-year, $25 million contract for IT services from CGI Group, a Canadian information technology company. If you were the manager of the division, how would you justify the long-term nature of your contract with CGI Group? (LO2, LO3)

15. The Wall Street Journal reported that Juniper Networks, Inc.—a maker of company network equipment—plans to offer its more than 1,000 employees the opportunity to reprice their stock options. Juniper’s announcement comes at a time when its stock price is down 90 percent, leaving many employees’ stock options worthless. How do you think Juniper’s CEO justified repricing the employees’ stock options to the sharehold- ers? (LO4, LO5)

16. Suppose that Honda is on the verge of signing a 15-year contract with TRW to supply airbags. The terms of the contract include providing Honda with 85 percent of the air- bags used in new automobiles. Just prior to signing the contract, a manager reads that one of TRW’s competitors has introduced a comparable airbag using a new technology that reduces the cost by 30 percent. How would this information affect Honda’s optimal contract length with TRW? (LO3)

17. EFI—a material handling company—pays each of its salespersons a base salary plus a percentage of revenues generated. To reduce overhead, EFI has switched from giving

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each salesperson a company car to reimbursing them $0.35 for each business-related mile driven. Accounting records show that, on average, each salesperson drives 100 business-related miles per day, 240 days per year. Can you think of an alternative way to restructure the compensation of EFI’s sales force that could potentially enhance profits? Explain. (LO6, LO7)

18. Teletronics reported record profits of $100,000 last year and is on track to exceed those profits this year. Teletronics competes in a very competitive market where many of the firms are merging in an attempt to gain competitive advantages. Currently, the compa- ny’s top manager is compensated with a fixed salary that does not include any perfor- mance bonuses. Explain why this manager might nonetheless have a strong incentive to maximize the firm’s profits. (LO4, LO5)

19. Recently, Air Liquide signed a long-term contract with Yan’an Energy and Chemical Co., a subsidiary of Yanchang Petroleum Group—one of China’s largest firms engaged in oil and natural gas exploration and production as well as oil refining. The new con- tract specifies that Air Liquide invest approximately 80 million euros in two air separa- tion units (ASUs), which will supply air gases for Yan’an’s production of plastics. Air Liquide is a French multinational firm that supplies industrial gases to a wide range of industries, including chemical manufacturers. Why is a long-term contract preferable to a spot exchange or vertical integration between Yan’an and Air Liquide? (LO1, LO2, LO3)

20. A few years ago, the Boston Globe reported that the city of Boston planned to spend $14 million to convert the FleetCenter sports arena and entertainment center into an appro- priate venue for the Democratic National Convention (DNC). The city engaged Shawmut Design and Construction in a contractual relationship to complete the work, which was supposed to start 48 days prior to the commencement of the DNC on July 26. However, when negotiations between Boston’s mayor and the police union broke down, the Boston Police Patrolmen’s Association took to the picket lines surrounding the FleetCenter and prevented construction crews from beginning the work. The Globe reported that “a truck attempting to deliver steel turned around after a crowd of union members stood at a chain-link gate in front of the arena, shouting ‘back it up,’ and ‘respect the line, buddy.’” Moreover, the Globe reported that “On-duty police officers, who had been instructed to prevent pickets from restricting access, did not intervene.” Given the tight construction schedule, construction delays reportedly cost about $100,000 per day. Identify the princi- pal–agent problem in this situation. Did the mayor and the city of Boston face the classi- cal “hold-up problem” or another problem? Explain. (LO2, LO6)

21. Business-process outsourcing (BPO) is a type of outsourcing that consists of contracting operations and responsibilities of a specific business process (e.g., human resources) to a third-party service provider. Such outsourcing generally began with manufactur- ing firms outsourcing their supply chain but has grown into a much wider range of processes, including marketing, finance, sales, and accounting. According to a recent Forbes article, the revenue of the global outsourced services industry rose from $45 billion in 2000 to nearly $100 billion in 2012. Competition among firms in the BPO market is strong. Companies based in the United States include HP Enterprise Services, Affiliated Computer Services, and Automated Data Processing (ADP). A number of Indian companies, however, also provide worldwide BPO services, such as Infosys, Wipro, and Genpact. An article in BusinessWeek suggested that BPO can save end users anywhere from 15 to 85 percent. International BPO service providers are particularly attractive since offshore labor offers an additional 25 to 30 percent cost savings. Furthermore, approximately 25 percent of the cost savings results from BPO firms’ proprietary products. The remaining 10 to 30 percent in cost reduction accrues from consolidated operations. Suppose you are the manager of a U.S.-based company

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and must decide whether to outsource your human resources department. Outline argu- ments supporting and opposing a decision to outsource this function of your business. From a purely business standpoint, do any issues arise from contracting with an interna- tional-based versus U.S.-based BPO service firm? Explain. (LO1, LO3)

22. You are a management consultant for a 30-year-old partner in a large law firm. In a meeting, your client says: “According to an article in The New York Times, 57 percent of large law firms have a mandatory retirement age for partners in the firm. Before they retire, partners are paid directly for the work that they do, and, as owners, they are enti- tled to a share of the profits of the firm. Once they retire, partners do not receive either form of compensation. In light of this, I think we should eliminate mandatory retirement in order to gain a ‘competitive advantage’ in attracting high-quality lawyers to work for our firm. Of course, you are the expert.” What do you recommend? Explain. (LO4, LO5)

23. Automated Data Processing (ADP) provides computer software and services to a host of companies, including automobile dealerships. ADP charges dealerships a monthly lease for hardware, software, and support services but does not charge for training the dealerships’ employees. Dealerships need only pay for their employees’ time and travel to ADP headquarters, where they attend “Software U” at no additional charge. Discuss the specialized investments (if any) made by an automobile dealership, its employees, and ADP—and identify two potential vulnerabilities that a dealership faces under this arrangement. (LO2)

24. Andrew has decided to open an online store that sells home and garden products. After searching around, he chooses the software company Initech to provide the software for his website since its product required the least amount of specialized investments for him to use it. They agreed upon a price of $3,000. To use Initech’s software, Andrew makes $1,000 in sunk capital investments and spends 40 hours learning how to use Initech’s software, which is very different from other software packages. Both Andrew and Initech view Andrew’s time as worth $25 per hour, and Initech is fully aware of the investments Andrew must make to use its product. After Andrew’s investments were made, Initech came to Andrew and asked for more money. How much do you think its asked for? (LO2)

25. HomeGrown is a small restaurant that specializes in serving local fruits, vegeta- bles, and meats. The company has chosen to enter into a long-term relationship with Family Farms, a local farming operation. The two parties have decided to enter into a long-term contract, where Family Farms will supply produce to HomeGrown at spec- ified prices and volume each year. Before signing a contract, HomeGrown is trying to decide how long the contract should be. It estimates that each year the contract covers saves the restaurant $1,000 in bargaining and opportunism costs. However, each year the contract covers also requires more legal fees. HomeGrown estimates that the number of hours required from lawyers, L, has a quadratic relationship with the num- ber of years on the contract, so that L = Y2, where Y is the number of years for the contract. If HomeGrown’s lawyers charge $100 per hour, how long should the con- tract be? (LO3)

26. Jim’s diner is just about to open in Memphis, Tennessee. However, Jim is trying to decide whether he wants to offer Coke or Pepsi soda products. He determines that, to offer either product, he will have to spend $1,800 in sunk costs to purchase and install the appropriate paraphernalia, e.g., a large Coca-Cola or Pepsi sign out front. Ultimately, he chooses to offer Coke products and agrees to pay Coke 5 cents per ounce of Coke sold for the right to use its product. After Jim makes the investments specific to his soda choice, Coke returns and asks for a fixed (one-time) fee in addition to the 5 cents per ounce. What is the most Jim should be willing to pay? (LO2)

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27. Recently, the owner of a Trader Joe’s franchise decided to change how she compensated her top manager. Last year, she paid him a fixed salary of $65,000, and her store made $120,000 in profits (not counting payment to her top manager). She suspected the store could do much better and feared the fixed salary was causing her top manager to shirk on the job. Therefore, this year she decided to offer him a fixed salary of $30,000 plus 15 percent of the store’s profits. Since the change, the store is performing much better, and she forecasts profits this year to be $280,000 (again, not counting the payment to her top manager). Assuming the change in compensation is the reason for the increased profits, and that the forecast is accurate, how much more money will the owner make (net of payment to her top manager) because of this change? Does the manager make more money under the new payment scheme? (LO4, LO5)

SELECTED READINGS

Alchian, Armen A., and Demsetz, Harold, “Production, Information Costs, and Economic Organization.” American Economic Review 62, December 1972, pp. 777–95.

Antle, Rick, and Smith, Abbie, “An Empirical Investigation of the Relative Performance Evaluation of Corporate Executives.” Journal of Accounting Research 24(1), Spring 1986, pp. 1–39.

Coase, R. H., “The Nature of the Firm.” Economica, November 1937, pp. 366–405.

Gibbons, Robert, and Murphy, Kevin J., “Relative Performance Evaluation for Chief Executive Officers.” Industrial and Labor Relations Review 43, February 1990, pp. 30–51.

Jensen, Michael C., “Takeovers: Their Causes and Consequences.” Journal of Economic Perspectives 1, Winter 1988, pp. 21–48.

Jensen, Michael C., and Murphy, Kevin J., “Performance Pay and Top Management Incentives.” Journal of Political Economy 98(2), April 1990, pp. 225–64.

Klein, Benjamin; Crawford, Robert G.; and Alchian, Armen A., “Vertical Integration, Appropriable Rents, and the Competitive Contracting Process.” Journal of Law and Economics 21(2), October 1978, pp. 297–326.

Lewis, Tracy R., and Sappington, David E. M., “Incentives for Monitoring Quality.” RAND Journal of Economics 22(3), Autumn 1991, pp. 370–84.

Williamson, Oliver E., “Markets and Hierarchies: Some Elementary Considerations.” American Economic Review 63, May 1973, pp. 316–25.

Winn, Daryl N., and Shoenhair, John D., “Compensation Based (Dis)incentives for Revenue Maximizing Behavior: A Test of the ‘Revised’ Baumol Hypothesis.” Review of Economics and Statistics 70(1), February 1988, pp. 154–58.

APPENDIX

AN INDIFFERENCE CURVE APPROACH TO MANAGERIAL INCENTIVES

The essence of the problem with compensation payments that are not tied to performance is depicted graphically in Figure 6–6. The manager views both leisure and income to be goods. Moreover, the manager is willing to substi- tute between leisure on the job (shirking) and income. This is why his indifference curve has the usual shape in Figure 6–6, where we measure the quantity of leisure con- sumed at the workplace on the horizontal axis and income on the vertical axis. Note that while the manager enjoys shirking, the owner does not want the manager to shirk.

When the manager is offered a fixed salary of $50,000, his opportunity set becomes the shaded area in Figure 6–6. The reason is simple: Since the owner is not physically present at the workplace, the manager will receive the

same $50,000 regardless of whether he works a full eight hours (and hence doesn’t shirk) or spends the entire day at home (and shirks eight hours). If profits are low, the owner will not know whether this is due to poor mana- gerial effort or simply bad luck. The manager can take advantage of the separation of ownership from control by pushing his indifference curve as far to the northeast as possible until he is in equilibrium at point A, where he shirks the entire day every day of the year but still collects the $50,000.

From the viewpoint of the firm’s owner, the fixed sal- ary has an adverse effect on profits because it does not provide the manager with an incentive to monitor other employees. To see this, suppose the profits of the firm are

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a simple linear function of the amount of shirking done by the manager during each eight-hour period. Such a rela- tionship is graphed in Figure 6–7. The line through point C defines the level of firm profits, which depends on the manager’s degree of shirking. For example, if the manager spends the entire day on the job monitoring other employ- ees, shirking is zero and firm profits are $3 million. If the manager spends the entire day shirking, profits are zero. If the manager shirks two hours and thus works six hours, the profits of the firm are $2.25 million. Since the fixed salary of $50,000 provides the manager with an incentive to shirk eight hours, the profits of the firm will be zero if it uses that compensation plan.

How can the owner get the manager to spend time monitoring the production process? You might think that

if she paid the manager a bigger salary, the manager would work harder. But this is not correct; a larger salary would simply shift the vertical intercept of the opportunity set in Figure 6–6 above $50,000, but the equilibrium would still imply eight hours of shirking. In essence, the employment contract is such that there is absolutely no cost to the man- ager of shirking.

Suppose the owner offers the manager the following type of employment contract: a fixed salary of $50,000, plus a bonus of 10 percent of the profits. In this instance, if the manager spends eight hours shirking, profits are zero and the manager gets only $50,000. If the manager does not shirk at all, the firm earns $3 million in profits and the manager gets a bonus equal to 10 percent of those profits. In this instance, the bonus is $300,000. The bonus to the manager, as a function of his level of shirking, is depicted in Figure 6–7 as the line through point D. Note that when the manager shirks for two hours each day, the firm earns $2.25 million in gross profits and the manag- er’s bonus is $225,000.

The effect of a salary-plus-bonus compensation plan on managerial behavior is illustrated in Figure 6–8. The manager’s opportunity set is now given by the line through points A and B. For example, if the manager shirks eight hours, profits are zero and he receives no bonus; therefore, his income is $50,000. If the manager does not shirk at all, a bonus of $300,000 is added to his fixed salary; thus, the manager can earn $350,000 if he does not shirk.

Exactly what the manager does under the salary-plus- bonus plan depends on his preferences. But as we see in Figure 6–8, this manager can attain a higher indiffer- ence curve by shirking less and moving from point A to

Figure 6–8 A Profit-Sharing Incentive Scheme Increases Managerial Effort

Figure 6–6 Impact of a Fixed Salary on Managerial Behavior

0

Manager’s income

Shirking (leisure on

the job)

$50,000

8

Manager’s highest indifference curve given the $50,000

fixed salary

Opportunity set given fixed salary

A

Figure 6–7 A Profit-Sharing Incentive Bonus

0

$

Shirking (leisure on

the job)8

D

$3 million

$300,000

$2.25 million

$225,000

2

C

Firm profits depend on manager’s level

of shirking

Manager’s bonus depends on firm’s

profitability

Time shirking

Time managing

0

$

Shirking (leisure on

the job)8

A

$350,000

$50,000

2

B

Manager’s choice with fixed salary

Time shirking

Time managing

$275,000

Manager’s choice with profit sharing

Opportunity set with

bonus scheme

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202

point B. At point B, the manager earns $275,000 in income—$225,000 in the form of a bonus payment and $50,000 as a fixed salary. The manager clearly prefers this compensation scheme. Note also that the manager still shirks two hours each day, but this is considerably less than under the fixed-salary/no-bonus plan.

What is the impact of the bonus on the owner of the firm? In Figure 6–7, we see that when the manager shirks

two hours each day, the firm earns $2.25 million in gross profits. Thus, the salary plus bonus increases the owner’s gross profits from zero (under the fixed salary) to $2.25 million. The bonus has increased the welfare not only of the manager but of the owner; profits, net of managerial compensation, are

$2,250,000 − $275,000 = $1,975,000

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headLINE AT&T Puts Halt to T-Mobile Merger A few years ago, the U.S. Justice Department filed suit to block the merger between AT&T and T-Mobile USA. Estimated reports placed AT&T’s share of the wireless subscrip- tion market at 32 percent, while T-Mobile’s share was 10 percent. This market had two other major competitors: Verizon, with a 34 percent share, and Sprint, with a 17 percent share. After spending millions on merger plans, AT&T decided to call off the deal. The impact on AT&T’s bottom line was so significant that its CEO saw his pay cut by $2 million as a result.

Do you think AT&T should have spent millions on merger plans in the first place? Explain.

The Nature of Industry 7

LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Calculate alternative measures of industry structure, conduct, and perfor- mance, and discuss their limitations.

LO2 Describe examples of vertical, horizontal, and conglomerate mergers, and explain the economic basis for each type of merger.

LO3 Explain the relevance of the Herfindahl-Hirschman index for antitrust policy under the horizontal merger guidelines.

LO4 Describe the structure–conduct–performance paradigm, the feedback cri- tique, and their relation to the five forces framework.

LO5 Identify whether an industry is best described as perfectly competitive, a monopoly, monopolistically competitive, or an oligopoly.

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INTRODUCTION

Managers of firms do not make decisions in a vacuum. Numerous factors affect decisions such as how much output to produce, what price to charge, and how much to spend on research and development, advertising, and so on. Unfortunately, no single theory or methodology pro- vides managers with the answers to these questions. The optimal pricing strategy for an auto- mobile manufacturer generally will differ from that of a computer firm; the level of research and development will differ for food manufacturers and defense contractors. In this chapter we highlight important differences that exist among industries. In subsequent chapters, we will see why these differences arise and examine how they affect managerial decisions.

Much of the material in this chapter is factual and is intended to acquaint you with aspects of the “real world” that are relevant for managers. You will be exposed to statistics for numer- ous industries. Some of these statistics summarize how many firms exist in various industries; others indicate which firms and industries are the largest and which industries tend to charge the highest markups.

The numbers presented in this chapter will change over time; the largest firm today is unlikely to be the largest firm in 40 years. Consequently, the most important thing for you to grasp in this chapter is that industries differ substantially in nature; not all industries are created equal. Our task in the remaining chapters of this book is to determine what it is about firms and industries that gives rise to systematic differences in price–cost margins, advertising expendi- tures, and other managerial decision variables. This will be particularly valuable to you as a manager since you do not know in which industry you will work during the next 40 years of your career. An effective manager is able to adapt to the nature of the industry in which his or her firm competes. As the nature of the industry changes, so will the manager’s optimal decisions.

MARKET STRUCTURE

Market structure refers to factors such as the number of firms that compete in a market, the relative size of the firms (concentration), technological and cost conditions, demand condi- tions, and the ease with which firms can enter or exit the industry. Different industries have different structures, and these structures affect the decisions the prudent manager will make. The following subsections provide an overview of the major structural variables that affect managerial decisions.

Firm Size It will come as no surprise to you that some firms are larger than others. Consider Table 7–1, which provides a snapshot of the sales of companies in a variety of different industries. Notice that there are considerable differences in the size of the largest firm in each industry. In 2015, for instance, Walmart was the largest general merchandiser with sales of approximately $486 billion. In contrast, International Paper was the largest producer of packaging and con- tainers, but it had sales of only $26 billion.

Industries are also dynamic. Over time, changes in competitors’ strategies or changes in market conditions can change a firm’s relative position within an industry—or potentially change the viability of the industry itself. For instance, Verizon Communications had the largest sales of any telecommunications firm in 2006, but by 2012, AT&T was the industry leader, and continued to lead with sales of $132 billion in 2015. Also, in 2008 Google was the leader in Internet services and retailing, but it had been overtaken by Amazon.com by 2012.

market structure Factors that affect managerial decisions, including the number of firms competing in a market, the relative size of firms, technological and cost considerations, demand conditions, and the ease with which firms can enter or exit the industry.

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Table 7–1 Largest Firms in Selected Industries

Industry Largest Company Sales (millions)

Advertising/Marketing Omnicon Group $  15,318

Aerospace and Defense Boeing 90,762

Airlines American Airlines Group 42,650

Apparel Nike 27,799

Beverages Coca-Cola 45,998

Chemicals Dow Chemical 58,167

Computer Software Microsoft 86,833

Computers, Office Equipment Apple 182,795

Electronics, Electrical Equipment Honeywell International 40,306

Entertainment Disney 48,813

General Merchandisers Walmart 485,651

Household and Personal Products Procter & Gamble 84,537

Industrial Machinery Illinois Tool Works 15,282

Information Technology Services IBM 94,128

Internet Services and Retailing Amazon.com 88,988

Motor Vehicles and Parts General Motors 155,929

Packaging, Containers International Paper 26,221

Real Estate CBRE Group 9,050

Telecommunications AT&T 132,447

Tobacco Philip Morris International 29,767

Transportation and Logistics C.H. Robinson Worldwide 13,470

SOURCE: Fortune 500 List, November 19, 2015; authors’ calculations.

What drives these differences in sales across industries, and why do firms’ relative posi- tions tend to change over time? Are they driven by differences or changes in market structure? Did firms become “large” by combining activities through mergers? To what extent do they stem from differences (or changes) in research and development (R&D) or advertising expen- ditures? The remainder of this chapter, and indeed the remainder of this book, takes a deeper look at these and other questions.

Industry Concentration The data in Table 7–1 reveal considerable variation in the size of the largest firm in various industries. Another factor that affects managerial decisions is the size distribution of firms within an industry; that is, are there many small firms within an industry or only a few large firms? This question is important because, as we will see in later chapters, the optimal deci- sions of a manager who faces little competition from other firms in the industry will differ from those of a manager who works in an industry in which there are many firms.

Some industries are dominated by a few large firms, while others are composed of many small firms. Before presenting concentration data for various U.S. industries, we examine two measures that economists use to gauge the degree of concentration in an industry.

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Measures of Industry Concentration Concentration ratios measure how much of the total output in an industry is produced by the largest firms in that industry. The most common concentration ratio is the four-firm concen- tration ratio (C4). The four-firm concentration ratio is the fraction of total industry sales produced by the four largest firms in the industry.

Let S1, S2, S3, and S4 denote the sales of the four largest firms in an industry, and let ST denote the total sales of all firms in the industry. The four-firm concentration ratio is given by

C 4 = S 1 + S 2 + S 3 + S 4 _____________

S T

Equivalently, the four-firm concentration ratio is the sum of the market shares of the top four firms: C 4 = w 1 + w 2 + w 3 + w 4

where

w 1 = S 1 / S T ,

w 2 = S 2 / S T , w 3 = S 3 / S T , and

w 4 = S 4 / S T

When an industry is composed of a very large number of firms, each of which is very small, the four-firm concentration ratio is close to zero. When four or fewer firms produce all of an industry’s output, the four-firm concentration ratio is 1. The closer the four-firm con- centration ratio is to zero, the less concentrated is the industry; the closer the ratio is to 1, the more concentrated is the industry.

four-firm concentration ratio The fraction of total industry sales generated by the four largest firms in the industry.

DEMONSTRATION PROBLEM 7–1

Suppose an industry is composed of six firms. Four firms have sales of $10 each, and two firms have sales of $5 each. What is the four-firm concentration ratio for this industry?

ANSWER: Total industry sales are ST = $50. The sales of the four largest firms are

S 1 + S 2 + S 3 + S 4 = $40

Therefore, the four-firm concentration ratio is

C 4 = 40

___ 50

= .80

This means that the four largest firms in the industry account for 80 percent of total industry output.

Concentration ratios provide a very crude measure of the size structure of an industry. Four-firm concentration ratios that are close to zero indicate markets in which there are many sellers, giving rise to much competition among producers for the right to sell to consumers. Industries with four-firm concentration ratios close to 1 indicate markets in which there is little competition among producers for sales to consumers.

Another measure of concentration is the Herfindahl-Hirschman index. The Herfindahl- Hirschman index (HHI) is the sum of the squared market shares of firms in a given industry,

Herfindahl-Hirschman index (HHI) The sum of the squared market shares of firms in a given industry multiplied by 10,000.

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multiplied by 10,000 to eliminate the need for decimals. By squaring the market shares before adding them up, the index weights firms with high market shares more heavily.

Suppose firm i’s share of the total market output is wi = Si /ST, where Si is firm i’s sales and ST is total sales in the industry. Then the Herfindahl-Hirschman index is

HHI = 10,000  Σw i 2

The value of the Herfindahl-Hirschman index lies between 0 and 10,000. A value of 10,000 arises when a single firm (with a market share of w1 = 1) exists in the industry. A value of zero results when there are numerous infinitesimally small firms.

DEMONSTRATION PROBLEM 7–2

Suppose an industry consists of three firms. Two firms have sales of $10 each, and one firm has sales of $30. What is the Herfindahl-Hirschman index for this industry? What is the four-firm concentra- tion ratio?

ANSWER: Since total industry sales are ST = $50, the largest firm has a market share of w1 = 30/50 and the other two firms have a market share of 10/50 each. Thus, the Herfindahl-Hirschman index for this industry is

HHI = 10,000 [ ( 30

___ 50

) 2

+ ( 10

___ 50

) 2

+ ( 10

___ 50

) 2

] = 4,400

The four-firm concentration ratio is 1 since the top three firms account for all industry sales.

The Concentration of U.S. Industry Now that you understand the algebra of industry concentration and Herfindahl-Hirschman indexes, we may use these indexes to examine the concentration of representative indus- tries within the United States. Table 7–2 provides concentration ratios (in percentages) and Herfindahl-Hirschman indexes for selected U.S. industries. Notice that there is considerable variation among industries in the degree of concentration. The top four producers of elec- tronic computers account for 87 percent of the industry’s total output, suggesting considerable concentration. Distilleries, as well as the industry that makes motor vehicles, also have high four-firm concentration ratios. In contrast, the four-firm concentration ratios for the jewelry, ready-mix concrete, and women’s and girls’ apparel industries are low, suggesting greater competition among sellers. For example, the four largest producers of ready-mix concrete account for only 23 percent of the total market.

On balance, the Herfindahl-Hirschman indexes reported in Table 7–2 reveal a similar pat- tern: The industries with high four-firm concentration ratios tend to have higher Herfindahl- Hirschman indexes. There are exceptions, however. Notice that according to the four-firm concentration ratio, the motor vehicle industry is more concentrated than the snack food industry. However, the Herfindahl-Hirschman index for the snack food industry is higher than that for the motor vehicle industry.

There are several reasons that inferences drawn about an industry’s level of concentra- tion may differ, depending on whether one uses the four-firm concentration or Herfindahl- Hirschman index. First, the four-firm concentration ratio is based on the market shares of only the four largest firms in an industry, while the Herfindahl-Hirschman index is based on the market shares of all firms in an industry. In other words, the four-firm concentration ratio does

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Table 7–2 Four-Firm Concentration Ratios and Herfindahl-Hirschman Indexes for Selected U.S. Manufacturing Industries

Industry C4

(percentage) HHI

Breweries 90 NA

Distilleries 70 1,519

Electronic computers 87 NA

Fluid milk 46 1,075

Furniture and related products 11 62

Jewelry (excluding costume) 29 347

Men’s and boys’ cut and sew apparel 27 324

Motor vehicles 68 1,744

Ready-mix concrete 23 313

Semiconductor and other electronic components 34 476

Snack foods 53 1,984

Soap and cleaning compound 47 848

Soft drinks 52 891

Women’s and girls’ cut and sew apparel 20 174

SOURCE: Concentrations Ratios: 2007, U.S. Bureau of the Census, 2012.

NOTE: The U.S. Bureau of the Census approximates the HHI by using only data on the top 50 firms in the industry

not take into account the fifth largest firm, whereas the Herfindahl-Hirschman index does. Second, the HHI is based on squared market shares, while the four-firm concentration ratio is not. Consequently, the Herfindahl-Hirschman index places a greater weight on firms with large market shares than does the four-firm concentration ratio. These two factors can lead to differences in the ranking of firms by the C4 and the HHI.

Limitations of Concentration Measures Statistics and other data should always be interpreted with caution, and the preceding mea- sures of concentration are no exception. For instance, the HHI indexes reported in Table 7–2 are only approximations because the Census Bureau uses data on only the top 50 firms in the industry rather than data on all firms in the industry. In concluding our discussion of the concentration of U.S. industries, it is important to point out three additional limitations of the numbers reported in Table 7–2.

Global Markets. The four-firm concentration ratios and Herfindahl-Hirschman indexes reported in Table 7–2 are based on a definition of the product market that excludes foreign imports. That is, in calculating C4 and HHI, the Bureau of the Census does not take into account the penetration by foreign firms into U.S. markets. This tends to overstate the true level of concentration in industries in which a significant number of foreign producers serve the market.

For example, consider the four-firm concentration ratio for the brewery industry. Based on Table 7–2, the top four U.S. firms account for 90 percent of industry sales. However, this figure ignores beer produced by the many well-known breweries in Mexico, Canada, Europe,

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Australia, and Asia. The four-firm concentration ratio based on both domestic and imported beer would be considerably lower.

National, Regional, and Local Markets. A second deficiency in the numbers reported in Table 7–2 is that they are based on figures for the entire United States. In many industries, the relevant markets are local and may be composed of only a few firms. When the relevant markets are local, the use of national data tends to understate the actual level of concentration in the local markets.

For example, suppose that each of the 50 states had only one gasoline station. If all gas- oline stations were the same size, each firm would have a market share of only 1/50. The four-firm concentration ratio, based on national data, would be 4/50, or 8 percent. This would suggest that the market for gasoline services is not very concentrated. However, it does a consumer in central Texas little good to have gas stations in 49 other states since the relevant market for buying gasoline for this consumer is his or her local market. Thus, geographical differences among markets can lead to biases in concentration measures.

In summary, indexes of market structure based on national data tend to understate the degree of concentration when the relevant markets are local.

Industry Definitions and Product Classes. We already emphasized that the geographic definition of the relevant market (local or national) can lead to a bias in concentration ratios. Similarly, the definition of product classes used to define an industry also affects indexes.

Specifically, in constructing indexes of market structure, there is considerable aggrega- tion across product classes. Consider the four-firm concentration ratio for soft drinks, which is 52 percent in Table 7–2. This number may seem surprisingly low when one considers how Coca-Cola and Pepsi dominate the market for cola. However, the concentration ratio of 52 percent is based on a much more broadly defined notion of soft drinks. In fact, the product classes the Bureau of the Census uses to define the industry include many more types of bot- tled and canned drinks, including birch beer, root beer, fruit drinks, ginger ale, iced tea, and lemonade.

How does one determine which products belong in which industry? As a general rule, products that are close substitutes (have large, positive cross-price elasticities) are considered to belong to a given industry class. Indeed, one might view soft drinks to be close substitutes for cola drinks, thus justifying their inclusion into the industry before calculating concentra- tion ratios.

Technology Industries also differ with regard to the technologies used to produce goods and services. Some industries are very labor intensive, requiring much labor to produce goods and services. Other industries are very capital intensive, requiring large investments in plant, equipment, and machines to be able to produce goods or services. These differences in technology give rise to differences in production techniques across industries. In the petroleum-refining industry, for example, firms utilize approximately one employee for each $5 million in sales. In contrast, the beverage industry utilizes roughly 15 workers for each $5 million in sales.

Technology is also important within a given industry. In some industries, firms have access to identical technologies and therefore have similar cost structures. In other industries, one or two firms have access to a technology that is not available to other firms. In these instances, the firms with superior technology will have an advantage over other firms. When this technological advantage is significant, the technologically superior firm (or firms) will

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Industry classification systems provide information about different businesses in the U.S. economy. For instance, if you were interested in starting a business that sells tablets, you might want to know how many companies were already in that business. Or you might want to know about the number of people employed in the industry and the total value of shipments. The answers to these and other questions can be found by using classification systems such as the North American Industry Classification System (NAICS).

The NAICS is a standardized classification system for the three partners of the North American Free Trade Agreement (NAFTA): Canada, Mexico, and the United States. It uses a six-digit code to classify industries into 20 different sectors. Since the first five digits of the NAICS code are the same for Canada, Mexico, and the United States, you can compare industry trends among NAFTA partners. The sixth digit of the NAICS code is country-specific; it varies to accommo- date special identification needs in different countries.

The six-digit NAICS code contains varying levels of spec- ificity about a classification. The first two digits comprise the economic sector code, the third digit comprises the subsec- tor, the fourth the industry group, the fifth the NAICS indus- try, and the sixth digit designates the national industry. The

broadest classification is the two-digit code, which simply classifies firms into one of 20 possible sectors. The six-digit code provides the most specific information about a firm’s classification: It places firms into a country-specific industry.

To illustrate, suppose a U.S. firm is assigned an NAICS code of 512131. As shown in the accompanying table, the first two digits (51) of this code tell us that the firm belongs to the sector called Information (51). This is a very broad classification that includes publishing industries (newspa- pers, periodicals, books, and software); motion pictures and sound recording industries; TV and radio broadcasting; telecommunications; and data processing, hosting, and related services. The first three digits provide a more spe- cific classification: The firm belongs to a subsector called Motion Picture and Sound Recording (512). Looking at the first four digits further refines the nature of the firm’s prod- uct: The firm belongs to an industry group called Motion Picture and Video Industries (5121). Moving to the five-digit code, we see that the firm belongs to the NAICS industry called Motion Picture and Video Exhibition (51213). All digits together tell us that the firm belongs to the national industry that the United States calls Motion Picture Theaters except Drive-Ins (512131).

INSIDE BUSINESS 7–1

The 2012 North American Industry Classification System (NAICS)

Interpreting NAICS Code

NAICS Level NAICS Code Description

Sector 51 Information

Subsector 512 Motion Picture and Sound Recording

Industry Group 5121 Motion Picture and Video Industries

NAICS Industry 51213 Motion Picture and Video Exhibition

National Industry 512131 Motion Picture Theaters (except Drive-Ins)

completely dominate the industry. In the remaining chapters, we will see how such differences in technologies affect managerial decisions.

Demand and Market Conditions Industries also differ with regard to the underlying demand and market conditions. In indus- tries with relatively low demand, the market may be able to sustain only a few firms. In industries where demand is great, the market may require many firms to produce the quantity

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demanded. One of our tasks in the remaining chapters is to explain how the degree of market demand affects the decisions of managers.

The information accessible to consumers also tends to vary across markets. It is very easy for a consumer to find the lowest airfare on a flight from Washington to Los Angeles; all one has to do is call a travel agent or surf the Internet to obtain price quotes. In contrast, it is much more difficult for consumers to obtain information about the best deal on a used car. The consumer not only has to bargain with potential sellers over the price but also must attempt to ascertain the quality of the used car. As we will learn in subsequent chapters, the optimal deci- sions of managers will vary depending on the amount of information available in the market.

Finally, the elasticity of demand for products tends to vary from industry to industry. Moreover, the elasticity of demand for an individual firm’s product generally will differ from the market elasticity of demand for the product. In some industries, there is a large discrep- ancy between an individual firm’s elasticity of demand and the market elasticity. The reason for this can be easily explained.

In Chapter 3 we learned that the demand for a specific product depends on the number of close substitutes available for the product. As a consequence, the demand for a particu- lar brand of product (e.g., 7Up) will be more elastic than the demand for the product group in general (soft drinks). In markets where there are no close substitutes for a given firm’s product, the elasticity of demand for that product will coincide with the market elasticity of demand for the product group (since there is only one product in the market). In industries where many firms produce substitutes for a given firm’s product, the demand for the individ- ual firm’s product will be more elastic than the overall industry demand.

One measure of the elasticity of industry demand for a product relative to that of an indi- vidual firm is the Rothschild index. The Rothschild index provides a measure of the sensitiv- ity to price of the product group as a whole relative to the sensitivity of the quantity demanded of a single firm to a change in its price.

The Rothschild index is given by

R = E T ___ E F

where ET is the elasticity of demand for the total market and EF is the elasticity of demand for the product of an individual firm.

The Rothschild index takes on a value between 0 and 1. When the index is 1, the indi- vidual firm faces a demand curve that has the same sensitivity to price as the market demand curve. In contrast, when the elasticity of demand for an individual firm’s product is much greater (in absolute value) than the elasticity of the market demand, the Rothschild index is close to zero. In this instance, an individual firm’s quantity demanded is more sensitive to a price increase than is the industry as a whole. In other words, when the Rothschild index is less than 1, a 10 percent increase in one firm’s price will decrease that firm’s quantity demanded by more than the total industry quantity would fall if all firms in the industry increased their prices by 10 percent. The Rothschild index therefore provides a measure of how price sensitive an individual firm’s demand is relative to the entire market. When an industry is composed of many firms, each producing similar products, the Rothschild index will be close to zero.

Table 7–3 provides classical estimates of the firm and market elasticities of demand and the Rothschild indexes for 10 U.S. industries. The table reveals that firms in some industries are more sensitive to price increases than firms in other industries. Notice that the Rothschild indexes for tobacco and for chemicals are unity. This means that the representative firm in the industry faces a demand curve that has exactly the same elasticity of demand as the total industry demand. In contrast, the Rothschild index for food is 0.26, which means that the

Rothschild index A measure of the sensitivity to price of a product group as a whole relative to the sensitivity of the quantity demanded of a single firm to a change in its price.

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Table 7–3 Market and Representative Firm Demand Elasticities and Corresponding Rothschild Indexes for Selected U.S. Industries

Industry Own Price Elasticity of Market Demand

Own Price Elasticity of Demand for Representative Firm’s Product Rothschild Index

Food −1.0 −3.8 0.26 Tobacco −1.3 −1.3 1.00 Textiles −1.5 −4.7 0.32 Apparel −1.1 −4.1 0.27 Paper −1.5 −1.7 0.88 Printing and publishing −1.8 −3.2 0.56 Chemicals −1.5 −1.5 1.00 Petroleum −1.5 −1.7 0.88 Rubber −1.8 −2.3 0.78 Leather −1.2 −2.3 0.52

SOURCE: Matthew D. Shapiro, “Measuring Market Power in U.S. Industry,” National Bureau of Economic Research, Working Paper No. 2212, 1987.

demand for an individual food producer’s product is roughly four times more elastic than that of the industry as a whole. Firms in the food industry face a demand curve that is much more sensitive to price than the industry as a whole.

DEMONSTRATION PROBLEM 7–3

The industry elasticity of demand for airline travel is −3 and the elasticity of demand for an individ- ual carrier is −4. What is the Rothschild index for this industry?

ANSWER: The Rothschild index is

R = −3

__ −4

= 0.75

Potential for Entry The final structure variable we discuss in this chapter is the potential for entry into an indus- try. In some industries, it is relatively easy for new firms to enter the market; in others, it is more difficult. The optimal decisions by firms in an industry will depend on the ease with which new firms can enter the market.

Numerous factors can create a barrier to entry, making it difficult for other firms to enter an industry. One potential barrier to entry is the explicit cost of entering an industry, such as capital requirements. Another is patents, which give owners of patents the exclusive right to sell their products for a specified period of time.

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In general, the demand for an individual firm’s product is more elastic than that for the industry as a whole. The exception is the case of monopoly, where a single firm comprises the mar- ket (the demand for a monopolist’s product is the same as the industry demand). How much more elastic is the demand for an individual firm’s product compared to that for the market?

Table 7–4 provides an answer to this question. The second column gives the own price elasticity of the market demand for a given industry. This elasticity measures how responsive total industry quantity demanded is to an industrywide price increase. The third column provides the elasticity of demand for an individual firm’s product. Thus, that column measures how responsive the quantity demanded of an individual firm’s product is to a change in that firm’s price.

Notice in Table 7–4 that the market elasticity of demand in the agriculture industry is −1.8. This means that a 1 percent increase in the industrywide price would lead to a 1.8 percent reduction in the total quantity demanded of agricultural products. In contrast, the elasticity of demand for a representative firm’s product is −96.2. If an individual firm raised its price by 1 percent, the quantity demanded of the firm’s product would fall by a whopping 96.2 percent. The demand for an individual agricultural firm’s product is very elastic indeed because there are numerous firms in the industry selling close substitutes. The more competition among producers in an indus- try, the more elastic will be the demand for an individual firm’s product.

INSIDE BUSINESS 7–2

The Elasticity of Demand at the Firm and Market Levels

Table 7–4 Market and Representative Firm Demand Elasticities for Selected U.S. Industries

Industry Own Price Elasticity of Market Demand

Own Price Elasticity of Demand for Representative

Firm’s Product

Agriculture −1.8 −96.2 Construction −1.0 −5.2 Durable manufacturing −1.4 −3.5 Nondurable manufacturing −1.3 −3.4 Transportation −1.0 −1.9 Communication and utilities −1.2 −1.8 Wholesale trade −1.5 −1.6 Retail trade −1.2 −1.8 Finance −0.1 −5.5 Services −1.2 −26.4

SOURCE: Matthew D. Shapiro, “Measuring Market Power in U.S. Industry,” National Bureau of Economic Research, Working Paper No. 2212, 1987.

Economies of scale also can create a barrier to entry. In some markets, only one or two firms exist because of economies of scale. If additional firms attempted to enter, they would be unable to generate the volume necessary to enjoy the reduced average costs associated with economies of scale. As we will learn in subsequent chapters, barriers to entry have important implications for the long-run profits a firm will earn in a market.

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CONDUCT

In addition to structural differences across industries, the conduct, or behavior, of firms also tends to differ across industries. Some industries charge higher markups than other indus- tries. Some industries are more susceptible to mergers or takeovers than others. In addition, the amount spent on advertising and research and development tends to vary across indus- tries. The following subsections describe important differences in conduct that exist across industries.

Pricing Behavior Firms in some industries charge higher markups than firms in other industries. To illustrate this fact, we introduce what economists refer to as the Lerner index. The Lerner index is given by

L = P – MC

______ P

where P is price and MC is marginal cost. Thus, the Lerner index measures the difference between price and marginal cost as a fraction of the price of the product.

When a firm sets its price equal to the marginal cost of production, the Lerner index is zero; consumers pay a price for the product that exactly equals the cost to the firm of producing another unit of the good. When a firm charges a price that is higher than mar- ginal cost, the Lerner index takes on a value greater than zero, with the maximum possible value being unity. The Lerner index therefore provides a measure of how much firms in an industry mark up their prices over marginal cost. The higher the Lerner index, the greater the firm’s markup. In industries in which firms rigorously compete for consumer sales by attempting to charge the lowest price in the market, the Lerner index is close to zero. When firms do not rigorously compete for consumers through price competition, the Lerner index is closer to 1.

The Lerner index is related to the markup charged by a firm. In particular, we can rear- range the formula for the Lerner index to obtain

P = ( 1 _

1 – L ) MC

In this equation, 1/(1 − L) is the markup factor. It defines the factor by which marginal cost is multiplied to obtain the price of the good. When the Lerner index is zero, the markup factor is 1, and thus the price is exactly equal to marginal cost. If the Lerner index is 1/2, the markup factor is 2. In this case, the price charged by a firm is two times the marginal cost of production.

Table 7–5 provides estimates of the Lerner index and markup factor for 10 U.S. indus- tries. Notice that there are considerable differences in Lerner indexes and markup factors across industries. The industry with the highest Lerner index and markup factor is the tobacco industry. In this industry, the Lerner index is 76 percent. This means that for each $1 paid to the firm by consumers, $0.76 is markup. Alternatively, the price is 4.17 times the actual mar- ginal cost of production.

Lerner index A measure of the difference between price and marginal cost as a fraction of the product’s price.

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Table 7–5 Lerner Indexes and Markup Factors for Selected U.S. Industries

Industry Lerner Index Markup Factor

Food 0.26 1.35

Tobacco 0.76 4.17

Textiles 0.21 1.27

Apparel 0.24 1.32

Paper 0.58 2.38

Printing and publishing 0.31 1.45

Chemicals 0.67 3.03

Petroleum 0.59 2.44

Rubber 0.43 1.75

Leather 0.43 1.75

SOURCES: Michael R. Baye and Jae-Woo Lee, “Ranking Industries by Performance: A Synthesis,” Texas A&M University, Working Paper No. 90-20, March 1990; Matthew D. Shapiro, “Measuring Market Power in U.S. Industry,” National Bureau of Economic Research, Working Paper No. 2212, 1987.

DEMONSTRATION PROBLEM 7–4

A firm in the airline industry has a marginal cost of $200 and charges a price of $300. What are the Lerner index and markup factor?

ANSWER: The Lerner index is

L = P – MC

______ P

= 300 – 200

_______ 300

= 1 __

3

The markup factor is

1 ____

1 – L =

1 _____

1 – 1 / 3 = 1.5

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

In contrast, the Lerner index and markup factor for apparel are much lower. Based on the Lerner index for apparel, we see that for each $1 a clothing manufacturer receives, only $0.24 is markup. Alternatively, the price of an apparel product is only 1.32 times the actual marginal cost of production. Again, the message for managers is that the markup charged for a product will vary depending on the nature of the market in which the product is sold. An important goal in the remaining chapters is to help managers determine the optimal markup for a product.

Integration and Merger Activity Integration and merger activity also differ across industries. Integration refers to uniting pro- ductive resources. Integration can occur through a merger, in which two or more existing firms “unite,” or merge, into a single firm. Alternatively (and as discussed in Chapter 6), integration can occur during the formation of a firm. By its very nature, integration results in larger firms than would exist in the absence of integration.

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Mergers can result from an attempt by firms to reduce transaction costs, reap the benefits of economies of scale and scope, increase market power, or gain better access to capital mar- kets. Some mergers are “friendly” in that both firms desire to merge into a single firm. Others are “hostile,” meaning that one of the firms does not desire the merger to take place.

In some instances, mergers or takeovers occur because it is perceived that the manage- ment of one of the firms is doing an inadequate job of managing the firm. In this instance, the benefit of the takeover is the increased profits that result from “cleaning house,” that is, firing the incompetent managers. Many managers fear mergers and acquisitions because they are uncertain about the impact of a merger on their positions.

Economists distinguish among three types of integration, or mergers: vertical, horizontal, and conglomerate.

Vertical Integration Vertical integration refers to a situation where various stages in the production of a single product are carried out in a single firm. For instance, an automobile manufacturer that pro- duces its own steel, uses the steel to make car bodies and engines, and finally sells an automo- bile is vertically integrated. This is in contrast to a firm that buys car bodies and engines from other firms and then assembles all the parts supplied by the different suppliers. A vertical merger is the integration of two or more firms that produce components for a single product. We learned in Chapter 6 that firms vertically integrate to reduce the transaction costs associ- ated with acquiring inputs.

Horizontal Integration Horizontal integration refers to the merging of the production of similar products into a single firm. For example, if two computer firms merged into a single firm, horizontal integration would occur. Horizontal integration involves merging two or more final products into a single firm, whereas vertical integration involves merging two or more phases of production into a single firm.

In contrast to vertical integration, which occurs because this strategy reduces transaction costs, the primary reasons firms engage in horizontal integration are (1) to enjoy the cost sav- ings of economies of scale or scope and (2) to enhance their market power. In some instances, horizontal integration allows firms to enjoy economies of scale and scope, thus leading to cost savings in producing the good. As a general rule, these types of horizontal mergers are socially beneficial. On the other hand, a horizontal merger, by its very definition, reduces the number of firms that compete in the product market. This tends to increase both the four-firm concentration ratio and the Herfindahl-Hirschman index for the industry, which reflects an increase in the mar- ket power of firms in the industry. The social benefits of the reduced costs due to a horizontal merger must be weighed against the social costs associated with a more concentrated industry.

When the benefits of cost reductions are small relative to the gain in market power enjoyed by the horizontally integrated firm, the government may challenge the merger. Specifically, the Federal Trade Commission (FTC) and the Antitrust Division of the U.S. Department of Justice (DOJ) are empowered to file a lawsuit to prevent firms from merging into a single firm. Under their current Horizontal Merger Guidelines, these antitrust authorities view industries with Herfindahl-Hirschman indexes in excess of 2,500 to be “highly concentrated” and may attempt to block a horizontal merger if it will increase the Herfindahl-Hirschman index by more than 200. It is important to stress, however, that these are merely guidelines. In the absence of evi- dence that a merger is likely to harm consumers, the FTC and DOJ may decide not to challenge a merger even though the HHI (and its change) exceed these thresholds. In addition, anti- trust authorities sometimes permit mergers in industries that have high Herfindahl-Hirschman

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indexes when there is evidence of significant foreign competition, an emerging new technol- ogy, or increased efficiency, or when one of the firms has financial problems.

Industries with Herfindahl-Hirschman indexes below 1,500 after a merger generally are considered “unconcentrated” by the FTC and DOJ, and horizontal mergers usually are not challenged. Also, if a merger changes the Herfindahl-Hirschman index by less than 100, it usually goes unchallenged. If the Herfindahl-Hirschman index is between 1,500 and 2,500 after a merger, and the merger increases the Herfindahl-Hirschman index by more than 100, the FTC and DOJ may potentially challenge the merger. A challenge is also possible if the Herfindahl-Hirschman index exceeds 2,500 and the merger increases the Herfindahl- Hirschman index by 100 to 200. However, in these last two cases, the agencies generally rely more heavily on other factors, such as economies of scale and ease of entry into an industry, in determining whether to attempt to block a horizontal merger. In Chapter 14, we will discuss these and other government actions designed to reduce market power.

Conglomerate Mergers Finally, a conglomerate merger involves the integration of different product lines into a single firm. For example, if a cigarette maker and a cookie manufacturer merged into a single firm, a conglomerate merger would result. A conglomerate merger is similar to a horizontal merger in that it involves merging final products into a single firm. It differs from a horizontal merger because the final products are not related.

The economic rationale for conglomerates is far from clear; merging completely differ- ent business lines is often counterproductive because doing so leads to a loss of specializa- tion without offsetting beneficial synergies. Some have argued that conglomerate mergers can create synergies through improved cash flows for products with cyclical demands. Revenues derived from one product line can be used to generate working capital when the demand for another product is low. While this is a potential rationale when imperfections in capital mar- kets prevent a firm from using financial markets to obtain working capital, engaging in a con- glomerate merger for this purpose should be viewed as a last resort. Others have argued that, when the supply of superior managerial talent is tight, the overall profits of a conglomer- ate managed by a superior CEO can exceed the combined profits of several independent (but highly focused) firms that are managed by different CEOs with only average managerial talent.

Research and Development Earlier we noted that firms and industries differ with respect to the underlying technologies used to produce goods and services. One way firms gain a technological advantage is by engaging in research and development (R&D) and then obtaining a patent for the technology developed through the R&D. Table 7–6 provides R&D spending as a percentage of sales for selected firms. Notice the variation in R&D spending across industries. In the pharmaceutical industry, for example, Bristol-Myers Squibb reinvested 19.7 percent of sales revenue in R&D; in the food industry, Kellogg reinvested only 1.5 percent of sales revenue in R&D.

The message for managers is clear: The optimal amount to spend on R&D will depend on the characteristics of the industry in which the firm operates. One goal in the remaining chapters is to examine the major determinants of R&D spending.

Advertising As Table 7–6 reveals, there is also considerable variation across firms in the level of adver- tising utilized. Firms in the food industry, such as Kellogg, spend about 9 percent of their

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Table 7–6 R&D, Advertising, and Profits as a Percentage of Sales for Selected Firms

Company Industry

R&D as Percentage

of Sales

Advertising as

Percentage of Sales

Profit as Percentage of

Sales

Bristol-Myers Squibb Pharmaceuticals 19.7 4.9 15.9

Ford Motor vehicle and parts 4.1 3.2 5.1

Goodyear Tire and Rubber Rubber and plastic parts 2.0 2.5 Negative

Kellogg Food 1.5 9.2 10.1

Procter & Gamble Soaps and cosmetics 2.5 11.7 16.0

SOURCE: Annual reports of the companies; authors’ calculation.

sales revenue on advertising. In contrast, firms in the rubber and plastic parts industry, such as Goodyear, spend about 2 percent of their sales revenue on advertising. Another goal of the remaining chapters is to examine why advertising intensities vary across firms in different industries. We will also see how firms determine the optimal amount and type of advertising to utilize.

PERFORMANCE

Performance refers to the profits and social welfare that result in a given industry. It is import- ant for future managers to recognize that profits and social welfare vary considerably across industries.

Profits Table 7–6 highlights differences in profits across firms in different industries. Ford’s sales were among the highest in the group, yet its profits as a percentage of sales were second low- est in the group. One task in the next several chapters is to examine why “big” firms do not always earn big profits. As a manager, it would be a mistake to believe that just because your firm is large, it will automatically earn profits.

Social Welfare Another gauge of industry performance is the amount of consumer and producer surplus gen- erated in a market. While this type of performance is difficult to measure, R. E. Dansby and R. D. Willig have proposed a useful index. The Dansby-Willig (DW) performance index measures how much social welfare (defined as the sum of consumer and producer surplus) would improve if firms in an industry expanded output in a socially efficient manner. If the DW index for an industry is zero, there are no gains to be obtained by inducing firms in the industry to alter their outputs; consumer and producer surplus are maximized given indus- try demand and cost conditions. When the index is greater than zero, social welfare would improve if industry output were expanded.

Dansby-Willig performance index Ranks industries according to how much social welfare would improve if the output in an industry were increased by a small amount.

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Table 7–7 Dansby-Willig Performance Indexes for Selected U.S. Industries

Industry Dansby-Willig Index

Food 0.51

Textiles 0.38

Apparel 0.47

Paper 0.63

Printing and publishing 0.56

Chemicals 0.67

Petroleum 0.63

Rubber 0.49

Leather 0.60

SOURCE: Michael R. Baye and Jae-Woo Lee, “Ranking Industries by Performance: A Synthesis,” Texas A&M Working Paper No. 90–20, March 1990.

The DW index thus allows one to rank industries according to how much social welfare would rise if the industry altered its output. Industries with large index values have poorer performance than industries with lower values. In Table 7–7, for instance, we see that the chemical industry has the highest DW index. This suggests that a slight change in output in the chemical industry would increase social welfare more than would a slight change in the output in any of the other industries. The textile industry has the lowest DW index, which reveals the best performance.

DEMONSTRATION PROBLEM 7–5

Suppose you are the manager of a firm in the textile industry. You have just learned that the gov- ernment has placed the textile industry at the top of its list of industries it plans to regulate and intends to force the industry to expand output and lower the price of textile products. How should you respond?

ANSWER: You should point out to government’s counsel that the textile industry has the lowest Lerner index out of the 10 major industries listed in Table 7–5; only $0.21 of each $1 paid by consumers is markup. Furthermore, the Dansby-Willig index for the textile industry is the lowest of nine industries listed in Table 7–7. The efficient way for government to improve social welfare is to alter output in the other industries first.

THE STRUCTURE–CONDUCT– PERFORMANCE PARADIGM

You now have a broad overview of the structure, conduct, and performance of U.S. industry. The structure of an industry refers to factors such as technology, concentration, and market conditions. Conduct refers to how individual firms behave in the market; it involves pricing

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decisions, advertising decisions, and decisions to invest in research and development, among other factors. Performance refers to the resulting profits and social welfare that arise in the market. The structure–conduct–performance paradigm views these three aspects of industry as being integrally related.

The Causal View The causal view of industry asserts that market structure “causes” firms to behave in a certain way. In turn, this behavior, or conduct, “causes” resources to be allocated in certain ways, leading to either “good” or “poor” market performance. To better understand the causal view, consider a highly concentrated industry in which only a few firms compete for the right to sell products to consumers. According to the causal view, this structure gives firms market power, enabling them to charge high prices for their products. The behavior (charging high prices) is caused by market structure (the presence of few competitors). The high prices, in turn, “cause” high profits and poor performance (low social welfare). Thus, according to the causal view, a concentrated market “causes” high prices and poor performance.

The Feedback Critique Today most economists recognize that the causal view provides, at best, an incomplete view of the relation among structure, conduct, and performance. According to the feedback cri- tique, there is no one-way causal link among structure, conduct, and performance. The con- duct of firms can affect market structure; market performance can affect conduct as well as market structure. To illustrate the feedback critique, let us apply it to the previous analysis, which stated that concentration causes high prices and poor performance.

According to the feedback critique, the conduct of firms in an industry may itself lead to a concentrated market. If the (few) existing firms are charging low prices and earning low economic profits, there will be no incentive for additional firms to enter the market. If this is the case, it could actually be low prices that “cause” the presence of few firms in the industry. In summary, then, it is a simplification of reality to assert that concentrated markets cause high prices. Indeed, the pricing behavior of firms can affect the number of firms. As we will see in subsequent chapters, low prices and good performance can occur even if only one or two firms are operating in an industry. A detailed explanation of this possibility will have to wait until we develop models for various market structures.

Relation to the Five Forces Framework The structure–conduct–performance paradigm and the feedback critique are closely related to the five forces framework discussed in Chapter 1. Recall that the five forces frame- work suggests that five interrelated “forces” affect the level, growth, and sustainability of industry profits: (1) entry, (2) power of input suppliers, (3) power of buyers, (4) industry rivalry, and (5) substitutes and complements. These five forces capture elements of the structure and conduct of firms in the industry, while the level, growth, and sustainability of industry profits are elements of performance. In light of the feedback critique, the five forces framework can be modified as shown in Figure 7–1 to illustrate that these forces are interconnected.

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OVERVIEW OF THE REMAINDER OF THE BOOK

In the remaining chapters of this book, we examine the optimal managerial conduct under a variety of market structures. To have some terminology that will enable us to distinguish among various types of market structures, it is useful to introduce the four basic models we will use to accomplish this goal. Recognize, however, that our discussion of these four mod- els provides only an overview; indeed, entire chapters will be devoted to making managerial decisions in each of these situations.

Perfect Competition In markets characterized by perfect competition, there are many firms, each of which is small relative to the entire market. The firms have access to the same technologies and pro- duce similar products, so no firm has any real advantage over other firms in the industry. Firms in perfectly competitive markets do not have market power; that is, no individual firm has a perceptible impact on the market price, quantity, or quality of the product produced in the market. In perfectly competitive markets, both concentration ratios and Rothschild indexes tend to be close to zero. We will study perfectly competitive markets in detail in the next chapter.

∙ Concentration ∙ Switching Costs ∙ Price, Quantit y, Quality, ∙ Timing of Decisions or Service Competition ∙ Information ∙ Degree of Differentiation ∙ Government Restraint s

∙ Price/Value of Surrogate ∙ Network Effects Products or Services ∙ Government ∙ Price/Value of Complementary Restraints Products or Services

Entry

Power of Buyers

Level, Growth, and Sustainability of Industry Profits

Industry Rivalry Substitutes and Complements

∙ Entry Costs ∙ Network Effects ∙ Speed of Adjustment ∙ Reputation ∙ Sunk Costs ∙ Switching Costs ∙ Economies of Scale ∙ Government Restraints

∙ Buyer Concentration ∙ Price/Value of Substitute Products or Services ∙ Relationship-Specific Investments ∙ Customer Switching Costs ∙ Government Restraints

Power of Input Suppliers ∙ Supplier Concentration ∙ Price/Productivity of Alternative Inputs ∙ Relationship-Specific Investments ∙ Supplier Switching Costs ∙ Government Restraints

Figure 7–1 The Five Forces Framework with Feedback Effects

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Monopoly A monopoly is a firm that is the sole producer of a good or service in the relevant market. For instance, most local utility companies are the sole providers of electricity and natural gas in a given city. Some towns have a single gasoline station or movie theater that serves the entire local market. All of these constitute local monopolies.

When there is a single provider of a good or service in a market, there is a tendency for the seller to capitalize on the monopoly position by restricting output and charging a price above marginal cost. Because there are no other firms in the market, consumers cannot switch to another producer in the face of higher prices. Consequently, consumers either buy some of the product at the higher price or go without it. In monopolistic markets, there is extreme concentration and the Rothschild index is unity.

Monopolistic Competition In a market characterized by monopolistic competition, there are many firms and consumers, just as in perfect competition. Thus, concentration measures are close to zero. Unlike in perfect competition, however, each firm produces a product that is slightly different from the products produced by other firms; Rothschild indexes are greater than zero. Those who manage restau- rants in a city containing numerous food establishments operate in a monopolistically competi- tive industry.

A firm in a monopolistically competitive market has some control over the price charged for the product. By raising the price, some consumers will remain loyal to the firm due to a preference for the particular characteristics of its product. But some consumers will switch to other brands. For this reason, firms in monopolistically competitive industries often spend considerable sums on advertising in an attempt to convince consumers that their brands are “better” than other brands. This reduces the number of customers who switch to other brands when a firm raises the price for its product.

Oligopoly In an oligopolistic market, a few large firms tend to dominate the market. Firms in highly concentrated industries such as the airline, automobile, and aerospace industries operate in an oligopolistic market.

When one firm in an oligopolistic market changes its price or marketing strategy, not only its own profits but the profits of the other firms in the industry are affected. Consequently, when one firm in an oligopoly changes its conduct, other firms in the industry have an incen- tive to react to the change by altering their own conduct. Thus, the distinguishing feature of an oligopolistic market is mutual interdependence among firms in the industry.

The interdependence of profits in an oligopoly gives rise to strategic interaction among firms. For example, suppose the manager of an oligopoly is considering increasing the price charged for the firm’s product. To determine the impact of the price increase on profits, the manager must consider how rival firms in the industry will respond to the price increase. Thus, the strategic plans of one firm in an oligopoly depend on how that firm expects other firms in the industry to respond to the plans, if they are adopted. For this reason, it is very difficult to manage a firm that operates in an oligopoly. Because large rewards are paid to managers who know how to operate in oligopolistic markets, we will devote two chapters to an analysis of managerial decisions in such markets.

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Industries can change dramatically over time. During the course of its evolution, a given industry may go through phases that include monopoly, oligopoly, monopolistic competition, and perfect competition. For this reason, it is important to understand how to make decisions in all four environments, even if you “know” you will work for a monopoly when you graduate. The following description of the evolution in the computer industry should convince you of this fact.

In the 1960s, a few large firms produced mainframe computers for universities, scientific think tanks, and large business applications. Each computer was designed almost exclusively for a specific user, and its cost often was over $100,000. Because each computer kept its own standards, a customer whose computer needed repair was forced to go to the original manufacturer or write off the original purchase. This allowed the few companies that produced computers to act as virtual monopolists once they had a customer base. The early computer firms enjoyed high profit margins, some as high as 50 to 60 percent. These large profits induced several new firms to enter the com- puter market.

With entry came innovations in technology that reduced the size of mainframes, lowered the cost of production, and, because of increased competition, reduced the price to the customer. This influx of new competitors and prod- ucts brought the market for computers into an oligopolistic- type structure. As a result, each firm became acutely aware of competitors and their actions. However, each firm held on to the specialized hardware and software for each user. Because of the specialized nature of the smaller machines, customers were still subject to their original purchases when it came to upgrades. However, since the price of the original machines was lower in the new environment, it was less costly to write off the original purchase and shift from one company to another. Of course, suppliers recognized this fact, which led to more vigorous competition. In the 1970s, the combination of lower prices and more competi- tion decreased the returns in the market to 20 to 40 percent for the industry.

The 1980s brought the personal computer into many medium-size businesses that previously could not afford a computer. Along with the PC came workstations and mini- computers. Although profit margins had dropped in the 1970s, they were still high enough in the 1980s to entice new entry. The computer market of the 1980s was moving toward monopolistic competition, with a few large firms and many small firms, each producing slightly different styles of comput- ers. Computers became affordable to many households and smaller businesses. As more firms entered the market, profit margins dropped drastically and copycat firms began open- ing the systems; thus, many parts became interchangeable among machines. Economic profits still were being earned, but profit margins had dropped to around 10 to 20 percent.

During the 1990s, computer makers attempted to main- tain margins by differentiating their products. This tactic was of limited success, as the open systems of the 1990s led to standardized technology at virtually all levels of the computer industry. By the early 2000s, many components of PCs had become “commodities” that were bought and sold in mar- kets resembling those with perfect competition. As a conse- quence, there were few dimensions other than price for PC makers to use in differentiating their products. This height- ened price competition in the 2000s significantly reduced the profits of computer manufacturers, including key players such as Dell and Gateway. By the end of the first decade of the 21st century, competitive strains have led some firms to abandon their “direct sales” approach in favor of distributing computers through popular retailers. The strain on profits is being translated into exit and consolidation within the indus- try. Further changes in industry structure are almost certain in the upcoming years as more of these firms attempt to expand their business to high-mobility devices (e.g., smart- phones and tablets). The computer industry thus provides an enlightening look at the dynamics of industry.

SOURCES: Simon Forge, “Why the Computer Industry Is Restructuring Now,” Futures 23 (November 1991), pp. 960–77; “Gateway CEO Out after Profit Miss,” Ecommerce Times, November 26, 2006; Roger Kay, “The PC Industry Is Digging Its Own Grave,” Forbes (April 2013); annual reports of the companies.

INSIDE BUSINESS 7–3

The Evolution of Market Structure in the Computer Industry

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ANSWERING THE headLINE Given that AT&T was unwilling to fight the battle in court, the safe strategy would have been not to spend the millions on the merger plans in the first place. Given the high concentration of the market, AT&T should have realized that the merger might be heav- ily scrutinized by antitrust authorities and that strong justifications might be needed to overcome the presumption that the merger would harm consumers. As we learned in this chapter, the FTC and DOJ Horizontal Merger Guidelines suggest that U.S. antitrust authorities are more likely to challenge a merger when the relevant Herfindahl-Hirschman index is greater than 2,500 and the resulting increase in the index as a result of the merger is more than 200. Based on the reported market shares of the four largest firms in this industry, the Herfindahl-Hirschman index for the wireless subscription market was at least 2,569 before the proposed merger and would have increased to at least 3,209 after the merger. Thus, it seems that AT&T should have realized that the Justice Department might attempt to block the merger. Spending millions attempting to justify the merger on technological or efficiency grounds was a gamble that did not pay off for AT&T.

SUMMARY

This chapter reveals that different industries have different market structures and require different types of manage- rial decisions. The structure of an industry, and therefore the job of the manager, is dependent on the number of firms in the industry, the structure of demand and costs, the availability of information, and the behavior of other firms in the industry.

The four-firm concentration ratio is one measure of market structure. If the ratio equals one, the industry is a monopoly or oligopoly; if it is zero, the industry is competitive. Another measure of market structure is the Herfindahl-Hirschman index (HHI), which can range from 10,000 for a monopoly to zero for a perfectly com- petitive industry. Of course, these indexes must be used in conjunction with other information, including whether

the market is local and whether the firm competes with foreign firms.

Other summary statistics include the Lerner index, the Rothschild index, and the Dansby-Willig index. These indexes provide a manager information about industry cost and demand conditions. For instance, the greater the Lerner index in an industry, the greater the ability of a firm in the industry to charge a high markup on its product.

The data presented in this chapter reveal industrywide differences in activities such as advertising and research and development. The remainder of the book will explain why these differences exist and the optimal managerial decisions for alternative market structures. The next chapter begins with a study of managerial decisions under perfect competition, monopoly, and monopolistic competition.

KEY TERMS AND CONCEPTS

barrier to entry conduct conglomerate merger Dansby-Willig performance index feedback critique five forces framework four-firm concentration ratio Herfindahl-Hirschman index (HHI)

horizontal integration horizontal merger integration Lerner index market structure monopolistic competition monopoly oligopoly

perfect competition performance Rothschild index structure structure–conduct–performance

paradigm vertical merger

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CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. Ten firms compete in a market to sell product X. The total sales of all firms selling the product are $2 million. Ranking the firms’ sales from highest to lowest, we find the top four firms’ sales to be $260,000, $220,000, $150,000, and $130,000, respectively. Calculate the four-firm concentration ratio in the market for product X. (LO1)

2. An industry consists of three firms with sales of $300,000, $700,000, and $250,000. (LO3) a. Calculate the Herfindahl-Hirschman index (HHI). b. Calculate the four-firm concentration ratio (C4). c. Based on the FTC and DOJ Horizontal Merger Guidelines described in the text,

do you think the Department of Justice would attempt to block a horizontal merger between two firms with sales of $300,000 and $250,000? Explain.

3. Suppose the own price elasticity of market demand for retail gasoline is −0.8, the Rothschild index is 0.5, and a typical gasoline retailer enjoys sales of $1.5 million annu- ally. What is the price elasticity of demand for a representative gasoline retailer’s prod- uct? (LO1)

4. A firm has $1.5 million in sales, a Lerner index of 0.57, and a marginal cost of $50, and competes against 800 other firms in its relevant market. (LO1) a. What price does this firm charge its customers? b. By what factor does this firm mark up its price over marginal cost? c. Do you think this firm enjoys much market power? Explain.

5. Evaluate the following statement: “Managers should specialize by acquiring only the tools needed to operate in a particular market structure. That is, managers should spe- cialize in managing either a perfectly competitive, monopoly, monopolistically competi- tive, or oligopoly firm.” (LO1)

6. Under what conditions might the Justice Department approve a merger between two companies that operate in an industry with a premerger Herfindahl-Hirschman index of 2,900 if the postmerger index is expected to increase by 225? (LO5)

7. Based only on the knowledge that the premerger market share of two firms proposing to merge was 30 percent each, an economist working for the Justice Department was able to determine that, if approved, the postmerger HHI would increase by 1,800. How was the economist able to draw this conclusion without knowledge of the other firms’ market shares? From this information, can you devise a general rule explaining how the Herfindahl-Hirschman index is affected when exactly two firms in the market merge? (Hint: Compare a2 + b2 with [a + b]2.) (LO3, LO4)

8. Consider a firm that operates in a market that competes aggressively in prices. Due to the high fixed cost of obtaining the technology associated with entering this market, only a limited number of other firms exist. Furthermore, over 70 percent of the products sold in this market are protected by patents for the next eight years. Does this industry conform to an economist’s definition of a perfectly competitive market? (LO3)

9. Based on the information given, indicate whether the following industry is best char- acterized by the model of perfect competition, monopoly, monopolistic competition, or oligopoly. (LO5) a. Industry A has a four-firm concentration ratio of 0.005 percent and a Herfindahl-

Hirschman index of 75. A representative firm has a Lerner index of 0.45 and a Rothschild index of 0.34.

b. Industry B has a four-firm concentration ratio of 0.0001 percent and Herfindahl- Hirschman index of 55. A representative firm has a Lerner index of 0.0034 and Rothschild index of 0.00023.

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c. Industry C has a four-firm concentration ratio of 100 percent and Herfindahl- Hirschman index of 10,000. A representative firm has a Lerner index of 0.4 and Rothschild index of 1.0.

d. Industry D has a four-firm concentration ratio of 100 percent and Herfindahl- Hirschman index of 5,573. A representative firm has a Lerner index equal to 0.43 and Rothschild index of 0.76.

10. The four-firm concentration ratios for industries X and Y are 81 percent and 74 percent, respectively, while the corresponding Herfindahl-Hirschman indexes are 3,100 and 1,600. The Dansby-Willig performance index for industry X is 0.7, while that for indus- try Y is 0.55. Based on this information, which would lead to the greater increase in social welfare: a slight increase in industry X’s output or a slight increase in industry Y’s output? (LO5)

PROBLEMS AND APPLICATIONS

11. You work at a firm on Wall Street that specializes in mergers, and you are the team leader in charge of getting approval for a merger between two major beer manufacturers in the United States. While Table 7–2 in the text indicates that the four-firm concentra- tion ratio for all of the breweries operating in the United States is 90 percent, your team has put together a report suggesting that the merger does not present antitrust concerns even though the two firms each enjoys a 15 percent share of the U.S. market. Provide an outline of your report. (LO1)

12. Forey, Inc., competes against many other firms in a highly competitive industry. Over the last decade, several firms have entered this industry and, as a consequence, Forey is earning a return on investment that roughly equals the interest rate. Furthermore, the four-firm concentration ratio and the Herfindahl-Hirschman index are both quite small, but the Rothschild index is significantly greater than zero. Based on this informa- tion, which market structure best characterizes the industry in which Forey competes? Explain. (LO3, LO4)

13. Firms like Papa John’s, Domino’s, and Pizza Hut sell pizza and other products that are differentiated in nature. While numerous pizza chains exist in most locations, the differ- entiated nature of these firms’ products permits them to charge prices above marginal cost. Given these observations, is the pizza industry most likely a monopoly, perfectly competitive, monopolistically competitive, or an oligopoly industry? Use the causal view of structure, conduct, and performance to explain the role of differentiation in the market for pizza. Then apply the feedback critique to the role of differentiation in the industry. (LO1, LO5)

14. Which of the following would most likely be scrutinized under the FTC and DOJ Horizontal Merger Guidelines? (LO4, LO5) a. Two major players in Internet services and retailing—Amazon.com and

eBay—merge. b. Cigarette maker Philip Morris merges with the Miller Brewing Company. c. Lockheed Martin, a large firm that manufactures aircraft, merges with United

States Steel. 15. Nationwide Bank has approached Hometown Bank with a proposal to merge. The fol-

lowing table lists the sales of the banks in the area. Use this information to calculate the four-firm concentration ratio and the Herfindahl-Hirschman index. Based on the FTC and DOJ Horizontal Merger Guidelines, do you think the Justice Department is likely to challenge the proposed merger? (LO2)

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16. Suppose Fiat recently entered into an Agreement and Plan of Merger with Case for $4.3 billion. Prior to the merger, the market for four-wheel-drive tractors consisted of five firms. The market was highly concentrated, with a Herfindahl-Hirschman index of 2,765. Case’s share of that market was 22 percent, while Fiat comprised just 12 percent of the market. If approved, by how much would the postmerger Herfindahl-Hirschman index increase? Based only on this information, do you think the Justice Department would challenge the merger? Explain. (LO3)

17. Use the estimated elasticities in Table 7–4 to calculate the Rothschild index for each industry. Based on these calculations, which industry most closely resembles perfect competition? Which industry most closely resembles monopoly? (LO3)

18. Recently, Pfizer and Allergan—the makers of Viagra and Botox, respectively—initiated a $160 billion merger. Pharmaceutical companies tend to spend a greater percentage of sales on R&D activities than other industries. The government encourages these R&D activities by granting companies patents for drugs approved by the Food and Drug Administration. For instance, Allergan spent large sums of money developing its pop- ular wrinkle-removing neurotoxin, Botox, which is currently protected under a patent. Botox sells for about $15 per vial. Calculate the Lerner index if the marginal cost of producing Botox is $1.50 per vial. Does the Lerner index make sense in this situation? Explain. (LO1, LO5)

19. Many MBAs who ventured into the “dot-com” world of the late 1990s found themselves unemployed by 2001 as many firms in that industry ceased to exist. However, during their tenure with these companies, these managers gained valuable skills in how to operate within a highly competitive environment. Based on the numbers in Table 7–3 in this chapter, which industries represent the best match for these managers’ expertise? Looking at the industries listed in Table 7–3, what factors give rise to the varying levels of market power? (LO1, LO5)

20. In 2006, the five leading suppliers of digital cameras in the United States were Canon, Sony, Kodak, Olympus, and Samsung. The combined market share of these five firms was 60.9 percent. The leading firm was Canon, with a market share of 18.7 percent. The own price elasticity for Canon’s cameras was –4.0 and the market elasticity of demand was –1.6. Suppose that in 2006, the average retail price of a Canon digital camera was $240 and that Canon’s marginal cost was $180 per camera. Based on this information, discuss industry concentration, demand and market conditions, and the pricing behav- ior of Canon in 2006. Do you think the industry environment is significantly different today? Explain. (LO1, LO5)

21. Del Monte has a long and rich tradition in the American food processing industry. It is perhaps best known for packaging canned fruits and vegetables. Part of its success has involved acquiring other brands of canned fruits and vegetables. Suppose that Del

Bank Name Sales (in millions)

MegaBank $1,100

City Bank  950

Nationwide Bank  845

Atlantic Savings  785

Bulk Bank  665

Metropolitan Bank  480

American Bank  310

Hometown Bank  260

Urban Bank  140

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Monte is continuing its business plan of expansion by acquisition and that the following table summarizes potential acquisition targets. As the CEO’s horizontal merger and acquisition advisor, it is your task to guide the decision-making process. Based only on the information contained in the table, is a horizontal merger with one of these com- panies likely to pass the U.S. government’s scrutiny and enhance Del Monte’s perfor- mance? Justify your conclusion. (LO2, LO3)

Company Product Line

Profit as % of Sales C4 HHI

Rothschild Index

Lerner Index

Dansby- Willig Index

Unilever Dove—personal care 5.2 24.1% 874 0.11 0.94 0.01

TricorBraun Food-grade cans 6.8 32.7% 1,065 0.64 0.67 0.40

Goya Canned tomatoes 7.1 86.3% 3,297 0.74 0.32 0.66

Dole Canned pineapple 8.7 94.2% 5,457 0.76 0.14 0.72

22. In January 2007, XM enjoyed about 58 percent of satellite radio subscribers, and Sirius had the remaining 42 percent. Both firms were suffering losses, despite their dominance in the satellite radio market. In 2008, the DOJ decided not to challenge a merger, and these two firms united to become Sirius XM. If you were an economic consultant for Sirius, what economic arguments would you have presented to the DOJ to persuade it not to challenge the merger? Explain. (LO3, LO4)

23. Not long ago, the Federal Communications Commission (FCC) implemented “local number portability” rules allowing cellular phone consumers to switch cellular provid- ers within the same geographic area and maintain the same phone number. How would you expect this change to affect the Rothschild index for the cellular service industry? (LO1, LO4)

SELECTED READINGS

Conant, John L., “The Role of Managerial Discretion in Union Mergers.” Journal of Economic Behavior and Organization 20(1), January 1993, pp. 49–62.

Dansby, R. E., and Willig, R. D., “Industry Performance Gradient Indexes.” American Economic Review 69, 1979, pp. 249–60.

Davis, Douglas D., and Holt, Charles A., “Market Power and Mergers in Laboratory Markets with Posted Prices.” RAND Journal of Economics 25(3), Autumn 1994, pp. 467–87.

Golbe, Devra L., and White, Lawrence J., “Catch a Wave: The Time Series Behavior of Mergers.” Review of Economics and Statistics 75(3), August 1993, pp. 493–99.

Hirschman, Albert O., “The Paternity of an Index.” American Economic Review 54(5), September 1964, p. 761.

Johnson, Ronald N., and Parkman, Allen M., “Premerger Notification and the Incentive to Merge and Litigate.”

Journal of Law, Economics and Organization 7(1), Spring 1991, pp. 145–62.

Kim, E. Han, and Singal, Vijay, “Mergers and Market Power: Evidence from the Airline Industry.” American Economic Review 83(3), June 1993, pp. 549–69.

Lerner, A. P., “The Concept of Monopoly and the Measurement of Monopoly Power.” Review of Economic Studies, October 1933, pp. 157–75.

O’Neill, Patrick B., “Concentration Trends and Profitability in U.S. Manufacturing: A Further Comment and Some New (and Improved) Evidence.” Applied Economics 25(10), October 1993, pp. 1285–86.

Rothschild, K. W., “The Degree of Monopoly.” Economica 9, 1942, pp. 24–39.

“Symposia: Horizontal Mergers and Antitrust.” Journal of Economic Perspectives 1(2), Fall 1987.

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headLINE McDonald’s New Buzz: Specialty Coffee Not long ago, McDonald’s unveiled plans to roll out McCafé in the United States, a pre- mium line of coffee that includes cappuccino, latte, and iced mocha. The recession during the late 2000s in the United States left some analysts questioning whether it was the right time for McDonald’s to roll out its line of new specialty drinks. However, McDonald’s quickly saw a tripling of its share of U.S. coffee sales.

Why do you think McDonald’s embarked on the program, and related, what do you think was the source of its success? Do you think this new product line will sustain its impact on the company’s bottom line? Explain.

SOURCES: J. Adamy, “McDonald’s Coffee Strategy Is a Tough Sell,” The Wall Street Journal, October 27, 2008; M. Brandau, “McDonald’s McCafé: An Evolution,” Nation’s Restaurant News, August 16, 2011; www.mcdonalds.com/mccafe

Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets

8 LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Identify the conditions under which a firm operates as perfectly competitive, monopolistically competitive, or a monopoly.

LO2 Identify sources of (and strategies for obtaining) monopoly power. LO3 Apply the marginal principle to determine the profit-maximizing price and output. LO4 Show the relationship between the elasticity of demand for a firm’s product

and its marginal revenue. LO5 Explain how long-run adjustments impact perfectly competitive, monopoly,

and monopolistically competitive firms; discuss the ramifications of each of these market structures on social welfare.

LO6 Decide whether a firm making short-run losses should continue to operate or shut down its operations.

LO7 Illustrate the relationship between marginal cost, a competitive firm’s short- run supply curve, and the competitive industry supply; explain why supply curves do not exist for firms that have market power.

LO8 Calculate the optimal output of a firm that operates two plants and the opti- mal level of advertising for a firm that enjoys market power.

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INTRODUCTION

In Chapter 7, we examined the nature of industries and saw that industries differ with respect to their underlying structures, conduct, and performances. In this chapter, we characterize the optimal price, output, and advertising decisions of managers operating in environments of (1) perfect competition, (2) monopoly, and (3) monopolistic competition. We will analyze oligopoly decisions in Chapters 9 and 10 and examine more sophisticated pricing strategies in Chapter 11. With an understanding of the concepts presented in these chapters, you will be prepared to manage a firm that operates in virtually any environment.

Because this is the beginning of our analysis of output decisions of managers operating in an industry, it is logical to start with the simplest case: a situation where managerial deci- sions have no perceptible impact on the market price. Thus, in the first section of this chapter, we will analyze output decisions of managers operating in perfectly competitive markets. In subsequent sections, we will examine output decisions by firms that have market power: monopoly and monopolistic competition. The analysis in this chapter will serve as a building block for the analyses in the remainder of the book.

PERFECT COMPETITION

We begin our analysis by examining the output decisions of managers operating in perfectly competitive markets. The key conditions for perfect competition are as follows:

1. There are many buyers and sellers in the market, each of which is “small” relative to the market.

2. Each firm in the market produces a homogeneous (identical) product. 3. Buyers and sellers have perfect information. 4. There are no transaction costs. 5. There is free entry into and exit from the market.

Taken together, the first four assumptions imply that no single firm can influence the price of the product. The fact that there are many small firms, each selling an identical prod- uct, means that consumers view the products of all firms in the market as perfect substitutes. Because there is perfect information, consumers know the quality and price of each firm’s product. There are no transaction costs (such as the cost of traveling to a store); if one firm charged a slightly higher price than the other firms, consumers would not shop at that firm but instead would purchase from a firm charging a lower price. Thus, in a perfectly competitive market all firms charge the same price for the good, and this price is determined by the inter- action of all buyers and sellers in the market.

The assumption of free entry and exit simply implies that additional firms can enter the market if economic profits are being earned, and firms are free to leave the market if they are sustaining losses. As we will show later in this chapter, this assumption implies that in the long run, firms operating in a perfectly competitive market earn zero economic profits.

One classic example of a perfectly competitive market is agriculture. There are many farmers and ranchers, and each is so small relative to the market that he or she has no per- ceptible impact on the prices of corn, wheat, pork, or beef. Agricultural products tend to be homogeneous; there is little difference between corn produced by farmer Jones and corn produced by farmer Smith. The retail market for several types of computer hardware (i.e., the

perfectly competitive market A market in which (1) there are many buyers and sellers; (2) each firm produces a homogeneous product; (3) buyers and sellers have perfect information; (4) there are no transaction costs; and (5) there is free entry and exit.

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physical components of a computer, such as memory) also is close to perfect competition. A quick look at any price comparison site online reveals that there are many computer hardware retailers, each selling identical brands of computer hardware and charging a similar price for a given product. The reason there is so little price variation is that if one retailer charged a higher price than a competitor, consumers would purchase from another retailer.

Demand at the Market and Firm Levels No single firm operating in a perfectly competitive market exerts any influence on price; price is determined by the interaction of all buyers and sellers in the market. The firm manager must charge this “market price” or consumers will purchase from a firm charging a lower price. Before we characterize the profit-maximizing output decisions of managers operat- ing in perfectly competitive markets, it is important to explain more precisely the relation between the market demand for a product and the demand for a product produced by an indi- vidual perfectly competitive firm.

In a competitive market, price is determined by the intersection of the market supply and demand curves. Because the market supply and demand curves depend on all buyers and sellers, the market price is outside the control of a single perfectly competitive firm. In other words, because the individual firm is “small” relative to the market, it has no perceptible influence on the market price.

Figure 8–1 illustrates the distinction between the market demand curve and the demand curve facing a perfectly competitive firm. The left-hand panel depicts the market, where the equilibrium price, Pe, is determined by the intersection of the market supply and demand curves. From the individual firm’s point of view, the firm can sell as much as it wishes at a price of Pe; thus, the demand curve facing an individual perfectly competitive firm is given by the horizontal line in the right-hand panel, labeled Df. The fact that the individual firm’s demand curve is perfectly elastic reflects the fact that if the firm charged a price even slightly above the market price, it would sell nothing. Thus, in a perfectly competitive market, the demand curve for an individual firm’s product is simply the market price.

Since the demand curve for an individual perfectly competitive firm’s product is per- fectly elastic, the pricing decision of the individual firm is trivial: Charge the price that every other firm in the industry charges. All that remains is to determine how much output should be produced to maximize profits.

firm demand curve The demand curve for an individual firm’s product; in a perfectly competitive market, it is simply the market price.

Figure 8–1 Demand at the Market and Firm Levels under Perfect Competition

P

S

0Market output Firm’s output

P

P e

D

Df=Pe

Market Firm

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Short-Run Output Decisions Recall that the short run is the period of time in which there are some fixed factors of produc- tion. For example, suppose a building is leased at a cost of $10,000 for a one-year period. In the short run (for one year) these costs are fixed, and they are paid regardless of whether the firm produces zero or one million units of output. In the long run (after the lease is up), this cost is variable; the firm can decide whether or not to renew the lease. To maximize profits in the short run, the manager must take as given the fixed inputs (and thus the fixed costs) and determine how much output to produce given the variable inputs that are within his or her control. The next subsection characterizes the profit-maximizing output decision of the manager of a perfectly competitive firm.

Maximizing Profits Under perfect competition, the demand for an individual firm’s product is the market price of output, which we denote P. If we let Q represent the output of the firm, the total revenue to the firm of producing Q units is R = PQ. Since each unit of output can be sold at the market price of P, each unit adds exactly P dollars to revenues. As Figure 8–2 illustrates, there is a linear relation between revenues and the output of a competitive firm. Marginal revenue is the change in revenue attributable to the last unit of output. Geometrically, it is the slope of the revenue curve. Expressed in economic terms, the marginal revenue for a competitive firm is the market price.

A C A L C U L U S A L T E R N A T I V E Marginal revenue is the derivative of the revenue function. If revenues are a function of output,

R = R(Q) then

MR = dR

___ dQ

marginal revenue The change in revenue attributable to the last unit of output; for a competitive firm, MR is the market price.

Figure 8–2 Revenue, Costs, and Profits for a Perfectly Competitive Firm

0 Firm’s output

$

Q*

A E

B

Profit-maximizing output

Slope of R = MR = P

R = P × Q Revenue

C(Q) Costs

Maximum profits

Slope of C(Q) = MC

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A C A L C U L U S A L T E R N A T I V E Marginal revenue is the derivative of the revenue function. For a perfectly competitive firm, revenue is

R = PQ

where P is the market equilibrium price. Thus,

MR = dR

___ dQ

= P

The profits of a perfectly competitive firm are simply the difference between revenues and costs: π = PQ − C(Q)

Geometrically, profits are given by the vertical distance between the cost function, labeled C(Q) in Figure 8–2, and the revenue line. Note that for output levels to the left of point A, the cost curve lies above the revenue line, which implies that the firm would incur losses if it produced any output to the left of point A. The same is true of output levels to the right of point B.

For output levels between points A and B, the revenue line lies above the cost curve. This implies that these outputs generate positive levels of profit. The profit-maximizing level of output is the level at which the vertical distance between the revenue line and the cost curve is greatest. This is given by the output level Q* in Figure 8–2.

There is a very important geometric property at the profit-maximizing level of output. As we see in Figure 8–2, the slope of the cost curve at the profit-maximizing level of output (point E) exactly equals the slope of the revenue line. Recall that the slope of the cost curve is marginal cost and the slope of the revenue line is marginal revenue. Therefore, the profit- maximizing output is the output at which marginal revenue equals marginal cost. Since marginal revenue is equal to the market price for a perfectly competitive firm, the manager must equate the market price with marginal cost to maximize profits.

An alternative way to express the competitive output rule is depicted in Figure 8–3, where standard average and marginal cost curves have been drawn. If the market price is given by Pe, this price intersects the marginal cost curve at an output of Q*. Thus, Q* rep- resents the profit-maximizing level of output. For outputs below Q*, price exceeds marginal cost. This implies that by expanding output, the firm can sell additional units at a price that exceeds the cost of producing the additional units. Thus, a profit-maximizing firm will not choose to produce output levels below Q*. Similarly, output levels above Q* correspond to the situation in which marginal cost exceeds price. In this instance, a reduction in output would reduce costs by more than it would reduce revenue. Thus, Q* is the profit-maximizing level of output.

The shaded rectangle in Figure 8–3 represents the maximum profits of the firm. To see this, note that the area of the shaded rectangle is given by its base (Q*) times the height

P R I N C I P L E

Competitive Firm’s Demand The demand curve for a competitive firm’s product is a horizontal line at the market price. This price is the competitive firm’s marginal revenue.

D f = P = MR

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[P e − ATC(Q*)]. Recall that ATC(Q*) = C(Q*)/Q*; that is, average total cost is total cost divided by output. The area of the shaded rectangle is

Q* [ P e −

C ( Q* ) ______

Q* ] = P

e Q* − C ( Q* )

which is the definition of profits. Intuitively, [Pe − ATC(Q*)] represents the profits per unit produced. When this is multiplied by the profit-maximizing level of output (Q*), the result is the amount of total profits earned by the firm.

P R I N C I P L E

Competitive Output Rule To maximize profits, a perfectly competitive firm produces the output at which price equals mar- ginal cost in the range over which marginal cost is increasing:

P = MC ( Q )

A C A L C U L U S A L T E R N A T I V E The profits of a perfectly competitive firm are

π = PQ − C(Q)

The first-order condition for maximizing profits requires that the marginal profits be zero:

dπ

___ dQ

= P − dC ( Q )

______ dQ

= 0

Thus, we obtain the profit-maximizing rule for a firm in perfect competition:

P = dC

___ dQ

or

P = MC

Figure 8–3 Profit Maximization under Perfect Competition

0

$

Q*

MC

ATC(Q*)

P e ATC

Firm’s output

D f = P e = MR

Profits

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DEMONSTRATION PROBLEM 8–1

The cost function for a firm is given by

C ( Q ) = 5 + Q 2

If the firm sells output in a perfectly competitive market and other firms in the industry sell output at a price of $20, what price should the manager of this firm put on the product? What level of output should be produced to maximize profits? How much profit will be earned?

(Hint: Recall that for a cubic cost function

C ( Q ) = f + aQ + b Q 2 + c Q 3

the marginal cost function is

MC ( Q ) = a + 2bQ + 3c Q 2

Since a = 0, b = 1, and c = 0 for the cost function in this problem, we see that the marginal cost function for the firm is MC(Q) = 2Q.)

ANSWER: Since the firm competes in a perfectly competitive market, it must charge the same price other firms charge; thus, the manager should price the product at $20. To find the profit-maximizing output, we must equate price with marginal cost. This firm’s marginal costs are MC = 2Q. Equating this with price yields

20 = 2Q

so the profit-maximizing level of output is 10 units. The maximum profits are thus

π = ( 20 ) ( 10 ) − ( 5 + 10 2 ) = 200 − 5 − 100 = $95

Competition in international markets is often more keen than in domestic markets. This is especially true in devel- oping economies, where price rather than product differen- tiation is the main driver of consumer purchase decisions.

Consider, for instance, the French automaker PSA Peugeot-Citroën. In the mid-2000s, its Citroën division had a minuscule share of China’s auto market—especially com- pared to the market share it enjoyed in France and Europe. In an interview regarding the Chinese market, one of its managers remarked, “If prices fall, we will also follow suit, but not by more than the decrease in the market.” Another manager added, “This is a very competitive market . . . we have to think about the capacity at the factory.”

These remarks suggest that, in China, Citroën had very little control over price; in essence, it operated as a “price-taker” in the Chinese market for automobiles. As a price-taker, it had no incentive to price below the market price. Furthermore, Citroën would lose customers to other

automakers if it attempted to charge a price premium in the developing Chinese market.

As a price-taker, Citroën’s main decision was how many cars to produce at the market price. Managers in China had to ensure that the capacity at factories was sufficient for producing the optimal volume of cars. More recently, Citroën has seen its market share in China increase but con- tinues to face aggressive competition from other interna- tional firms as well as domestic Chinese firms. In light of the large capacities of GM and other automakers with opera- tions in China, Peugeot-Citroën is likely to continue to have limited power over its price for many years to come.

SOURCES: “Citroën Forecasts Slowdown in Sales Growth in China This Year,” Channel News Asia, June 9, 2004; “General Motors’ China Success,” BusinessWeek, January 8, 2006; “China: One of the Group’s Regions of Development Priority,” PSA Peugeot-Citroën website, December 2015; “China Auto Brands Vulnerable to Price Cuts, Group Says,” Bloomberg Business, June 2015.

INSIDE BUSINESS 8–1

Peugeot-Citroën of France: A Price-Taker in China’s Auto Market

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Minimizing Losses In the previous section, we demonstrated the optimal level of output to maximize profits. In some instances, short-run losses are inevitable. Here we analyze procedures for minimizing losses in the short run. If losses are sustained in the long run, the best thing for the firm to do is exit the industry.

Short-Run Operating Losses. Consider first a situation where there are some fixed costs of production. Suppose the market price, Pe, lies below the average total cost curve but above the average variable cost curve, as in Figure 8–4. In this instance, if the firm produces the out- put Q*, where Pe = MC, a loss of the shaded area will result. However, since the price exceeds the average variable cost, each unit sold generates more revenue than the cost per unit of the variable inputs. Thus, the firm should continue to produce in the short run, even though it is incurring losses.

Expressed differently, notice that the firm in Figure 8–4 has fixed costs that would have to be paid even if the firm decided to shut down its operation. Therefore, the firm would not earn zero economic profits if it shut down but would instead realize a loss equal to these fixed costs. Since the price in Figure 8–4 exceeds the average variable cost of producing Q* units of output, the firm earns revenues on each unit sold that are more than enough to cover the variable cost of producing each unit. By producing Q* units of output, the firm is able to put an amount of money into its cash drawer that exceeds the variable costs of producing these units and thus contributes toward the firm’s payment of fixed costs. In short, while the firm in Figure 8–4 suffers a short-run loss by operating, this loss is less than the loss that would result if the firm completely shut down its operation.

The Decision to Shut Down. Now suppose the market price is so low that it lies below the average variable cost, as in Figure 8–5. If the firm produced Q*, where Pe = MC in the range of increasing marginal cost, it would incur a loss equal to the sum of the two shaded rectangles in Figure 8–5. In other words, for each unit sold, the firm would lose

ATC(Q*) − P e

Figure 8–4 Loss Minimization

0

$

Q*

MC

ATC(Q*)

ATC

AVC

D f = P e = MR Loss

P e

Firm’s output

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P R I N C I P L E

Short-Run Output Decision under Perfect Competition To maximize short-run profits, a perfectly competitive firm should produce in the range of increas- ing marginal cost where P = MC, provided that P ≥ AVC. If P < AVC, the firm should shut down its plant to minimize its losses.

Figure 8–5 The Shut-Down Case

0

$

Q*

MC

ATC(Q*)

ATC

AVC

D f = P e = MR

Loss if produce

P e AVC(Q*)

Loss if shut down

Fixed cost

Firm’s output

When this per-unit loss is multiplied by Q*, negative profits result that correspond to the sum of the two shaded rectangles in Figure 8–5.

Now suppose that instead of producing Q* units of output, this firm decided to shut down its operation. In this instance, its losses would equal its fixed costs; that is, those costs that must be paid even if no output is produced. Geometrically, fixed costs are represented by the top rectangle in Figure 8–5 since the area of this rectangle is

[ATC(Q*) − AVC(Q*)] Q*

which equals fixed costs. Thus, when price is less than the average variable cost of produc- tion, the firm loses less by shutting down its operation (and producing zero units) than it does by producing Q* units. To summarize, we have demonstrated the following principle:

DEMONSTRATION PROBLEM 8–2

Suppose the cost function for a firm is given by C(Q) = 100 + Q2. If the firm sells output in a per- fectly competitive market and other firms in the industry sell output at a price of $10, what level of output should the firm produce to maximize profits or minimize losses? What will be the level of profits or losses if the firm makes the optimal decision?

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The Short-Run Firm and Industry Supply Curves Now that you understand how perfectly competitive firms determine their output, we will examine how to derive firm and industry short-run supply curves.

Recall that the profit-maximizing perfectly competitive firm produces the output at which price equals marginal cost. For example, when the price is given by P0 as in Figure 8–6, the firm produces Q0 units of output (the point where P = MC in the range of increasing mar- ginal cost). When the price is P1, the firm produces Q1 units of output. For prices between P0 and P1, output is determined by the intersection of price and marginal cost.

When the price falls below the AVC curve, however, the firm produces zero units because it does not cover the variable costs of production. Thus, to determine how much a perfectly competitive firm will produce at each price, we simply determine the output at which mar- ginal cost equals that price. To ensure that the firm will produce a positive level of output, price must be above the average variable cost curve.

ANSWER: First, note that there are fixed costs of 100 and variable costs of Q2, so the question deals with a short-run scenario. If the firm produces a positive level of output, it will produce where price equals marginal cost. The firm’s marginal costs are MC = 2Q. Equating this with price yields 10 = 2Q, or Q = 5 units. The average variable cost of producing 5 units of output is AVC = 52/5 = 25/5 = 5. Since P ≥ AVC, the firm should produce 5 units in the short run. By producing 5 units of output, the firm incurs a loss of

π = (10)(5) − (100 + 5 2 ) = 50 − 100 − 25 = − $75

which is less than the loss of $100 (fixed costs) that would result if the firm shut down its plant in the short run.

Figure 8–6 The Short-Run Supply Curve for a Competitive Firm

0

$

Q0

MC

AVC

Q1

P0

P1

Short-run supply curve of individual

firm

Firm’s output

P R I N C I P L E The Firm’s Short-Run Supply Curve The short-run supply curve for a perfectly competitive firm is its marginal cost curve above the minimum point on the AVC curve, as illustrated in Figure 8–6.

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The market (or industry) supply curve is closely related to the supply curve of individual firms in a perfectly competitive industry. Recall that the market supply curve reveals the total quantity that will be produced in the market at each possible price. Since the amount an indi- vidual firm will produce at a given price is determined by its marginal cost curve, the horizon- tal sum of the marginal costs of all firms determines how much total output will be produced at each price. More specifically, since each firm’s supply curve is the firm’s marginal cost curve above the minimum AVC, the market supply curve for a perfectly competitive industry is the horizontal sum of the individual marginal costs above their respective AVC curves.

Figure 8–7 illustrates the relation between an individual firm’s supply curve (MCi) and the market supply curve (S) for a perfectly competitive industry composed of 500 firms. When the price is $10, each firm produces zero units, and thus total industry output also is zero. When the price is $12, each firm produces 1 unit, so the total output produced by all 500 firms is 500 units. Notice that the industry supply curve is flatter than the supply curve of an individual firm and that the more firms in the industry, the farther to the right is the market supply curve.

Long-Run Decisions One important assumption underlying the theory of perfect competition is that of free entry and exit. If firms earn short-run economic profits, in the long run additional firms will enter the industry in an attempt to reap some of those profits. As more firms enter the industry, the industry supply curve shifts to the right. This is illustrated in Figure 8–8 as the shift from S0 to S1,which lowers the equilibrium market price from P0 to P1. This shifts down the demand curve for an individual firm’s product, which in turn lowers its profits.

If firms in a competitive industry sustain short-run losses, in the long run they will exit the industry since they are not covering their opportunity costs. As firms exit the industry, the market supply curve decreases from S0 in Figure 8–8 to S2, thus increasing the market price from P0 to P2. This, in turn, shifts up the demand curve for an individual firm’s product, which increases the profits of the firms remaining in the industry.

The process just described continues until ultimately the market price is such that all firms in the market earn zero economic profits. This is the case in Figure 8–9. At the price of Pe, each firm receives just enough to cover the average costs of production (AC is used because in the long run there is no distinction between fixed and variable costs), and economic profits

Figure 8–7 The Market Supply Curve

P

Market output

$10

Individual firm’s supply

curve

$12

1 500

MC i

S

Market supply curve

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P R I N C I P L E

Long-Run Competitive Equilibrium In the long run, perfectly competitive firms produce a level of output such that

1. P = MC 2. P = minimum of AC

Figure 8–8 Entry and Exit: The Market and Firm’s Demand

0

P

P1

P0

P2

S2 S 0

S1EntryExit

Market

0

P

D f = P2 = MR2

Entry

Exit

Firm

D f = P0 = MR0

D f = P1 = MR1

D

Market output Firm’s output

are zero. If economic profits were positive, entry would occur and the market price would fall until the demand curve for an individual firm’s product was just tangent to the AC curve. If economic profits were negative, exit would occur, increasing the market price until the firm demand curve was tangent to the AC curve.

Figure 8–9 Long-Run Competitive Equilibrium

0

$

Q*

MC

AC

P e

Long-run competitive equilibrium

D f = P e= MR

Firm’s output

These long-run properties of perfectly competitive markets have two important welfare implications. First, note that the market price is equal to the marginal cost of production. The market price reflects the value to society of an additional unit of output. This valua- tion is based on the preferences of all consumers in the market. Marginal cost reflects the cost to society of producing another unit of output. These costs represent the resources that would have to be taken from some other sector of the economy to produce more output in this industry.

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To see why it is important, from a social perspective, that price equal marginal cost, sup- pose price exceeded marginal cost in equilibrium. This would imply that society would value another unit of output more than it would cost to produce another unit of output. If the indus- try produced at a level such that price exceeded the marginal cost of the last unit produced, it would thus be inefficient; social welfare would be improved by expanding output. Since in a competitive industry price equals marginal cost, the industry produces the socially efficient level of output.

The second thing to note about long-run competitive equilibrium is that price equals the minimum point on the average cost curve. This implies not only that firms are earning zero economic profits (that is, just covering their opportunity costs) but also that all economies of scale have been exhausted. There is no way to produce the output at a lower average cost of production.

It is important to remember the distinction we made in Chapters 1 and 5 between eco- nomic profits and accounting profits. The fact that a firm in a perfectly competitive industry earns zero economic profits in the long run does not mean that accounting profits are zero; rather, zero economic profits implies that accounting profits are just high enough to offset any implicit costs of production. The firm earns no more, and no less, than it could earn by using the resources in some other capacity. This is why firms continue to produce in the long run even though their economic profits are zero.

MONOPOLY

In the previous section we characterized the optimal output decisions of firms that are small relative to the total market. In this context, small means the firms have no control whatsoever over the prices they charge for the product. In this section, we will consider the opposite extreme: monopoly. Monopoly refers to a situation where a single firm serves an entire mar- ket for a good for which there are no close substitutes.

Monopoly Power In determining whether a market is characterized by monopoly, it is important to specify the relevant market for the product. For example, some utilities, such as electric or water compa- nies, are local monopolies in that only one utility offers service to a given neighborhood. Even though there may be similar companies serving other towns, they do not directly compete against one another for customers. The substitutes for electric services in a given city are poor and, short of moving to a different city, consumers must pay the price for local utility services or go without electricity. It is in this sense that a utility company may be a monopoly in the local market for utility services.

When one thinks of a monopoly, one usually envisions a very large firm. This needn’t be the case, however; the relevant consideration is whether there are other firms selling close substitutes for the good in a given market. For example, a gas station located in a small town that is several hundred miles from another gas station is a monopolist in that town. In a large town there typically are many gas stations, and the market for gasoline is not characterized by monopoly.

The fact that a firm is the sole seller of a good in a market clearly gives that firm greater market power than it would have if it competed against other firms for consumers. Since there is only one producer in the market, the market demand curve is the demand curve for the monopolist’s product. This is in contrast to the case of perfect competition, where the demand

monopoly A market structure in which a single firm serves an entire market for a good that has no close substitutes.

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curve for an individual firm is perfectly elastic. A monopolist does not have unlimited power, however.

Figure 8–10 depicts the demand curve for a monopolist. Since all consumers in the mar- ket demand the good from the monopolist, the market demand curve, DM, is the same as the demand for the firm’s product, D f. In the absence of legal restrictions, the monopolist is free to charge any price for the product. But this does not mean the firm can sell as much as it wants to at that price. Given the price set by the monopolist, consumers decide how much to purchase. For example, if the monopolist sets the relatively low price of P1, the quantity demanded by consumers is Q1. The monopolist can set a higher price of P0, but there will be a lower quantity demanded of Q0 at that price.

In summary, the monopolist is restricted by consumers to choose only those price–quan- tity combinations along the market demand curve. The monopolist can choose a price or a quantity, but not both. The monopolist can sell higher quantities only by lowering the price. If the price is too high, consumers may choose to buy nothing at all.

Sources of Monopoly Power The next issue we will address is how a firm obtains monopoly power, that is, why a monop- olist has no competitors. There are four primary sources of monopoly power. One or more of these sources create a barrier to entry that prevents other firms from entering the market to compete against the monopolist.

Economies of Scale The first source of monopoly power we will discuss is technological in nature. First, however, it is useful to recall some important terminology. Economies of scale exist whenever long-run average costs decline as output increases. Diseconomies of scale exist whenever long-run aver- age costs increase as output increases. For many technologies, there is a range over which econ- omies of scale exist and a range over which diseconomies exist. For example, in Figure 8–11 there are economies of scale for output levels below Q* (since ATC is declining in this range) and diseconomies of scale for output levels above Q* (since ATC is increasing in this range).

diseconomies of scale Exist whenever long-run average costs increase as output increases.

economies of scale Exist whenever long-run average costs decline as output increases.

Figure 8–10 The Monopolist’s Demand

0

P

Q Q1

A

B

D f = D M

Q0

P0

P1

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Notice in Figure 8–11 that if the market were composed of a single firm that produced QM units, consumers would be willing to pay a price of PM per unit for the QM units. Since PM> ATC(QM), the firm sells the goods at a price that is higher than the average cost of production and thus earns positive profits. Now suppose another firm entered the market and the two firms ended up sharing the market (each firm producing QM/2). The total quantity produced would be the same, and thus the price would remain at PM. But with two firms, each produc- ing only QM/2 units, each firm has an average total cost of ATC(QM/2)—a higher average total cost than when a single firm produced all the output. For example, in a market with overhead costs and two firms, each firm must incur these costs of production, and each can only spread the costs over half as much output as a monopolist. Also notice in Figure 8–11 that each firm’s average cost is greater than PM, which is the price consumers are willing to pay for the total QM units produced in the market. Having two firms in the industry leads to losses, but a single firm can earn positive profits because it has higher volume and enjoys reduced average costs due to economies of scale. Thus, we see that economies of scale can lead to a situation where a single firm services the entire market for a good.

This analysis of economies of scale also reveals why it is so important to define the rel- evant market when determining whether or not a firm is a monopolist. As we noted earlier, a gas station may be a monopolist in a small town located several hundred miles from another gas station, whereas a gas station situated in a large city is unlikely to be a monopolist. In terms of Figure 8–11, the demand for gasoline in a small town typically is low relative to Q*, which gives rise to economies of scale in the relevant range (outputs below Q*). In large cities the demand for gasoline is large relative to Q*, which makes it possible for several gas stations to coexist in the market.

Economies of Scope Recall that economies of scope exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms, that is, when it is cheaper to produce outputs Q1 and Q2 jointly. Pharmaceutical companies often enjoy economies of scope in their development of new drugs; breakthroughs in developing a product that cures one disease may reduce the cost of developing additional products that cure other illnesses.

economies of scope Exist when the total cost of producing two products within the same firm is lower than when the products are produced by separate firms.

Figure 8–11 Economies of Scale and Minimum Prices

$

Q Q M

Average cost with a single

firm

ATC(Q M 2)

ATC

P M

ATC(Q M)

Q M

2 Q*

Demand

Average cost when two firms share the market

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In the presence of economies of scope, efficient production requires that a firm produce several products jointly. While multiproduct firms do not necessarily have more market power than firms producing a single product, economies of scope tend to encourage “larger” firms. In turn, this may provide greater access to capital markets, where working capital and funds for investment are obtained. To the extent that smaller firms have more difficulty obtain- ing funds than do larger firms, the higher cost of capital may serve as a barrier to entry. In extreme cases, economies of scope can lead to monopoly power.

Cost Complementarity Cost complementarities exist in a multiproduct cost function when the marginal cost of pro- ducing one output is reduced when the output of another product is increased; that is, when an increase in the output of product 2 decreases the marginal cost of producing output 1. A simple example of a multiproduct cost function with cost complementarities involves the production of doughnuts and doughnut holes.

Multiproduct firms that enjoy cost complementarities tend to have lower marginal costs than firms producing a single product. This gives multiproduct firms a cost advantage over single-product firms. Thus, in the presence of cost complementarities, firms must produce several products to be able to compete against the firm with lower marginal costs. To the extent that greater capital requirements exist for multiproduct firms than for single-product firms, this requirement can limit the ability of small firms to enter the market. In extreme cases, monopoly power can result.

Patents and Other Legal Barriers The sources of monopoly power just described are technological in nature. In some instances, government may grant an individual or a firm a monopoly right. For example, a city may prevent another utility company from competing against the local utility company. Another example is the potential monopoly power generated by the patent system.

The patent system gives the inventor of a new product the exclusive right to sell the product for a given period of time (see Inside Business 8–2). The rationale behind granting monopoly power to a new inventor is based on the following argument: Inventions take many years and considerable sums of money to develop. Once an invention becomes public infor- mation, in the absence of a patent system, other firms could produce the product and compete against the individual or firm that developed it. Since these firms do not have to expend resources developing the product, they would make higher profits than the original developer. In the absence of a patent system, there would be a reduced incentive on the part of firms to develop new technologies and products.

It is important to stress that patents rarely lead to absolute monopoly because competi- tors are often quick to develop similar products or technologies in order to get a piece of the action. Furthermore, several firms taking different R&D paths may each obtain a patent for a product that is a close substitute for other patented products. For example, the two best- selling erectile dysfunction medications—Pfizer’s Viagra and Eli Lilly’s Cialis—are competitors even though both have “enjoyed” patents. For these reasons, managers enjoying patent protec- tion are by no means immune from competitive pressures.

Maximizing Profits Now that you know what monopoly power is and the factors that lead to monopoly power, we will see how the manager of a monopoly may exploit this power to maximize profits. In particular, in this section we presume that the manager is in charge of a firm that is

cost complementarities Exist when the marginal cost of producing one output is reduced when the output of another product is increased.

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Figure 8–12 Elasticity of Demand and Total Revenues

0 Q

R 0

Q 0

0

P

Q

(a)

P 0

Q 0

D

Unitary

Elastic

Inelastic

Demand

Elastic

MR

R (Q) (Total revenue)

Inelastic

(b)

Maximum revenues = P 0 × Q 0

Unitary

a monopoly. Our goal is to characterize the price and output decisions that maximize the monopolist’s profits.

Marginal Revenue Suppose the monopolist faces a demand curve for its product such as the one in Figure 8–12(a). In Chapter 3, we learned that a linear demand curve is elastic at high prices and inelastic at low prices. If the monopolist produces zero units of output, its revenues are zero. As output is increased above zero, demand is elastic and the increase in output (which implies a lower price) leads to an increase in total revenue, as shown in Figure 8–12(b). This follows from the total revenue test. As output is increased beyond Q0 into the inelastic region of demand, fur- ther increases in output actually decrease total revenue, until at point D the price is zero and revenues are again zero. This is depicted in Figure 8–12(b). Thus, total revenue is maximized at an output of Q0 in Figure 8–12(b). This corresponds to the price of P0 in Figure 8–12(a), where demand is unitary elastic.

The line labeled MR in Figure 8–12(a) is the marginal revenue schedule for the monopolist. Recall that marginal revenue is the change in total revenue attributable to the last unit of output; geometrically, it is the slope of the total revenue curve. As Figure 8–12(a) shows, the marginal rev- enue schedule for a monopolist lies below the demand curve; in fact, for a linear demand curve, the marginal revenue schedule lies exactly halfway between the demand curve and the vertical axis. This means that for a monopolist, marginal revenue is less than the price charged for the good.

There are two ways to understand why the marginal revenue schedule lies below the monop- olist’s demand curve. Consider first a geometric explanation. Marginal revenue is the slope of the total revenue curve [R(Q)] in Figure 8–12(b). As output increases from zero to Q0, the slope of the total revenue curve decreases until it becomes zero at Q0. Over this range, marginal revenue

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Formula: Monopolist’s Marginal Revenue. The marginal revenue of a monopolist is given by the formula

MR = P [ 1 + E

_ E

]

where E is the elasticity of demand for the monopolist’s product and P is the price charged for the product.

A C A L C U L U S A L T E R N A T I V E The monopolist’s revenue is

R ( Q ) = P ( Q ) Q

Taking the derivative with respect to Q yields

dR

___ dQ

=

dP

___ dQ

Q + P

=

P [ ( dP

_ dQ

) ( Q

_ P

) + 1 ]

=

P [ 1 _

E + 1 ]

=

P [ 1 + E

_ E

]

where E is the elasticity of demand. Since dR/dQ = MR, this means that

MR = P [ 1 + E

_ E

]

The United States grants inventors three types of patent protection: utility, design, and plant patents. A “utility pat- ent” protects the way an invention is used and works, while a “design patent” protects the way an invention looks. A “plant patent” protects an inventor who has discovered and asexually reproduced a distinct and new variety of plant (excluding tuber propagated plants or plants found in uncul- tivated states). Utility and plant patents provide 20 years of protection, while design patents last 14 years.

Trademarks are different from patents in that they protect words, names, symbols, or images that are used in connec- tion with goods or services. Similarly, a copyright protects a creator’s form of expression (including literary, dramatic, musical, and artistic works). Patents and trademarks are administered through the U.S. Patent and Trademark Office, while the U.S. Copyright Office handles copyrights.

SOURCES: United States Patent and Trademark Office; United States Copyright Office.

INSIDE BUSINESS 8–2

Patent, Trademark, and Copyright Protection

decreases until it reaches zero when output is Q0. As output expands beyond Q0, the slope of the total revenue curve becomes negative and gets increasingly negative as output continues to expand. This means that marginal revenue is negative for outputs in excess of Q0.

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An alternative explanation for why marginal revenue is less than price for a monopolist is as follows: Suppose a monopolist sells one unit of output at a price of $4 per unit, for a total revenue of $4. What happens to revenue if the monopolist produces one more unit of output? Revenue increases by less than $4. To see why, note that the monopolist can sell one more unit of output only by lowering price, say, from $4 to $3 per unit. But the price reduction necessary to sell one more unit lowers the price received on the first unit from $4 to $3. The total revenue associated with two units of output thus is $6. The change in revenue due to producing one more unit is therefore $2, which is less than the price charged for the product.

Since the price a monopolist can charge for the product depends on how much is pro- duced, let P(Q) represent the price per unit paid by consumers for Q units of output. This relation summarizes the same information as a demand curve, but because price is expressed as a function of quantity instead of the other way around, it is called an inverse demand func- tion. The inverse demand function, denoted P(Q), indicates the price per unit as a function of the firm’s output. The most common inverse demand function is the linear inverse demand function. The linear inverse demand function is given by

P ( Q ) = a + bQ

where a is a number greater than zero and b is a number less than zero. In addition to the general formula for marginal revenue that is valid for all demand func-

tions, it is useful to have the following formula for marginal revenue, which is valid for the special case of a linear inverse demand function.

Formula: MR for Linear Inverse Demand. For the linear inverse demand function, P(Q) = a + bQ, marginal revenue is given by

MR = a + 2bQ

DEMONSTRATION PROBLEM 8–3

Show that if demand is elastic (say, E = −2), marginal revenue is positive but less than price. Show that if demand is unitary elastic (E = −1), marginal revenue is zero. Finally, show that if demand is inelastic (say, E = −0.5), marginal revenue is negative.

ANSWER: Setting E = −2 in the marginal revenue formula yields

MR = P [ 1 − 2

_ − 2

] = − 1

___ − 2

P

so MR = 0.5P. Thus, when demand is elastic, marginal revenue is positive but less than price (in this example, marginal revenue is one-half of the price).

Setting E = −1 in the marginal revenue formula yields

MR = P [ 1 − 1

_ − 1

] = 0

so MR = 0. Thus, when demand is unitary elastic, marginal revenue is zero. Finally, setting E = −0.5 in the marginal revenue formula yields

MR = P [ 1 − .5

_ − .5

] = P [ .5 _

− .5 ] = − P

so MR = −P. Thus, when demand is inelastic, marginal revenue is negative and less than price (in this example, marginal revenue is the negative of the price).

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A C A L C U L U S A L T E R N A T I V E With a linear inverse demand function, the revenue function is

R ( Q ) = ( a + bQ ) Q

Marginal revenue is

MR = dR

___ dQ

= a + 2bQ

DEMONSTRATION PROBLEM 8–4

Suppose the inverse demand function for a monopolist’s product is given by

P = 10 − 2Q

What is the maximum price per unit a monopolist can charge to be able to sell 3 units? What is mar- ginal revenue when Q = 3?

ANSWER: First, we set Q = 3 in the inverse demand function (here a = 10 and b = −2) to get

P = 10 − 2(3) = 4

Thus, the maximum price per unit the monopolist can charge to be able to sell 3 units is $4. To find marginal revenue when Q = 3, we set Q = 3 in the marginal revenue formula for linear inverse demand to get

MR = 10 − [(2)(2)(3)] = − 2

The Output Decision Revenues are one determinant of profits; costs are the other. Since the revenue a monopolist receives from selling Q units is R(Q) = Q[P(Q)], the profits of a monopolist with a cost func- tion of C(Q) are

π = R ( Q ) – C ( Q )

Typical revenue and cost functions are graphed in Figure 8–13(a). The vertical dis- tance between the revenue and cost functions in panel (a) reflects the profits to the monop- olist of alternative levels of output. Output levels below point A and above point B imply losses since the cost curve lies above the revenue curve. For output levels between points A and B, the revenue function lies above the cost function, and profits are positive for those output levels.

Figure 8–13(b) depicts the profit function, which is the difference between R and C in panel (a). As Figure 8–13(a) shows, profits are greatest at an output of QM, where the vertical distance between the revenue and cost functions is the greatest. This corresponds to the maximum profit point in panel (b). A very important property of the profit- maximizing level of output (QM) is that the slope of the revenue function in panel (a) equals the slope of the cost function. In economic terms, marginal revenue equals marginal cost at an output of QM.

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Figure 8–13 Costs, Revenues, and Profits under Monopoly

0

Profits (π)

Q QM

0

$

Q

(a)

QM

Slope of R = MR

Maximum profits

Slope of C(Q) = MC

R = P(Q)×Q Revenue function

π = R – C Profit function

C(Q) Cost function

A

B

(b)

A C A L C U L U S A L T E R N A T I V E The profits for a monopolist are

π = R ( Q ) − C ( Q ) where R(Q) is total revenue. To maximize profits, marginal profits must be zero:

dπ

___ dQ

= dR ( Q )

______ dQ

− dC ( Q )

______ dQ

= 0 or

MR = MC

P R I N C I P L E

Monopoly Output Rule A profit-maximizing monopolist should produce the output QM such that marginal revenue equals marginal cost:

MR( Q M ) = MC( Q M )

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The economic intuition behind this important rule is as follows: If marginal revenue was greater than marginal cost, an increase in output would increase revenues more than it would increase costs. Thus, a profit-maximizing manager of a monopoly should continue to expand output when MR > MC. On the other hand, if marginal cost exceeded marginal revenue, a reduction in output would reduce costs by more than it would reduce revenue. A profit-maximizing manager thus is motivated to produce where marginal revenue equals marginal cost.

An alternative characterization of the profit-maximizing output decision of a monopoly is presented in Figure 8–14. The marginal revenue curve intersects the marginal cost curve when QM units are produced, so the profit-maximizing level of output is QM. The maximum price per unit that consumers are willing to pay for QM units is PM, so the profit-maximizing price is PM. Monopoly profits are given by the shaded rectangle in the figure, which is the base (QM) times the height [PM − ATC(QM)].

Figure 8–14 Profit Maximization under Monopoly

$

Q

ATC

P M

ATC(Q M)

Q M

Profits = [P M – ATC(QM)] × Q M

Profits

MC

D

MR

P R I N C I P L E

Monopoly Pricing Rule Given the level of output, QM, that maximizes profits, the monopoly price is the price on the demand curve corresponding to the QM units produced:

P M = P( Q M )

DEMONSTRATION PROBLEM 8–5

Suppose the inverse demand function for a monopolist’s product is given by

P = 100 − 2Q

and the cost function is given by

C ( Q ) = 10 + 2Q

Determine the profit-maximizing price and quantity and the maximum profits.

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

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ANSWER: Using the marginal revenue formula for linear inverse demand and the formula for marginal cost, we see that

MR = 100 − ( 2 ) ( 2 ) ( Q ) = 100 − 4Q MC = 2

Next, we set MR = MC to find the profit-maximizing level of output:

100 − 4Q = 2

or

4Q = 98

Solving for Q yields the profit-maximizing output of QM = 24.5 units. We find the profit-maximizing price by setting Q = QM in the inverse demand function:

P = 100 − 2 ( 24.5 ) = 51

Thus, the profit-maximizing price is $51 per unit. Finally, profits are given by the difference between revenues and costs:

π

=

P M Q M − C( Q M )

= ( 51 ) ( 24.5 ) − [ 10 + 2 ( 24.5 ) ]

=

$1,190.50

The Absence of a Supply Curve Recall that a supply curve determines how much will be produced at a given price. Since perfectly competitive firms determine how much output to produce based on price (P = MC), supply curves exist in perfectly competitive markets. In contrast, a monopolist determines how much to produce based on marginal revenue, which is less than price (P > MR = MC). This is because a change in quantity by a monopolist actually changes the market price. Consequently, there is no way to express how a monopolist’s quantity choice would change for different given prices, so there is no supply curve for a monopolist. In fact there is no sup- ply curve in markets served by firms with market power, such as monopolistic competition, which we discuss in the next section.

Multiplant Decisions Up until this point, we have assumed that the monopolist produces output at a single loca- tion. In many instances, however, a monopolist has different plants at different locations. An important issue for the manager of such a multiplant monopoly is the determination of how much output to produce at each plant.

Suppose the monopolist produces output at two plants. The cost of producing Q1 units at plant 1 is C1(Q1), and the cost of producing Q2 units at plant 2 is C2(Q2). Further, suppose the products produced at the two plants are identical, so the price per unit consumers are willing to pay for the total output produced at the two plants is P(Q), where

Q = Q 1 + Q 2

Profit maximization implies that the two-plant monopolist should produce output in each plant such that the marginal cost of producing in each plant equals the marginal revenue of total output.

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P R I N C I P L E

Multiplant Output Rule Let MR(Q) be the marginal revenue of producing a total of Q = Q1 + Q2 units of output. Suppose the marginal cost of producing Q1 units of output in plant 1 is MC1(Q1) and that of producing Q2 units in plant 2 is MC2(Q2). The profit maximization rule for the two-plant monopolist is to allo- cate output among the two plants such that

MR ( Q ) = M C 1 ( Q 1 ) MR ( Q ) = M C 2 ( Q 2 )

A C A L C U L U S A L T E R N A T I V E If profits are

π = R ( Q 1 + Q 2 ) − C 1 ( Q 1 ) − C 2 ( Q 2 )

the first-order conditions for maximizing profits are

dπ

____ d Q 1

= dR ( Q 1 + Q 2 ) __________

d Q 1 −

d C 1 ( Q 1 ) _______ d Q 1

= 0

dπ

____ d Q 2

= dR ( Q 1 + Q 2 ) __________

d Q 2 −

d C 2 ( Q 2 ) _______ d Q 2

= 0

The economic intuition underlying the multiplant output rule is precisely the same as all of the profit maximization principles. If the marginal revenue of producing output in a plant exceeds the marginal cost, the firm will add more to revenue than to cost by expanding output in the plant. As output is expanded, marginal revenue declines until it ultimately equals the marginal cost of producing in the plant.

The conditions for maximizing profits in a multiplant setting imply that

M C 1 ( Q 1 ) = M C 2 ( Q 2 )

This too has a simple economic explanation. If the marginal cost of producing in plant 1 is lower than that of producing in plant 2, the monopolist could reduce costs by producing more output in plant 1 and less in plant 2. As more output is produced in plant 1, the marginal cost of producing in the plant increases until it ultimately equals the marginal cost of producing in plant 2.

DEMONSTRATION PROBLEM 8–6

Suppose the inverse demand for a monopolist’s product is given by

P ( Q ) = 70 − .5Q

The monopolist can produce output in two plants. The marginal cost of producing in plant 1 is MC1 = 3Q1, and the marginal cost of producing in plant 2 is MC2 = Q2. How much output should be produced in each plant to maximize profits, and what price should be charged for the product?

ANSWER: To maximize profits, the firm should produce output in the two plants such that

MR ( Q ) = M C 1 ( Q 1 ) MR ( Q ) = M C 2 ( Q 2 )

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In this instance, marginal revenue is given by

MR ( Q ) = 70 − Q

where Q = Q1 + Q2. Substituting these values into the formula for the multiplant output rule, we get

70 − ( Q 1 + Q 2 ) = 3 Q 1 70 − ( Q 1 + Q 2 ) = Q 2

Thus, we have two equations and two unknowns, and we must solve for the two unknowns. The first equation implies that

Q 2 = 70 − 4 Q 1

Substituting this into the second equation yields

70 − ( Q 1 + 70 − 4 Q 1 ) = 70 − 4 Q 1

Solving this equation, we find that Q1 = 10. Next, we substitute this value of Q1 into the first equation:

70 − ( 10 + Q 2 ) = 3 ( 10 )

Solving this equation, we find that Q2 = 30. Thus, the firm should produce 10 units in plant 1 and 30 units in plant 2 for a total output of Q = 40 units.

To find the profit-maximizing price, we must find the maximum price per unit that consumers will pay for 40 units of output. To do this, we set Q = 40 in the inverse demand function:

P = 70 − .5 ( 40 ) = 50

Thus, the profit-maximizing price is $50.

Implications of Entry Barriers Our analysis of monopoly reveals that a monopolist may earn positive economic profits. If a monopolist is earning positive economic profits, the presence of barriers to entry prevents other firms from entering the market to reap a portion of those profits. Thus, monopoly prof- its, if they exist, will continue over time so long as the firm maintains its monopoly power. It is important to note, however, that the presence of monopoly power does not imply posi- tive profits; it depends solely on where the demand curve lies in relation to the average total cost curve. For example, the monopolist depicted in Figure 8–15 earns zero economic profits because the optimal price exactly equals the average total cost of production. Moreover, in the short run a monopolist may even experience losses.

The monopoly power a monopolist enjoys often implies some social costs to society. Consider, for example, the monopolist’s demand, marginal revenue, and marginal cost curves graphed in Figure 8–16. For simplicity, these curves are graphed as linear functions of out- put, and the position of the average cost curve is suppressed for now. The profit-maximizing monopolist produces QM units of output and charges a price of PM.

The first thing to notice about monopoly is that price exceeds the marginal cost of pro- duction: PM > MC. The price in a market reflects the value to society of another unit of out- put. Marginal cost reflects the cost to society of the resources needed to produce an additional unit of output. Since price exceeds marginal cost, the monopolist produces less output than is socially desirable. In effect, society would be willing to pay more for one more unit of output than it would cost to produce the unit. Yet the monopolist refuses to do so because it would reduce the firm’s profits. This is because marginal revenue for a monopolist lies below the demand curve, and thus MR < MC at this level of output.

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Figure 8–15 A Monopolist Earning Zero Profits

$

Q

ATC

P M

Q M

MC

D

MR 0

In contrast, given the same demand and cost conditions, a firm in a perfectly competitive industry would continue to produce output up to the point where price equals marginal cost; this corresponds to an industry output and price of QC and PC under perfect competition. Thus, the monopolist produces less output and charges a higher price than would a perfectly competitive industry. The shaded area in Figure 8–16 represents the deadweight loss of monopoly, that is, the welfare loss to society due to the monopolist producing output below the competitive level. To see this, recall from Chapter 2 that the vertical difference between demand and marginal cost (competitive supply) at each quantity represents the change in social welfare associated with each incremental unit of output. Summing these vertical distances for all units between the monopoly (QM) and competitive (QC) outputs yields the shaded triangle in Figure 8–16 and thus represents the welfare loss to society (in dollars) due to the monopolization of the market.

deadweight loss of monopoly The consumer and producer surplus that is lost due to the monopolist charging a price in excess of marginal cost.

Figure 8–16 Deadweight Loss of Monopoly

P

Q Q C

Deadweight loss

P C

Q M

P M

D

MC

MR

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MONOPOLISTIC COMPETITION

A market structure that lies between the extremes of monopoly and perfect competition is monopolistic competition. This market structure exhibits some characteristics present in both perfect competition and monopoly.

Conditions for Monopolistic Competition An industry is monopolistically competitive if:

1. There are many buyers and sellers. 2. Each firm in the industry produces a differentiated product. 3. There is free entry into and exit from the industry.

There are numerous industries in which firms produce products that are close substitutes, and the market for hamburgers is a prime example. Many fast-food restaurants produce ham- burgers, but the hamburgers produced by one firm differ from those produced by other firms. Moreover, it is relatively easy for new firms to enter the market for hamburgers.

The key difference between the models of monopolistic competition and perfect competi- tion is that in a market with monopolistic competition, each firm produces a product that dif- fers slightly from other firms’ products. The products are close, but not perfect, substitutes. For example, other things being equal, some consumers prefer McDonald’s hamburgers, whereas others prefer to eat at Wendy’s, Burger King, or one of the many other restaurants that serve hamburgers. As the price of a McDonald’s hamburger increases, some consumers will substi- tute toward hamburgers produced by another firm. But some consumers may continue to eat at McDonald’s even if the price is higher than at other restaurants. The fact that the products are not perfect substitutes in a monopolistically competitive industry thus implies that each firm faces a downward-sloping demand curve for its product. To sell more of its product, the firm must lower

monopolistic competition A market in which (1) there are many buyers and sellers; (2) each firm produces a differentiated product; and (3) there is free entry and exit.

In 1896, Colgate dental cream was introduced in tubes similar to those we use now. Today, the Colgate-Palmolive Company’s brand of toothpaste is the best-selling tooth- paste in the world (ahead of the Crest brand marketed by Procter & Gamble, which was introduced in 1955).

While Colgate and Crest enjoy the lion’s share of the toothpaste market, if you view the oral care shelf at your local drugstore or supermarket, you will find over a hun- dred different varieties of toothpaste. Colgate alone sells over 40 different varieties that are marketed under names ranging from Shrek Bubble Fruit to Colgate Total Advanced Whitening.

Why would a dominant company like Colgate choose to sell so many different varieties of toothpaste—varieties that compete against each other for consumers’ dollars?

The high level of product differentiation in the tooth- paste market stems from firms introducing new varieties in an attempt to boost their economic profits. In environments where makers of other brands (such as Crest) can easily enter profitable segments of the market, a profitable strat- egy is to attempt to quickly cover that segment (introducing Shrek Bubble Fruit toothpaste, for instance) in order to earn short-run profits until other firms enter to steal a share of that segment. While introducing new varieties may canni- balize sales of your existing products, cannibalizing your own sales is better than having them stolen by a hungry competitor.

SOURCES: Corporate websites of the Colgate-Palmolive Company and Procter & Gamble and Hoover’s Online.

INSIDE BUSINESS 8–3

Product Differentiation, Cannibalization, and Colgate’s Smile

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Figure 8–17 Profit Maximization under Monopolistic Competition

$

Q

ATC P*

Q*

MC

D

MR 0

Profits = [P* – ATC(Q*)] × Q*

ATC(Q*)

the price. In this sense, the demand curve facing a monopolistically competitive firm looks more like the demand for a monopolist’s product than like the demand for a competitive firm’s product.

There are two important differences between a monopolistically competitive market and a market serviced by a monopolist. First, while a monopolistically competitive firm faces a downward-sloping demand for its product, there are other firms in the industry that sell simi- lar products. Second, in a monopolistically competitive industry, there are no barriers to entry. As we will see later, this implies that firms will enter the market if existing firms earn positive economic profits.

Profit Maximization The determination of the profit-maximizing price and output under monopolistic competition is precisely the same as for a firm operating under monopoly. To see this, consider the demand curve for a monopolistically competitive firm presented in Figure 8–17. Since the demand curve slopes downward, the marginal revenue curve lies below it, just as under monopoly. To maximize profits, the monopolistically competitive firm produces where marginal revenue equals marginal cost. This output is given by Q* in Figure 8–17. The profit-maximizing price is the maximum price consumers are willing to pay for Q* units of the firm’s output. The firm’s profits are given by the shaded region.

Now that you understand that the basic principles of profit maximization are the same under monopolistic competition and monopoly, it is important to highlight one important difference in the interpretation of our analysis. The demand and marginal revenue curves used to determine the monopolistically competitive firm’s profit-maximizing output and price are based not on the market demand for the product but on the demand for the individual firm’s product. The demand curve facing a monopolist, in contrast, is the market demand curve.

In fact, because the firms in a monopolistically competitive industry produce differentiated products, the notion of an industry or market demand curve is not well defined. To find market demand, one must add up the total quantities purchased from all firms in the market at each price. But in monopolistically competitive markets, each firm produces a product that differs from other firms’ products. Adding up these different products would be like adding up apples and oranges.

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P R I N C I P L E

Profit Maximization Rule for Monopolistic Competition To maximize profits, a monopolistically competitive firm produces where its marginal revenue equals marginal cost. The profit-maximizing price is the maximum price per unit that consumers are willing to pay for the profit-maximizing level of output. In other words, the profit-maximizing output, Q*, is such that

MR(Q*) = MC(Q*)

and the profit-maximizing price is

P* = P(Q*)

DEMONSTRATION PROBLEM 8–7

Suppose the inverse demand function for a monopolistically competitive firm’s product is given by

P = 100 − 2Q

and the cost function is given by

C ( Q ) = 5 + 2Q

Determine the profit-maximizing price and quantity and the maximum profits.

ANSWER: Using the marginal revenue formula for linear inverse demand and the formula for marginal cost, we see that

MR = 100 − ( 2 ) ( 2 ) ( Q ) = 100 − 4Q MC = 2

Next, we set MR = MC to find the profit-maximizing level of output:

100 − 4Q = 2

or

4Q = 98

Solving for Q yields the profit-maximizing output of Q* = 24.5 units. The profit-maximizing price is found by setting Q = Q* in the inverse demand function:

P* = 100 − 2 × 24.5 = 51

Thus, the profit-maximizing price is $51 per unit. Finally, profits are given by the difference between revenues and costs:

π

=

P*Q* − C ( Q* )

= ( 51 ) ( 24.5 ) − [ 5 + 2 ( 24.5 ) ]

=

$1,195.50

Long-Run Equilibrium Because there is free entry into monopolistically competitive markets, if firms earn short-run profits in a monopolistically competitive industry, additional firms will enter the industry in the long run to capture some of those profits. Similarly, if existing firms incur losses, in the long run some firms will exit the industry.

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Figure 8–18 Effect of Entry on a Monopolistically Competitive Firm’s Demand

$

Q

ATC

P*

Q*

MC

D1

MR1 0 MR

0

D0

Due to entry of new firms selling

other brands

(Brand X)

To explain the impact of entry and exit in monopolistically competitive markets, suppose a monopolistically competitive firm is earning positive economic profits. The potential for profits induces other firms to enter the market and produce slight variations of the existing firm’s product. As additional firms enter the market, some consumers who were buying the firm’s product will begin to consume one of the new firms’ products. Thus, one would expect the existing firms to lose a share of the market when new firms enter.

To make this notion more precise, suppose a monopolistically competitive firm that sells brand X faces an initial demand curve of D0 in Figure 8–18. Since this demand curve lies above the ATC curve, the firm is earning positive economic profits. This, of course, lures more firms into the industry. As additional firms enter, the demand for this firm’s product will decrease because some consumers will substitute toward the new products offered by the entering firms. Entry continues until the demand curve decreases to D1, where it is just tangential to the firm’s average cost curve. At this point, firms in the indus- try are earning zero economic profits, and there is no incentive for additional firms to enter the industry.

The story is similar if firms in the industry initially are incurring losses. However, in this instance firms will exit the industry, and the demand for the products offered by the firms that remain will increase. This process leads to increased profits (or, more accurately, reduced losses) for the remaining firms. Ultimately, firms stop leaving the industry when the remain- ing firms earn zero economic profits.

Thus, the long-run equilibrium in a monopolistically competitive industry is character- ized by the situation in Figure 8–19. Each firm earns zero economic profits but charges a price that exceeds the marginal cost of producing the good.

P R I N C I P L E

The Long Run and Monopolistic Competition In the long run, monopolistically competitive firms produce a level of output such that

1. P > MC. 2. P = ATC > minimum of average costs.

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As in the case of monopoly, the fact that price exceeds marginal cost implies that monop- olistically competitive firms produce less output than is socially desirable. In essence, con- sumers are willing to pay more for another unit than it would cost the firm to produce another unit; yet the firm will not produce more output because of its concern with profits.

Because price equals average costs, firms earn zero economic profits just as firms in perfectly competitive markets do. Even though the firms have some control over price, com- petition among them leads to a situation where no firm earns more than its opportunity cost of producing.

Finally, note that the price of output exceeds the minimum point on the average cost curve. This implies that firms do not take full advantage of economies of scale in production. In a sense, there are too many firms in the industry to enable any individual firm to take full advantage of economies of scale in production. On the other hand, some argue that this is sim- ply the cost to society of having product variety. If there were fewer firms, economies of scale could be fully exploited, but there would be less product variety in the market.

Implications of Product Differentiation The key difference between perfect competition and monopolistic competition is the assump- tion that firms produce differentiated products. Since there are many products in a monopo- listically competitive industry, the only reason firms have any control over their price is that consumers view the products as differentiated. The demand for a firm’s product is less elastic when consumers view other firms’ products as poor substitutes for it. The less elastic the demand for a firm’s product, the greater the potential for earning profits.

For this reason, many firms in monopolistically competitive industries continually attempt to convince consumers that their products are better than those offered by other firms. A number of examples of such industries come readily to mind: fast-food restaurants, tooth- paste, mouthwash, gasoline, aspirin, car wax—undoubtedly you can add other industries to the list. Each of these industries consists of many firms, and the different brands offered by firms in each industry are very close substitutes. In some instances, firms introduce several varieties of products; each soft-drink producer, for example, produces a variety of cola and noncola drinks.

Figure 8–19 Long-Run Equilibrium under Monopolistic Competition

P

Q

AC

P*

Q*

MC

MR 0

D

Long-run monopolistically competitive equilibrium

(Brand X)

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Firms in monopolistically competitive industries employ two strategies to persuade con- sumers that their products are better than those offered by competitors. First, monopolistically competitive firms spend considerable amounts on advertising campaigns. Very typically, these campaigns involve comparative advertising designed to differentiate a given firm’s brand from brands sold by competing firms. Comparative advertising is common in the fast- food industry. For example, Subway attempts to stimulate demand for its food by differenti- ating itself as the healthy fast-food alternative. To the extent that comparative advertising is effective, it may induce consumers to pay a premium for a particular brand. The additional value that a brand adds to the product is known as brand equity.

Second, firms in monopolistically competitive industries frequently introduce new prod- ucts into the market to further differentiate their products from other firms. These include not only “new, improved” products, such as an “improved” version of laundry detergent, but com- pletely different product lines. Monopolistically competitive firms may also attempt to create and advertise new products that fill special needs in the market. This strategy—called niche marketing—involves products or services targeted to a specific group of consumers. Through green marketing, for instance, firms create and advertise “environmentally friendly” prod- ucts in an attempt to capture the segment of the market that is concerned with environmental issues. Examples of green marketing include package labels that prominently indicate that a toy is made from recycled plastic or a particular brand of laundry detergent is biodegradable.

Unfortunately, successful differentiation and branding strategies sometimes make man- agers myopic. A brand myopic manager is satisfied with an existing brand, is slow to launch new products, and is not aware of emerging industry trends or changes in consumer prefer- ences. Essentially, a brand myopic company rests on its past laurels and, in so doing, misses opportunities to enhance (and hence protect) its brand. A few decades ago, for instance, Crest became the best-selling toothpaste through advertising campaigns that touted Crest as the brand that helps fight cavities. In recent years, however, fresh breath, white teeth, and gum sensitivity emerged as issues that consumers care about. Colgate capitalized on Crest’s brand myopia by exploiting these new trends in consumer preferences and recently surpassed Crest as the leading toothpaste in the market.

As the manager of a firm in a monopolistically competitive industry, it is important for you to remember that, in the long run, additional firms will enter the market if your firm earns short-run profits with its product. Thus, while you may make short-run profits by introducing a new product line, in the long run other firms will mimic your product and/or introduce new product lines, and your economic profits will decrease to zero.

OPTIMAL ADVERTISING DECISIONS

How much should a firm spend on advertising in order to maximize profits? The answer depends, in part, on the nature of the industry in which the firm operates. Firms that operate in perfectly competitive markets generally do not find it profitable to advertise because con- sumers already have perfect information about the large number of substitutes that exist for any given firm’s product. A wheat farmer who operates a small family farm, for instance, is unlikely to profit by spending family funds on an advertising campaign designed to increase the demand for the family’s wheat. In contrast, firms that have market power—such as monop- olists and monopolistically competitive firms—will generally find it profitable to spend a fraction of their revenues on advertising.

As with any economic decision, the optimal amount of advertising balances marginal benefits and marginal costs: To maximize these profits, managers should advertise up to the

comparative advertising A form of advertising where a firm attempts to increase the demand for its brand by differentiating its product from competing brands.

brand equity The additional value added to a product because of its brand.

niche marketing A marketing strategy where goods and services are tailored to meet the needs of a particular segment of the market.

green marketing A form of niche marketing where firms target products toward consumers who are concerned about environmental issues.

brand myopic A manager or company that rests on a brand’s past laurels instead of focusing on emerging industry trends or changes in consumer preferences.

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point where the incremental revenue from advertising equals the incremental cost. The incre- mental cost of advertising is simply the dollar cost of the resources needed to increase the level of advertising. These costs include fees paid for additional advertising space and the opportunity cost of the human resources needed to put together the advertising campaign. The incremental revenue is the extra revenue the firm gets as a result of the advertising cam- paign. These extra revenues depend on the number of additional units that will be sold as a result of an advertising campaign and how much is earned on each of these units. Fortunately, a simple formula is available that permits managers to easily determine the optimal level of advertising.

Formula: The Profit-Maximizing Advertising-to-Sales Ratio. The profit-maximizing advertising-to-sales ratio (A/R) is given by

A

__ R

= E Q, A ______

− E Q, P

where EQ,P represents the own-price elasticity of demand for the firm’s product, EQ,A is the advertising elasticity of demand for the firm’s product, A represents the firm’s expenditures on advertising, and R = PQ denotes the dollar value of the firm’s sales (that is, the firm’s revenues).

A C A L C U L U S A L T E R N A T I V E A firm’s profits are revenues minus production costs and advertising expenditures. If we let A represent advertising expenditures, Q = Q(P, A) denote the demand for the firm’s product, and C(Q) denote production costs, firm profit is a function of P and A:

π (P, A) = Q ( P, A ) P − C [ Q ( P, A ) ] − A

The first-order conditions for maximizing profits require

∂ π

___ ∂ P

= ∂ Q

___ ∂ P

P + Q − ∂ C

___ ∂ Q

∂ Q

___ ∂ P

= 0 (8–1)

and

∂ π

___ ∂ A

= ∂ Q

___ ∂ A

P − ∂ C

___ ∂ Q

∂ Q

___ ∂ A

− 1 = 0 (8–2)

Noting that ∂C/∂Q = MC and EQ, P = (∂Q/∂P)(P/Q), we may write Equation 8–1 as

P − MC

______ P

= − 1

____ E Q, P

(8–3)

Similarly, using the fact that EQ, A = (∂Q/∂A)(A/Q), Equation 8–2 implies

A

__ R

= ( P − MC

_ P

) E Q, A (8–4)

Substituting Equation 8–3 into Equation 8–4 yields the above formula.

Two aspects of this formula are worth noting. First, the more elastic the demand for a firm’s product, the lower the optimal advertising-to-sales ratio. In the extreme case where EQ,P = −∞ (perfect competition), the formula indicates that the optimal advertising-to-sales ratio is zero. Second, the greater the advertising elasticity, the greater the optimal advertising-to-sales ratio. Firms that have market power (such as monopolists and monopolistically competitive firms)

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262 CHAPTER 8 Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets

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face a demand curve that is not perfectly elastic. As a consequence, these firms will generally find it optimal to engage in some degree of advertising. Exactly how much such firms should spend on advertising, however, depends on the quantitative impact of advertising on demand. The more sensitive demand is to advertising (that is, the greater the advertising elasticity), the greater the number of additional units sold because of a given increase in advertising expendi- tures, and thus the greater the optimal advertising-to-sales ratio.

DEMONSTRATION PROBLEM 8–8

Corpus Industries produces a product at constant marginal cost that it sells in a monopolistically competitive market. In an attempt to bolster profits, the manager hired an economist to estimate the demand for its product. She found that the demand for the firm’s product is log-linear, with an own price elasticity of demand of –10 and an advertising elasticity of demand of 0.2. To maximize prof- its, what fraction of revenues should the firm spend on advertising?

ANSWER: To find the profit-maximizing advertising-to-sales ratio, we simply plug EQ, P = −10 and EQ, A = 0.2 into the formula for the optimal advertising-to-sales ratio:

A

__ R

= E Q, A ______

− E Q, P =

0.2 ___

10 = 0.02

Thus, Corpus Industries’ optimal advertising-to-sales ratio is 2 percent—to maximize profits, the firm should spend 2 percent of its revenues on advertising.

ANSWERING THE headLINE As noted earlier in this chapter, the fast-food restaurant business has many features of monopolistic competition. Indeed, the owner of a typical McDonald’s franchise competes not only against Burger King and Wendy’s but against a host of other establishments. While each of these restaurants offers quick meals at reasonable prices, the products offered are clearly differentiated. Product differentiation gives these businesses some market power.

The McCafé program discussed in the opening headline was designed to further dif- ferentiate McDonald’s from the competition. In so doing, McDonald’s hoped to increase its own demand by attracting customers away from traditional coffee shops and other fast-food restaurants. In fact, this is exactly what happened, as McDonald’s saw a large increase in its coffee sales over a short period of time. While a monopolistically competi- tive business like McDonald’s might benefit in the short run by introducing new products more quickly than its rivals, in the long run its competitors will attempt to mimic the strate- gies that are profitable. For example, Starbucks recently acquired the La Boulange bakery brand, allowing it to offer more food options along with its coffee—an apparent response to McDonald’s invading its turf. This type of entry by rival firms would likely reduce the demand for meals (and coffee) at McDonald’s and ultimately result in long-run economic profits of zero. It is worth noting that a similar chain of events occurred in 1978 when McDonald’s successfully launched its Egg McMuffin. Other fast-food restaurants eventually responded by launching their own breakfast items, which ultimately reduced McDonald’s share of the breakfast market and its economic profits. For these reasons, it is unlikely that McDonald’s McCafé program will have a sustainable impact on its bottom line.

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SUMMARY

In this chapter, we examined managerial decisions in three market environments: perfect competition, monopoly, and monopolistic competition. Each of these market structures provides a manager with a different set of variables that can influence the firm’s profits. A manager may need to pay particularly close attention to different decision parameters because different market structures allow con- trol of only certain variables. Managers who recognize which variables are relevant for a particular industry will make more profits for their firms.

Managers in perfectly competitive markets should concentrate on producing the proper quantity and keeping costs low. Because perfectly competitive markets contain

a very large number of firms that produce perfect substi- tutes, a manager in this market has no control over price. A manager in a monopoly, in contrast, needs to recognize the relation between price and quantity. By setting a quan- tity at which marginal cost equals marginal revenue, the manager of a monopoly will maximize profits. This is also true for the manager of a firm in a monopolistically com- petitive market, who also must evaluate the firm’s product periodically to ensure that it is differentiated from other products in the market. In many instances, the manager of a monopolistically competitive firm will find it advanta- geous to slightly change the product from time to time to enhance product differentiation.

KEY TERMS AND CONCEPTS

brand equity brand myopic comparative advertising cost complementarities deadweight loss of monopoly diseconomies of scale economies of scale economies of scope

firm demand curve free entry free exit green marketing inverse demand function linear inverse demand function marginal revenue monopolistic competition

monopoly multiplant monopoly niche marketing patents perfectly competitive market product differentiation

CONCEPTUAL AND COMPUTATIONAL QUESTIONS

1. The following graph summarizes the demand and costs for a firm that operates in a per- fectly competitive market. (LO1, LO6) a. What level of output should

this firm produce in the short run?

b. What price should this firm charge in the short run?

c. What is the firm’s total cost at this level of output?

d. What is the firm’s total variable cost at this level of output?

e. What is the firm’s fixed cost at this level of output?

f. What is the firm’s profit if it produces this level of output?

g. What is the firm’s profit if it shuts down?

h. In the long run, should this firm continue to operate or shut down?

$48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

ATC

Quantity

MC

AVC

D f = MR

AFC

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$220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Quantity

MC

MR D

ATC

4. You are the manager of a monopoly, and your demand and cost functions are given by P = 300 − 3Q and C(Q) = 1,500 + 2Q2, respectively. (LO3, LO4) a. What price–quantity combination maximizes your firm’s profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price–quantity

combination? d. What price–quantity combination maximizes revenue? e. Calculate the maximum revenues. f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price–quantity

combination? 5. You are the manager of a firm that produces a product according to the cost function

C(qi) = 160 + 58qi − 6qi 2 + qi

3. Determine the short-run supply function if: (LO1, LO7) a. You operate a perfectly competitive business. b. You operate a monopoly. c. You operate a monopolistically competitive business.

6. The accompanying diagram shows the demand, marginal revenue, and marginal cost of a monopolist. (LO1, LO3, LO5) a. Determine the profit-maximizing output and price. b. What price and output would prevail if this firm’s product were sold by price-taking

firms in a perfectly competitive market? c. Calculate the deadweight loss of this monopoly.

2. A firm sells its product in a perfectly competitive market where other firms charge a price of $90 per unit. The firm’s total costs are C(Q) = 50 + 10Q + 2Q2. (LO3) a. How much output should the firm produce in the short run? b. What price should the firm charge in the short run? c. What are the firm’s short-run profits? d. What adjustments should be anticipated in the long run?

3. The following graph summarizes the demand and costs for a firm that operates in a monopolistically competitive market. (LO1, LO3, LO5) a. What is the firm’s optimal output? b. What is the firm’s optimal price? c. What are the firm’s maximum profits? d. What adjustments should the manager be anticipating?

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265

7. You are the manager of a monopolistically competitive firm, and your demand and cost functions are given by Q = 36 − 4P and C(Q) = 4 + 4Q + Q2. (LO1, LO3, LO5) a. Find the inverse demand function for your firm’s product. b. Determine the profit-maximizing price and level of production. c. Calculate your firm’s maximum profits. d. What long-run adjustments should you expect? Explain.

8. The elasticity of demand for a firm’s product is –2.5 and its advertising elasticity of demand is 0.2. (LO8) a. Determine the firm’s optimal advertising-to-sales ratio. b. If the firm’s revenues are $40,000, what is its profit-maximizing level of advertising?

9. A monopolist’s inverse demand function is P = 150 − 3Q. The company produces out- put at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2. (LO1, LO8) a. Provide the equation for the monopolist’s marginal revenue function. (Hint: Recall

that Q1 + Q2 = Q.) b. Determine the profit-maximizing level of output for each facility. c. Determine the profit-maximizing price.

10. The manager of a local monopoly estimates that the elasticity of demand for its product is con- stant and equal to –3. The firm’s marginal cost is constant at $20 per unit. (LO1, LO3, LO4) a. Express the firm’s marginal revenue as a function of its price. b. Determine the profit-maximizing price.

$120 110 100 90 80 70 60 50 40 30 20 10 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Quantity

DMR

MC

PROBLEMS AND APPLICATIONS

11. The CEO of a major automaker overheard one of its division managers make the following statement regarding the firm’s production plans: “In order to maximize profits, it is essen- tial that we operate at the minimum point of our average total cost curve.” If you were the CEO of the automaker, would you praise or chastise the manager? Explain. (LO3)

12. You are the manager of a small U.S. firm that sells nails in a competitive U.S. market (the nails you sell are a standardized commodity; stores view your nails as identical to those available from hundreds of other firms). You are concerned about two events you recently learned about through trade publications: (1) the overall market supply of nails will decrease by 2 percent, due to exit by foreign competitors, and (2) due to a growing U.S. economy, the overall market demand for nails will increase by 2 percent. Based on this information, should you plan to increase or decrease your production of nails? Explain. (LO1, LO7)

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266

13. When the first Pizza Hut opened its doors back in 1958, it offered consumers one style of pizza: its Original Thin Crust Pizza. Since its modest beginnings, Pizza Hut has established itself as the leader of the $25 billion pizza industry. Today, Pizza Hut offers six styles of pizza, including Pan Pizza, Stuffed Crust Pizza, and its Hand-Tossed Style. Explain why Pizza Hut has expanded its offerings of pizza over the past six decades, and discuss the long-run profitability of such a strategy. (LO1, LO2, LO5)

14. You are the manager of a small pharmaceutical company that received a patent on a new drug three years ago. Despite strong sales ($150 million last year) and a low marginal cost of producing the product ($0.50 per pill), your company has yet to show a profit from selling the drug. This is, in part, due to the fact that the company spent $1.7 billion developing the drug and obtaining FDA approval. An economist has esti- mated that, at the current price of $1.50 per pill, the own price elasticity of demand for the drug is –2. Based on this information, what can you do to boost profits? Explain. (LO1, LO3, LO4)

15. The second-largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet the monthly demand for electricity in these coun- ties, which is given by the inverse demand function P = 1,200 − 4Q, the utility company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing elec- tricity at each facility are given by C1(Q1) = 8,000 + 6Q1

2 and C2(Q2) = 6,000 + 3Q2 2,

respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profits. (LO1, LO8)

16. You are the manager of College Computers, a manufacturer of customized computers that meet the specifications required by the local university. Over 90 percent of your clientele consists of college students. College Computers is not the only firm that builds computers to meet this university’s specifications; indeed, it competes with many manufacturers online and through traditional retail outlets. To attract its large student clientele, College Computers runs a weekly ad in the student paper advertising its “free service after the sale” policy in an attempt to differentiate itself from the competition. The weekly demand for computers produced by College Computers is given by Q = 800 − 2P, and its weekly cost of producing computers is C(Q) = 1,200 + 2Q2. If other firms in the industry sell PCs at $300, what price and quantity of computers should you produce to maximize your firm’s profits? What long-run adjustments should you anticipate? Explain. (LO1, LO2, LO3, LO5)

17. You are the general manager of a firm that manufactures personal computers. Due to a soft economy, demand for PCs has dropped 50 percent from the previous year. The sales manager of your company has identified only one potential client, who has received several quotes for 10,000 new PCs. According to the sales manager, the client is willing to pay $800 each for 10,000 new PCs. Your production line is currently idle, so you can easily produce the 10,000 units. The accounting department has provided you with the following information about the unit (or average) cost of producing three potential quan- tities of PCs:

10,000 PCs 15,000 PCs 20,000 PCs

Materials (PC components) $     600 $600 $600

Depreciation 300 225 150

Labor        150    150    150

Total unit cost $1,050 $975 $900

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267

Based on this information, should you accept the offer to produce 10,000 PCs at $800 each? Explain. (LO6)

18. You are a manager at Spacely Sprockets—a small firm that manufactures Type A and Type B bolts. The accounting and marketing departments have provided you with the following information about the per-unit costs and demand for Type A bolts:

Accounting Data for Type A Bolts Marketing Data for

Type A Bolts

Item Unit Cost Quantity Price

Materials and labor $2.75 0 $10

Overhead   5.00 1 9

2 8

Total cost per unit $7.75 3 7

4 6

5 5

Materials and labor are obtained in a competitive market on an as-needed basis, and the reported costs per unit for materials and labor are constant over the relevant range of output. The reported unit overhead costs reflect the $10 spent last month on machines, divided by the projected output of 2 units that was planned when the machines were purchased. In addition to the above information, you know that the firm’s assembly line can produce no more than five bolts. Since the firm also makes Type B bolts, this means that each Type A bolt produced reduces the number of Type B bolts that can be produced by one unit; the total number of Types A and B bolts pro- duced cannot exceed 5 units. A call to a reputable source has revealed that unit costs for producing Type B bolts are identical to those for producing Type A bolts and that Type B bolts can be sold at a constant price of $4.75 per unit. Determine your relevant marginal cost of producing Type A bolts and your profit-maximizing production of Type A bolts. (LO3)

19. In a statement to Gillette’s shareholders, its CEO indicated, “Despite several new prod- uct launches, Gillette’s advertising-to-sales declined dramatically . . . to 7.5 percent last year. Gillette’s advertising spending, in fact, is one of the lowest in our peer group of consumer product companies.” If the elasticity of demand for Gillette’s consumer products is similar to that of other firms in its peer group (which averages –4), what is Gillette’s advertising elasticity? Is Gillette’s demand more or less responsive to advertis- ing than other firms in its peer group? Explain. (LO8)

20. Recently, the spot market price of U.S. hot rolled steel plummeted to $400 per ton. Just one year ago, this same ton of steel cost $700. According to Metals Monitor, the drop in price was due to falling oil prices, along with a rise in cheap imports and excess capacity. These dramatic market changes have greatly impacted the supply of raw steel. Suppose that last year the supply for raw steel was QSraw = 600 + 4P, but this year it has shifted to QSraw = 4,200 + 4P. Assuming the market for raw steel is competitive and that the current worldwide demand for steel is Qdraw = 9,000 – 8P, compute the equilibrium price and quantity for the steel market one year ago, and the equilibrium price–quantity combination for the current steel market. Suppose the cost function of a representative steel producer is C(Q) = 1,200 + 15Q2. Compare the change in the quantity of raw steel exchanged at the market level with the change in raw steel produced by a representative firm. How do you explain this difference? (LO1, LO3, LO7)

21. The French government announced plans to convert state-owned power firms EDF and GDF into separate limited companies that operate in geographically distinct markets.

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268

BBC News reported that France’s CFT union responded by organizing a mass strike, which triggered power outages in some Paris suburbs. Union workers are concerned that privatizing power utilities would lead to large-scale job losses and power outages similar to those experienced in parts of the eastern coast of the United States and parts of Italy in 2003. Suppose that prior to privatization, the price per kilowatt-hour of electricity was €0.13 and that the inverse demand for electricity in each of these two regions of France is P = 1.35 − 0.002Q (in euros). Furthermore, to supply electricity to its particular region of France, it costs each firm C(Q) = 120 + 0.13Q (in euros). Once privatized, each firm will have incentive to maximize profits. Determine the number of kilowatt-hours of electricity each firm will produce and supply to the market and the per-kilowatt-hour price. Compute the price elasticity of demand at the profit-maximizing price–quantity combination. Explain why the price elasticity makes sense at the profit-maximizing price–quantity combination. Compare the price–quantity combina- tion before and after privatization. How much more profit will each firm earn as a result of privatization? (LO2, LO3)

22. The owner of an Italian restaurant has just been notified by her landlord that the monthly lease on the building in which the restaurant operates will increase by 20 percent at the beginning of the year. Her current prices are competitive with nearby restaurants of similar quality. However, she is now considering raising her prices by 20 percent to offset the increase in her monthly rent. Would you recommend that she raise prices? Explain. (LO3)

23. Last month you assumed the position of manager for a large car dealership. The distin- guishing feature of this dealership is its “no hassle” pricing strategy; prices (usually well below the sticker price) are posted on the windows, and your sales staff has a reputation for not negotiating with customers. Last year, your company spent $2 million on adver- tisements to inform customers about its “no hassle” policy and had overall sales revenue of $40 million. A recent study from an agency on Madison Avenue indicates that, for each 3 percent increase in TV advertising expenditures, a car dealer can expect to sell 12 percent more cars—but that it would take a 4 percent decrease in price to generate the same 12 percent increase in units sold. Assuming the information from Madison Avenue is correct, should you increase or decrease your firm’s level of advertising? Explain. (LO1, LO2, LO8)

SELECTED READINGS

Gal-Or, Esther, and Spiro, Michael H., “Regulatory Regimes in the Electric Power Industry: Implications for Capacity.” Journal of Regulatory Economics 4(3), September 1992, pp. 263–78.

Gius, Mark Paul, “The Extent of the Market in the Liquor Industry: An Empirical Test of Localized Brand Rivalry, 1970–1988.” Review of Industrial Organization 8(5), October 1993, pp. 599–608.

Lamdin, Douglas J., “The Welfare Effects of Monopoly versus Competition: A Clarification of Textbook Presentations.” Journal of Economic Education 23(3), Summer 1992, pp. 247–53.

Malueg, David A., “Monopoly Output and Welfare: The Role of Curvature of the Demand Function.” Journal

of Economic Education 25(3), Summer 1994, pp. 235–50.

Nguyen, Dung, “Advertising, Random Sales Response, and Brand Competition: Some Theoretical and Econometric Implications.” Journal of Business 60(2), April 1987, pp. 259–79.

Simon, Herbert A., “Organizations and Markets.” Journal of Economic Perspectives 5(2), Spring 1991, pp. 25–44.

Stegeman, Mark, “Advertising in Competitive Markets.” American Economic Review 81(1), March 1991, pp. 210–23.

Zupan, Mark A., “On Cream Skimming, Coase, and the Sustainability of Natural Monopolies.” Applied Economics 22(4), April 1990, pp. 487–92.

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269

APPENDIX

THE CALCULUS OF PROFIT MAXIMIZATION

PERFECT COMPETITION

The profits of a perfectly competitive firm are

π = PQ − C ( Q )

The first-order conditions for maximizing profits require that marginal profits be zero:

dπ

___ dQ

= P − dC ( Q )

______ dQ

= 0

Thus, we obtain the profit-maximizing rule for a firm in perfect competition:

P = dC

___ dQ

or

P = MC The second-order condition for maximizing profits requ ires that

d 2 π

____ d Q 2

= − d 2 C

____ d Q 2

= − dMC

_____ dQ

< 0

This means that d(MC)/dQ > 0, or that marginal cost must be increasing in output.

MONOPOLY AND MONOPOLISTIC COMPETITION

MR = MC RULE The profits for a firm with market power are

π = R ( Q ) − C ( Q )

where R(Q) = P(Q)Q is total revenue. To maximize prof- its, marginal profits must be zero:

dπ

___ dQ

= dR ( Q )

______ dQ

− dC ( Q )

______ dQ

= 0

or

MR = MC

The second-order condition requires that

d 2 π

____ d Q 2

= d 2 R ( Q )

_______ d Q 2

− d 2 C ( Q )

_______ d Q 2

< 0

which means that

dMR

_____ dQ

< dMC

_____ dQ

But this simply means that the slope of the marginal revenue curve must be less than the slope of the marginal cost curve.

APPENDIX

THE ALGEBRA OF PERFECTLY COMPETITIVE SUPPLY FUNCTIONS

This appendix shows how to obtain the short-run firm and industry supply functions from cost data. Suppose there are 500 firms in a perfectly competitive industry, with each firm having a cost function of

C ( q i ) = 50 + 2 q i + 4 q i 2 The corresponding average total cost (ATC), average vari- able cost (AVC), and marginal cost (MC) functions are

AT C i = 50

___ q i + 2 + 4 q i

AV C i = 2 + 4 q i and

M C i = 2 + 8 q i Recall that a firm’s supply curve is the firm’s marginal cost curve above the minimum of average variable cost. Since AVC is at its minimum where it equals marginal cost, to find the quantity where average variable cost equals marginal cost, we must set the two functions equal

to each other and solve for qi. When we do this for the given equations, we find that the quantity at which mar- ginal cost equals average variable cost is qi = 0.

Next, we recognize that an individual firm maximizes profits by equating P = MCi, so

P = 2 + 8 q i Solving for qi gives us the individual firm’s supply function:

q i = − 2 __

8 +

1 __

8 P

To find the supply curve for the industry, we simply sum the above equation over all 500 firms in the market:

Q = ∑ i=1

500

q i = 500 ( − 2 _

8 +

1 _

8 P ) = −

1,000 _____

8 +

500 ____

8 P

or

Q = − 125 + 62.5P

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270

Basic Oligopoly Models 9

headLINE Crude Oil Prices Fall, but Consumers in Some Areas See No Relief at the Pump Thanks to a recent decline in crude oil prices, consumers in most locations recently enjoyed lower gasoline prices. In a few isolated areas, however, consumers cried foul because gasoline retailers did not pass on the price reductions to those who pay at the pump. Consumer groups argued that this corroborated their claim that gasoline retailers in these areas were colluding in order to earn monopoly profits. For obvious reasons, the gasoline retailers involved denied the allegations.

Based on the evidence, do you think that gasoline stations in these areas were colluding in order to earn monopoly profits? Explain.

LEARNING OBJECTIVES

After completing this chapter, you will be able to:

LO1 Explain how beliefs and strategic interaction shape optimal decisions in oligopoly environments.

LO2 Identify the conditions under which a firm operates in a Sweezy, Cournot, Stackelberg, or Bertrand oligopoly, and the ramifications of each type of oligopoly for optimal pricing decisions, output decisions, and firm profits.

LO3 Apply reaction (or best-response) functions to identify optimal decisions and likely competitor responses in oligopoly settings.

LO4 Identify the conditions for a contestable market, and explain the ramifica- tions for market power and the sustainability of long-run profits.

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Managerial Economics and Business Strategy 271

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INTRODUCTION

Up until now, our analysis of markets has not considered the impact of strategic behavior on managerial decision making. At one extreme, we examined profit maximization in perfectly competitive and monopolistically competitive markets. In these types of markets, so many firms are competing with one another that no individual firm has any effect on other firms in the market. At the other extreme, we examined profit maximization in a monopoly market. In this instance there is only one firm in the market, and strategic interactions among firms thus are irrelevant.

This chapter is the first of two chapters in which we examine managerial decisions in oli- gopoly markets. Here we focus on basic output and pricing decisions in four specific types of oligopolies: Sweezy, Cournot, Stackelberg, and Bertrand. In the next chapter, we will develop a more general framework for analyzing other decisions, such as advertising, research and development, entry into an industry, and so forth. First, let us briefly review what is meant by the term oligopoly.

CONDITIONS FOR OLIGOPOLY

Oligopoly refers to a situation where there are relatively few large firms in an industry. No explicit number of firms is required for oligopoly, but the number usually is somewhere between 2 and 10. The products the firms offer may be either identical (as in a perfectly com- petitive market) or differentiated (as in a monopolistically competitive market). An oligopoly composed of only two firms is called a duopoly.

Oligopoly is perhaps the most interesting of all market structures; in fact, the next chapter is devoted entirely to the analysis of situations that arise under oligopoly. But from the view- point of the manager, a firm operating in an oligopoly setting is the most difficult to manage. The key reason is that there are few firms in an oligopolistic market and the manager must consider the likely impact of her or his decisions on the decisions of other firms in the indus- try. Moreover, the actions of other firms will have a profound impact on the manager’s opti- mal decisions. It should be noted that due to the complexity of oligopoly, there is no single model that is relevant for all oligopolies.

THE ROLE OF BELIEFS AND STRATEGIC INTERACTION

To gain an understanding of oligopoly interdependence, consider a situation where several firms selling differentiated products compete in an oligopoly. In determining what price to charge, the manager must consider the impact of his or her decisions on other firms in the industry. For example, if the price for the product is lowered, will other firms lower their prices or maintain their existing prices? If the price is increased, will other firms do likewise or main- tain their current prices? The optimal decision of whether to raise or lower price will depend on how the manager believes other managers will respond. If other firms lower their prices when the firm lowers its price, it will not sell as much as it would if the other firms maintained their existing prices.

As a point of reference, suppose the firm initially is at point B in Figure 9–1, charging a price of P0. Demand curve D1 is based on the assumption that rivals will match any price

oligopoly A market structure in which there are only a few firms, each of which is large relative to the total industry.

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change, while D2 is based on the assumption that they will not match a price change. Note that demand is more inelastic when rivals match a price change than when they do not. The reason for this is simple. For a given price reduction, a firm will sell more if rivals do not cut their prices (D2) than it will if they lower their prices (D1). In effect, a price reduction increases quantity demanded only slightly when rivals respond by lowering their prices. Similarly, for a given price increase, a firm will sell more when rivals also raise their prices (D1) than it will when they maintain their existing prices (D2).

Figure 9–1 A Firm’s Demand Depends on Actions of Rivals

Price

Q

Demand if rivals do not match price changes

C

Q0

Demand if rivals match price changes

P0

B A

D1

D2

0

DEMONSTRATION PROBLEM 9–1

Suppose the manager is at point B in Figure 9–1, charging a price of P0. If the manager believes rivals will not match price reductions but will match price increases, what does the demand for the firm’s product look like?

ANSWER: If rivals do not match price reductions, prices below P0 will induce quantities demanded along curve D2. If rivals do match price increases, prices above P0 will generate quantities demanded along D1. Thus, if the manager believes rivals will not match price reductions but will match price increases, the demand curve for the firm’s product is given by CBD2.

DEMONSTRATION PROBLEM 9–2

Suppose the manager is at point B in Figure 9–1, charging a price of P0. If the manager believes rivals will match price reductions but will not match price increases, what does the demand for the firm’s product look like?

ANSWER: If rivals match price reductions, prices below P0 will induce quantities demanded along curve D1. If rivals do not match price increases, prices above P0 will induce quantities demanded along D2. Thus, if the manager believes rivals will match price reductions but will not match price increases, the demand curve for the firm’s product is given by ABD1.

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The preceding analysis reveals that the demand for a firm’s product in oligopoly depends critically on how rivals respond to the firm’s pricing decisions. If rivals will match any price change, the demand curve for the firm’s product is given by D1. In this instance, the manager will maximize profits where the marginal revenue associated with demand curve D1 equals marginal cost. If rivals will not match any price change, the demand curve for the firm’s product is given by D2. In this instance, the manager will maximize profits where the mar- ginal revenue associated with demand curve D2 equals marginal cost. In each case, the profit- maximizing rule is the same as that under monopoly; the only difficulty for the firm manager is determining whether or not rivals will match price changes.

PROFIT MAXIMIZATION IN FOUR OLIGOPOLY SETTINGS

In the following subsections, we will examine profit maximization based on alternative assumptions regarding how rivals will respond to price or output changes. Each of the four models has different implications for the manager’s optimal decisions, and these differences arise because of differences in the ways rivals respond to the firm’s actions.

Sweezy Oligopoly The Sweezy model is based on a very specific assumption regarding how other firms will respond to price increases and price cuts. An industry is characterized as a Sweezy oligopoly if

1. There are few firms in the market serving many consumers. 2. The firms produce differentiated products. 3. Each firm believes rivals will cut their prices in response to a price reduction but will

not raise their prices in response to a price increase. 4. Barriers to entry exist.

Because the manager of a firm competing in a Sweezy oligopoly believes other firms will match any price decrease but not match price increases, the demand curve for the firm’s prod- uct is given by ABD1 in Figure 9–2. For prices above P0, the relevant demand curve is D2; thus, marginal revenue corresponds to this demand curve. For prices below P0, the relevant demand curve is D1, and marginal revenue corresponds to D1. Thus, the marginal revenue curve (MR) the firm faces is initially the marginal revenue curve associated with D2; at Q0, it jumps down to the marginal revenue curve corresponding to D1. In other words, the Sweezy oligopolist’s marginal revenue curve, denoted MR, is ACEF in Figure 9–2.

The profit-maximizing level of output occurs where marginal revenue equals marginal cost, and the profit-maximizing price is the maximum price consumers will pay for that level of output. For example, if marginal cost is given by MC0 in Figure 9–2, marginal revenue equals marginal cost at point C. In this case the profit-maximizing output is Q0 and the opti- mal price is P0. Since price exceeds marginal cost (P0 > MC0), output is below the socially efficient level. This situation translates into a deadweight loss (lost consumer and producer surplus) that does not arise in a perfectly competitive market.

An important implication of the Sweezy model of oligopoly is that there will be a range (CE) over which changes in marginal cost do not affect the profit-maximizing level of output. This is in contrast to competitive, monopolistically competitive, and monopolistic firms, all of which increase output when marginal costs decline.

Sweezy oligopoly An industry in which (1) there are few firms serving many consumers; (2) firms produce differentiated products; (3) each firm believes rivals will respond to a price reduction but will not follow a price increase; and (4) barriers to entry exist.

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To see why firms competing in a Sweezy oligopoly may not increase output when mar- ginal cost declines, suppose marginal cost decreases from MC0 to MC1 in Figure 9–2. Marginal revenue now equals marginal cost at point E, but the output corresponding to this point is still Q0. Thus the firm continues to maximize profits by producing Q0 units at a price of P0.

In a Sweezy oligopoly, firms have an incentive not to change their pricing behavior provided marginal costs remain in a given range. The reason for this stems purely from the assumption that rivals will match price cuts but not price increases. Firms in a Sweezy oligop- oly do not want to change their prices because of the effect of price changes on the behavior of other firms in the market.

The Sweezy model has been criticized because it offers no explanation of how the industry settles on the initial price P0 that generates the kink in each firm’s demand curve. Nonetheless, the Sweezy model does show us that strategic interactions among firms and a manager’s beliefs about rivals’ reactions can have a profound impact on pricing decisions. In practice, the initial price and a manager’s beliefs may be based on a manager’s experience with the pricing patterns of rivals in a given market. If your experience suggests that rivals will match price reductions but will not match price increases, the Sweezy model is probably the best tool to use in formulating your pricing decisions.

Cournot Oligopoly Imagine that a few large oil producers must decide how much oil to pump out of the ground. The total amount of oil produced will certainly affect the market price of oil, but the underly- ing decision of each firm is not a pricing decision but rather the quantity of oil to produce. If each firm must determine its output level at the same time other firms determine their output levels, or, more generally, if each firm expects its own output decision to have no impact on rivals’ output decisions, then this scenario describes a Cournot oligopoly.

More formally, an industry is a Cournot oligopoly if

1. There are few firms in the market serving many consumers. 2. The firms produce either differentiated or homogeneous products.

Cournot oligopoly An industry in which (1) there are few firms serving many consumers; (2) firms produce either differentiated or homogeneous products; (3) each firm believes rivals will hold their output constant if it changes its output; and (4) barriers to entry exist.

Figure 9–2 Sweezy Oligopoly

P

Q

P0

Q0

MC0

D 1MR

0 MR 1

D 2

A MC1

B

MR2

C

E

F

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3. Each firm believes rivals will hold their output constant if it changes its output. 4. Barriers to entry exist.

Thus, in contrast to the Sweezy model of oligopoly, the Cournot model is relevant for decision making when managers make output decisions and believe that their decisions do not affect the output decisions of rival firms. Furthermore, the Cournot model applies to situa- tions in which the products are either identical or differentiated.

Reaction Functions and Equilibrium To highlight the implications of Cournot oligopoly, suppose there are only two firms compet- ing in a Cournot duopoly: Each firm must make an output decision, and each firm believes that its rival will hold output constant as it changes its own output. To determine its optimal output level, firm 1 will equate marginal revenue with marginal cost. Notice that since this is a duopoly, firm 1’s marginal revenue is affected by firm 2’s output level. In particular, the greater the output of firm 2, the lower the market price and thus the lower is firm 1’s marginal revenue. This means that the profit-maximizing level of output for firm 1 depends on firm 2’s output level: A greater output by firm 2 leads to a lower profit-maximizing output for firm 1. This relationship between firm 1’s profit-maximizing output and firm 2’s output is called a best-response or reaction function.

A best-response function (also called a reaction function) defines the profit-maximizing level of output for a firm for given output levels of the other firm. More formally, the profit- maximizing level of output for firm 1 given that firm 2 produces Q2 units of output is

Q 1 = r 1 ( Q 2 )

Similarly, the profit-maximizing level of output for firm 2 given that firm 1 produces Q1 units of output is given by

Q 2 = r 2 ( Q 1 )

Cournot reaction (best-response) functions for a duopoly are illustrated in Figure 9–3, where firm 1’s output is measured on the horizontal axis and firm 2’s output is measured on the vertical axis.

best-response (or reaction) function A function that defines the profit-maximizing level of output for a firm for given output levels of another firm.

Figure 9–3 Cournot Reaction Functions

Q2

Q1

Q2*

Q1*0 Q M 1

Q M2

(Reaction function of firm 1)r1

r2 (Reaction function of firm 2)

E

D C

B A

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To understand why reaction functions are shaped as they are, let us highlight a few important points in the diagram. First, if firm 2 produced zero units of output, the profit- maximizing level of output for firm 1 would be Q 1

M  since this is the point on firm 1’s reaction function (r1) that corresponds to zero units of Q2. This combination of outputs corresponds to the situation where only firm 1 is producing a positive level of output; thus, Q 1

M corresponds to the situation where firm 1 is a monopolist. If instead of producing zero units of output firm 2 produced Q 2

* units, the profit-maximizing level of output for firm 1 would be Q 1 *  since this

is the point on r1 that corresponds to an output of Q 2 * by firm 2.

The reason the profit-maximizing level of output for firm 1 decreases as firm 2’s output increases is as follows: The demand for firm 1’s product depends on the output produced by other firms in the market. When firm 2 increases its level of output, the demand and marginal revenue for firm 1 decline. The profit-maximizing response by firm 1 is to reduce its level of output.

DEMONSTRATION PROBLEM 9–3

In Figure 9–3, what is the profit-maximizing level of output for firm 2 when firm 1 produces zero units of output? What is it when firm 1 produces Q 1

* units?

ANSWER: If firm 1 produces zero units of output, the profit-maximizing level of output for firm 2 will be Q 2

M  since this is the point on firm 2’s reaction function that corresponds to zero units of Q1. The out- put of Q 2

M corresponds to the situation where firm 2 is a monopolist. If firm 1 produces Q 1 * units, the

profit-maximizing level of output for firm 2 will be Q 2 * , since this is the point on r2 that corresponds

to an output of Q 1 * by firm 1.

To examine equilibrium in a Cournot duopoly, suppose firm 1 produces Q 1 M units of out-

put. Given this output, the profit-maximizing level of output for firm 2 will correspond to point A on r2 in Figure 9–3. Given this positive level of output by firm 2, the profit-maximizing level of output for firm 1 will no longer be Q 1

M , but will correspond to point B on r1. Given this reduced level of output by firm 1, point C will be the point on firm 2’s reaction function that maximizes profits. Given this new output by firm 2, firm 1 will again reduce output to point D on its reaction function.

How long will these changes in output continue? Until point E in Figure 9–3 is reached. At point E, firm 1 produces Q 1

* and firm 2 produces Q 2 * units. Neither firm has an incentive to

change its output given that it believes the other firm will hold its output constant at that level. Point E thus corresponds to the Cournot equilibrium. Cournot equilibrium is the situation where neither firm has an incentive to change its output given the output of the other firm. Graphically, this condition corresponds to the intersection of the reaction curves.

Thus far, our analysis of Cournot oligopoly has been graphical rather than algebraic. However, given estimates of the demand and costs within a Cournot oligopoly, we can explic- itly solve for the Cournot equilibrium. How do we do this? To maximize profits, a manager in a Cournot oligopoly produces where marginal revenue equals marginal cost. The calculation of marginal cost is straightforward; it is done just as in the other market structures we have analyzed. The calculation of marginal revenues is a little more subtle. Consider the following formula:

Formula: Marginal Revenue for Cournot Duopoly. If the (inverse) market demand in a homogeneous-product Cournot duopoly is

P = a − b ( Q 1 + Q 2 )

Cournot equilibrium A situation in which neither firm has an incentive to change its output given the other firm’s output.

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where a and b are positive constants, then the marginal revenues of firms 1 and 2 are

M R 1 ( Q 1 , Q 2 ) = a − b Q 2 − 2b Q 1 M R 2 ( Q 1 , Q 2 ) = a − b Q 1 − 2b Q 2

A C A L C U L U S A L T E R N A T I V E Firm 1’s revenues are

R 1 = P Q 1 = [ a − b ( Q 1 + Q 2 ) ] Q 1 Thus,

M R 1 ( Q 1 , Q 2 ) = ∂ R 1 ____ ∂ Q 1

= a − b Q 2 − 2b Q 1

A similar analysis yields the marginal revenue for firm 2.

Notice that the marginal revenue for each Cournot oligopolist depends not only on the firm’s own output but also on the other firm’s output. In particular, when firm 2 increases its output, firm 1’s marginal revenue falls. This is because the increase in output by firm 2 lowers the market price, resulting in lower marginal revenue for firm 1.

Since each firm’s marginal revenue depends on its own output and that of the rival, the output where a firm’s marginal revenue equals marginal cost depends on the other firm’s output level. If we equate firm 1’s marginal revenue with its marginal cost and then solve for firm 1’s output as a function of firm 2’s output, we obtain an algebraic expression for firm 1’s reaction function. Similarly, by equating firm 2’s marginal revenue with marginal cost and performing some algebra, we obtain firm 2’s reaction function. The results of these computations are summarized as follows.

Formula: Reaction Functions for Cournot Duopoly. For the linear (inverse) demand function P = a − b ( Q 1 + Q 2 ) and cost functions,

C 1 ( Q 1 ) = c 1 Q 1 C 2 ( Q 2 ) = c 2 Q 2

the reaction functions are

Q 1 = r 1 ( Q 2 ) =

a − c 1 _____ 2b

− 1 __

2 Q 2

Q 2 = r 2 ( Q 1 ) =

a − c 2 _____ 2b

− 1 __

2 Q 1

To see how the preceding formulas are derived, note that firm 1 sets output such that M R 1 ( Q 1 , Q 2 ) = M C 1 For the linear (inverse) demand and cost functions, this means that a − b Q 2 − 2b Q 1 = c 1 Solving this equation for Q1 in terms of Q2 yields

Q 1 = r 1 ( Q 2 ) = a − c 1 _____

2b −

1 __

2 Q 2

The reaction function for firm 2 is computed similarly.

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DEMONSTRATION PROBLEM 9–4

Suppose the inverse demand function for two Cournot duopolists is given by

P = 10 − ( Q 1 + Q 2 )

and their costs are zero.

1. What is each firm’s marginal revenue? 2. What are the reaction functions for the two firms? 3. What are the Cournot equilibrium outputs? 4. What is the equilibrium price?

ANSWER:

1. Using the formula for marginal revenue under Cournot duopoly, we find that

M R 1 ( Q 1 , Q 2 ) = 10 − Q 2 − 2 Q 1

M R 2 ( Q 1 , Q 2 ) = 10 − Q 1 − 2 Q 2

2. Similarly, the reaction functions are

Q 1 = r 1 ( Q 2 ) = 10

___ 2 −

1 __

2 Q 2

= 5 − 1 __

2 Q 2

Q 2 = r 2 ( Q 1 ) = 10

___ 2 −

1 __

2 Q 1

= 5 − 1 __

2 Q 1

3. To find the Cournot equilibrium, we must solve the two reaction functions for the two unknowns:

Q 1 = 5 −

1 __

2 Q 2

Q 2 = 5 −

1 __

2 Q 1

Inserting Q2 into the first reaction function yields

Q 1 = 5 − 1 _

2 [ 5 −

1 _

2 Q 1 ]

Solving for Q1 yields

Q 1 = 10

___ 3

To find Q2, we plug Q1 = 10/3 into firm 2’s reaction function to get

Q 2 = 5 − 1 _

2 (

10 _

3 )

= 10

___ 3

For a video walkthrough of this problem, visit www.mhhe.com/baye9e

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4. Total industry output is

Q = Q 1 + Q 2 = 10

___ 3 +

10 ___

3 =

20 ___

3

The price in the market is determined by the (inverse) demand for this quantity:

P = 10 − ( Q 1 + Q 2 )

= 10 − 20

___ 3

= 10

___ 3

Regardless of whether Cournot oligopolists produce homogeneous or differentiated prod- ucts, industry output is lower than the socially efficient level. This inefficiency arises because the equilibrium price exceeds marginal cost. The amount by which price exceeds marginal cost depends on the number of firms in the industry as well as the degree of product differ- entiation. The equilibrium price declines toward marginal cost as the number of firms rises. When the number of firms is arbitrarily large, the equilibrium price in a homogeneous prod- uct Cournot market is arbitrarily close to marginal cost, and industry output approximates that under perfect competition (there is no deadweight loss).

Isoprofit Curves Now that you have a basic understanding of Cournot oligopoly, we will examine how to graph- ically determine the firm’s profits. Recall that the profits of a firm in an oligopoly depend not only on the output it chooses to produce but also on the output produced by other firms in the oligopoly. In a duopoly, for instance, increases in firm 2’s output will reduce the price of the output. This is due to the law of demand: As more output is sold in the market, the price consumers are willing and able to pay for the good declines. This will, of course, alter the profits of firm 1.

The basic tool used to summarize the profits of a firm in Cournot oligopoly is an isoprofit curve, which defines the combinations of outputs of all firms that yield a given firm the same level of profits.

Figure 9–4 presents the reaction function for firm 1 (r1), along with three isoprofit curves (labeled π0, π1, and π2). Four aspects of Figure 9–4 are important to understand:

1. Every point on a given isoprofit curve yields firm 1 the same level of profits. For instance, points F, A, and G all lie on the isoprofit curve labeled π0; thus, each of these points yields profits of exactly π0 for firm 1.

2. Isoprofit curves that lie closer to firm 1’s monopoly output Q 1 M are associated with

higher profits for that firm. For instance, isoprofit curve π2 implies higher profits than does π1, and π1 is associated with higher profits than π0. In other words, as we move down firm 1’s reaction function from point A to point C, firm 1’s profits increase.

3. The isoprofit curves for firm 1 reach their peak where they intersect firm 1’s reaction function. For instance, isoprofit curve π0 peaks at point A, where it intersects r1; π1 peaks at point B, where it intersects r1; and so on.

4. The isoprofit curves do not intersect one another.

isoprofit curve A function that defines the combinations of outputs produced by all firms that yield a given firm the same level of profits.

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With an understanding of these four aspects of isoprofit curves, we now provide fur- ther insights into managerial decisions in a Cournot oligopoly. Recall that one assumption of Cournot oligopoly is that each firm takes as given the output decisions of rival firms and simply chooses its output to maximize profits given other firms’ output. This is illustrated in Figure 9–5, where we assume firm 2’s output is given by Q 2

* . Since firm 1 believes firm 2 will produce this output regardless of what firm 1 does, it chooses its output level to maxi- mize profits when firm 2 produces Q 2

* . One possibility is for firm 1 to produce Q 1 A units of

output, which would correspond to point A on isoprofit curve π 1 A . However, this decision does

not maximize profits because by expanding output to Q 1 B , firm 1 moves to a higher isoprofit

curve ( π 1 B , which corresponds to point B). Notice that profits can be further increased if firm

1 expands output to Q 1 C , which is associated with isoprofit curve π 1

C .

Figure 9–4 Isoprofit Curves for Firm 1

Q2

Q1 Q M1

π0 < π1 < π2

Monopoly point for firm 1

0

Isoprofit curves for

firm 1

r1 (Firm 1’s reaction function)

π0

π2

π1

F A G

B

C

Figure 9–5 Firm 1’s Best Response to Firm 2’s Output

Q2

Q1

Q2*

r1 (Firm 1’s reaction function)

0 QA1 Q B 1 Q

C 1 Q

D 1 Q

M 1

Monopoly point for firm 1

Q2* is the output firm 1 thinks firm 2 will choose

A B C

D πA1

πB1 πC1

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It is not profitable for firm 1 to increase output beyond Q 1 C , given that firm 2 produces Q 2

* . To see this, suppose firm 1 expanded output to, say, Q 1

D . This would result in a combination of outputs that corresponds to point D, which lies on an isoprofit curve that yields lower profits. We conclude that the profit-maximizing output for firm 1 is Q 1

C whenever firm 2 produces Q 2

* units. This should not surprise you: This is exactly the output that corresponds to firm 1’s reaction function.

To maximize profits, firm 1 pushes its isoprofit curve as far down as possible (as close as possible to the monopoly point), until it is just tangential to the given output of firm 2. This tangency occurs at point C in Figure 9–5.

DEMONSTRATION PROBLEM 9–5

Graphically depict isoprofit curves for firm 2, and explain the relation between points on the isoprofit curves and firm 2’s reaction function.

ANSWER: Isoprofit curves for firm 2 are the mirror image of those for firm 1. Representative isoprofit curves are depicted in Figure 9–6. Points G, A, and F lie on the same isoprofit curve and thus yield the same level of profits for firm 2. These profits are π1, which are less than those of curves π2 and π3. As the isoprofit curves get closer to the monopoly point, the level of profits for firm 2 increases. The isoprofit curves begin to bend backward at the point where they intersect the reaction function.

Figure 9–6 Firm 2’s Reaction Function and Isoprofit Curves

Q2

Q1

Q M2

r2 (Firm 2’s reaction function)

0

C

π2

π3

Monopoly point for firm 2

B

π1

A

F

π3 > π2 > π1

G

We can use isoprofit curves to illustrate the profits of each firm in a Cournot equilibrium. Recall that Cournot equilibrium is determined by the intersection of the two firms’ reaction functions, such as point C in Figure 9–7. Firm 1’s isoprofit curve through point C is given by π 1

C , and firm 2’s isoprofit curve is given by π 2 C .

Changes in Marginal Costs In a Cournot oligopoly, the effect of a change in marginal cost is very different than in a Sweezy oligopoly. To see why, suppose the firms initially are in equilibrium at point E in

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Figure 9–8, where firm 1 produces Q 1 * units and firm 2 produces Q 2

* units. Now suppose firm 2’s marginal cost declines. At the given level of output, marginal revenue remains unchanged but marginal cost is reduced. This means that for firm 2, marginal revenue exceeds the lower marginal cost, and it is optimal to produce more output for any given level of Q1. Graphically, this shifts firm 2’s reaction function up from r2 to r 2

** , leading to a new Cournot equilibrium at point F. Thus, the reduction in firm 2’s marginal cost leads to an increase in firm 2’s output, from Q 2

* to Q 2 ** , and a decline in firm 1’s output from Q 1

* to Q 1 ** . Firm 2 enjoys a larger market

share due to its improved cost situation. The reason for the difference between the preceding analysis and the analysis of Sweezy

oligopoly is the difference in the way a firm perceives how other firms will respond to a change in its decisions. These differences lead to differences in the way a manager should optimally respond to a reduction in the firm’s marginal cost. If the manager believes other firms will follow price reductions but not price increases, the Sweezy model applies. In this instance, we learned that it may be optimal to continue to produce the same level of output even if marginal cost declines. If the manager believes other firms will maintain their existing

Figure 9–7 Cournot Equilibrium

Q2

Q1

QM2

r2

0

C

πC2

pC1Q C 2

QC1 Q M 1

r1

Figure 9–8 Effect of Decline in Firm 2’s Marginal Cost on Cournot Equilibrium

Q2

Q1

Q *2*

r1

0 Q*1* Q*1 Q M 1

Due to decline in firm 2’s marginal cost

E

r2 r *2*

Q*2

F

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output levels if the firm expands output, the Cournot model applies. In this case, it is optimal to expand output if marginal cost declines. The most important ingredient in making manage- rial decisions in markets characterized by interdependence is obtaining an accurate grasp of how other firms in the market will respond to the manager’s decisions.

Collusion Whenever a market is dominated by only a few firms, firms can benefit at the expense of consumers by “agreeing” to restrict output or, equivalently, to charge higher prices. Such an act by firms is known as collusion. In the next chapter, we will devote considerable attention to collusion; for now, it is useful to use the model of Cournot oligopoly to show why such an incentive exists.

In Figure 9–9, point C corresponds to a Cournot equilibrium; it is the intersection of the reaction functions of the two firms in the market. The equilibrium profits of firm 1 are given by isoprofit curve π 1

C and those of firm 2 by π 2 C . Notice that the shaded lens-shaped area in

Figure 9–9 contains output levels for the two firms that yield higher profits for both firms than they earn in a Cournot equilibrium. For example, at point D each firm produces less output and enjoys greater profits since each of the firms’ isoprofit curves at point D are closer to the respective monopoly point. In effect, if each firm agreed to restrict output, the firms could charge higher prices and earn higher profits. The reason is easy to see. Firm 1’s profits would be highest at point A, where it is a monopolist. Firm 2’s profits would be highest at point B, where it is a monopolist. If each firm “agreed” to produce an output that in total equaled the monopoly output, the firms would end up somewhere on the line connecting points A and B. In other words, any combination of outputs along line AB would maximize total industry profits.

The outputs on the line segment containing points E and F in Figure 9–9 thus maximize total industry profits, and since they are inside the lens-shaped area, they also yield both firms higher profits than would be earned if the firms produced at point C (the Cournot equi- librium). If the firms colluded by restricting output and splitting the monopoly profits, they would end up at a point like D, earning higher profits of π 1

collude and π 2 collude . At this point,

Figure 9–9 The Incentive to Collude in a Cournot Oligopoly

Q2

Q1

QM2

r1

0 QM1

r2

B