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The economics of sporTs
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The economics of sporTs
F i f t h E d i t i o n
Michael A. Leeds Temple University
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Peter von Allmen Skidmore College
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Library of Congress Cataloging-in-Publication Data Leeds, Michael (Michael A.) The economics of sports/Michael A. Leeds, Peter von Allmen.— 5th ed. p. cm. ISBN-13: 978-0-13-302292-6 ISBN-10: 0-13-302292-7 1. Sports—Economic aspects. I. Allmen, Peter von. II. Title. GV716.L44 2013 338.4’3796—dc23
2012032292
ISBN-10: 0-13-302292-7 ISBN-13: 978-0-13-302292-6
10 9 8 7 6 5 4 3 2 1
For Daniel, Melanie, Dan, Tom, and Eric, who make everyday a treasure.
BRIEF CONTENTS
Preface xvii
Part 1 Introduction and review of Economic Concepts 1
Chapter 1 Economics and Sports 3
Chapter 2 Review of the Economist’s Arsenal 13
Part 2 the Industrial Organization of Sports 61 Chapter 3 Sports Franchises as Profit-Maximizing Firms 63
Chapter 4 Monopoly and Antitrust 111
Chapter 5 Competitive Balance 151
Part 3 Public Finance and Sports 181 Chapter 6 The Public Finance of Sports: Who Benefits
and How? 183
Chapter 7 The Public Finance of Sports: Who Pays and Why? 219
Part 4 the Labor Economics of Sports 249 Chapter 8 An Introduction to Labor Markets in Professional
Sports 251
Chapter 9 Labor Market Imperfections 289
Chapter 10 Discrimination 323
Part 5 Sports in the Not-for-Profit Sector 357 Chapter 11 The Economics of Amateurism and College
Sports 359
Works Cited 399
Photo Credits 423
Index 425
viii
CONTENTS
Preface xvii
Part 1 Introduction and review of Economic Concepts 1
Chapter 1 ECONOmICS aNd SPOrtS 3 Introduction 3
1.1 The Organization of the Text 4
Special Features and Additional Resources 5
1.2 Babe Ruth and Comparative Advantage 6
Opportunity Costs 6
Absolute and Comparative Advantage 7 ■ Biographical Sketch: Babe Didrikson Zaharias 9
Summary 11 • Discussion Questions 11 • Problems 12
Chapter 2 rEvIEw OF thE ECONOmISt’S arSENaL 13 Introduction 13
Learning Objectives 13
2.1 The Supply and Demand Model 14
Demand, Supply, and Equilibrium 14
Changes in Supply and Demand 17
2.2 Producing Output and the Production Function 27
A Note on the Definition of Output 27
The Production Function 27
Price Ceilings and the Economics of Scalping 30
2.3 Market Structures: From Perfect Competition to Monopoly 32
Perfect Competition 32
Monopoly and Other Imperfectly Competitive Market Structures 34
The Impact of an Increase in Costs 37
2.4 The Rise of Professional Sports 39 ■ Biographical Sketch: Silvio Berlusconi 41
Summary 43 • Discussion Questions 44 • Problems 44
ix
x Contents
Appendix 2a UtILIty FUNCtIONS, INdIFFErENCE CUrvES, aNd BUdgEt CONStraINtS 45 2A.1 Constrained Maximization 45
2A.2 Using Indifference Curves and Budget Constraints: The Rise of Soccer and Baseball 52
Appendix 2B rEgrESSION aNaLySIS IN BrIEF 54 Multiple Regression and Dummy Variables 59
Part 2 the Industrial Organization of Sports 61
Chapter 3 SPOrtS FraNChISES aS PrOFIt-maxImIzINg FIrmS 63 Introduction 63
Learning Objectives 64
3.1 Maximizing Profits or Maximizing Wins? 65
Maximizing Profit 66
Maximizing Wins 67
3.2 A Closer Look at Revenues, and Costs 68
A Detailed Look at Revenue 71
The Distributional Effects of Revenue Sharing 82
Cost 84
Opportunity Cost and Team Movement 85
3.3 Taxes, Profit, and Owner Behavior 86
Finding Profit in Losses 86
Operating Income, Taxes, and Profit 88
Vertical Integration 88
3.4 The Importance of Leagues 90
The Origin of Leagues in American Sports 91
Setting the Rules 92
Limiting Entry 94
Limited Entry as Cooperative Behavior 98
Advertising 98 ■ SportS and the law: The Limits of Leagues 101
3.5 Soccer’s Alternative Business Model 102
Profit-Maximization in Soccer 103
The Impact of Promotion and Relegation 104
The Financial Dangers of an Open System 106
The Single-Entity Ownership Model 106
Contents xi
■ Biographical Sketch: Bill Veeck 107 Summary 108 • Discussion Questions 109 • Problems 109
Chapter 4 mONOPOLy aNd aNtItrUSt 111 Introduction 111
Learning Objectives 112
4.1 What’s Wrong with Monopoly? 112
Monopolists and Deadweight Loss 112
Do Monopolies Always Charge Monopoly Prices? 115
Promotion, Relegation, and Monopoly Power 116
4.2 Strategic Pricing and Price Discrimination 117
Variable and Dynamic Ticket Pricing 117
Bundling 120
Price Discrimination and Two-part Pricing 121
Monopoly Stood on Its Head: A Brief Introduction to Monopsony 124
4.3 What’s Right with Monopoly? 125
4.4 Barriers to Entry that Leagues Create 127 ■ SportS and the law: Franchise Location 128
4.5 Society’s Response to Monopoly and Monopsony: Antitrust Laws 129
An Important Anomaly: Baseball’s Antitrust Exemption 130
Leagues That Lack an Antitrust Exemption 134
Limited Exemptions: The NFL and Television 135
4.6 The NCAA: An Incidental Cartel 136
4.7 Prisoner’s Dilemma: How Rational Actions Lead to Irrational Outcomes 139
■ Biographical Sketch: Alvin “Pete” Rozelle 142 Summary 144 • Discussion Questions 145 • Problems 145
Appendix 4a OvErvIEw OF BaSIC gamE thEOry 146 An Alternative Application of Game Theory 147
Chapter 5 COmPEtItIvE BaLaNCE 151 Introduction 151
Learning Objectives 152
5.1 Why Fans and Owners Want Competitive Balance 152
The Fans’ Perspective 152
xii Contents
The Owners’ Perspective 153
The Effect of Market Size 154
The Influence of Diminishing Returns 156
A Brief History of Competitive Balance 157
5.2 Measuring Competitive Balance 158
Within-Season Variation 158
Between-Season Variation 162
Illustrating Competitive Imbalance 164
5.3 Attempts to Alter Competitive Balance 167
The Invariance Principle 167
Revenue Sharing 169
Salary Caps and Luxury Taxes 171
The Reverse-Order Entry Draft 173
Schedule Adjustments in the NFL 176
Promotion and Relegation 176 ■ Biographical Sketch: Bud Selig 177
Summary 178 • Discussion Questions 179 • Problems 179
Part 3 Public Finance and Sports 181
Chapter 6 thE PUBLIC FINaNCE OF SPOrtS: whO BENEFItS aNd hOw? 183 Introduction 183
Learning Objectives 184
6.1 How Teams Benefit from New Facilities 184
Facilities, Attendance, and Profits 185
6.2 How Fans Benefit from a New Facility 187
The Size and Shape of Baseball and Football Stadiums 188
The Size and Shape of Basketball and Hockey Arenas 194
Do New Facilities Create Better Teams? 196
Teams as Public Goods 197
6.3 How Cities Benefit from Teams, Facilities, and Events 199
Positive and Negative Externalities 200
Facilities, Spending, and Tax Revenue 203
Location, Location, Location 211
The Impact of Special Events 212
Contents xiii
■ Biographical Sketch: Al Davis 215 Summary 217 • Discussion Questions 217 • Problems 217
Chapter 7 thE PUBLIC FINaNCE OF SPOrtS: whO PayS aNd why? 219 Introduction 220
Learning Objectives 220
7.1 How Cities Came to Fund Stadiums 220
Teams on the Move 221
The Three Eras of Stadium Construction 222 ■ SportS and the law: Who Can Move? 223
7.2 How Teams Exploit Monopoly Power 224
Leagues, Cities, and Market Power 225
The Winner’s Curse 229
7.3 Stadium Location and Costs 230
How Exchange Rates Affect Costs 231
Why Most Stadiums Are Not in the Center of Town 232
7.4 Stadium Costs and Financing 234
7.5 Paying for Stadiums 237
Who Pays a Sales Tax? 240
Incremental Financing 242
Taxes That Spread the Burden 243
The Benefits of Debt 243 ■ Biographical Sketch: Williard “Mitt” Romney 246
Summary 247 • Discussion Questions 248 • Problems 248
Part 4 the Labor Economics of Sports 249
Chapter 8 aN INtrOdUCtION tO LaBOr markEtS IN PrOFESSIONaL SPOrtS 251 Introduction 251
Learning Objectives 253
8.1 An Overview of Labor Supply and Labor Demand 253
Labor Supply 254
Labor Demand 256
Labor Market Equilibrium 261
8.2 The Economics of Tournaments and Superstars 265
xiv Contents
8.3 Tournaments, Cheating, and the Distribution of Income 269
More Potential Pitfalls of High Rewards: The Case of NASCAR 270
Too Much of a Good Thing 272
Performance-Enhancing Drugs 273
The Distribution of Income 277 ■ Biographical Sketch: Scott Boras 278
Summary 280 • Discussion Questions 280 • Problems 281
Appendix 8a thE LaBOr–LEISUrE ChOICE mOdEL OF INdIFFErENCE CUrvES 282
The Labor–Leisure Model When Hours Are Fixed 286
Chapter 9 LaBOr markEt ImPErFECtIONS 289 Introduction 289
Learning Objectives 290
9.1 The Monopsony Power of Sports Leagues 290
The Economics of Monopsony 290
The Reserve Clause 292
9.2 Unions in Professional Sports 293
A Brief Introduction to the Economics of Unions 294
■ SportS and the law: McNeil v. The National Football League 299
Salary Arbitration 302
Measuring Monopsony Power 303
Salary Caps 304
Luxury or Competitive Balance Taxes 308
The Impact of Rival Leagues 309
9.3 Labor Conflict and Compromise in Collective Bargaining 311
Comparing the 2011 NBA and NFL Negotiations 315
Professional Tennis Associations 318 ■ Biographical Sketch: Marvin Miller 320
Summary 321 • Discussion Questions 322 • Problems 322
Contents xv
Chapter 10 dISCrImINatION 323 Introduction 323
Learning Objectives 324
10.1 Becker’s Theory of Labor Discrimination 326
10.2 Different Forms of Discrimination in Professional Sports 327
Employer Discrimination 327
Does Anyone Win with Employer Discrimination? 332
Employee Discrimination 337
Consumer Discrimination 340
Discrimination by National Origin in European Soccer 342
Positional Discrimination or Hiring Discrimination 344
Gender Equity—A Special Case? 348
10.3 Title IX and Discrimination in College Sports 349 ■ Biographical Sketch: Branch Rickey 352
Summary 354 • Discussion Questions 354 • Problems 355
Part 5 Sports in the Not-for-Profit Sector 357
Chapter 11 thE ECONOmICS OF amatEUrISm aNd COLLEgE SPOrtS 359 Introduction 359
Learning Objectives 360
11.1 The Troublesome Concept of Amateurism 360
A Brief History of Amateurism and the Olympic Ideal 360
11.2 The Costs and Benefits of College Athletics 366
The Revenue from Intercollegiate Athletics 366
The Revenue from Bowl Games 369
The Cost of Intercollegiate Athletics 373
Do Colleges Profit from Athletics? 375
Spillovers from Athletics to the University 376
11.3 The Role of the NCAA 380
The NCAA as a Regulatory Agency 380
The NCAA as a Club 382
xvi Contents
The NCAA as a Cartel 383
Academic Standards: A Basis of Academic Integrity or Monopoly Power? 387
11.4 The Returns to the Athlete 389
Pay for Play: The Grant-in-Aid 389
Measuring the Net Value of Athletes to Colleges 391
College as an Investment for the Student-Athlete 391 ■ Biographical Sketch: Anita Defrantz 396
Summary 397 • Discussion Questions 398 • Problems 398
Works Cited 399
Photo Credits 423
Index 425
PREFACE
As The Economics of Sports reaches its fifth edition, it is interesting for us to reflect back on the almost fifteen years since we began work on the first edition. When the first edition was published, the field was relatively new but rapidly growing. Undergraduate sports economics courses were popular, but not widely offered. Today, sports economics stands as a vital subdiscipline within applied micro- economics, with new and exciting research being produced by economists from around the world. Along with the increased research, the number of sports eco- nomics courses has grown as well. Throughout this process of growth and change, sports economics continues to serve as both a mirror and a lens, reflecting our broader culture and values, while at the same time bringing into focus such fun- damental issues as fairness and the legitimacy of free markets. With the passing of each season, new events unfold in professional and amateur sports that deserve analysis and explanation. Finally, in the context of this book, sports economics remains a vital and interesting area of study for students of economics. Sports provides a seemingly endless set of examples from every area of microeconomics, giving students the opportunity to study public finance, industrial organization, and labor markets in a context that holds student interest like no other industry.
Over the many years that we have worked on this project, we have enjoyed continuous help and support from students and colleagues at colleges and univer- sities across the United States and around the world. Our colleagues continue to offer encouragement, share classroom experiences, and suggest new and different coverage as the industry evolves. For all of this support and help, we are most grateful. And as we have said many times, we hope that our own enthusiasm, as well as the enthusiasm others have shared with us, is reflected in the text.
In recent years, many outstanding books that concentrate on specific sports or particular aspects of the economics of sports have been published. This text stands apart from the others in that it has the instruction of economic concepts as its central focus. We hope you find it useful and interesting.
new to thiS edition
The fifth edition represents our most comprehensive revision and update of the text since the first edition appeared in 2001. In doing so, we have retained the fea- tures from previous editions that made learning about sports economics meaning- ful as well as enjoyable, while at the same time incorporating many recent events in the sports industry and the broader economy.
• We have introduced a new feature for the fifth edition: Sports and the Law. Though we discuss the important decisions that have shaped the sports industry throughout the text, we’ve chosen four specific cases that particu- larly highlight the profound impact of the law in this industry. You will find these features in Chapters 3, 4, 7, and 9.
xvii
xviii Preface
• Chapter 2 now contains a full review of production theory in the context of team rosters as well as a review of the relationship between marginal prod- uct and marginal cost.
• Chapter 3 has been rearranged to highlight the differences between profit- maximization and win maximization as owner strategies. It also places greater emphasis on the role of the theory of clubs as an explanation for the recent turmoil in intercollegiate athletic conferences.
• We have supplemented our presentation of advanced profit-maximizing strategies with a discussion of dynamic ticket pricing, including a compari- son to variable ticket pricing and ticket bundling.
• The most significant change for this edition is the reorganization of Chapters 6 and 7. Chapter 6 now covers the benefits of public support for stadiums and events such as the Olympics to owners, fans, and cities. Chapter 7 covers the economics of financing these facilities and events. While much of the discus- sion that users liked from previous editions has been retained, the new orga- nization should lead to improved student understanding.
• Chapter 9 has been revised to provide a comprehensive explanation of the process and outcomes of the new collective bargaining agreements in the NBA and NFL.
• We have integrated Chapter 11 more fully into the rest of the book by emphasizing such concepts as profit-maximization and spillovers that appear elsewhere. This allows us to show more clearly how athletic depart- ments resemble—and do not resemble—professional sports teams.
As with the previous editions, our goal for the fifth edition is to keep the text comprehensive yet accessible. The text is designed to serve as the foundation for undergraduate courses in sports economics. The nature of the subject matter makes this a unique challenge. Unlike area courses such as industrial organiza- tion or labor economics, which are self-contained fields in the broader area of economics, sports economics cuts across a wide array of economic disciplines. To deal with this problem, we have split the text into five parts, three of which are devoted to illustrating prominent areas of economics: industrial organiza- tion, public finance, and labor economics. We hope that this division provides students with an overview of much of economics and inspires them to pursue each field in its own right. Because we focus largely on professional sports in the first four parts of the book, we include a closing section devoted to amateur sports. This final part provides insights into theories related to the not-for-profit sector of the economy, such as the theory of bureaucracy. Each of the five parts of this text presents significant economic theory and recent evidence and research for that area of economics.
To make the text accessible, we assume that students have had one semester of microeconomics principles. Balancing accessibility against an economist’s desire for theoretical rigor remains a challenge. In order to help the students understand the economics and to make the treatment more entertaining, we have included a generous component of sports history to place the events and economic theory in perspective.
Preface xix
intended audience
Economics of sports classes are taught at a variety of levels, ranging from undergrad- uate courses, with principles of economics as the only prerequisites, to the graduate level. This text is designed to offer a high level of flexibility to the instructor. All the material in the main body of the text should be accessible to students with a single semester of microeconomics principles. In order to enrich courses taught at a higher level, we have included appendices containing intermediate-level material at the end of several chapters. To ensure that all students begin the course with a common back- ground, we provide a substantial review of principles-level material in Chapter 2. This material can either be covered explicitly with lecture support or left to the students to read on their own, as needed. For instructors interested in presenting the results of econometric research, Chapter 2 contains an appendix on the fundamen- tals of regression. In advanced undergraduate- and graduate-level courses, the text can serve as a foundation for common understanding of basic concepts.
organization of the text and coverage optionS
As stated previously, the text is divided into five parts. The first two chapters pro- vide an introduction to sports economics, a review of principles-level tools, and an illustration of how economic principles apply to the sports industry. Chapters 3, 4, and 5 focus on the industrial organization of the sports industry. Here, we discuss the competitive landscape, the implications of monopoly power, profit- maximization, and competitive balance. Chapter 4 focuses specifically on issues of antitrust and regulation and discusses how they have impacted the formation, success, and, sometimes, the failure of leagues. Chapter 5 describes why leagues are concerned about competitive balance, how competitive balance is measured, and how leagues might attempt to alter the balance of competition in a league. Chapters 6 and 7 focus on public finance. In this portion of the text, students learn the benefits and costs of providing public support for stadiums and events, why teams seem to have so much power over municipalities and why municipalities fight so hard to keep the teams they have as well as court new ones. Chapters 8 through 10 focus on labor issues related to sports. Chapter 8 introduces the fundamental theories of labor markets, including human capital theory and tour- nament theory. Chapter 9 covers monopoly unions and monopsony, two labor market imperfections that profoundly impact the functioning of most sports labor markets. Chapter 10 discusses discrimination. Finally, Chapter 11 focuses on the economics of amateur sports, especially major collegiate sports. Because major college sports is really an industry itself, this chapter serves as a capstone to the text, incorporating the theories and concepts from many of the previous chapters.
additional reSourceS
The text is accompanied by an online Instructor’s Manual, updated for the fifth edition by George Diemer of Chestnut Hill College. We are pleased to provide PowerPoint slides, written by Eva Marikova Leeds of Moravian College that
xx Preface
contain all figures and tables in the text as well as lecture notes for classroom presentation. We are also pleased to offer a Test Bank for the fifth edition of the text, written by, David Chaplin of Northwest Nazarene University which contains additional questions and suggested answers for further classroom or test use. The Instructor’s Manual, PowerPoint slides, and Test Bank may be accessed via the Instructor’s Resource Center at www.pearsonhighered.com/irc.
Students and instructors may also access the text’s companion Web site at www.pearsonhighered.com/leeds. Updated for the fifth edition, the Web site fea- tures chapter quizzes, current Web links, and additional sports data.
acknowledgmentS
In a project such as this, the list of people who contributed to its completion extends far beyond those whose names appear on the cover. We owe personal and profes- sional debts of sincere gratitude to a great many people. First, we thank our team at Pearson including Noel Seibert, Emily Brodeur, Maggie Brobeck, and Carolyn Terbush. We also are grateful for the advice, encouragement, and suggestions from the ever-growing community of sports economists who use this book. Their input and support serve as a continuing source of motivation and assistance. We would particularly like to thank all of those who read and reviewed the manuscript as we prepared the fifth edition, including Andrew Zimbalist, Smith College; Bruce K. Johnson, Centre College; Mary N. Gade, Oklahoma State University; Nancy Jianakoplos, Colorado State University; Phil Miller, Minnesota State University– Mankato; Joshua Price, University of Texas–Arlington; and Wayne A. Grove, Le Moyne College. Their suggestions for improvements were excellent, and we tried our best to incorporate them wherever possible. A special thanks to Eva Marikova Leeds for her diligent review of the manuscript during the revision process. Finally, as always, we thank our families: Eva, Daniel, Melanie, Heather, Daniel, Thomas, and Eric, all of whom provided unwavering support.
Michael A. Leeds Peter von Allmen
www.pearsonhighered.com/irc
www.pearsonhighered.com/leeds
The economics of sporTs
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P a r t O n e
Introduction and Review of Economic
Concepts
Chapter 1 Economics and Sports Chapter 2 Review of the Economist’s Arsenal
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3
C h a p t e r 1
Economics and Sports
All I remember about my wedding day in 1967 is that the Cubs dropped a double-header.
—George Will1
1George F. Will, Bunts (New York: Scribner, 1998), p. 22. 2“El Clasico TV ratings break record,” December 13, 2011, at http://www.insidespanishfootball.com/el-clasico-tv-ratings- break-record/, viewed March 6, 2012.
IntroductIon
On December 10, 2011, in a game watched by over 60 percent of Spanish television viewers and millions more around the world, the two most successful teams in the top Spanish soccer league, La Liga, faced off in a game that has come to symbolize much more than a soccer contest.2 Real Madrid, long allied with Spanish conservatism, jumped to an early 1–0 lead, only to lose 3–1 to its archrival, FC Barcelona. “Barça” is so much a symbol of Catalan pride that the team motto is “More than a club.” As always, the win touched off an enormous celebration in the winning city. Just a few months later, more than a million New York Giants fans filled the streets of Manhattan for the ulti- mate celebration—a ticker tape parade—following the Giants Super Bowl victory, while at the same time the city of Boston was awash in the excitement brought on by the annual “Beanpot” hockey tournament between Northeastern, Harvard, Boston College, and Boston University.
Sports occupy a unique position in the human psyche. Athletic contests around the world have long been a way for individuals, institutions, cities, and nations to define themselves. Sports can bring out the best and the worst in people. As early as the 19th century, universities used football to give their students a sense of identity. Cities feel that they have achieved “big-time” status once
http://www.insidespanishfootball.com/el-clasico-tv-ratings-break-record/
http://www.insidespanishfootball.com/el-clasico-tv-ratings-break-record/
4 Part 1 • Introduction and Review of Economic Concepts
they have attracted a major league franchise. At the national level, Japan’s perfor- mance in the 2011 Women’s World Cup provided a much-needed lift to a country devastated by the earthquake and tsunami and shaken by a near nuclear disaster. At the same time, police have had to quell riots on campuses in the wake of heart- breaking losses—or big victories. Reports of domestic violence rise in cities when “their” team is upset in the Super Bowl. In their pursuit of national pride, coun- tries have sometimes sacrificed the physical well-being of their young athletes by giving them performance-enhancing drugs that have had dire side-effects.3
Sports can also serve as tools by which nations conduct foreign policy. They have brought people together, as was the case in 1971 when a team of American table tennis players and their “ping-pong diplomacy” marked the first step in the reopening of relations between the United States and China. They have also kept people apart, as demonstrated by the boycotts that disrupted the 1976, 1980, and 1984 Olympics.
The clamor over sports might lead one to think that the sports industry domi- nates the world economy. In fact, compared to many firms, let alone industries, it is a very small operation. According to Forbes Magazine, the total revenues gener- ated by the four major North American sports leagues (basketball, baseball, football, and hockey) totaled about $21 billion in 2010, which would not rank among the top 100 revenue-generating companies. The sports’ revenues are about one-twentieth of those of Walmart and roughly equal to the $21.6 billion generated by Northwestern Mutual, yet, unlike sports, Walmart does not have its own section in any newspaper, and the local insurance company does not merit a segment on the evening news.4
This book harnesses this enthusiasm for sports and uses it to introduce a variety of economic concepts. These concepts frequently have applications beyond the business of sports. For example, understanding how sports leagues exercise monopoly power provides deeper insight into the policies followed by the Organization of the Petroleum Exporting Countries (OPEC) or Google, and learning about the impact of free agency on team payrolls shows how free markets affect the distribution of incomes in an economy. Studying sports economics thus provides more than an appreciation for the sports industry. It also demonstrates how economic reasoning helps us understand the world around us.
1.1 the organIzatIon of the text
The text is divided into five parts. The remainder of this part provides an extensive review of basic economic theory, particularly supply and demand, the basics of production theory, and models of perfect competition and monopoly.
3See Katie Kindelain, “Kentucky Students Riot after NCAA Championship Win,” abcnews.com, April 3, 2012, at http://abcnews.go.com/blogs/headlines/2012/04/kentucky-students-riot-after-ncaa- championship-win; David Card and Gordon B. Dahl, “Family Violence and Football: The Effect of Unexpected Emotional Cues on Violent Behavior,” Quarterly Journal of Economics, vol. 126, no.1 (February 2011), pp. 103–143; Steven Ungerleider, Faust’s Gold: Inside the East German Doping Machine (New York: Thomas Dunne Books, 2001). 4“Fortune 500,” Fortune, May 12, 2012, at http://money.cnn.com/magazines/fortune/fortune500/ 2011/full_list/index.html, viewed March 8, 2012.
http://abcnews.go.com/blogs/headlines/2012/04/kentucky-students-riot-after-ncaa-championship-win;
http://abcnews.go.com/blogs/headlines/2012/04/kentucky-students-riot-after-ncaa-championship-win;
http://money.cnn.com/magazines/fortune/fortune500/2011/full_list/index.html
http://money.cnn.com/magazines/fortune/fortune500/2011/full_list/index.html
Chapter 1 • Economics and Sports 5
The tools introduced in Chapter 2 are used throughout the text to inform a wide variety of questions in the broader sports industry.
The next three parts of the text are devoted to showing how three particular areas of economics provide insight into how sports function. Part Two presents the industrial organization of sports. Industrial organization is the study of how firms maximize profit. In Chapter 3, we discuss the purpose and structure of a variety of professional leagues. We also review the competitive and monopoly market structures and discuss the implications for profit maximization in each case. In Chapter 4, we extend the discussion of monopoly and analyze the chal- lenges that concentrated markets create for consumers. In Chapter 5, we investi- gate the desirability of competitive balance, how it can be measured, how it has changed over time, and how leagues have dealt with unbalanced competition.
Part Three contains two chapters on the public finance of sports. Public finance asks how and why governments provide goods and services and how they raise the funds to pay for them. In Chapter 6, we discuss the potential benefits of new arenas for both teams and the cities in which they play and describe how the size and shape of facilities have evolved. In Chapter 7, we turn to the cost of these facilities, includ- ing an analysis of why local governments might pay some or all of these costs as a form of investment and, if the investment is made, how to best fund it.
Part Four covers the labor economics of professional sports. Labor economics analyzes how markets determine the level of employment and compensation. In Chapter 8, we use labor markets to explain why professional athletes receive such high salaries. In doing so, we introduce basic labor market concepts, such as human capital, and analyze the potential impact of teams and leagues as pow- erful employers on wages. Chapter 9 explores labor market institutions, such as player associations, which also affect salaries and working conditions of players. In Chapter 10, we discuss the history and implications of discrimination in profes- sional sports. From the informal yet strictly enforced “color lines” that marked the National Football League (NFL) and Major League Baseball (MLB) until 1946 and 1947, respectively, to the limits that such leagues as Nippon Professional Baseball still place on how many foreign players are permitted on team rosters, sports pro- vide many examples of discriminatory behavior.
Finally, in Part Five (Chapter 11), we broaden our study of sports to include amateur athletics at the Olympic and major college levels. We present the history of amateurism and the consequences that misperceptions about this history have had for the National Collegiate Athletic Association (NCAA). This chapter also examines the effects of recent changes in admissions and eligibility standards on schools and athletes.
Special features and additional resources
There are two types of feature boxes in the text. The first highlights specific legal decisions that have had a major impact on the structure of professional sports. Economics does not exist in a vacuum, and these cases are vitally important to understanding how certain groups have used or tried to use economic power to their advantage, sometimes in conflict with laws such as those that apply to dis- crimination, antitrust, and fair labor standards. The second contains biographical
6 Part 1 • Introduction and Review of Economic Concepts
sketches. The world of sports is filled with colorful personalities that add to our enjoyment of the game. Some of these people are well known to even the casual sports fan. Others are less known, but all have played an important role in the evo- lution of the economics of sports. These biographical sketches, the first of which appears in this chapter, highlight both their accomplishments in the context of the chapter and their character as individuals.
As you progress through the course, we encourage you to make full use of the Internet as a powerful and easy-to-use source of further reading. First and foremost, the publisher of this text, Addison Wesley, maintains a Web site specifi- cally designed to support the book. Log on to www.aw-bc.com/leeds_vonallmen and you will find a set of interesting links to other valuable sites as well as infor- mation that we provide directly to assist you. The site is updated regularly so that it contains links to sites and stories that are sure to be of interest.
In addition, virtually every major (and almost every minor) league team and individual sports league or association has its own Web site. These sites are continu- ally updated with information about news (including economic events) from around the league. Finally, many sports magazines maintain Web sites that have current and archived information that can be very useful for term papers, projects, and general information. One caution: Beware of unreliable information that is rampant on non- commercial, individual blogs and private Web sites. The information they convey is often based on opinion rather than on fact and is of little or no value.
Let the games begin!
1.2 BaBe ruth and comparatIve advantage
Economics can often help to resolve what at first glance seems to be puzzling behavior. We begin most chapters by posing a few puzzles that people have faced in the sports world. The material that we present in each chapter then helps us to solve the puzzles that we raise at the outset. This section provides a taste of what is to come. We use the theory of comparative advantage, a concept normally used by specialists in international trade, to explain why the Boston Red Sox stopped using the best left-handed pitcher in baseball in 1918.
opportunity costs
In 1915, a young left-hander for the Boston Red Sox emerged as one of the domi- nant pitchers in the game, helping the Red Sox to World Series championships in 1916 and 1918. In the 1918 World Series, he won two games and set a record for consecutive scoreless innings that stood until 1961. From 1915 through 1918, he won 78 games and lost only 40, and he allowed slightly over 2 runs per game. In 1919, he pitched in only 17 games and won only 16 more games in the rest of his career, yet no fans complained. The reason was that the young pitcher was none other than George Herman “Babe” Ruth, who went on to redefine baseball as a power-hitting rightfielder for the Red Sox and later for the New York Yankees.
Babe Ruth confronted the Red Sox with the classic economic problem of opportunity costs. An opportunity cost is the value of the best forgone alternative.
www.aw-bc.com/leeds_vonallmen
Chapter 1 • Economics and Sports 7
We all face opportunity costs in our everyday lives. Our limited time, income, and energy constantly force us to choose among alternative actions. When we go to the movies on Saturday night, we no longer have the time or the money to go to a concert that evening. When the Red Sox used Babe Ruth as a rightfielder, they gave up the chance to use him as a pitcher. (Because the main contribution of a rightfielder is as a hitter, we will use the term “hitter” rather than rightfielder from now on.) If the goal of a team is to win as many games as possible (an objective we will explore later in this text) then the opportunity cost of using a player at one position is the wins that the team sacrifices by not using him at another position. When the Red Sox used Babe Ruth as an outfielder, they sacrificed wins by not having a great pitcher in their rotation. If they had kept Ruth as a pitcher, they would have sacrificed wins by not having a great hitter in their lineup.
absolute and comparative advantage
It is usually easy to decide where to use a player, as only a few players make good pitchers, and pitchers are typically bad hitters. Babe Ruth, however, was an exception. He was the best pitcher and the best hitter on the team. Being the best at everything meant that Babe Ruth had an absolute advantage at both pitching and hitting. A person or country has an absolute advantage in an activity when it is more efficient at that activity than another person or country. For example, if the United States can make cancer drugs using fewer resources than Japan can, it has an absolute advantage in making cancer drugs. Because Babe Ruth was a better pitcher and hitter than any other player on the Red Sox, he had an absolute advantage over all his teammates in both pitching and hitting.
The Red Sox decided to use Babe Ruth as a hitter because, although he had an absolute advantage as both a hitter and a pitcher, his absolute advantage as a hitter was much larger than his absolute advantage as a pitcher. This meant that Babe Ruth had a comparative advantage as a hitter. A person or country has a comparative advantage when the opportunity cost of an activity is lower than it is for another person or country. Because Babe Ruth was such a good hitter, the opportunity cost of using him as a pitcher (the number of wins the team would sacrifice) was extremely high, much higher than for other players on the team. This meant that, even though Babe Ruth had an absolute advantage over his teammates as a pitcher, he did not have a comparative advantage as a pitcher.5
To see the gains from moving Babe Ruth from the pitcher’s mound to the outfield more clearly, we compare the opportunity cost of using Babe Ruth at each position in 1918. The opportunity cost of using Ruth as an outfielder was the additional runs given up by Red Sox pitchers, which would result in more losses. The opportunity cost of using Ruth as a pitcher was the reduction in runs scored by the Red Sox, which also might have led to more losses. Ruth’s switch
5For a more complete explanation of Babe Ruth’s comparative advantage during his career with the New York Yankees, see Edward Scahill, “Did Babe Ruth Have a Comparative Advantage as a Pitcher?” Journal of Economic Education, vol. 21, no. 4 (Fall 1990), pp. 402–410.
8 Part 1 • Introduction and Review of Economic Concepts
from pitcher to outfielder probably displaced Tilly Walker, arguably the worst of the Red Sox starting outfielders in 1917, and made room for Dutch Leonard, who had the highest earned run average (ERA) among the regular starting pitchers in 1918.6 Ruth’s last year as a full-time pitcher—1917—was an amazing one; he won 24 games, lost 13, and gave up about 2 runs per game. The first year that Ruth played mostly in the outfield was even more amazing. He led the league in slug- ging percentage (the average number of bases advanced per at bat), and his 11 home runs not only led the league but also were almost twice as many as the 6 hit by the entire Red Sox starting outfield in 1917.
Table 1.1 shows that replacing Ruth, who had a 2.01 ERA in 1917, with Leonard, who had a (still low) 2.72 ERA, meant that the Sox gave up 0.71 more runs per 9 innings than they would have if Ruth had had an identical year in 1918. Over the 14 games that Leonard pitched, that meant that the Red Sox’ opportu- nity cost of using Babe Ruth in the field was about 10 runs over the course of the 1918 season.7 Using the formula for runs produced (runs scored + runs batted in − home runs) shows that Ruth produced 29 more runs in 1918 than Walker had produced in 1917. Thus, the Red Sox came out 19 runs ahead from the switch.
At this point, one might ask why the Red Sox did not use Babe Ruth as a pitcher every four or five days and as a hitter every day in between. In baseball, the skills of pitching and hitting are so different that one cannot develop both at the same time. No player has ever managed to play every day and pitch every fourth or fifth day. Acquiring the skills needed to become an elite hitter or pitcher demands a great deal of intensive practice. This pre-commitment generally does not leave enough time or energy to develop alternative skills.
More generally, one of the most important conclusions of the theory of com- parative advantage is that developing particular skills and specializing in activi- ties that use these skills makes individuals, firms, and nations better off. Professors employ research assistants and working parents hire day care providers because
6The earned run average is the average number of runs a pitcher gives up per nine innings, the normal length of a ballgame.
taBle 1.1 The Gain and Loss from Moving Babe Ruth
Player Runs Sacrificed Runs Produced
Babe Ruth 2.01 per game 105 per season Dutch Leonard 2.72 per game — Tilly Walker — 76 per season Net change +9.94 per seasona +29 per season aUses 14 starts for the 1918 season. Source: Baseball Almanac, at http://www.baseball-almanc.com.
7The Boston Red Sox played only 126 games in 1918 because the season was terminated on September 1 due to the United States’ entry into World War I.
http://www.baseball-almanc.com
Chapter 1 • Economics and Sports 9
BioGRaPhicaL SkeTch
Babe Didrikson Zaharias (1911–1956)
I knew exactly what I wanted to be when I grew up. My goal was to be the greatest athlete that ever lived.
—Babe Didrikson Zaharias1
The theory of comparative advantage tells us that athletes are better off when they specialize. A quick look at athletes from the professional ranks to middle schools seems to bear this hy- pothesis out. “Two-way” football players have become a rarity, and athletes who play more than one sport have all but disap- peared. It is thus unlikely that the athletic world will ever see another Babe Didrikson Zaharias. Zaharias dominated the ath- letic world like no athlete before or since, achieving star status in the disparate worlds of basketball, track and field, and golf.
Mildred Ella Didriksen was born in 1911 to impoverished Norwegian immigrants in Port Arthur, Texas. The sixth of seven
children and the youngest girl, Mildred got the nickname “Babe” while a young girl and still the “baby” of the family, though she later attributed the nickname to comparisons with baseball hero Babe Ruth. Her last name was changed to “Didrikson” as a result of a spelling error in her school records.
As a youth, Zaharias was drawn to sports at a time when sexual stereotypes still discouraged women from participating in “manly” sports, but Zaharias’ working-class upbringing freed her from many of the restrictions that would have constrained her development as an athlete. She did not participate in organized sports, however, until she left high school in 1930 to play basketball for the Employers Casualty Insurance Company.
It may seem odd today for an athlete to advance her career by taking a job as a secretary for $75 a month with an insurance company, but at that time, many col- leges did not offer athletic programs for women, and the fledging National Collegiate Athletic Association (NCAA) was openly disdainful of women’s athletics. Employers
(Continued)
trying to do everything would take them away from the activities that they perform best. It is cheaper (more efficient) for them to pay other people to provide the goods or services than to try to do everything themselves.
At the national level, if the United States has a comparative advantage in the production of cancer drugs, it is better off specializing in cancer drugs and importing TVs even if it has an absolute advantage over Japan in both products. The opportunity cost of sacrificing cancer drugs in order to make TVs ourselves is higher than the cost of sending cancer drugs to Japan in exchange for TVs. Like Babe Ruth, we are better off specializing in what we are relatively best at and leav- ing the rest to others.
10 Part 1 • Introduction and Review of Economic Concepts
Casualty played in the 45-member Women’s National Basketball League, which played under the auspices of the Amateur Athletic Union (AAU). The AAU was then the domi- nant athletic body; it oversaw competitions by a few schools and by companies that sponsored teams.
The Employers Casualty “Golden Cyclones” were one of the best amateur teams in the nation. When the first All-American women’s basketball team was announced in 1929, eight of its members were from Employers Casualty. Zaharias quickly established herself as a star among stars, being named an All-American for three straight years.
As good as she was on the basketball court, Zaharias found her greatest success in track and field. It was here that she recorded the greatest single performance in the history of track and field and perhaps of any athletic competition. The 1932 National Track and Field Competition served as the trials for the 1932 Los Angeles Olympic Games. Zaharias was the sole representative of the Employers Casualty team. In one afternoon, she ensured that Employers Casualty won the team championship by winning the shot put, the baseball throw, the javelin throw, the 80-meter hurdles, and the broad jump. She also tied for first in the high jump and finished fourth in the discus, an event in which she normally did not compete. In all, she won six gold medals and broke four world records in about three hours. Zaharias hardly skipped a beat in the Olympics, setting world records in the javelin throw and the 80-meter hurdles. She also tied for first in the high jump, though her then-unorthodox style (the so-called Western Roll that soon became the dominant style) caused a controversy among some of the judges, who thought it illegal. As a compromise, she was declared the second-place finisher and given the only half-gold-half-silver medal in the history of the modern Olympics.
As the dominant performer and personality of the 1932 “Hollywood Games,” Zaharias quickly became a national celebrity. Her publicity, however, came at a con- siderable cost. The public did not know what to make of a woman who defied sexual stereotypes of the time. Zaharias seemed destined to fade from public view when the AAU stripped her of her amateur status for appearing in an automobile advertise- ment (even though, apparently, she had not given permission for the firm to use her likeness). After a year or so of stunts and exhibition tours, she returned to work for Employers Casualty.
Over the next several years, Zaharias reconstructed her personal and athletic lives. Stung by her treatment in the press, she strove to develop a more feminine image, playing up her role as a wife following her marriage to professional wrestler (and later sports promoter) George Zaharias in 1938, but she was anything but a typical housewife. Having picked up golf as a teenager, Zaharias threw herself into her new, more socially acceptable sport. In 1935, she won the Texas State Women’s Golf Championship and was ready to enter full-time competition when the United States Golf Association banned her from amateur competition because of her appearance in the automobile advertisement. She responded by turning pro, but she quickly realized that professional golf provided neither adequate competition nor adequate remuneration. She succeeded in having her amateur status reinstated in 1943. Though she would have to wait until the end of World War II to enter the next stage of her athletic career, it was worth the wait.
Zaharias burst onto the women’s golf tour in 1945, winning the Texas Women’s Open and the Western Open, and being named “Woman Athlete of the Year” by the Associated Press (an award she had won 13 years earlier for her Olympic exploits). This proved merely a warm-up for 1946, when she won 14 straight tournaments. In 1947,
(Continued)
Chapter 1 • Economics and Sports 11
Summary
Sports occupy a unique place in the public psyche. Although sports generate less revenue than many other industries, sports results are predicted, reported, and analyzed in newspapers, magazines, books, and TV and radio programs. This text presents economic models from industrial organization, public finance, and labor economics to provide insight into the economics of sports. One of the most important economic models is that of comparative advantage. Despite having an absolute advantage as both a pitcher and an outfielder, Babe Ruth specialized in playing the outfield because that was where he had a comparative advantage. He had a comparative advantage in playing every day as an outfielder because the opportunity cost of his playing outfield—the additional runs that other teams would score against a lesser Red Sox pitcher—was less than the opportunity cost of his playing every four to five days as a pitcher—the lower number of runs the Red Sox would score from playing a lesser outfielder. Following the law of com- parative advantage made Babe Ruth and the Red Sox better off.
Discussion Questions 1. Why do sports generate so much more news coverage than other industries that are
much larger in financial terms? 2. The theory of comparative advantage predicts that athletes perform better when they
specialize. Studies show that young athletes are increasingly focusing on a single sport. Do you think this is a good idea?
Zaharias became the first American woman to win the British Women’s Amateur golf championship in the 55-year history of the event.
After her victory in the British Amateur event, Zaharias again turned pro and a year later became a charter member of the newly formed Ladies Professional Golf Association (LPGA—it chose the term “Ladies” to avoid conflict with the unsuccess- ful Women’s PGA). Her talents led her to be a dominant figure in the LPGA—she won about two of every three events she entered in 1950 and 1951—and her showmanship, while not always appreciated by her competitors, helped market the new tour.
In 1953, Zaharias was diagnosed with cancer, and doctors told her family and friends (but not Zaharias herself) that she had less than a year to live. Within four months, however, she was back on the tour, finishing as the sixth-highest money winner for 1953. She did even better in 1954, winning five tournaments and having the lowest average on the tour. The cancer reappeared in 1955, and Babe Didrikson Zaharias, argu- ably the greatest athlete of the twentieth century, died in 1956. 1Susan Cayleff, Babe: The Life and Legend of Babe Didrikson Zaharias (Urbana, I.L.: University of Illinois Press, 1995), p. 46.
Source: Susan Cayleff, Barbe: The Life and Legend of Babe Didrikson Zaharias (Urbana, I.L.: University of Illinois Press, 1995).
12 Part 1 • Introduction and Review of Economic Concepts
Problems 1.1. Use an appropriate economic theory to explain why Kobe Bryant might employ some-
one to answer his fan mail even if he can read the letters and type the responses more quickly than the person he employs?
1.2. Is the following statement true or false? Explain your reasoning. “I am attending college on a full athletic scholarship, so the opportunity cost of attending college is zero for me.”
1.3. From 1946 through 1967, the placekicker for the Cleveland Browns, Lou Groza, was successful on 54.9 percent of his field goal attempts. From 1999 through 2008, the Browns’ kicker was Phil Dawson, who was successful on 82.8 percent of his attempts. Use the theory of comparative advantage to explain the massive improvement in the Browns’ kicking game.
1.4. The term “figure skating” refers to the shapes that skaters used to trace in the ice as part of skating competitions. In the 1970s, this aspect of the sport was deemphasized and eventually eliminated. Use the theory of comparative advantage to show why eliminating this part of the competition has led skaters to perform much more difficult and sophisticated jumps and spins.
13
C h a p t e r 2
Review of the Economist’s Arsenal
To be a sports fan these days is to be taking a course in economics.
—Allen Barra1
1Allen Barra, “In Anti-Trust We Trust,” Salon Magazine, May 19, 2000, at http://www.salon.com/news/feature/2000/05/19/ antitrust/index.html.
IntroductIon
As noted in Chapter 1, many aspects of sports business are hard to explain from a casual fan’s per- spective. In this chapter, we review some of the basic economic models that allow us to formalize our analysis and, in turn, explain why these markets behave as they do.
Learning Objectives
after reading this chapter, you will be able to:
• Use the basic model of supply and demand to explain the relationship between prices and quantity, such as why collectors pay much more for Mickey Mantle baseball cards than for Hank Aaron baseball cards, even though Aaron had better career statistics.
• Describe how teams use their most fundamental input—player talent—to generate wins, and how the law of diminishing marginal returns impacts teams’ decisions on how to allocate that talent.
http://www.salon.com/news/feature/2000/05/19/antitrust/index.html
http://www.salon.com/news/feature/2000/05/19/antitrust/index.html
14 Part 1 • Introduction and Review of Economic Concepts
• Distinguish the various market structures that are present in the sports industry and apply the appropriate model for analyzing questions such as why the Chicago White Sox do not lower their ticket prices when doing so would allow them to sell out like their neighbors, the Chicago Blackhawks.
• Explain why the era of professional sports began at the same time in two different countries with two different sports.
2.1 the Supply and demand model
The supply and demand model is the first and simplest model that we encounter. Recall that a model is a simplification of reality that allows economists to isolate particular economic forces. A good model allows economists to make predictions and provide explanations about the world quickly and easily.
Unlike physicists and chemists, economists and other social scientists find it difficult to conduct experiments: It is far more difficult to control what people do than it is to control substances in a test tube. Even if economists were physi- cally able to control what people do, ethical and legal considerations would make most experiments unfeasible. For example, it would be very hard—and certainly undesirable—for an economist studying bankruptcy to force a person or firm to go bankrupt. Instead, economists rely on theoretical and statistical models of market structure to make reliable predictions about behavior.
For all its simplicity, the supply and demand model has remarkable power to explain the world around us. At the same time, we must be careful to use the model under the appropriate circumstances. The supply and demand model is most suitable when there are many buyers and sellers of a homogeneous good (i.e., all suppliers are selling the same product), and consumers have good infor- mation about available prices across sellers.
Supply and demand show us how producers and consumers respond to price changes. Together, they determine how much of a good or service is pro- duced and what value society places on it. In a different course, we might use these tools to analyze the financial meltdown of 2008 or the impact of a higher minimum wage on employment. In this section, we introduce the concepts of sup- ply and demand and use them to show why Mickey Mantle cards cost so much more than Hank Aaron cards.
demand, Supply, and equilibrium
An individual consumer’s demand for baseball cards (or for any good or service) is the relationship between the price of those cards and the number of cards that he or she is willing and able to buy. It is a sequence of answers to the question, “If baseball cards cost this much, how many of them would you buy?” Or, from the firm’s perspective, “How many would we be able to sell?” We compute the market demand, which shows the quantity that all consumers combined pur- chase at each price by summing the individual demand curves, that is, by adding the quantity that each consumer purchases at each price. Figure 2.1 shows the market demand curve for a specific player’s baseball card. Note that the curve
Chapter 2 • Review of the Economist’s Arsenal 15
is downward sloping, as the relationship between price and quantity is invariably negative. As the price of cards falls, the number of cards that consumers buy rises. Economists call the negative relationship between price and quantity the law of demand. A change in a good’s price causes a change in quantity demanded, moving quantity up along the demand curve when the price rises and down the demand curve when the price falls.
The supply of baseball cards relates price to the number of cards that sellers are willing and able to provide. Unlike consumers, who view the price of an item as the sacrifice they must make, producers view the price as a reward. As a result, higher prices encourage producers (sellers) to offer more cards. For existing cards, an increase in the price gives more card owners an incentive to offer their cards for sale. In addition, sellers have an incentive to produce more new cards as the price rises. At the same time, other producers have an incentive to stop what they are doing and start producing cards. Some economists call the positive relationship between price and quantity the law of supply.
Similar to market demand, the market supply curve is the sum of the indi- vidual supply curves. The market supply curve is typically upward sloping, as seen in Figure 2.2. Again, if the price of cards changes, the quantity moves along the supply curve, a movement that economists call a change in quantity supplied.
Taken alone, market demand says nothing about the amount consumers actually buy or the price they pay. Similarly, market supply alone does not say how much producers sell or the price they receive. To find out what happens in the marketplace, one must look at supply and demand together. Figures 2.3a and 2.3b show that the two curves cross at the point labeled e. Economists call e the equilibrium point because at that point, the actions of consumers and produc- ers are in balance. Consumers are willing and able to buy Qe cards at the price
D
p ($ per card)
Q (quantity of cards)0
FIgure 2.1 The Demand for Baseball Cards As the price of baseball cards falls, the quantity demanded rises.
16 Part 1 • Introduction and Review of Economic Concepts
pe, which is exactly the quantity that producers are willing and able to sell at that price. As a result, neither consumers nor producers have any desire to alter their actions; thus, the price stays at pe, and the quantity at Qe.
Figure 2.3a shows that, at a price higher than pe (such as ph), disequilibrium occurs because producers want to sell Qs while consumers want to buy only Qd.
S
0
p ($ per card)
Q (quantity of cards)
FIgure 2.2 The Supply of Baseball Cards As the price of baseball cards rises, the quantity supplied also rises.
QdQeQe Qs
pe
p l
S
D
ee
0
p ($ per card)
Q (quantity of cards)
QsQd
ph
pe
S
D
0
p ($ per card)
Q (quantity of cards)
(a) A price of ph results in excess supply (b) A price of pl results in excess demand
FIgure 2.3 Equilibrium in the Baseall Card Market Equilibrium occurs at price pe, where the supply and demand curves meet.
Chapter 2 • Review of the Economist’s Arsenal 17
Unable to sell all the cards they want, producers face a surplus or excess supply. Frustrated producers lower their prices in order to attract more customers. The lower price encourages consumers to buy more cards and discourages producers from selling them. As Qd rises and Qs falls, the excess supply falls until it equals zero, and equilibrium is restored at pe.
Figure 2.3b shows that, at a price below the equilibrium (p1), buyers want to purchase Qd cards while sellers want to sell only Qs. The shortage or excess demand for cards at p1 drives the price upward until the shortage disappears at pe.
We cannot actually see the supply and demand curves of the products we consume. We do, however, observe equilibrium prices. For example, baseball trading card prices are published regularly in price guides. In 1955, the Bowman Company produced a set of cards known as the “TV set,” with pictures of players appearing on the face of the card bordered by what appears to be a television set. Included in that set are the cards of Mickey Mantle, perhaps the greatest switch- hitting power hitter ever, and Hank Aaron, who was Major League Baseball’s all- time home run leader from 1974 to 2007.
According to the Beckett Baseball price guide, which tracks card values, the March 2012 prices of Mantle and Aaron cards from the 1955 Bowman set were $800 and $250, respectively.2 Such a large difference in price is difficult to justify, given that Hank Aaron had more home runs (HR), hits (H), runs scored (R), runs batted in (RBI), and a higher batting average (Avg) than Mantle (see Table 2.1). We can use the simple supply and demand model as an analytical tool to investigate the difference in prices. Because the forces of supply and demand determine prices, the explanation must lie in differences in supply, in demand, or in both.
changes in Supply and demand
The supply and demand relationships are not permanently fixed. They can change for many different reasons. This section reviews why the supply or demand curve might shift and the effects that shifts have on the equilibrium price and quantity.
FactorS that aFFect the locatIon oF the demand curve Economists call a shift of the demand curve a change in demand. A change in demand stems from a change in any of the five underlying factors: consumer income, the prices
table 2.1 Career Statistics of Hank Aaron and Mickey Mantle
AB H R HR RBI Avg Card Price
Hank Aaron 12,364 3,771 2,174 755 2,297 .305 $250 Mickey Mantle 8,102 2,415 1,677 536 1,509 .298 $800
Sources: Player statistics are from MLB.com; Card prices are from Beckett Baseball, March 2012, p. 34.
2Beckett Baseball, March 2012, p. 34.
18 Part 1 • Introduction and Review of Economic Concepts
of substitutes or complements, consumer tastes, the number of consumers in the market, and the expectations that consumers hold.
We have seen that consumers typically buy more of a good if their incomes increase, but frequent exceptions exist. If a hockey fan living in Providence, Rhode Island, gets a raise, he might buy more hockey cards of the Providence Bruins, the local minor league team. Alternatively, he might buy fewer cards of the Providence Bruins and more cards of the National Hockey League’s (NHL’s) Boston Bruins. If he buys more cards of the Providence Bruins as his income rises, then the cards are normal goods. normal goods get their name because consum- ers normally buy more of a good or service when their incomes rise. If the fan buys fewer cards, then the cards are inferior goods. inferior goods need not be undesirable or poorly made. One simply buys less of them as one’s income rises.
If hockey fans buy fewer Providence Bruins cards when their incomes fall, it seems reasonable to conclude that they would go to fewer hockey games as well. We can also ask whether the recession of 2008–2009 had a negative impact on professional sports or are sports “recession-proof”? The evidence from the recent recession is mixed. Attendance at the four major sports in 2008 and early 2009 was not significantly below previous levels, but all else was not held equal, as incomes fell. Some NBA teams sold tickets at significant discounts to prop up attendance. According to ESPN.com, the Memphis Grizzlies drew about as many fans in 2008–2009 (about 12,600 per game) as they did in 2007–2008 (12,770), but they sold their tickets so cheaply that the team’s gross revenue per game was only $300,000, an average of less than $24 per fan.3 Similarly, some Major League Baseball teams discounted 2009 season tickets by up to 25 percent, and the New York Yankees were forced to cut the prices of some premium seats in the new ballpark by half.4
The major North American sports leagues do have a safety net in the form of long-term TV contracts. As long as recessions do not outlast these contracts, the guaranteed income of these contracts helps to sustain teams. Sports and ath- letes that rely heavily on year-to-year sponsorships, such as golf and tennis, are in a more vulnerable position. Formula-1 and the National Association for Stock Car Auto Racing (NASCAR) were particularly hard-hit by the downturn, as they rely heavily on sponsorships by car manufacturers that were devastated by the recession.5 Similarly, the Ladies Professional Golf Association (LPGA) reduced its tournament schedule from 34 events in 2008 to 31 in 2009 and total prize money fell by about $5 million.6
3Bill Simmons, “Welcome to the No Benjamins Association,” ESPN.com, February 27, 2009, at http:// www.espn.go.com.
6Ron Sirak, “LPGA Facing Economic Realities,” Golf Digest, November 18, 2008, at http://www. golfdigest.com/golf-tours-news/2008-11/20081119sirak, viewed April 30, 2012.
5Sean Gregory and Steve Goldberg, “Daytona Drag: NASCAR Tries to Outrace the Recession,” Time, February 12, 2009, at http://www.time.com/time/business/article/0,8599,1879136,00.html.
4Jon Birger, “Baseball Battles the Slump,” CNNMoney.com, February 19, 2009, at http://money.cnn. com/2009/02/18/magazines/fortune/birger_baseball.fortune/index.htm; and Richard Sandomir, “Yankees Slash the Price of Top Tickets,” The New York Times, April 28, 2009, at http://www. nytimes.com/2009/04/29/sports/baseball/29tickets.html?_r=1&scp=4&sq=+%20yankees%20+% 20%22ticket%20prices%22&st=cse.
http://www.espn.go.com
http://www.espn.go.com
http://www.golfdigest.com/golf-tours-news/2008-11/20081119sirak
http://www.golfdigest.com/golf-tours-news/2008-11/20081119sirak
http://www.time.com/time/business/article/0,8599,1879136,00.html
http://money.cnn.com/2009/02/18/magazines/fortune/birger_baseball.fortune/index.htm
http://money.cnn.com/2009/02/18/magazines/fortune/birger_baseball.fortune/index.htm
http://www.nytimes.com/2009/04/29/sports/baseball/29tickets.html?_r=1&scp=4&sq=+%20yankees%20+%20%22ticket%20prices%22&st=cse
http://www.nytimes.com/2009/04/29/sports/baseball/29tickets.html?_r=1&scp=4&sq=+%20yankees%20+%20%22ticket%20prices%22&st=cse
http://www.nytimes.com/2009/04/29/sports/baseball/29tickets.html?_r=1&scp=4&sq=+%20yankees%20+%20%22ticket%20prices%22&st=cse
Chapter 2 • Review of the Economist’s Arsenal 19
When the price of a substitute good increases, the demand curve shifts to the right. If a card collector views Mickey Mantle cards and Yogi Berra cards as rea- sonable substitutes, an increase in the price of Yogi Berra cards causes the demand curve for Mickey Mantle cards to shift to the right.
The opposite effect occurs when the price of a complement increases. For example, older cards need protection from bending and other mishaps that reduce the value of the card. The best way to prevent such accidents is to keep the cards in protective sleeves. If the price of the sleeves rises, the demand for cards falls. This occurs because collectors use the two products together and think of them as a single commodity. When the price of sleeves rises, the price of a card with a sleeve also rises, reducing demand for cards. Figure 2.4a shows the impact of an increase in income and a reduction in the price of a substitute good on the demand curve.
In his book The Blind Side, Michael Lewis provides an interesting example of how tastes can affect the demand for a specific service.7 Lewis notes that, until the 1980s, offensive linemen were regarded largely as interchangeable units and were among the lowest paid players on a football team. Today, left tackles are among the most highly paid players on the team. The premium paid to left tackles repre- sents a change in tastes by football teams that have increasingly emphasized the forward pass.
The growing emphasis on the forward pass has made quarterbacks the stars of their teams and made protecting them a priority. It has become particularly
Increase in cost
S1
S0
S2
D2
D0
D1
D
0
Improvement in technology
p ($ per card)
Q (quantity of cards)
Increase in income
Decrease in price of substitute
S
0
p ($ per card)
Q (quantity of cards)
(a) Demand (b) Supply
FIgure 2.4 Changes in the Demand for and Supply of Baseball Cards Demand and supply curves can shift left or right.
7Michael Lewis, The Blind Side: Evolution of a Game (New York: W. W. Norton, 2006).
20 Part 1 • Introduction and Review of Economic Concepts
important to protect quarterbacks from behind, their “blind side,” where they cannot see oncoming defenders. This required players big enough to stand up to defensive ends but fast enough to move over to block linebackers. Left tackle (which protects a right-handed quarterback’s blind side) thus became a unique— and highly paid—position.
Another example of the impact of tastes on prices can be found in ticket prices charged by Major League Baseball teams. Traditionally, teams have charged a fixed price for a given seat location, regardless of the opponent. Recently, they have started to behave more like European soccer teams or Japanese baseball teams by charging higher prices when more popular teams, such as the New York Yankees or the Boston Red Sox, come to town in a strategy known as vari- able ticket pricing. Some teams, such as the San Francisco Giants, even change ticket prices based on pitching matchups. The practice of altering ticket prices after the season begins is known as dynamic pricing. We will return to this con- cept in Chapter 4, but even with our simple model of supply and demand, we can predict that, because the supply of seats is the same regardless of whom the visiting team is, differences in price must reflect changes in the demand curve. The demand curve for teams like the Red Sox and Yankees is farther to the right than for most other teams because of the greater taste of fans for seeing these teams play.8
Finally, expectations of future prices can affect demand. A collector who believes that the prices of cards will rise in the near future is willing to buy more cards at any given price than a collector who believes that prices will remain stable. The expectation of a price increase shifts the collector’s demand curve to the right. Similarly, if the collector believes that prices will fall, his demand curve shifts to the left.
FactorS that aFFect the locatIon oF the Supply curve As was the case for demand, the position of the supply curve also depends on several underlying fac- tors. A change in supply results from a change in input prices, technology, taxes, expectations held by producers, and natural events that destroy or promote prod- ucts or resources.
In the case of baseball cards, if the price of paper products rises, the cost of producing each baseball card rises as well. At any given price, the net return to making and selling cards is lower than before, and the incentive to provide cards falls. Card manufacturers produce fewer cards at any given price, and the supply curve shifts to the left from S0 to S1 in Figure 2.4b.
A technological innovation that reduces the cost of making cards increases the profitability of making cards and encourages producers to make and sell more cards. The increase in technology shifts the supply curve rightward to S2.
A sales tax on cards introduces a wedge between the price the consumer pays and the price the producer receives. The difference between what the consumer
8Joshua Brustein, “Star Pitchers in a Duel? Tickets Will Cost More,” New York Times, June 27, 2010, at http://www.nytimes.com/2010/06/28/technology/28tickets.html, viewed February 23, 2012.
http://www.nytimes.com/2010/06/28/technology/28tickets.html
Chapter 2 • Review of the Economist’s Arsenal 21
pays and what the producer receives means that the market has two supply curves, as seen in Figure 2.5. Figure 2.5 shows that the vertical difference between the two supply curves equals the amount of the per-unit tax. For example, a $0.10 per-card tax on producers results in a new supply curve that lies $0.10 above the original. The price that consumers must pay (pt) is determined by the intersection of the demand curve with the supply curve that includes the tax. Quantity decreases to Qt because consumers are willing to purchase fewer cards at the higher price. The price that sellers receive is the price for Qt cards on the original supply curve and is equal to the price that consumers pay minus the tax (pt - t). The difference between the price that consumers pay and the price that sellers receive is the per- unit tax, t. Multiplying the per-unit tax by the number of cards sold, Qt, yields the tax revenue collected by the government. In Figure 2.5, this area is shaded gray.
Natural disasters can also affect the location of the supply curve. If a hur- ricane damaged the card factory, it would temporarily reduce the availability of new cards. The world saw stark evidence of this type of event when a major earthquake struck Japan in 2011. The quake and ensuing tsunami damaged many factories and a major nuclear energy facility, temporarily disrupting the produc- tion of products such as autos worldwide, as even non-Japanese automakers scrambled to find alternative suppliers of parts normally produced in Japan.9
D
S0 S0 + tax
0
p t
p t− t p0
Q0Q t
tax
p ($ per card)
Q (quantity of cards)
FIgure 2.5 A Change in Supply Due to a Tax A tax causes consumers to see the curve S0 + tax while producers still act along S0.
9“Japan’s Earthquake and Tsunami Hit Parts Supplies,” Motor Trend, June 2011, at http://www. motortrend.com/features/auto_news/2011/1106_japan_earthquake_tsunami_hit_parts_supplies/ viewall.html, viewed February 23, 2011.
http://www.motortrend.com/features/auto_news/2011/1106_japan_earthquake_tsunami_hit_parts_supplies/viewall.html
http://www.motortrend.com/features/auto_news/2011/1106_japan_earthquake_tsunami_hit_parts_supplies/viewall.html
http://www.motortrend.com/features/auto_news/2011/1106_japan_earthquake_tsunami_hit_parts_supplies/viewall.html
22 Part 1 • Introduction and Review of Economic Concepts
Closer to home, the New Orleans Saints were unable to play any home games during the 2005 season due to the damage to their home stadium caused by hurricane Katrina, reducing the supply of NFL games in New Orleans to zero for the season.10
Finally, if producers expect prices to rise in the future, they have an incentive to wait until prices rise before selling their product. At any price, producers are willing to provide less today, thinking that they will be able to sell for more tomor- row, and the supply curve shifts to the left.
elaStIcIty oF Supply Economists are often less interested in how much produc- ers produce than in how sensitive their production decisions are to changes in price. At first, one might be tempted to express this sensitivity in terms of slope. If card producers had a steep supply curve, such as S0 in Figure 2.6, then it appears that firms do not respond very much to an increase in price. As price rises from p0 to p1, output grows from Q0 cards to only Q1. If the supply curve is relatively flat (S1), producers respond to the price increase by expanding output from Q=0 to Q=1. Slope, however, is a misleading measure of sensitivity.
Suppose, for example, that the price of a pack of baseball cards rises from $0.10 to $0.11 and that firms respond by printing 200 more packs of cards. The slope of the supply curve is the change in price divided by the change in quantity, or $0.01/200 packs.
10Associated Press, “Saints’ home games: 4 at LSU, 3 in Alamodome,” September 12, 2005, at http:// sports.espn.go.com/nfl/news/story?id=2159595, viewed April 30, 2012.
S0
p ($ per card)
Q (quantity of cards)
p1
p0
Q0 Q1 Q0′ Q1′
S1
0
A B
FIgure 2.6 Relatively Elastic versus Inelastic Supply Elasticity depends on more than just the slope of the curve.
http://sports.espn.go.com/nfl/news/story?id=2159595
http://sports.espn.go.com/nfl/news/story?id=2159595
Chapter 2 • Review of the Economist’s Arsenal 23
The problem is that 200 packs can represent a big change in the number of packs produced or a very small change, depending on how many packs firms had been printing to begin with. Increasing production by 200 packs means much more to producers if they expand from 1,000 packs to 1,200 than if they expand from 10,000 packs to 10,200. As a result, slope cannot tell us how meaningful the increase of 200 packs really is. Thus, while the supply of cards appears to be more sensitive to price changes at point B on supply curve S1 because of its relatively flat slope, supply might actually be more sensitive at point A on curve S0 because the initial quantity of cards is lower.
Economists account for the producers’ starting point by using percentage changes in price and output rather than absolute changes.11 They use these per- centage changes to measure the sensitivity of production to changes in price. We call this measure the elasticity of supply (which we denote as es). The elasticity of supply is the percentage change in quantity that results from a given percentage change in price:
es = %∆Qs
%∆p
In the above example, the $0.01 increase in the price of a pack of cards cor- responds to a percentage change of +0.01/+0.10 = 0.10, or 10 percent. If firms originally produced 1,000 packs of cards, then the percentage change in quan- tity is (1,200 - 1,000)/1,000 = 0.2, or 20 percent, and the elasticity of supply is es = 0.2/0.1 = 2.0. When the price of a pack of cards rises by 10 percent, produc- ers increase their output by 20 percent. The percentage increase in output is twice the percentage rise in price.
If firms originally produced 10,000 packs of cards, the percentage increase in output is (10,200 - 10,000)/10,000 = 0.02, or 2 percent, and the elasticity of sup- ply becomes es = 0.02/0.10 = 0.20. In this case, a 10 percent increase in the price of a pack of cards brings only a 2 percent increase in production, and firms are much less responsive to changes in price.
Although the supply curve’s location and elasticity are important for many of the issues we deal with later in the book, they cannot resolve our question about the relative prices of Mantle and Aaron cards. To simplify the analysis, we will make two weak assumptions and one strong assumption. A weak assumption is likely to be true in real life, while a strong assumption is often not true. Strong assumptions can be valuable, however, as long as the conclusions we draw are valid even when the assumption is not strictly true. In this case, our weak assumptions are that the Bowman Company produced the same number of Mickey Mantle and Hank Aaron cards and that the same number of Mantle and Aaron cards have survived in per- fect (mint) condition. Our strong assumption is that the owners of these cards are willing and able to sell a fixed number of cards regardless of the price they receive.
11We define the percentage change of the variable X(%∆X) as ∆X/X = (X1 - X0)/X0. We use point elasticity rather than arc elasticity, which would replace the denominator with the mean of X0 and X1. If X0 and X1 are close together, the difference is negligible.
24 Part 1 • Introduction and Review of Economic Concepts
In this case, the supply curve is a vertical line. Because price changes do not affect the quantity supplied, the supply curve in Figure 2.7 is perfectly inelastic.
elaStIcIty oF demand As with supply, we are often interested in the sensitivity of demand to changes in price rather than absolute levels of price and quantity. The elasticity of demand (ed) is the percentage change in quantity demanded for a given percentage change in price. The only difference between the elasticity of demand and the elasticity of supply is that the elasticity of demand measures the price sensitivity of consumers rather than producers
ed = %∆Qd
%∆p
For example, if the price of a card increases from $0.10 to $0.11 and the quan- tity demanded falls from 1,000 to 750 cards, the elasticity of demand is
(1,000 - 750)/1,000 (0.10 - 0.11)/0.10
= -2.5
Elasticities of demand fall between zero (perfectly inelastic) and minus infinity (infinitely elastic).12 When the elasticity lies between 0 and -1, we say that demand is inelastic, because the percentage change in quantity is less than the percentage change in price. When the elasticity is less than -1, we say that demand is elastic.
S
Qs0
p ($ per card)
Q (quantity of cards)
FIgure 2.7 Perfectly Inelastic Supply When the supply curve is vertical, quantity does not change, and the elasticity of supply is zero.
12Some microeconomics textbooks eliminate the negative sign by taking the absolute value of the elas- ticity formula. We use the negative number because it reinforces the notion that price and quantity move in opposite directions along the demand curve.
Chapter 2 • Review of the Economist’s Arsenal 25
explaInIng the dIFFerence In card prIceS We can now use the simple supply and demand model to show that the difference in value between Mickey Mantle and Hank Aaron cards stems from economic forces rather than accident or error. We previously noted that there is no reason to believe that the supply curves of Mantle and Aaron cards differ from each other. Because a fixed number of cards of each player were produced, we assume that supply is perfectly inelastic. As a result, differences in price must be the result of differences in demand. What fac- tors might contribute to such a large difference in demand?
Mickey Mantle spent his entire career in New York, while Aaron spent his career in Milwaukee and Atlanta, which are much smaller cities. Even if Aaron and Mantle are equally popular with their hometown fans, the difference in popu- lation causes the demand curve for Mickey Mantle cards to lie far to the right of the demand curve for Hank Aaron cards. To see why, assume that a typical fan prefers players and memorabilia for his hometown team. We are not, how- ever, interested in how many cards each individual Braves or Yankees fan buys at each price. We want to know how many cards all Braves fans combined buy at each price and how many cards all Yankees fans combined buy at each price. The total market demand curve is thus the horizontal sum of the individual demand curves. Figure 2.8 shows the individual demand curves for baseball cards by two baseball fans, Ray and Roy, and the market demand curve that would result if they were the only consumers. Because New York is a much larger city, adding all of the individual demand curves for Mickey Mantle cards results in a market demand curve for his cards that is farther to the right than the demand curve for Hank Aaron cards, increasing their price relative to Hank Aaron cards.
In addition to having more people, the New York metropolitan area has fans who are, on average, wealthier than Braves fans in either Milwaukee or Atlanta.
S
Dmarket
250
22
p ($ per card)
Q (quantity of cards) 28 50
DRoy DRay
0
FIgure 2.8 The Relationship between Individual Demand and Market Demand for Baseball Cards Market demand is the horizontal sum of the individual demands.
26 Part 1 • Introduction and Review of Economic Concepts
If baseball cards are normal goods, the higher level of income causes the demand curve for Mickey Mantle cards to shift out still farther relative to the demand for Hank Aaron cards.
Finally, one must account for the unfortunate possibility that the tastes of baseball fans for baseball cards reflect the prejudices of the population at large. As we shall see in Chapter 10, most economists regard discrimination as a taste or distaste for members of a particular group. If some card collectors prefer Mickey Mantle, who was white, to Hank Aaron, who is black, simply because of their races, the demand for Mantle cards would be greater than the demand for Aaron cards.
Figure 2.9 shows that the combined effects of the differences in market size, income, and tastes and preferences of individuals with a taste for discrimination result in greater demand for Mantle cards than for Aaron cards. The differences in demand coupled with the identical, perfectly inelastic supply curves create the difference in equilibrium price. Several studies of trading card prices have established that race plays a significant role in determining the price of playing cards. Nardinelli and Simon (1990) were the first to establish such a link. Gabriel, Johnson, and Stanton (1999) found that discrimination was less likely to occur for rookie cards, when the future performance of a player was unknown, but reap- peared as the player’s ability was revealed over the course of his career.13
13Clark Nardinelli and Curtis Simon, “Customer Racial Discrimination in the Market for Memorabilia: The Case of Baseball,” Quarterly Journal of Economics, vol. 105, no. 3 (1990), pp. 575–595; and Paul E. Gabriel, Curtis D. Johnson, and Timothy J. Stanton, “Customer Racial Discrimination for Baseball Memorabilia,” Applied Economics, vol. 31, no. 11 (1999), pp. 1331–1335.
S
D
800
p ($ per card)
Q (quantity of cards) 50
(a) Mickey Mantle
S
D 250
p ($ per card)
Q (quantity of cards) 50
(b) Hank Aaron
0 0
FIgure 2.9 Differences in Demand for Hank Aaron and Mickey Mantle Cards Create Differences in Price
Chapter 2 • Review of the Economist’s Arsenal 27
2.2 producIng output and the productIon FunctIon
Producing a sporting contest, such as a football game, is much different from pro- ducing a pizza. Most obviously, a football game is service, like a play or movie, not a physical object. In addition, output must be produced in concert with another producer (team). Despite these differences, we can still apply the economic theory of production to sports. In this section, we review the basics of production theory, including why these concepts are so important to the study of team sports and the special nature of sports relative to other goods and services.
a note on the definition of output
Before analyzing a market, economists must determine how to measure output. In some markets, such as the pizza market, defining output (Q) is easy. It is the number of pizzas produced in a given time period. In sports markets, defining and measuring output is more complicated. If we think of output as what a firm sells in order to obtain revenue, we could measure output as attendance or tele- vision appearances. If we focus on production, it may be more useful to mea- sure output as games, because the team must combine inputs to produce games throughout the course of the season. Finally, if a team’s popularity, and hence its revenue, depend on its performance, the appropriate output is wins or win- ning percentage rather than simply games played. Our problem resembles that facing those who study higher education. From the standpoint of revenue, a col- lege or university may define output as the number of students enrolled. From the standpoint of input utilization, it may define output as the amount that its students learn, perhaps measured by their future incomes. Unfortunately, there is no simple resolution to this issue. To force a universal definition of output would cloud the issue as often as it would clarify it. In this text, we address this thorny issue by defining output according to the aspect of the market under consider- ation. For the remainder of this section, we consider output to be the number of wins produced per season.
the production Function
Production transforms inputs into output. A production function shows the relationship between the quantity of inputs used and the quantity of output pro- duced. This relationship is an expression of the technology of production and typ- ically includes labor and capital as inputs because the firm can substitute between them. In sports, however, capital (the need for a field of play, for example) is fixed. In addition, the number of players is set by rule. Thus, as we consider a team’s attempt to produce wins (Q), it makes more sense to speak in terms of units of tal- ent. The more talent a team has on the roster, the more games it can expect to win. We can show a production function in which a football team can invest in either offensive talent (TO) or defensive talent (TD) as:
Q = f(TO, TD)
28 Part 1 • Introduction and Review of Economic Concepts
Another term for Q is the total product of labor. In order to evaluate the impact of increases in either input on the number of wins, we must hold the other input constant. Figure 2.10a shows the typical relationship between one variable input, offensive talent in this case, and output while holding the quan- tity of defensive talent constant. As TO rises from 0 to TO1, each successive unit of talent adds more to wins than the last. The intuition behind this is fairly sim- ple. If a football team only has one or two talented players out of the starting 11, the team will benefit enormously from additional talent on the field. From TO1 to TO2, wins continue to rise but at a decreasing rate. These players still improve the team but not as much as the first few talented players. Beyond TO2, addi- tional talent might actually cause the team to win less. Is this possible? Perhaps you are familiar with the saying, “there’s only one ball” as a reference to the fact that having too many players want to carry the ball can damage team chemistry and reduce wins.
When coaches and general managers consider adding talent to a roster, they think like economists—by focusing on the margin. If they add one more talented player, how many more games might the team win? To focus on the change in output resulting from a small increase in one input, economists evaluate the play- er’s marginal product. The marginal product of an input indicates the increase in output that results from a one-unit increase in that input, holding the other input constant. For both offense and defense we thus have:
MPT = ∆Q/∆T
Figure 2.10b shows the marginal product of offensive talent. From 0 to TO1, as the slope of the total product curve increases, the marginal product increases. Again, the number of games the team wins increases quickly as the coach adds talent to the roster. From TO1 to TO2, the slope of the total product curve decreases, and marginal product falls. The decline in marginal product, known
Q (Q = TP = wins)
TP
0 TO1 TO2 OT (offensive talent)
FIgure 2.10a The Total Product Curve
Chapter 2 • Review of the Economist’s Arsenal 29
as the law of diminishing returns, is one of the most important concepts in all of economics. The law of diminishing returns states that as a firm (team) con- tinually increases one input while holding the other fixed, the marginal product of that input must eventually fall. This concept explains why, for example, a baseball team with five good starting pitchers does sign yet another starter and why the Giants do not sign both Eli Manning and Tom Brady to play in the same year. Other than for a few trick plays, a team can use only one quarterback at a time, and, barring injury, additional quarterbacks rarely play. Finally, beyond TO2, where the total product curve is downward sloping, the marginal product
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