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MICROECONOMIC THEORY

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Microeconomic Theory Basic Principles and Extensions TWELFTH EDITION

WALTER NICHOLSON Amherst College

CHRISTOPHER SNYDER Dartmouth College

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Microeconomic Theory: Basic Principles and Extensions, Twelfth Edition Walter Nicholson, Christopher Snyder

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Walter: To Beth, Sarah, David, Sophia, Abby, Nate, Christopher, and Ava

Christopher: To Maura

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Walter Nicholson is the Ward H. Patton Professor of Economics (Emeritus) at Amherst College. He received a B.A. in mathematics from Williams College and a Ph.D. in econom- ics from the Massachusetts Institute of Technology (MIT). Professor Nicholson’s primary research interests are in the econometric analyses of labor market problems, including wel- fare, unemployment, and the impact of international trade. For many years, he has been Senior Fellow at Mathematica, Inc. and has served as an advisor to the U.S. and Canadian governments. He and his wife, Susan, live in Naples, Florida, and Montague, Massachusetts.

Christopher M. Snyder is the Joel and Susan Hyatt Professor of Economics at Dartmouth College, currently serving as Chair of the Economics Department. He received his B.A. in economics and mathematics from Fordham University and his Ph.D. in eco- nomics from MIT. He is Research Associate in the National Bureau of Economic Research, Secretary-Treasurer of the Industrial Organization Society, and Associate Editor of the Review of Industrial Organization. His research covers various theoretical and empirical topics in industrial organization, contract theory, and law and economics.

Professor Snyder and his wife Maura Doyle (who also teaches economics at Dartmouth) live within walking distance of campus in Hanover, New Hampshire, with their three daughters.

Professors Nicholson and Snyder are also the authors of Intermediate Microeconom- ics and Its Application (Cengage Learning, 2015), an intuitive treatment of intermediate microeconomics emphasizing concepts and real-world applications over mathematical derivations.

About the Authors

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ix

Preface xix

PART ONE Introduction 1 CHAPTER 1 Economic Models 3 CHAPTER 2 Mathematics for Microeconomics 21

PART TWO Choice and Demand 87 CHAPTER 3 Preferences and Utility 89 CHAPTER 4 Utility Maximization and Choice 115 CHAPTER 5 Income and Substitution Effects 141 CHAPTER 6 Demand Relationships among Goods 183

PART ThrEE Uncertainty and Strategy 205 CHAPTER 7 Uncertainty 207 CHAPTER 8 Game Theory 247

PART FOUr Production and Supply 295 CHAPTER 9 Production Functions 297 CHAPTER 10 Cost Functions 325 CHAPTER 11 Profit Maximization 363

PART FivE Competitive Markets 399 CHAPTER 12 The Partial Equilibrium Competitive Model 401 CHAPTER 13 General Equilibrium and Welfare 449

PART SiX Market Power 489 CHAPTER 14 Monopoly 491 CHAPTER 15 Imperfect Competition 525

PART SEvEN Pricing in Input Markets 573 CHAPTER 16 Labor Markets 575 CHAPTER 17 Capital and Time 599

PART EiGhT Market Failure 631 CHAPTER 18 Asymmetric Information 633 CHAPTER 19 Externalities and Public Goods 683

Brief Answers to Queries 717 Solutions to Odd-Numbered Problems 727 Glossary of Frequently Used Terms 741 Index 749

Brief Contents

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Preface ..............................................................................................................................................xix

PART ONE Introduction CHAPTER 1 Economic Models ...............................................................................................................................3 Theoretical Models 3 Verification of Economic Models 4 General Features of Economic Models 5 Structure of Economic Models 6 Development of the Economic Theory of Value 9 Modern Developments 18

Summary 19 Suggestions for Further Reading 20

CHAPTER 2 Mathematics for Microeconomics................................................................................................21 Maximization of a Function of One Variable 21 Functions of Several Variables 26 Maximization of Functions of Several Variables 34 The Envelope Theorem 36 Constrained Maximization 40 Envelope Theorem in Constrained Maximization Problems 45 Inequality Constraints 46 Second-Order Conditions and Curvature 48 Homogeneous Functions 55 Integration 58 Dynamic Optimization 63 Mathematical Statistics 67

Summary 76 Problems 77

Contents

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xii Contents

Suggestions for Further Reading 81 Extensions: Second-Order Conditions and Matrix Algebra 82

PART TWO Choice and Demand

CHAPTER 3 Preferences and Utility ....................................................................................................................89 Axioms of Rational Choice 89 Utility 90 Trades and Substitution 92 The Mathematics of Indifference Curves 99 Utility Functions for Specific Preferences 102 The Many-Good Case 106

Summary 107 Problems 107 Suggestions for Further Reading 110

Extensions: Special Preferences 111

CHAPTER 4 Utility Maximization and Choice .................................................................................................115 An Initial Survey 116 The Two-Good Case: A Graphical Analysis 117 The n-Good Case 120 Indirect Utility Function 126 The Lump Sum Principle 127 Expenditure Minimization 129 Properties of Expenditure Functions 132

Summary 134 Problems 134 Suggestions for Further Reading 137

Extensions: Budget Shares 138

CHAPTER 5 Income and Substitution Effects ..................................................................................................141 Demand Functions 141 Changes in Income 143 Changes in a Good’s Price 145 The Individual’s Demand Curve 148 Compensated (Hicksian) Demand Curves and Functions 151 A Mathematical Development of Response to Price Changes 156 Demand Elasticities 159 Consumer Surplus 166

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Contents xiii

Revealed Preference and the Substitution Effect 171 Summary 173 Problems 173 Suggestions for Further Reading 176

Extensions: Demand Concepts and the Evaluation of Price Indices 178

CHAPTER 6 Demand Relationships among Goods .........................................................................................183 The Two-Good Case 183 Substitutes and Complements 186 Net (Hicksian) Substitutes and Complements 188 Substitutability with Many Goods 189 Composite Commodities 190 Home Production, Attributes of Goods, and Implicit Prices 193

Summary 196 Problems 197 Suggestions for Further Reading 200

Extensions: Simplifying Demand and Two-Stage Budgeting 202

PART ThrEE Uncertainty and Strategy

CHAPTER 7 Uncertainty ......................................................................................................................................207 Mathematical Statistics 207 Fair Gambles and the Expected Utility Hypothesis 208 Expected Utility 209 The Von Neumann–Morgenstern Theorem 210 Risk Aversion 212 Measuring Risk Aversion 216 Methods for Reducing Uncertainty and Risk 221 Insurance 221 Diversification 222 Flexibility 223 Information 230 The State-Preference Approach to Choice Under Uncertainty 231 Asymmetry of Information 237

Summary 237 Problems 238 Suggestions for Further Reading 241

Extensions: The Portfolio Problem 242

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xiv Contents

CHAPTER 8 Game Theory ....................................................................................................................................247 Basic Concepts 247 Prisoners’ Dilemma 248 Nash Equilibrium 250 Mixed Strategies 256 Existence of Equilibrium 260 Continuum of Actions 261 Sequential Games 263 Repeated Games 270 Incomplete Information 273 Simultaneous Bayesian Games 273 Signaling Games 278 Experimental Games 284 Evolutionary Games and Learning 286

Summary 287 Problems 287 Suggestions for Further Reading 290

Extensions: Existence of Nash Equilibrium 291

PART FOUr Production and Supply

CHAPTER 9 Production Functions .....................................................................................................................297 Marginal Productivity 297 Isoquant Maps and the Rate of Technical Substitution 300 Returns to Scale 304 The Elasticity of Substitution 307 Four Simple Production Functions 310 Technical Progress 314

Summary 318 Problems 319 Suggestions for Further Reading 321

Extensions: Many-Input Production Functions 322

CHAPTER 10 Cost Functions .................................................................................................................................325 Definitions of Costs 325 Relationship between Profit Maximization and Cost Minimization 327 Cost-Minimizing Input Choices 328 Cost Functions 333 Shifts in Cost Curves 337

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Contents xv

Short-Run, Long-Run Distinction 348 Summary 356 Problems 357 Suggestions for Further Reading 359

Extensions: The Translog Cost Function 360

CHAPTER 11 Profit Maximization ........................................................................................................................363 The Nature and Behavior of Firms 363 Profit Maximization 365 Marginal Revenue 367 Short-Run Supply by a Price-Taking Firm 372 Profit Functions 376 Profit Maximization and Input Demand 381

Summary 388 Problems 388 Suggestions for Further Reading 392

Extensions: Boundaries of the Firm 393

PART FivE Competitive Markets

CHAPTER 12 The Partial Equilibrium Competitive Model ..............................................................................401 Market Demand 401 Timing of the Supply Response 405 Pricing in the Very Short Run 405 Short-Run Price Determination 407 Shifts in Supply and Demand Curves: A Graphical Analysis 412 A Comparative Statics Model of Market Equilibrium 414 Long-Run Analysis 418 Long-Run Equilibrium: Constant Cost Case 419 Shape of the Long-Run Supply Curve 421 Long-Run Elasticity of Supply 424 Comparative Statics Analysis of Long-Run Equilibrium 424 Producer Surplus in the Long Run 428 Economic Efficiency and Applied Welfare Analysis 431 Price Controls and Shortages 434 Tax Incidence Analysis 435

Summary 440 Problems 440 Suggestions for Further Reading 444

Extensions: Demand Aggregation and Estimation 445

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xvi Contents

CHAPTER 13 General Equilibrium and Welfare ................................................................................................449 Perfectly Competitive Price System 449 A Graphical Model of General Equilibrium with Two Goods 450 Comparative Statics Analysis 460 General Equilibrium Modeling and Factor Prices 462 A Mathematical Model of Exchange 464 A Mathematical Model of Production and Exchange 475 Computable General Equilibrium Models 478

Summary 482 Problems 483 Suggestions for Further Reading 486

Extensions: Computable General Equilibrium Models 487

PART SiX Market Power

CHAPTER 14 Monopoly .........................................................................................................................................491 Barriers to Entry 491 Profit Maximization and Output Choice 493 Misallocated Resources under Monopoly 498 Comparative Statics Analysis of Monopoly 501 Monopoly Product Quality 502 Price Discrimination 504 Price Discrimination through Non-Uniform Schedules 510 Regulation of Monopoly 513 Dynamic Views of Monopoly 516

Summary 518 Problems 518 Suggestions for Further Reading 522

Extensions: Optimal Linear Two-Part Tariffs 523

CHAPTER 15 Imperfect Competition ...................................................................................................................525 Short-Run Decisions: Pricing and Output 525 Bertrand Model 527 Cournot Model 528 Capacity Constraints 534 Product Differentiation 535 Tacit Collusion 541 Longer-Run Decisions: Investment, Entry, and Exit 545

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Contents xvii

Strategic Entry Deterrence 550 Signaling 552 How Many Firms Enter? 555 Innovation 559

Summary 561 Problems 562 Suggestions for Further Reading 565

Extensions: Strategic Substitutes and Complements 567

PART SEvEN Pricing in Input Markets

CHAPTER 16 Labor Markets .................................................................................................................................575 Allocation of Time 575 A Mathematical Analysis of Labor Supply 578 Market Supply Curve for Labor 582 Labor Market Equilibrium 583 Wage Variation 585 Monopsony in the Labor Market 589 Labor Unions 592

Summary 595 Problems 595 Suggestions for Further Reading 598

CHAPTER 17 Capital and Time .............................................................................................................................599 Capital and the Rate of Return 599 Determining the Rate of Return 601 Pricing of Risky Assets 608 The Firm’s Demand for Capital 610 Present Discounted Value Criterion 613 Natural Resource Pricing 617

Summary 620 Problems 620 Suggestions for Further Reading 623

APPENDIX The Mathematics of Compound Interest ....................................................................................625

Present Discounted Value 625 Continuous Time 627

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xviii Contents

PART EiGhT Market Failure

CHAPTER 18 Asymmetric Information ................................................................................................................633 Complex Contracts as a Response to Asymmetric Information 633 Principal-Agent Model 635 Hidden Actions 637 Owner-Manager Relationship 638 Moral Hazard in Insurance 642 Hidden Types 647 Nonlinear Pricing 648 Adverse Selection in Insurance 658 Market Signaling 665 Auctions 667

Summary 671 Problems 671 Suggestions for Further Reading 674

Extensions: Using Experiments to Measure Asymmetric-Information Problems 675

CHAPTER 19 Externalities and Public Goods ...................................................................................................683 Defining Externalities 683 Externalities and Allocative Inefficiency 685 Partial-Equilibrium Model of Externalities 689 Solutions to Negative Externality Problems 691 Attributes of Public Goods 695 Public Goods and Resource Allocation 697 Lindahl Pricing of Public Goods 701 Voting and Resource Allocation 704 A Simple Political Model 706 Voting Mechanisms 709

Summary 710 Problems 711 Suggestions for Further Reading 713

Extensions: Pollution Abatement 715

Brief Answers to Queries ..............................................................................................................717 Solutions to Odd-Numbered Problems........................................................................................727 Glossary of Frequently Used Terms .............................................................................................741 Index ..................................................................................................................................................749

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xix

The 12th edition of Microeconomic Theory: Basic Principles and Extensions continues a suc- cessful collaboration between the authors starting with the 10th edition. This edition rep- resents our efforts to continue refining and modernizing our treatment of microeconomic theory. Despite the significant changes appearing in virtually every chapter, the text retains all of the elements that have made it successful for so many editions. The basic approach is to focus on building intuition about economic models while providing students with the mathematical tools needed to go further in their studies. The text also seeks to facilitate that linkage by providing many numerical examples, advanced problems, and extended discussions of empirical implementation—all of which are intended to show students how microeconomic theory is used today. New developments continue to keep the field excit- ing, and we hope this edition manages to capture that excitement.

NEW TO THE TWELFTH EDITION We took a fresh look at every chapter to make sure that they continue to provide clear and up-to-date coverage of all of the topics examined. The major revisions include the following.

• Many of the topics in our introductory chapter on mathematics (Chapter 2) have been further revised to conform more closely to methods encountered in the recent econom- ics literature. Significant new material has been added on comparative statics analysis (including the use of Cramer’s rule) and on the interpretation of the envelope theorem.

• New figures have been added to illustrate the most basic concepts (risk aversion, certainty equivalence) in Chapter 7 on uncertainty and the notation streamlined throughout.

• For all the figures exhibiting the game-theory examples in Chapter 8, detailed captions have been added providing synopses and further analytical points. We tightened the exposition by removing several extraneous examples.

• Passages have been added to Chapter 10 to help clear up perennial sources of student confusion regarding different categories of costs—economic versus accounting, fixed versus sunk, and so forth—illustrating with examples from real-world industries.

• Our discussion of the comparative statics of the competitive model in Chapter 12 has been extensively updated and expanded using the new mathematical material provided in Chapter 2.

Preface

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xx Preface

• Chapter 14 on monopoly has been extensively revised. A passage has been added mak- ing basic points about the monopoly problem, connecting it to general profit maximiza- tion from Chapter 11. Our revamped approach to comparative statics is now featured in several places in this chapter. We cover recent advances in price discrimination, tracta- ble functional forms, and innovation.

• A significant amount of new material has been added to Chapter 17 on capital by look- ing at savings decisions under uncertainty. The concept of the stochastic discount factor is introduced and used to describe a number of issues in modern finance theory.

• Coverage of behavioral economics has been further expanded with a number of added references throughout the relevant chapters. One or more new behavioral econom- ics problems have been added to most chapters covering topics such as decision util- ity, spurious product differentiation, and the role of competition and advertising in unshrouding information about prices to consumers. These appear at the end of the list of problems, highlighted by the icon of the head with psychological gears turning.

Many new problems have been added with the goal of sharpening the focus on ones that will help students to develop their analytical skills.

SUPPLEMENTS TO THE TExT The thoroughly revised ancillaries for this edition include the following.

• The Solutions Manual and Test Bank (by the text authors). The Solutions Manual con- tains comments and solutions to all problems, and the Test Bank has been revised to include additional questions. Both are available to all adopting instructors in electronic version on Instructor’s companion site.

• PowerPoint Lecture Presentation Slides. PowerPoint slides for each chapter of the text provide a thorough set of outlines for classroom use or for students as a study aid. The slides are available on Instructor’s companion site.

• MindTap® for Microeconomic Theory: Basic Principles & Extensions, 12th Edition, is a digital learning solution allowing instructors to chart paths of dynamic assignments and applications personalized for their own courses. MindTap also includes real-time course analytics and an accessible reader to help engage students and encourage their high- level thinking rather than memorization.

• Cengage Learning Testing powered by Cognero® is a flexible, online system that allows instructors to import, edit, and manipulate content from the text’s test bank or else- where, including the instructors own favorite test questions; create multiple test ver- sions in an instant; and deliver tests from learning management system used for the course, the classroom, or wherever the instructor wants.

ONLINE RESOURCES Cengage Learning provides instructors with a set of valuable online resources that are an effective complement to this text. Each new copy of the book comes with a registration card that provides access to Economic Applications and InfoTrac College Edition.

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Preface xxi

ACkNOWLEDgMENTS We are indebted to the team at Cengage, most importantly Anita Verma, for keeping all of the moving parts of this new edition moving and on schedule. The copyeditors at Lumina Datamatics, Inc did a great job of making sense of our messy manuscripts. Joseph Malcolm coordinated the copyediting and supervised the production of page proofs, deal- ing expertly with many of the technical problems that arise in going from text to print equations. We very much appreciate his attention to the complexities of this process and are grateful for his professionalism and hard work.

We thank our colleagues at Amherst and Dartmouth College for valuable conversa- tions and understanding. Several colleagues who used the book for their courses offered us detailed suggestions for revision. We have also benefitted from the reactions of gen- erations of students to the use of the book in our own microeconomics classes. Over the years, Amherst students Eric Budish, Adrian Dillon, David Macoy, Tatyana Mamut, Anoop Menon, katie Merrill, Jordan Milev, and Doug Norton and Dartmouth students Wills Begor, Paulina karpis, glynnis kearny, and Henry Senkfor worked with us revising various chapters.

Walter again gives special thanks to his wife Susan; after providing much-needed sup- port through twenty-four editions of his microeconomics texts, she is happy for the success but continues to wonder about his sanity. Walter’s children (kate, David, Tory, and Paul) still seem to be living happy and productive lives despite a severe lack of microeconomic education. Perhaps this will be remedied as the next generation grows older. At least he hopes they will wonder what the books dedicated to them are all about. He is offering a prize for the first to read the entire text.

Chris gives special thanks to his family—his wife, Maura Doyle, and their daughters, Clare, Tess, and Meg—for their patience during the revision process. Maura has extensive experience using the book in her popular microeconomics courses at Dartmouth College and has been a rich source of suggestions reflected in this revision.

Perhaps our greatest debt is to instructors who adopt the text, who share a similar view of how microeconomics should be taught. We are grateful for the suggestions that teachers and students have shared with us over the years. Special mention in this regard is due genevieve Briand, Ramez guirguis, Ron Harstad, Bradley Ruffle, and Adriaan Soetevent, who provided pages of detailed, perceptive comments on the previous edi- tion. We encourage teachers and students to continue to e-mail us with any comments on the text (wenicholson@amherst.edu or chris.snyder@dartmouth.edu.

Walter Nicholson Amherst, Massachusetts Christopher Snyder Hanover, New Hampshire

June 2016

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1

Introduction

Chapter 1 Economic Models

Chapter 2 Mathematics for Microeconomics

This part contains two chapters. Chapter 1 examines the general philosophy of how economists build models of economic behavior. Chapter 2 then reviews some of the mathematical tools used in the construction of these models. The mathematical tools from Chapter 2 will be used throughout the remainder of this book.

PART ONE

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3

CHAPTER ONE

Economic Models The main goal of this book is to introduce you to the models that economists use to explain the behavior of consumers, firms, and markets. These models are central to the study of all areas of economics. Therefore, it is essential to understand both the need for such models and the basic framework used to develop them. This chapter begins by outlining some of the ways in which economists study practically every question that interests them.

1.1 THEORETICAL MODELS A modern economy is a complicated place. Thousands of firms engage in producing mil- lions of different goods. Many millions of people work in all sorts of occupations and make decisions about which of these goods to buy. Let’s use peanuts as an example. Pea- nuts must be harvested at the right time and shipped to processors who turn them into peanut butter, peanut oil, peanut brittle, and numerous other peanut delicacies. These processors, in turn, must make certain that their products arrive at thousands of retail outlets in the proper quantities to meet demand.

Because it would be impossible to describe the features of even these peanut markets in complete detail, economists must abstract from the complexities of the real world and develop rather simple models that capture the “essentials.” Just as a road map is helpful, even though it does not record every house or every store, the economic models of, say, the market for peanuts are also useful, even though they do not record every minute fea- ture of the peanut economy. In this book, we will study the most widely used economic models. We will see that, even though these models often make significant abstractions from the complexities of the real world, they nonetheless capture the essential features that are common to all economic activities.

The use of models is widespread in the physical and social sciences. In physics, the notion of a “perfect” vacuum or an “ideal” gas is an abstraction that permits scientists to study real-world phenomena in simplified settings. In chemistry, the idea of an atom or a molecule is actually a simplified model of the structure of matter. Architects use mock-up models to plan buildings. Television repairers refer to wiring diagrams to locate problems. Economists’ models perform similar functions. They provide simplified portraits of the way individuals make decisions, the way firms behave, and the way in which these two groups interact to establish markets.

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4 Part 1: Introduction

1.2 VERIFICATION OF ECONOMIC MODELS Of course, not all models prove to be “good.” For example, the earth-centered model of planetary motion devised by Ptolemy was eventually discarded because it proved incapa- ble of accurately explaining how the planets move around the sun. An important purpose of scientific investigation is to sort out the “bad” models from the “good” models. Two general methods have been used to verify economic models: (1) a direct approach, which seeks to establish the validity of the basic assumptions on which a model is based, and (2) an indirect approach, which attempts to confirm validity by showing that a simplified model correctly predicts real-world events. To illustrate the basic differences between the two approaches, let’s briefly examine a model that we will use extensively in later chapters of this book—the model of a firm that seeks to maximize profits.

1.2.1 The profit-maximization model The model of a firm seeking to maximize profits is obviously a simplification of reality. It ignores the personal motivations of the firm’s managers and does not consider conflicts among them. It assumes that profits are the only relevant goal of the firm; other possi- ble goals, such as obtaining power or prestige, are treated as unimportant. The model also assumes that the firm has sufficient information about its costs and the nature of the market to which it sells to discover its profit-maximizing options. Most real-world firms, of course, do not have this information available, at least not at zero cost. Yet such shortcomings in the model are not necessarily serious. No model can exactly describe reality. The real question is whether this simple model has any claim to being a good one.

1.2.2 Testing assumptions One test of the model of a profit-maximizing firm investigates its basic assumption: Do firms really seek maximum profits? Some economists have examined this question by sending questionnaires to executives, asking them to specify the goals they pursue. The results of such studies have been varied. Businesspeople often mention goals other than profits or claim they only do “the best they can” to increase profits given their limited infor- mation. On the other hand, most respondents also mention a strong “interest” in profits and express the view that profit maximization is an appropriate goal. Therefore, testing the profit-maximizing model by testing its assumptions has provided inconclusive results.

1.2.3 Testing predictions Some economists, most notably Milton Friedman, deny that a model can be tested by inquir- ing into the “reality” of its assumptions.1 They argue that all theoretical models are based on “unrealistic” assumptions; the very nature of theorizing demands that we make certain abstrac- tions. These economists conclude that the only way to determine the validity of a model is to see whether it is capable of predicting and explaining real-world events. The ultimate test of an economic model comes when it is confronted with data from the economy itself.

Friedman provides an important illustration of that principle. He asks what kind of the- ory one should use to explain the shots expert pool players will make. He argues that the laws of velocity, momentum, and angles from theoretical physics would be a suitable model.

1See M. Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953), chap. 1. For an alternative view stressing the importance of using “realistic” assumptions, see H. A. Simon, “Rational Decision Making in Business Organizations,” American Economic Review 69, no. 4 (September 1979): 493–513.