principles of microeconomics
principles of microeconomics ECON-103
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CONTENTS Preface xix The Market Constructing a Model 1 Optimization and Equilibrium3 The De- riar Curve 3 The Supply Curve 5 Market Equilibrium 7 Com- parative Static9 Other Ways to Allocate Apartments11 The Dis- crzminati~~gMonopolist The Ordinary Ibfonopoliat Rent Control a Which Way Is Best? 14 Pareto Efficien15 Comparing Ways to Al- locate Apartrneri16 Equilibrium in the Long Run 17 Surnmary 18 Review Questions 19 BudgetConstraint The Budget Constraint 20 Two Goods Are Often Enough 21 Prop- erties of t,he Budget S22 How the Budget Line Changes 24 The Numeraire 26 Taxes, Subsidies, and Rationin26 Example: The FoodStamp Program Budget Line Changes 31 Summary 31 Review Questions 32 Vlll CONTENTS Preferences Corlsunler Preferences34 Assumptioris about Preferences 35 Indif- ference Curves 36 Examples of Preferences 37 Perfect Substitutes Perfect Complements Bads Neutrals Satiation Discrete Goods Well-Behaved Preferences 44 The Marginal Rate of Substitu- tion 48 Other Interpretations of the MRS 50 Behavior of the hfRS 51 Summary 52 Review Questions 52 Utility Cardinal Utility57 Constructing a Utility Function58 Some Exam- ples of Utility Function59 Example: Indzfference Curvesfrom Utility Perfect Substitutes Perfect Complements Quasilinear Preferences Cobb-Douglas Preferences Marginal Utility 65 Marginal Utility and MRS 66 Utility for Commuting 67 Summary 69 Review Questions 70 Appendix 70 Example: Cobb-DouglasPreferences Optimal Choice 73 Consurner Demand 78 Some Exarriples 78 Perfect Substitutes Perfect Complements Neutrals and Bads Discrete Goods Concave Preferences Cobb-DouglasPreferences Estimating Utility Functions83 Implications of the MRS Condition 85 Choosing Taxes 87 Summary 89 Review Questions 89 Appen- dix 90 Example: Cobb-DouglasDemand Functions Demand Normal and Inferior Goods 96 Income Offer Curves and Erlgel Curves 97 Some Examples 99 Perfect Substitutes Perfect Complements Cobb-Douglas Preferences Homothetic Preferences Quasilinear Preferences Ordinary Goods and Giffen Goods 104 The Price Offer Curve and the Demand Curve 106 Some Examples 107 Perfect Substitutes Perfect Complements A Discrete Good Substitutes and Complements 111 The Inverse Demand Function 112 Sumnlary 114 Review Questions 115 Appendix 115 CONTENTS IX 7 RevealedPreference The Idea of Revealed Preference 119 From Revealed Preference to Pref- erence 120 Recovering Preferences 122 The Weak Axiom of Re- vealed Preference 124 Checking WARP 125 The Strong Axiom of Revealed Preference 128 How to Check SARP 129 Index Numbers 130 Price Indices 132 Example: Indexing Social Security Payments Summary 135 Review Questions 135 8 SlutskyEquation The Substitution Effect 137 Example: Calculatingthe Substitution Ef- fect The Income Effect 141 Example: Calculating the Income Effect Sign of the Substitution Effect 142The Total Change in Dernand 143 Rates of Change 144 The Law of Demand 147 Exarrlples of Income and Substitution Effects 147 Example: Rebating a Tax Example: Voluntay Real Time Pricing Another Substitution Effect 153 Com- pensated Demand Curves 155 Summary 156 Review Questions 157 Appendix 157 Example: Rebating a Small Tax 9 Buyingand Selling Net and Gross Demands 160 The Budget Constraint 161 Changing the Endowment 163 Price Changes 164 Offer Curves and Demand Curves 167 The Slutsky Equation Revisited 168 Use of the Slut- sky Equation 172 Example: Calculatingthe Endowment Income Effect Labor Supply 173 The Budget Constraint 0 Comparative Statics of Labor Supply 174 Example: Overtime and the S7~pplyof Labor Sum- mary 178 R.eviewQuestions 179 Appendix 179 X CONTENTS Intertemporal Choice The Budget Constraint 182 Preferences for Consumption 185 Com- parative Statics186 The Slutsky Equation and Intertemporal Choice 187 Inflation 189 Present Value: A Closer Look 191 Analyz- ing Present Value for Several Periods193 Use of Present Value 194 Example: Valuinga Stream of Payments Example: The True Cost of a Credit Card Bonds 197 Example: Installment Loans Taxes 199 Example: Scholarships and Savings Choice of the Interest Rate 200 Summary 201 Review Questions 201 AssetMarkets Rates of Return 202 Arbitrage and Present Value204 Adjustments for Differences among Assets 204 Assets with Consumption Returns 205 Taxation of Asset Returns 206 Applications 207 Depletable Resources Whento Cut a Forest Example: Gasoline Prices during the Gulf War Financial Institutions211 Summary 212 Review Questions 213 Appendix 213 Uncertainty Contingent Consumption 215 Example: Catastrophe Bonds Utility Functions and Probabilities220 Example: Some Examples of Utility Functions Expected Utility 221 Why Expected Utility Is Reasonable 222 Risk Aversion 224 Example: The Demand for Insurance Di- versificatio228 Risk Spreading 228 Role of the Stock Market 229 Summary 230 Review Questions 230 Appendix 231 Example: The Effect of Taxation on Investmentin Risky Assets Risky Assets Mean-Variance Utility 234 Measuring Risk 239 Equilibrium in a Market for Risky Assets 241 How Returns Adjust 242 Example: Ranking Mutual Funds Summary 246 Review Questions 246 CONTENTS XI 14 Consumer's Surplus Denland for a Discrete Good 248 Constructing Utility from Demand 249 Other Interpretations of Consumer's Surplus 250 From Con- surner's Surplus to Consumers' Surplus 251 Approximat,ing a Continu- ous Demand 251 Quasilinear Utilit251 Interpreting the Change in Consumer's Surplus 252 Exam,ple: The Change in Consumer's Surplus Cornperisati~igand Equivalent Variation 254 Example: Compensating and Eq~~izialet ariations Example: Compensating and Equivalent Vari- ation for Quasilinear Preferencesroducer's Surplus 258 Benefit-Cost Analysis 260 Rationing Calculating Gains and Losses 262 Sum- inary 263 Review Questions 263 Appendix 264 Example: A FernDemand F~~nctions Example: CV, EV, and Consumer's Surplus 15 Market Demand From Individual to Market Demand 266 The Inverse Demand Function 268 Example: Adding Up "Linear" Demand Curves Discrete Goods 269 The Extensive and the Intensive Margin 269 Elasticity 270 Example: The Elasticity of a Linear Demand Curve Elasticity and De- mand 272 Elasticity and Revenue 273 Example: Strikes and Profits Constant Ela~t~icityDemands 276 Elasticity and Marginal Revenue 277 Example: Setting a Price Marginal Revenue Curves 279 Income Elas- ticit,y 280 Slirrlmary 281 Review Questions 282 Appendix 283 Example: The Laffer Curve Example: Another Expression for Elasticity 16 Equilibrium Supply 289 Market Equilibrium 289 Two Special Cases 290 In- verseDerrlarldand Supply Curves 291 Example: Equilibrium with Lin- ear Curves Comparative Statics 293 Example: Shifling Both Curves Taxes 294 Example: Taxation with Linear Demand and Supply Pass- ing Along a Tax 298 The Deadweight Loss of a Tax 300 Example: The Market for Loans Example: FoodSubsidies Example: Subsidies in Iraq Pareto Efficiency 306 Example: Waiting in Line Summary 309 Revicw Quest,ions 309 XI1 CONTENTS Auctions Classification of Auction312 Bidding Rules Auction Design 313 Other Auction Forms 316 Example: Late Bidding on eBay Example: Online Ad Auctions Problems with Auctions 319 The Winner's Curse 320 Summary 320 Review Questions 321 Technology Inputs and Outputs 322 Describing Technological Constraints 323 Examples of Technology 324 Fixed Proportions Perfect Substitutes Cobb-Douglas Properties ofTechnology326 The Marginal Product 328 The Technical Rate of Substitution 328 Diminishing Marginal Product 329 Diminishing Technical Rate of Substitution 329 The Long Run and the Short Run 330 Returns to Scale 330 Summary 332 Review Questions 333 Profit Maximization Profits334 The Organization of Firms 336 Profits and Stock Market Value 336 The Boundaries of the Firm 338 Fixed and Variable Fac- tors 339 Short-Run Profit Maximization 339 Comparative Statics 341 Profit Maximization in the Long Run 342 Inverse Factor Demand Curves 343 Profit Maximization and Returns to Scale344 Revealed Profitability345 Example: How Do Farmers React to Price Supports? Cost Minimization 349 Summary 349 Review Questions 350 Ap- pendix 351 CostMinimization Cost Minimization 353 Example: Minimizing Costsfor Specific Tech- nologies Revealed Cost Minimization 357 Returns to Scale and the Cost Function 358 Long-Run and Short-Run Costs 360 Fixed and Quasi-Fixed Costs 362 Sunk Costs 362 Summary 363 Review Questions 363 Appendix 364 CONTENTS Xlll 21 Cost Curves Average Costs 367 Marginal Costs 369 Marginal Costs and Variable Costs 371 Example: Specific Cost Curves Example: Marginal Cost Curvesfor Two Plants Long-Run Costs 375 Discrete Levels of Plant Size 377 Long-Run Marginal Costs 379 Summary 380 Review Questions 381 Appendix 381 22 FirmSupply Market Environments 383 Pure Competition 384 The Supply Deci- sion ofa Competitive Firm386 An Exception 388 Another Exception 389 Example: Pricing Operating Systems The Inverse Supply Func- tion 391 Profits and Producer's Surplus391 Example: The Supply Curvefor a SpecificCost FunctionThe Long-Run Supply Curve of a Firm 395 Long-Run Constant Average Costs 397 Summary 398 Review Questions 399 Appendix 399 23 IndustrySupply Short-Run Industry Supply 401 Industry Equilibrium in the Short Run 402 Industry Equilibrium in the Long Run 403 The Long-Run Supply Curve 405 Example: Taxation in the Long Run and in the Short Run The Meaning of Zero Profits 409 Fixed Factors and Economic Rent 410 Example: Taxi Licenses in New York City Economic Rent 412 Rental Rates and Prices 414 Example: Liquor Licenses The Politics of Rent 415 Example: Farming the Government Energy Policy 417 Two-Tiered Oil Pricing Price Controls The Entitlement Program Summary 421 Review Questions 422 XIV CONTENTS Monopoly Maximizing Profits 424 Linear Demand Curve and Monopoly 425 Markup Pricing 427 Example: The Impact of Taxes on a Monopo- list Inefficiency of Monopol429 Deadweight Loss of Monopoly 431 Example: The Optimal Life of a Patent Example: Patent Thickets Nat- ural Monopoly 435 What Causes Monopolies? 437 Example: Di- amonds Are Forever Example: Pooling in Auction Markets Example: Price Fixing in Computer Memory Markets Summary 441 Review Questions 442 Appendix 443 Monopoly Behavior Price Discrimination445 First-Degree Price Discriminati445 Ex- ample: First-degreePrice Discriminationn Practice Second-Degree Price Discrimination 448 Example: Price Discrimination in Airfares Ex- ample: Prescription Drug Prices Third-Degree Price Discriminatio452 Example: Linear Demand Curves Example: Calculating Optimal Price Discrimination Example: Price Discrimination in Academic Journals Bundling 457 Example: Software Suites Two-Part Tariff458 Mo- nopolistic Competitio459 A Location Model ofProduct Differentiation 463 Product Differentiatio465 More Vendors 466 Summary 467 Review Questions 467 FactorMarkets Monopoly in the Output Market 468 Monopsony 471 Example: The Minimum Wage Upstream and Downstream Monopolies 475 Summary 477 Review Questions 478 Appendix 478 CONTENTS XV 27 Oligopoly Choosing a Strategy 481 Quantity Leadership 481 The Follower's Problem rn The Leader'sProblem Price Leadership 487 Comparing Price Leadership and Quantity Leadership 489 Simultaneous Quantity Setting489 An Example of Cournot Equilibrium 491 Adjustment to Equilibrium 493 Many Firms in Cournot Equilibrium 493 Simulta- neous Price Setting494 Collusion 495 Punishment Strategies 498 Example: Price Matching and Competition Example: Voluntary Export RestraintsComparison of the Solutions 501 Summary 502 Review Questions 503 28 Came Theory The Payoff Matrix of a Game 504 Nash Equilibrium 506 Mixed Strategies07 Example: RockPaper Scissors The Prisoner's Dilemma 509 Repeated Games 511 Enforcing a Cartel 512 Example: Tit for fat in Airline Pricing Sequential Games 514 A Game of Entry Deterrence 516 Summary 518 Review Questions 519 29 Came Applications Best Response Curves 520 Mixed Strategies 522 Games of Coordi- nation 524 Battle of the SexesrnPrisoner's Dilemma rn Assurance Games rnChicken rn Hourto Coordinate Games of Competition 528 Games of Coexistence533 Games of Commitment 535 The Frogand the Scorpion rn The Kindly Kidnapper When Strength Is Weakness rn Savings and Social Securityrn Hold Up rnBargaining 543 The Ultimatum Game rnSummary 546 Review Questions 547 XVI CONTENTS BehavioralEconomics Framing Effects in Consumer Choice 549 The Disease Dilemma Anchoring Effects Bracketing * Too Much Choice Constructed Preferences Uncertainty 553 Law of Small Numbers Asset In- tegration andLoss Aversion * Time 556 Discounting * Self-control Example: Overconfidence Strategic Interaction and Social Norm558 Ultimatum Game Fairness Assessment of Behavioral Economics 560 Summary 561 ReviewQuestions 563 Exchange The Edgeworth Box 565 Trade 567 Pareto Efficient Allocations 568 Market Ti-ade 570 The Algebra of Equilibrium 572 Walras' Law 574 Relative Prices575 Example: An Algebraic Example of Equilibrium The Existence of Equilibrium577 Equilibrium and Effi- 578 The Algebra of Efficiency579 Example: Monopoly in ciency the EdgeworthBox Efficiency and Equilibriu582 Implications of the First Welfare Theorem 584 Implications ofthe SecondWelfare Theorem 586 Summary 588 Review Questions 589 Appendix 589 Production The Robinson Crusoe Economy 591 Crusoe, Inc.593 The Firrn 594 Robinson's Problem 595 Putting Them Together 595 Different Tech- nologies597 Production and the First Welfare Theorem599 Produc- tion and the Second Welfare Theorem000 Production Possibilitie600 Comparative Advantage 602 Pareto Efficiency604 Castaways, Inc. 606 Robinson and Friday as Consumers 608 Decentralized Resource Allocation 609 Summary 610 Review Questions 610 Appen- dix 611 CONTENTS XVll 33 Welfare Aggregation of Preferences614 Social Welfare Functions616 Welfare Maximization 618 Individualistic Social Welfare Functio620 Fair Allocations 621 Envy and Equity 622 Summary 624 Review Questions 624 Appendix 625 34 Externalities Smokers and Nonsmokers 627 Quasilinear Preferences and the Coase Theorem 630 Production Externalities 632 Example: Pollution Vouchers Interpretatiori of the Condition637 Market Signals 640 Example: Bees and Almonds The Tragedy of the Commons 641 Ex- ample: Overfishing Example: New England Lobsters Automobile Pollu- tion 645 Summary 647 Review Questions 647 35 Information Technology Systems Competition 650 The Problem of Complements 650 Re- lationships among Complementors Lock-In 654 A Model of Com- petition with Switching Costs e Example: Online Bill Payment Ex- ample: Number Portability on Cell Phones Network Externalities 658 Markets with Network Externalities658 Market Dynamics 660 Ex- ample: Network Externalities in Computer Software Implications of Net- work Externalities 664 Example: The Yellow Pages Rights Manage- ment 665 Example: Video Rental Sharing Intellectual Property667 Summary 669 Review Questions 669 36 PublicGoods When to Provide a Public Good? 671 Private Provision of the Public Good 675 Free Riding 675 Different Levels of the Public Go677 Example: Pollution Re- Quasilinear Preferences and Public Good679 visited The Free Rider Problem681 Comparison to Private Goods 683 Voting 684 Example: Agenda Manipulation Demand Revelation 687 Example: An Example of the Clarke Tax Problems with the Clarke Tax 691 Summary 692 Review Questions 692 Appendix 693 XVlllCONTENTS Asymmetric Information The Market for Lemons 695 Quality Choice 696 Choosingthe Qual- ity Adverse Selection 698 Moral Hazard 700 Moral Hazard and Adverse Selection 701 Signaling 702 Example: The SheepskinEflect Incentives 706 Example: VotingRights in the CorporationExample: Chinese Economic Reforms Asymmetric Information 711 Example: Monitoring Costs Example: The Grameen Banlc Summary 714 Re- view Questions 715 Mathematical Appendix Functions A1 Graphs A2 Properties of FunctionsA2 Inverse Functions A3 Equations and IdentitiesA3 Linear FunctionsA4 Changes and Rates of Change A4 Slopes and Intercepts A5 Absolute Values and Logarithms A6 Derivatives A6 Second Derivatives A7 The Product Rule and the Chain Rule A8 Partial DerivativeA8 Optimization A9 Constrained OptimizationA10 Answers ~11 PREFACE The success of the first six editions of Intermediate Microeconomics has pleased me very much. It has confirmed my belief that the market would welcome an analytic approach to microeconomics at the undergraduate level. My aim in writing the first edition was to present a treatment of the methods of microeconomics that would allow students to apply these tools on their own and not just passively absorb the predigested cases described in the text.I have found that the best way to do this is to emphasize the fundamental conceptual foundationof microeconomics and to provide concrete examples of their application rather than to attempt to provide an encyclopedia of terminology and anecdote. A challenge in pursuing this approach arises from the lack of mathemat- ical prerequisites for economics courses at many colleges and universities. The lack of calculus and problem-solving experience in general makes it difficult to present some of the analytical methods of economics. How- ever, it is not impossible. One can go a long way with a few simple facts about linear demand functions and supply functions and some elementary algebra. It is perfectly possible to be analytical wbeing excessively mathematical. The distinction is worth emphasizing. An analytical approacto eco- nomics is one that uses rigorous, logical reasoning. This does not neces- sarily require the use of advanced mathematical methodsThe language of mathematics certainly helps to ensure a rigorous analysis and using it is undoubtedly the best way to proceed when possible, but it may not be appropriate for all students. XX PREFACE Many undergraduate majors in economics are students who should know calculus, but don't-at least, not very well. For this reason I have kept cal- culus out of the main body of the text. However, I have provided complete calculus appendices to many of the chapters. This means that the calculus methods are there for the students who can handle them, but they do not pose a barrier to understanding for the others. I think that this approach manages to convey the idea that calculus is not just a footnote to the argument of the text, but is instead a deeper way to examine the same issues that one can also explore verbally and graphically. Many arguments are much simpler with a little mathematics, and all economics students should learn that. In many cases I've found that with a little motivation, and a few nice economic examples, students become quite enthusiastic about looking at things from an analytic per- spective. There are several other innovations in this text. First, the chapters are generally very short. I've tried to make most of them roughly "lecture size," so that they can be read at one sitting. I have followed the standard order of discussing first consumer theory and then producer theory, but I've spent a bit more time on consumer theory thpn is normally the case. This is not because I think that consumer theory is necessarily the most important part of microeconomics; rather, I have found that this is the material that students find the most mysterious, so I wanted to provide a more detailed treatment of it. Second, I've tried to put in a lot of examples of how to use the theory described here. In most books, students look at a lot of diagrams of shifting curves, but they don't see much algebra, or much calculation of anysort for that matter. But it is the algebra that is used to solve problems in practice. Graphs can provide insight, but the real power of economic analysis comes in calculating quantitative answers to economic problems. Every economics student should be able to translate an economic story into an equation or a numerical example, but all too often the development of this skill is neglected. For this reason I have also provided a workbook that I feel is an integral accompaniment to this book. The workbook was written with my colleague Theodore Bergstrom, and we have put a lot of effort into generating interesting and instructive problems. We think that it provides an important aid to the student of microeconomics. Third, I believe that the treatment of the topics in this book is more accurate than is usually the case in intermediate micro texts. It is true that I've sometimes chosen special cases to analyze when the general case is too difficult, but I've tried to be honest about that when I did it. In general, I've tried to spell out every step of each argument in detail. I believe that the discussion I'veprovided isnot only more complete and more accurate than usual, but this attention to detail also makes the arguments easier to understand than the loose discussion presented in many other books. PREFACE XXI There Are Many Pathsto Economic Enlightenment There is more material in this book than can comfortably be taught in one semester, so it is worthwhile picking and choosing carefully the material that you want to study. If you start on page 1 and proceed through the chapters in order, you will run out of time long before you reach the end of the book. The modular structure of the book allows the instructor a great deal of freedom in choosing how to present the material, and I hope that more people will take advantage of this freedom. The following chart illustrates the chapter dependencies. (AsymmetricInfor,k--o-- --- The dark colored chapters are "core" chapters-they should probably be covered in every intermediate microeconomics course. The light-colored chapt,ers are "optional" chapters: I cover some but not all of these every semester. The gray chapters are chapters I usually don't cover in my course, but they could easily be covered in other courses. A solid line going from Chapter A to Chapter B means that Chapter A should be read before chapter B. A broken line means that Chapter B requires knowing some material in Chapter A, but doesn't depend on it in a significant way. I generally cover consumer theory and markets and then proceed directly to producer theory. Another popular path is to do exchange right after XXll PREFACE consumer theory; many instructors prefer this route and I have gone to some trouble to make sure that this path is possible. Some people like to do producer theory before consumer theory. This is possible with this text, but if you choose this path, you will need to sup- plement the textbook treatment. The niaterial on isoquants, for example. assumes that the students have already seen indifference curves. Much of the material on public goods, externalities, law, and information can be introduced earlier in the course. I've arranged tlie material so that it is quite easy to put it pretty much wherever you desire. Similarly, the material on public goods can be irltroduced as an illus- tration of Edgeworth box analysis. Externalities can be introduced right after the discussion of cost curves, and topics from the information chapter can be introduced almost anywhere after students are familiar with thc approach of economic analysis. Changesfor the Seventh Edition consumer theory is still very useful in understanding economic phenomena, it is also important to understand its limitations and behavioral economics offers very useful insights for the economic analysis and policy. I have also added many new updated examples from current news events. My hope these examples will help students to learn to apply the concepts they learn to the stories they read in the newspaper or see on TV. In the fourth edition I added a chapter on information technology arid I have continued to develop that material in this edition. I describe some economic models of information networks, of switching costs, and of rights management for information goods. The point is to show how standard economic techniques of the sort developed in this book can lend significant insight into these issues. The TestBank and Workbook The workbook, Workouts in Intermediate Mzcroeconomzcs,is an integral part of the course. It contains hundreds of fill-in-the-blank exercises that lead the studentsthrough the steps of actually applying tlie tools they have learned in the textbook. In addition to the exercises, Workouts contains a collection of short multiple-choice quizzes based on the workbook problems in each chapter. Answers to the quizzes are also included in Workouts. These quizzes give a quick way for the student to review the material he or she has learned by working the problems in the workbook. But there is more ...instructors who have adopted Workouts for their course can make use of the Test Bank offered with the textbook. The PREFACE XXlll Test Bank contains several alternative versions of each Workouts quiz. The questions in these quizzes use different numerical values but the same internal logic. They can be used to provide additional problems for students to practice on, or to give quizzes to be taken in class. Grading is quick and reliable because the quizzes are multiple choice and can be graded electronically. In our course, we tell the students to work through all the quiz questions for each chapter, either by themselves or with a study group. Then during the term we have a short in-class quiz every other week or so, using the alternative versions from the Test Bank. These are essentially the Work- outs quizzes with different numbers. Hence, students who have done their homework find it easy to do well on the quizzes. We firmly believe that you can't learn economics without working some problems. The quizzes provided in Workouts and in the Test Bank make the learning process much easier for both the student and the teacher. A hard copy of the Test Bank is available from the publisher, as is the textbook's Instructor's Manual, which includes my teaching suggestions and lecture notes for each chapter of the textbook, and solutions to the exercises in Workouts. A nurnber of other useful ancillaries are also available with this text- book. These include a comprehensive set of Powerpoint slides, as well as the Norton Economic News Service, which alerts students to economic news related to specific ma,terial in the textbook. For information on these and other ancillaries, please visit the homepage for the book at http://www.wwnorton.com/varian. The Productionof the Book The entire book was typeset by the author using 'l?@C he wonderful type- setting system designed by Donald Knuth. I worked on a Linux system and using GNU emacs for editing, rcsfor version control and the T@Live system for processing. I used makeindex for the index, and Trevor Darrell's psfig software for inserting the diagrams. The book design was by Nancy Dale Muldoon, with some modifications by Roy Tedoff and the author. Anne Hellman was the manuscript editor, and Jack Repchek coordinated the whole effort in his capacity as editor. Acknowledgments Several people contributed to this project. First, I must thank my editorial assistants for the first edition, John Miller a,ndDebra Holt. John provided many comments, suggestions, and exercises based 011early drafts of this text and made a significant contribution to the coherence of the final prod- uct. Debra did a careful proofreading and consistency check during the final stages and helped in preparing the index. XXIV PREFACE The following individuals provided me with many useful suggestions and comments during the preparation of the first edition: Ken Binmore (Univer- sity of Michigan), Mark Bagnoli (Indiana University),Larry Chenault (Mi- ami University), Jonathan Hoag (Bowling Green State University), Allen Jacobs (M.I.T.), John McMillan (University of California at San Diego), Hal White (University of California at San Diego), and Gary Yohe (Wes- leyan University). In particular, I would like to thank Dr. Reiner Bucheg- ger, who prepared the German translation, for his close reading of the first edition and for providing me with a detailed list of corrections. Other in- dividuals to whom I owe thanks for suggestions prior to the first edition are Theodore Bergstrom, Jan Gerson, Oliver Landmann, Alasdair Smith, Barry Smith, and David Winch. My editorial assistants for the second edition were Sharon Parrott and Angela Bills. They provided much useful assistance with the writing and editing. Robert M. Costrell (University of Massachusetts at Amherst), Ash- ley Lyman (University of Idaho), Daniel Schwallie (Case-Western Reserve), A. D. Slivinskie (Western Ontario),and Charles Plourde (York University) provided me with detailedcomments and suggestions about how to improve the second edition. In preparing the third editionI received useful comments from the follow- ing individuals: Doris Cheng (San Jose), Imre Csek6 (Budapest), Gregory Hildebrandt (UCLA) , Jamie Brown Kruse (Colorado), Richard Manning (Brigham Young), Janet Mitchell (Cornell),Charles Plourde (YorkUniver- sity), Yeung-Nan Shieh (San Jose), John Winder (Toronto). I especially want to thank Roger F. Miller (University of Wisconsin), David Wildasin (Indiana) for their detailed comments, suggestions, and corrections. The fifth edition benefited from the comments by Kealoah Widdows (Wabash College),William Sims (ConcordiaUniversity), Jennifer R. Rein- ganum (Vanderbilt University), and Paul D. Thistle (Western Michigan University). I received comments that helped in preparation of the sixth edition from James S. Jordon (Pennsylvania State University), Brad Kamp (Univer- sity of South Florida), Sten Nyberg (Stockholm University), Matthew R. Roelofs (Western Washington University), Maarten-Pieter Schinkel (Uni- versity of Maastricht), and Arthur Walker (University of Northumbria). Finally, the seventh edition has benefited from reviews by Irina Khin- danova (Colorado School of Mines), Istvan Konya (Boston College), Shomu Banerjee (Georgia Tech) Andrew Helms (University of Georgia), Marc Melitz (Harvard University), Andrew Chatterjea (Cornell University), and Cheng-Zhong Qin (UC Santa Barbara). Berkeley, California October 2005 CHAPTER 1 THEMARKET The conventional first chapter of a microeconomics book is a discussion of the "scope and methods" of economics. Although this material can be very interesting, itseems appropriate to begin your study of economics with such materItis hard to appreciate such a discussion until you have seen some examples of economic analysis in action. So instead, we will begin this book with anonomic analysis. In this chapter we will examine a model of a the market market, of economics. Don't worry if it all goes by rather quickly. This chapterls is meant only to provide a quick overview of how these ideas can be used. Later on we will study them in substantially more detail. 1.1Constructinga Model Economics proceeds by developing models of socialBy anomena. model we mean a simplified representation of reality. The emphasis here is on the word "simple." Think about how useless a map on a one-to-one 2 THEMARKET (Ch.1) scale would be. The same is true of an economic model that attempts to de- scribe every aspect of reality. A model's power stems from the elimination of irrelevant detail, which allows the economist to focus on the essential features of the economic reality he or she is attempting to understand. Here we are interested in what. determines the price of apartments, so we want to have a simplified description of the apartment market. There is a certain art to choosing the right simplifications in building a model. In general we want to adopt the simplest model that is capable of describing the economic situation we are examining. We can then add complications one at a time, allowirig the model to become more complex and, we hope, more realistic. The particular example we want to consider is the market for apartments in a medium-size midwestern college town. In this town there are two sorts of apartments. There are some that are adjacent to the university, and others that are farther away. The adjacent apartments are generally considered to be more desirable by students, since they allow easier access to the university. The apartments that are farther away necessitate taking a bus, or a long, cold bicycle ride, so most students would prefer a nearby apartment .. if they can afford one. We will think of the apartments as being located in two large rings sur- rounding the university. The adjacent apartments are in the inner ring, while the rest are located in the outer ring. We will focus exclusively on the market for apa,rtments in the inner ring. The outer ring should be inter- preted as where people can go who don't find one of the closer apartments. We'll suppose that there are many apartments available in the outer ring, and t,heir price is fixed at some known level. We'll be concerned solely with the determination of the price of the inner-ring apartments and who gets to live there. An economist would describe the distinction between the prices ofthe two kinds of apartments in this model by saying that the price of the outer-ring apartments is an exogenous variable, while the price of the inner-ring apa,rtments is an endogenous variable. This means that the price of the outer-ring apartments is taken as determined by factors not discussed in this particular model, while the price of the inner-ring apartments is determined by forces described in the model. The first simplification that we'll make in our model is that all apart- ments are identical in every respect except for location. Thus it will make sense to speak of "the price" of apartments, without worrying about whether the apartments have one bedroom, or two bedrooms, or whatever. But what determines this price? What determines who will live in the inner-ring apartments and who will live farther out? What can be said about the desirability of different economic mechanisms for allocating apartments? What concepts can we use to judge the merit of different assignments of apartrnents to individuals? These are all questions that we want our model to address THE DEMAND CURVE 3 1.2 Optimization and Equilibrium Whenever we try to explain the behavior of human beings we need to have a framework on which our analysis can be based. In much of economics we use a framework built on the following two sirriple principles. The optimization principle: People try to choose the best patterns of consumptiori that they can afford. The equilibrium principle: Prices adjust until the amount that people demand of something is equal to the amount that is supplied. Let us consider these two principles. The first is almost tautological. If people are free to choose their actions, it is reasonable to assume that they try to choose things they want rather than things they don't want. Of course there are exceptions to this general principle, but they typically lie outside the domain of economic behavior. The second notion is a bit more problematic. It is at least conceivable that at any given time peoples' demands and supplies are not compati- ble, and hence something must be changing. These changes may take a long time to work themselves out, and, even worse, they niay induce other changes that might "destabilize" the whole system. This kind of thing can happen ...but it usually doesn't. frl the case of apartments, we typically see a fairly stable rental price froni month to month. It is this equilibrium price that we are interested in, not in how the market gets to this equilibrium or how it rnight change over long periods of time. It is worth observing that the definition used for equilibriurn may be different in different models. In the case of the simple market we will examine in this chapter, the demand and supply equilibrium idea will be adequate for our needs. But in more general models we will need more general definitions of equilibrium. Typically, equilibriurn will require that the eco~lornicagents' actions lliust be consisterit with each other. How do we use these two principles to determine the answers to the questions we raised above? It is time to introduce some economic concepts. 1.3 The Demand Curve Suppose that we consider all of the possible renters of the apartments and ask each of them the maximum amount that he or she would be willing to pay to rent one of the apartments. Let's start at the top. There must be someone who is willing to pay the highest price. Perhaps this person has a lot of money, perhaps he is 4 THE MARKET(Ch. 1) very lazy and doesn't want to walk far ... or whatever. Suppose that this person is willing to pay $500 a month for an apartment. If there is only orie person who is willing to pay $500 a rnonth to rent an apartment, then if the price for apartments were $500 a month, exactly one apartment would be rented-to the orie person who was willing to pay that price. Suppose that the next highest price that anyone is willing to pay is $490. Then if the market price were $499, there would still be only one apartment rented: the person who was willing to pay $500 would rent an apartment, but the person who was willing to pay $490 wouldn't. And so it goes. Only one apartrr~ent would be rented if the price were $498, $497, $496, and so on ...until we reach a price of $490. At that price, exactly two apartments would be rented: one to the $500 person and one to the $490 person. Similarly, two apartments would be rented until we reach the maximum price that the person with the third highest price would be willing to pay, and so on. Economists call a person's maximum willingness to pay for something that person's reservation price. The reservation price is the highest price that a given person will accept and still purchase the good. In other words, a person's reservation price is the price at which he or she is just indifferent between purchasing or not purchasing the good. In our example, if a person has a reservation price p it means that he or she would be just indifferent between living in the inner ring and paying a price p and living in the outer ring. Thus the number of apartments that will be rented at a given price p* will just be the number of people who have a reservation price greater than or equal to p*. For if the market price is p*, then everyone who is willing to pay at least p* for an apartment will want an apartment in the inner ring, and everyone who is not willing to pay p* will choose to live in the outer ring. We can plot these reservation prices in a diagram as in Figure 1.1. Here the price is depicted on the vertical axis and the number of people who are willing to pay that price or more is depicted on the horizontal axis. Another way to view Figure 1.1 is to think of it as measuring how many people would want to rent apartments at any particular price. Such a curve is an example of a demand curve-a curve that relates the quantity demanded to price. When the market price is above $500, zero apart- ments will be rented. When the price is between $500 and $490, one apartment will be rented. When it is between $490 and the third high- est reservation price, two apartments will be rented, and so on. The demand curve describes the quantity demanded at each of the possible prices. The demand curve for apartments slopes down: as the price of apart- ments decreases more people will be willing to rent apartments. If there are many people and their reservation prices differ only slightly from person to THESUPPLYCURVE .i Figure 1.1 person, it is reasonable to think of the demand curve as sloping smoothly downward, as in Figure 1.2. The curve in Figure 1.2 is what the demand curve in Figure 1.1 would look like if there were many people who want to rent the apartments. The "jumps" shown in Figure 1.1 are now so small relative to the size of the market that we can safely ignore them in drawing the market demand curve. 1.4 TheSupplyCurve We now have a nice graphical representation of demand behavior, so let us turn to supply behavior. Here we have to think about the nature of the market we are examining. The situation we wiI1consider is where there are many independent landlords who are each out to rent their apartments for the highest price the market will bear. We will refer to this as the case of a competitive market. Other sorts of market arrangements are certainly possible, and we will examine a few later. For now, let's consider the case where there are many landlords who all operate independently. It is clear that if all landlords are trying to do the best they can and if the renters are fully informed about the prices the landlords charge, then the equilibrium price of all apartments in the inner ring must be the same. The argument is not difficult. Suppose instead that there is some high price, ph, and some low price, pl, being charged 6 THE MARKET (Ch. 1) for apartments. The people who are renting their apartments for a high price could go to a landlord renting for a low price and offer to pay a rent somewhere between ph and pl. A transaction at such a price would make both the renter and the landlord better off. To the extent that all parties are seeking to further their own interests and are aware of the alternative prices being charged, a situation with different prices being charged for the same good cannot persist in equilibrium. But what will this single equilibrium price be? Let us try the method that we used in our construction of the demand curve: we will pick a price and ask how many apartments will be supplied at that price. The answer depends to some degree on the time frame in which we are examining the market. If we are considering a time fra~neof several years, so that new construction can take place, the number of apartments will certainly respond to the price that is charged. But in the "short run"- within a given year, say-the number of apartments is more or less fixed. If we consider only this short-run case, the supply of apartments will be constant at some predetermined level. The supply curve in this market is depicted in Figure 1.3 as a vertical line. Whatever price is being charged, the same number of apartments will be rented, namely, all the apartments that are available at that time. MARKETEQUILIBRIUM 7 1.5 Market Equilibrium We now have a way of representing the demand and the supply side of the apartment market. Let us put them together and ask what the equilibrium behavior of the market is. We do this by drawing both the demand and the supply curve on the same graph in Figure 1.4. In this graph we have used p* to denote the price where the quantity of apartments demanded equals the quantity supplied. This is the equi- librium price of apartments. At this price, each consumer who is willing to pay at leastp* is able to find an apartment to rent, and each landlord will be able to rent apartments at the going market price. Neither the con- sumers nor the landlords have any reason to change their behavior. This is why we refer to this as an equilibriu nm:change in behavior will be observed. To better understand this point, let us consider what would happen at a price other than p*. For example, consider some price p < p" where demand is greater than supply. Can this price persist? At this price at least some of the landlords will have more renters than they can handle. There will be lines of people hoping to get an apartment at that price; there are more people who are willing to pay the price p than there are apartments. Certainly some of the landlords would find it in their interest to raise the price of the apartments they are offering. Similarly, suppose that the price of apartments is some p greater than p*. 8 THE MARKET (Ch. 1) Then some of the apartments will be vacant: there are fewer people who are willing to pay p than there are apartments. Some of the landlords are now in danger of getting no rent at all for their apartments. Thus they will have an incentive to lower their price in order to attract more renters. If the price is above p* therearetoo few renters; if it is below p* there are too many renters. Only at the price of p* is the number of people who are willing to rent at that price equal to the number of apartments available for rent. Only at that price does demand equal supply. At the price p* the landlords' and the renters' behaviors are compatible in the sense that the number of apartments demanded by the renters at p* is equal to the number of apartments supplied by the landlords. This is the equilibrium price in the market for apartments. Once we've determined the market price for the inner-ring apartments, we can ask who ends up getting these apartments and who is exiled to the farther-away apartments. In our model there is a very simple answer to this question: in the market equilibrium everyone who is willing to pay p* or more gets an apartment in the inner ring, and everyone who is willing to pay less than p* gets one in the outer ring. The person who has a reser- vation price of p* is just indifferent between taking an apartment in the inner ring and taking one in the outer ring. The other people in the inner ring are getting theirapartments at less than the maximum they would be willing to pay for them. Thus the assignment of apartments to renters is determined by how much they are willing to pay. COMPARATIVESTATICS 9 1.6 ComparativeStatics Now that we have an economic model of the apartment market, we can begin to use it to analyze the behavior of the equilibrium price. For exam- ple, we can ask how the price of apartments changes when various aspects of the market change. This kind of an exercise is known as compara- tive statics, because it involves comparing two "static" equilibriawithout worrying about how the market moves from one equilibrium to another. The movement from one equilibrium to another can take a substantial amount of time, and questions about how such movement takes place can be very interesting and important. But we must walk before we can run, so we will ignore such dynamic questions for now. Comparative statics analysis is only concerned with comparing equilibria, and there will be enough questions to answer in this framework for the present. Let's start with a simple case. Suppose that the supply of apartments is increased, as in Figure 1.5. It is easy to see in this diagram that the equilibrium price of apartments will fall. Similarly, if the supply of apartments were reduced the equilibrium price would rise. 10 THEMARKET (Ch. 1) Let's try a more complicated-and more interesting-example. Suppose that a developer decides to turn several of the apartments into condomini- ums. What will happen to the price of the remaining apartments? Your first guess is probably that the price of apartments will go up, since the supply has been reduced. But this isn't necessarily right. It is true that the supply of apartments to rent has been reduced. But the de- mand for apartments has been reduced as well, since some of the people who were renting apartments may decide to purchase the new condomini- ums. It is natural to assume that the condominium purchasers come from those who already live in the inner-ring apartments-those people who are willing to pay more than p" for an apartment. Suppose, for example, that the demanders with the 10 highest reservation prices decide to buy condos rather than rent apartments. Then the new demand curve is just the old demand curve with 10 fewer demanders at each price. Since there are also 10 fewer apartments to rent, the new equilibrium price is just what it was before, and exactly the same people end up living in the inner- ring apartments. Thissituation is depicted in Figure 1.6. Both the demand curve and the supply curve shift left by 10 apartments, and the equilibrium price remains unchanged. OTHERWAYSTO ALLOCATEAPARTMENTS 11 Most people find this result surprising. They tend to see just the reduc- tion in the supply of apartments and don't think about the reduction in demand. The case we'veconsidered is an extreme one: all of the condo pur- chasers were former apartment dwellers. But the other case-where none of the condo purchasers were apartment dwellers-is even more extreme. The model, simple though it is, has led us to an important insight. If we want to determine how conversion to condominiums will affect the apart- ment market, we have to consider not only the effect on the supply of apartmentsbut also the effect on the demand for apartments. Let's consider another example of a surprising comparative statics anal- ysis: the effect of an apartment tax. Suppose that the city council decides that there should be a tax on apartments of $50 a year. Thus each landlord will have to pay $50 a year to the city for each apartment that he owns. What will this do to the price of apartments? Most people would think that at least some of the tax would get passed along to apartment renters. But, rather surprisingly, that is not the case. In fact, the equilibrium price of apartments will remain unchanged! In order to verify this, we have to ask what happens to the demand curve and the supply curve. The supply curve doesn't changethere are just as many apartments after the tax as before the tax. And the demand curve doesn't change either, since the number of apartments that will be rented at each different price will be the same as well. If neither the demand curve nor the supply curve shifts, the price can't change as a result of the tax. Here is a way to think about the effect of this tax. Before the tax is imposed, each landlord is charging the highest price that he can get that will keep his apartments occupied. The equilibrium price p* is the highest price that can be charged that is compatible with all of the apartments being rented. After thetax is imposed can the landlords raise their prices to compensate for the tax? The answer is no: if they could raise the price and keep their apartments occupied, they would have already done so. If they were charging the maximum price that the market could bear, the landlords couldn't raise their prices any more: none of the tax can get passed along to the renters. The landlords have to pay the entire amount of the tax. This analysis depends on the assumption that the supply of apartments remains fixed. If the number of apartments can vary as the tax changes, then the price paid by the renters will typically change. We'll examine this kind of behavior later on, after we've built up some more powerful tools for analyzing such problems. 1.7 Other Waysto Allocate Apartments In the previous section we described the equilibrium for apartments in a competitive market. But this is only one of many ways to allocate a 12 THE MARKET (Ch.1) resource; in this section we describe a few other ways. Some of these may sound rather strange, but each will illustrate an important economic point. -The DiscriminatingMonopolist First, let us consider a situation where there is one dominant landlord who owns all of the apartments. Or, alternatively, we could think of a number of individual landlords getting together and coordinating their actions to act as one. A situation where a market is dominated by a single seller of a product is known asa monopoly. In renting the apartments the landlord could decide to auction them off one by one to the highest bidders. Since this means that different people would end up paying different prices for apartments, we will call this the case of the discriminating monopolist. Let us suppose for simplicity that the discriminating monopolist knows each person's reservation price for apartments. (This is not terribly realistic, but it will serve to illustrate an important point.) This means that he would rent the first apartment to the fellow who would pay the most for it, in this case$500. The next apartment would go for $490 and so on as we moved down the demand curve. Each apartment would be rented to the person who was willing to pay the most for it. Here is the interesting feature of the discriminating monopolist: exactly the same people willget the apartments as in the case of the market solution, namely, everyone who valued an apartment at more than p*. The last person to rent an apartment pays the price p*-the same as the equilibrium price in a competitive market. The discriminating monopolist's attempt to maximize his own profits leads to the same allocation of apartments asthe supply and demand mechanism of the competitive market. The amount the people pay is different, but who gets the apartments is the same. It turns out that this is no accident, but we'll have to wait until later to explain the reason. The Orclinary Monopolist We assumed that the discriminating monopolist was able to rent each apart- ment at a different price. But what if he were forced to rent all apartments at the same price? In this case the monopolist faces a tradeoff: if he chooses a low price he will rent more apartments, but he may end up making less money than if he sets a higher price. Let us use D(p) to represent the demand function-the number of apart- ments demanded at price p. Then if the monopolist sets a price p, he will rent D(p) apartments and thus receive a revenue of pD(p). The revenue that the monopolist receives can be thought of as the area of a box: the OTHERWAYSTO ALLOCATE APARTMENTS 13 height of the box is the pricp and the width of the box is the number of apartments D(p). The product of the height and the width-the area of the box-is the revenue the monopolist receives. This is the box depicted in Figure 1.7. PRICE .. P s NUMBEROFAPARTMENTS Revenuebox. The revenuereceivedby the monopolistisjust the price times the quantity, whichcan be interpretedasthe areaof the box illustrated. If the monopolist has no costs associated with renting an apartment, he would want to choose a price that has the largest associated revenue box. The largest revenue box in Figure 1.7 occurs at the pricep. In this case the monopolist will find it in his interest to rent all of the apartments. In fact this will generally be the case for a monopolist.The monopolist will want to restrict the output available in order to maximize his profit. This means that the monopolist will generally want to charge a price that is higher than the equilibrium price in a competitive market, p*. In the case of the ordinary monopolist, fewer apartments will be rented, and each apartment will be rented at a higher price than in the competitive market. RentControl A third and final case that we will discuss will be the case of rent control. Suppose that the city decides to impose a maximum rent that can be 14 THE MARKET (Ch.1) charged for apartments, say p,,,. We suppose that the price p,,, is less than the equilibrium price in the competitive market, p*. If this is so we would have a situation of excess demand: there are more people who are willing to rent apartments at p,,, than there are apartments available. Who will end up with the apartments? The theory that we have described up until now doesn't have an answer to this question. We can describe what will happen when supply equals demand, but we don't have enough detail in the model to describe what will happen if supply doesn't equal demand. The answer to who gets the apartments under rent control depends on who has the most time to spend looking around, who knows the current tenants, and so on. All of these things are outside the scope of the simple model we've developed. It may be that exactly the same people get the apartments under rent control as under the competitive market. But that is an extremely unlikely outcome. It is much more likely that some of the formerly outer-ring people will end up in some of the inner-ring apartments and thus displace the people who would have been living there under the market system. So under rent control the same number of apartments will be rented at the rent-controlled price as were rented under the competitive price: they'll just be rent,ed to different people. 1.8 WhichWayIs Best? We've nowdescribed four possible ways of allocating apartments to people: The competitive market. A discriminating monopolist. An ordinary monopolist. Rent control. These are four different economic irlstitutio~ls for allocating apartments. Each method will result in different people getting apartments or in differ- ent prices being charged for apartments. We might well ask which economic institution is best. But first we have to define "best." What criteria might we use to compare these ways of allocating apartment,^? One thing we can do is to look at the economic positions of the people involved. It is pretty obvious that the owners of the apartments end up with the most money if they can act as discriminating monopolists: this would generate the most revenues for the apartment owner(s). Similarly the rent-control solution is probably the worst situation for the apartrrlent owners. What about the renters? They are probably worse off on average in the case of a discriminating monopolist-most of them would be paying a higher price than they would under the other ways of allocatirlg apartments. PARETO EFFICIENCY 15 Are the consumers better off in the case of rent control? Some of them are: the consumers who end up getting the apartments are better off than they would be under the market solution. But the ones who didn't get the apartments are worse off than they would be under the market solution. What we need here is a way to look at the economic position of all the parties involved-all the renters and all the landlords. How can weexamine the desirability of different ways to allocate apartments, taking everybody into account? What can be used as a criterion for a "good" way to allocate apartments taking into account all of the parties irivolved? 1.9 Pareto Efficiency One useful criterion for comparing the outcomes of different economic insti- tutions is a concept known as Pareto efficiency or economic efficiency.' We start with the following definition: if we can find a way to make somepeople better off without making anybody else worse off, we have a Pareto im- provement. If an allocation allows for a Pareto improvement, it is called Pareto inefficient; if an allocation is such that no Pareto improvements are possible, it is calledareto efficient. A Pareto inefficient allocation has the undesirable feature that there is some way to make somebody better off without hurting anyone else. There may be other positive things about the allocation, but the fact that it is Pareto inefficient is certainly one strike againit. If there is a way to make someone better off without hurting anyone else, why not do it? The idea of Pareto efficiency is an important one in economics and we will examine it; in some detail later on. It has many subtle implications that we will have to investigate more slowly, but we can get an inkling of what is involved even now. Here is a useful way to think about the idea of Pareto efficiency. Sup- pose that we assigned the renters to the inner- and outer-ring apartments randomly, but then allowed them to sublet their apartments to each other. Somepeople who really wanted to live closein might, through bad luck, end up with an outer-ring apartment. But then they could sublet an inner-ring apartment from someone who was assigned to such an apartment but who didn't value it as highly as the other person. If individuals were assigned randomly to apartments, there would generally be some who would want to trade apartments, if they were sufficiently compensated for doing so. For example,suppose that person A is assigned an apartment in the inner ring that lie feels isworth $200, and that there is some person B in the outer ring who would be willing to pay $300 for A's apartment. Then there is a Pareto efficiency is named after the nineteenth-ceneconomist and sociologist Vilfredo Pareto (1848-1923) who was one of the first to examine the implioftions this idea. 16 THEMARKET (Ch.1) "gain from trade" if these two agents swap apartments and arrange a side payment from B to A of some amount of money between $200 and $300. The exact amount of the transaction isn't important. What is important is that the people who are willing to pay the most for the apartments get them-otherwise, there would be an incentive for someone who attached a low value to an inner-ring apartment to make a trade with someone who placed a high value on an inner-ring apartment. Suppose that we think of all voluntary trades as being carried out so that all gains from trade ar
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