Intermediate Microeconomics - Eighth Edition PDF

This page intentionally left blank Intermediate Microeconomics A Modern Approach Eighth Edition W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter Norton ﬁrst published lec- tures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union. The ﬁrm soon expanded its program beyond the In- stitute, publishing books by celebrated academics from America and abroad. By mid-century, the two major pillars of Norton’s publishing program—trade books and college texts—were ﬁrmly established. In the 1950s, the Norton family trans- ferred control of the company to its employees, and today—with a staﬀ of four hundred and a comparable number of trade, college, and professional titles pub- lished each year—W. W. Norton & Company stands as the largest and oldest publishing house owned wholly by its employees. Copyright c 2010, 2006, 2003, 1999, 1996, 1993, 1990, 1987 by Hal R. Varian All rights reserved Printed in the United States of America EIGHTH EDITION Editor: Jack Repcheck Production Manager: Eric Pier–Hocking Editorial Assistant: Jason Spears TEXnician: Hal Varian ISBN 978-0-393-93424-3 W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110 W. W. Norton & Company, Ltd., Castle House, 75/76 Wells Street, London W1T 3QT www.wwnorton.com 1234567890 Intermediate Microeconomics A Modern Approach Eighth Edition Hal R. Varian University of California at Berkeley W. W. Norton & Company New York London This page intentionally left blank To Carol This page intentionally left blank CONTENTS Preface xix 1 The Market Constructing a Model 1 Optimization and Equilibrium 3 The De- mand Curve 3 The Supply Curve 5 Market Equilibrium 7 Com- parative Statics 9 Other Ways to Allocate Apartments 11 The Dis- criminating Monopolist The Ordinary Monopolist Rent Control Which Way Is Best? 14 Pareto Eﬃciency 15 Comparing Ways to Al- locate Apartments 16 Equilibrium in the Long Run 17 Summary 18 Review Questions 19 2 Budget Constraint The Budget Constraint 20 Two Goods Are Often Enough 21 Prop- erties of the Budget Set 22 How the Budget Line Changes 24 The Numeraire 26 Taxes, Subsidies, and Rationing 26 Example: The Food Stamp Program Budget Line Changes 31 Summary 31 Review Questions 32 VIII CONTENTS 3 Preferences Consumer Preferences 34 Assumptions 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 MRS 51 Summary 52 Review Questions 52 4 Utility Cardinal Utility 57 Constructing a Utility Function 58 Some Exam- ples of Utility Functions 59 Example: Indiﬀerence Curves from 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-Douglas Preferences 5 Choice Optimal Choice 73 Consumer Demand 78 Some Examples 78 Perfect Substitutes Perfect Complements Neutrals and Bads Discrete Goods Concave Preferences Cobb-Douglas Preferences Estimating Utility Functions 83 Implications of the MRS Condition 85 Choosing Taxes 87 Summary 89 Review Questions 89 Appen- dix 90 Example: Cobb-Douglas Demand Functions 6 Demand Normal and Inferior Goods 96 Income Oﬀer Curves and Engel 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 Summary 114 Review Questions 115 Appendix 115 CONTENTS IX 7 Revealed Preference 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 Slutsky Equation The Substitution Eﬀect 137 Example: Calculating the Substitution Ef- fect The Income Eﬀect 141 Example: Calculating the Income Eﬀect Sign of the Substitution Eﬀect 142 The Total Change in Demand 143 Rates of Change 144 The Law of Demand 147 Examples of Income and Substitution Eﬀects 147 Example: Rebating a Tax Example: Voluntary 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 Buying and 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: Calculating the Endowment Income Eﬀect Labor Supply 173 The Budget Constraint Comparative Statics of Labor Supply 174 Example: Overtime and the Supply of Labor Sum- mary 178 Review Questions 179 Appendix 179 X CONTENTS 10 Intertemporal Choice The Budget Constraint 182 Preferences for Consumption 185 Com- parative Statics 186 The Slutsky Equation and Intertemporal Choice 187 Inﬂation 189 Present Value: A Closer Look 191 Analyz- ing Present Value for Several Periods 193 Use of Present Value 194 Example: Valuing a Stream of Payments Example: The True Cost of a Credit Card Example: Extending Copyright Bonds 198 Exam- ple: Installment Loans Taxes 200 Example: Scholarships and Sav- ings Choice of the Interest Rate 201 Summary 202 Review Ques- tions 202 11 Asset Markets Rates of Return 203 Arbitrage and Present Value 205 Adjustments for Diﬀerences among Assets 205 Assets with Consumption Returns 206 Taxation of Asset Returns 207 Market Bubbles 208 Applica- tions 209 Depletable Resources When to Cut a Forest Example: Gasoline Prices during the Gulf War Financial Institutions 213 Sum- mary 214 Review Questions 215 Appendix 215 12 Uncertainty Contingent Consumption 217 Example: Catastrophe Bonds Utility Functions and Probabilities 222 Example: Some Examples of Utility Functions Expected Utility 223 Why Expected Utility Is Reasonable 224 Risk Aversion 226 Example: The Demand for Insurance Di- versiﬁcation 230 Risk Spreading 230 Role of the Stock Market 231 Summary 232 Review Questions 232 Appendix 233 Example: The Eﬀect of Taxation on Investment in Risky Assets 13 Risky Assets Mean-Variance Utility 236 Measuring Risk 241 Counterparty Risk 243 Equilibrium in a Market for Risky Assets 243 How Returns Adjust 245 Example: Value at Risk Example: Ranking Mutual Funds Summary 249 Review Questions 250 CONTENTS XI 14 Consumer’s Surplus Demand for a Discrete Good 252 Constructing Utility from Demand 253 Other Interpretations of Consumer’s Surplus 254 From Con- sumer’s Surplus to Consumers’ Surplus 255 Approximating a Continu- ous Demand 255 Quasilinear Utility 255 Interpreting the Change in Consumer’s Surplus 256 Example: The Change in Consumer’s Surplus Compensating and Equivalent Variation 258 Example: Compensating and Equivalent Variations Example: Compensating and Equivalent Vari- ation for Quasilinear Preferences Producer’s Surplus 262 Beneﬁt-Cost Analysis 264 Rationing Calculating Gains and Losses 266 Sum- mary 267 Review Questions 267 Appendix 268 Example: A Few Demand Functions Example: CV, EV, and Consumer’s Surplus 15 Market Demand From Individual to Market Demand 270 The Inverse Demand Function 272 Example: Adding Up “Linear” Demand Curves Discrete Goods 273 The Extensive and the Intensive Margin 273 Elasticity 274 Example: The Elasticity of a Linear Demand Curve Elasticity and De- mand 276 Elasticity and Revenue 277 Example: Strikes and Proﬁts Constant Elasticity Demands 280 Elasticity and Marginal Revenue 281 Example: Setting a Price Marginal Revenue Curves 283 Income Elas- ticity 284 Summary 285 Review Questions 286 Appendix 287 Example: The Laﬀer Curve Example: Another Expression for Elasticity 16 Equilibrium Supply 293 Market Equilibrium 293 Two Special Cases 294 In- verse Demand and Supply Curves 295 Example: Equilibrium with Lin- ear Curves Comparative Statics 297 Example: Shifting Both Curves Taxes 298 Example: Taxation with Linear Demand and Supply Pass- ing Along a Tax 302 The Deadweight Loss of a Tax 304 Example: The Market for Loans Example: Food Subsidies Example: Subsidies in Iraq Pareto Eﬃciency 310 Example: Waiting in Line Summary 313 Review Questions 313 XII CONTENTS 17 Auctions Classiﬁcation of Auctions 316 Bidding Rules Auction Design 317 Other Auction Forms 320 Example: Late Bidding on eBay Position Auctions 322 Two Bidders More Than Two Bidders Quality Scores Problems with Auctions 326 Example: Taking Bids Oﬀ the Wall The Winner’s Curse 327 Stable Marriage Problem 327 Mech- anism Design 329 Summary 331 Review Questions 331 18 Technology Inputs and Outputs 332 Describing Technological Constraints 333 Examples of Technology 334 Fixed Proportions Perfect Substi- tutes Cobb-Douglas Properties of Technology 336 The Marginal Product 338 The Technical Rate of Substitution 338 Diminishing Marginal Product 339 Diminishing Technical Rate of Substitution 339 The Long Run and the Short Run 340 Returns to Scale 340 Ex- ample: Datacenters Example: Copy Exactly! Summary 343 Review Questions 344 19 Proﬁt Maximization Proﬁts 345 The Organization of Firms 347 Proﬁts and Stock Market Value 347 The Boundaries of the Firm 349 Fixed and Variable Fac- tors 350 Short-Run Proﬁt Maximization 350 Comparative Statics 352 Proﬁt Maximization in the Long Run 353 Inverse Factor Demand Curves 354 Proﬁt Maximization and Returns to Scale 355 Revealed Proﬁtability 356 Example: How Do Farmers React to Price Supports? Cost Minimization 360 Summary 360 Review Questions 361 Ap- pendix 362 CONTENTS XIII 20 Cost Minimization Cost Minimization 364 Example: Minimizing Costs for Speciﬁc Tech- nologies Revealed Cost Minimization 368 Returns to Scale and the Cost Function 369 Long-Run and Short-Run Costs 371 Fixed and Quasi-Fixed Costs 373 Sunk Costs 373 Summary 374 Review Questions 374 Appendix 375 21 Cost Curves Average Costs 378 Marginal Costs 380 Marginal Costs and Variable Costs 382 Example: Speciﬁc Cost Curves Example: Marginal Cost Curves for Two Plants Cost Curves for Online Auctions 386 Long-Run Costs 387 Discrete Levels of Plant Size 389 Long-Run Marginal Costs 390 Summary 391 Review Questions 392 Appendix 393 22 Firm Supply Market Environments 395 Pure Competition 396 The Supply Deci- sion of a Competitive Firm 398 An Exception 400 Another Exception 401 Example: Pricing Operating Systems The Inverse Supply Func- tion 403 Proﬁts and Producer’s Surplus 403 Example: The Supply Curve for a Speciﬁc Cost Function The Long-Run Supply Curve of a Firm 407 Long-Run Constant Average Costs 409 Summary 410 Review Questions 411 Appendix 411 XIV CONTENTS 23 Industry Supply Short-Run Industry Supply 413 Industry Equilibrium in the Short Run 414 Industry Equilibrium in the Long Run 415 The Long-Run Supply Curve 417 Example: Taxation in the Long Run and in the Short Run The Meaning of Zero Proﬁts 421 Fixed Factors and Economic Rent 422 Example: Taxi Licenses in New York City Economic Rent 424 Rental Rates and Prices 426 Example: Liquor Licenses The Politics of Rent 427 Example: Farming the Government Energy Policy 429 Two-Tiered Oil Pricing Price Controls The Entitlement Program Carbon Tax Versus Cap and Trade 433 Optimal Production of Emis- sions A Carbon Tax Cap and Trade Summary 437 Review Questions 437 24 Monopoly Maximizing Proﬁts 440 Linear Demand Curve and Monopoly 441 Markup Pricing 443 Example: The Impact of Taxes on a Monopo- list Ineﬃciency of Monopoly 445 Deadweight Loss of Monopoly 447 Example: The Optimal Life of a Patent Example: Patent Thickets Ex- ample: Managing the Supply of Potatoes Natural Monopoly 451 What Causes Monopolies? 454 Example: Diamonds Are Forever Example: Pooling in Auction Markets Example: Price Fixing in Computer Memory Markets Summary 458 Review Questions 458 Appendix 459 25 Monopoly Behavior Price Discrimination 462 First-Degree Price Discrimination 462 Ex- ample: First-degree Price Discrimination in Practice Second-Degree Price Discrimination 465 Example: Price Discrimination in Airfares Ex- ample: Prescription Drug Prices Third-Degree Price Discrimination 469 Example: Linear Demand Curves Example: Calculating Optimal Price Discrimination Example: Price Discrimination in Academic Journals Bundling 474 Example: Software Suites Two-Part Tariﬀs 475 Mo- nopolistic Competition 476 A Location Model of Product Diﬀerentiation 480 Product Diﬀerentiation 482 More Vendors 483 Summary 484 Review Questions 484 CONTENTS XV 26 Factor Markets Monopoly in the Output Market 485 Monopsony 488 Example: The Minimum Wage Upstream and Downstream Monopolies 492 Summary 494 Review Questions 495 Appendix 495 27 Oligopoly Choosing a Strategy 498 Example: Pricing Matching Quantity Lead- ership 499 The Follower’s Problem The Leader’s Problem Price Leadership 504 Comparing Price Leadership and Quantity Leadership 507 Simultaneous Quantity Setting 507 An Example of Cournot Equilibrium 509 Adjustment to Equilibrium 510 Many Firms in Cournot Equilibrium 511 Simultaneous Price Setting 512 Collu- sion 513 Punishment Strategies 515 Example: Price Matching and Competition Example: Voluntary Export Restraints Comparison of the Solutions 519 Summary 519 Review Questions 520 28 Game Theory The Payoﬀ Matrix of a Game 522 Nash Equilibrium 524 Mixed Strategies 525 Example: Rock Paper Scissors The Prisoner’s Dilemma 527 Repeated Games 529 Enforcing a Cartel 530 Example: Tit for Tat in Airline Pricing Sequential Games 532 A Game of Entry Deterrence 534 Summary 536 Review Questions 537 29 Game Applications Best Response Curves 538 Mixed Strategies 540 Games of Coordi- nation 542 Battle of the Sexes Prisoner’s Dilemma Assurance Games Chicken How to Coordinate Games of Competition 546 Games of Coexistence 551 Games of Commitment 553 The Frog and the Scorpion The Kindly Kidnapper When Strength Is Weakness Savings and Social Security Hold Up Bargaining 561 The Ultimatum Game Summary 564 Review Questions 565 XVI CONTENTS 30 Behavioral Economics Framing Eﬀects in Consumer Choice 567 The Disease Dilemma Anchoring Eﬀects Bracketing Too Much Choice Constructed Preferences Uncertainty 571 Law of Small Numbers Asset In- tegration and Loss Aversion Time 574 Discounting Self-control Example: Overconﬁdence Strategic Interaction and Social Norms 576 Ultimatum Game Fairness Assessment of Behavioral Economics 578 Summary 579 Review Questions 581 31 Exchange The Edgeworth Box 583 Trade 585 Pareto Eﬃcient Allocations 586 Market Trade 588 The Algebra of Equilibrium 590 Walras’ Law 592 Relative Prices 593 Example: An Algebraic Example of Equilibrium The Existence of Equilibrium 595 Equilibrium and Eﬃ- ciency 596 The Algebra of Eﬃciency 597 Example: Monopoly in the Edgeworth Box Eﬃciency and Equilibrium 600 Implications of the First Welfare Theorem 602 Implications of the Second Welfare Theorem 604 Summary 606 Review Questions 607 Appendix 607 32 Production The Robinson Crusoe Economy 609 Crusoe, Inc. 611 The Firm 612 Robinson’s Problem 613 Putting Them Together 613 Diﬀerent Tech- nologies 615 Production and the First Welfare Theorem 617 Produc- tion and the Second Welfare Theorem 618 Production Possibilities 618 Comparative Advantage 620 Pareto Eﬃciency 622 Castaways, Inc. 624 Robinson and Friday as Consumers 626 Decentralized Resource Allocation 627 Summary 628 Review Questions 628 Appen- dix 629 CONTENTS XVII 33 Welfare Aggregation of Preferences 632 Social Welfare Functions 634 Welfare Maximization 636 Individualistic Social Welfare Functions 638 Fair Allocations 639 Envy and Equity 640 Summary 642 Review Questions 642 Appendix 643 34 Externalities Smokers and Nonsmokers 645 Quasilinear Preferences and the Coase Theorem 648 Production Externalities 650 Example: Pollution Vouchers Interpretation of the Conditions 655 Market Signals 658 Example: Bees and Almonds The Tragedy of the Commons 659 Ex- ample: Overﬁshing Example: New England Lobsters Automobile Pollu- tion 663 Summary 665 Review Questions 665 35 Information Technology Systems Competition 668 The Problem of Complements 668 Re- lationships among Complementors Example: Apple’s iPod and iTunes Example: Who Makes an iPod? Example: AdWords and AdSense Lock- In 674 A Model of Competition with Switching Costs Example: Online Bill Payment Example: Number Portability on Cell Phones Net- work Externalities 678 Markets with Network Externalities 678 Mar- ket Dynamics 680 Example: Network Externalities in Computer Soft- ware Implications of Network Externalities 684 Example: The Yellow Pages Example: Radio Ads Two-sided Markets 686 A Model of Two-sided Markets Rights Management 687 Example: Video Rental Sharing Intellectual Property 689 Example: Online Two-sided Markets Summary 692 Review Questions 693 XVIII CONTENTS 36 Public Goods When to Provide a Public Good? 695 Private Provision of the Public Good 699 Free Riding 699 Diﬀerent Levels of the Public Good 701 Quasilinear Preferences and Public Goods 703 Example: Pollution Revisited The Free Rider Problem 705 Comparison to Private Goods 707 Voting 708 Example: Agenda Manipulation The Vickrey- Clarke-Groves Mechanism 711 Groves Mechanism The VCG Mech- anism Examples of VCG 713 Vickrey Auction Clarke-Groves Mechanism Problems with the VCG 714 Summary 715 Review Questions 716 Appendix 716 37 Asymmetric Information The Market for Lemons 719 Quality Choice 720 Choosing the Qual- ity Adverse Selection 722 Moral Hazard 724 Moral Hazard and Adverse Selection 725 Signaling 726 Example: The Sheepskin Eﬀect Incentives 730 Example: Voting Rights in the Corporation Example: Chinese Economic Reforms Asymmetric Information 735 Example: Monitoring Costs Example: The Grameen Bank Summary 738 Re- view Questions 739 Mathematical Appendix Functions A1 Graphs A2 Properties of Functions A2 Inverse Functions A3 Equations and Identities A3 Linear Functions A4 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 Derivatives A8 Optimization A9 Constrained Optimization A10 Answers A11 Index A31 PREFACE The success of the ﬁrst seven 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 foundations of 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 without being excessively mathematical. The distinction is worth emphasizing. An analytical approach to eco- nomics is one that uses rigorous, logical reasoning. This does not neces- sarily require the use of advanced mathematical methods. The 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 than 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 any sort 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’ve provided is not 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 Paths to 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. The Market Budget Preferences Utility Uncertainty Choice Intertemporal Choice Demand Revealed Preference Asset Markets Consumer's Surplus Market Demand Slutsky Equation Risky Assets Buying and Selling Equilibrium Exchange Auctions Information Technology Profit Maximization Technology Production Welfare Cost Minimization Cost Curves Firm Supply Industry Supply Monopoly Behavior Monopoly Oligopoly Factor Markets Externalities Game Theory Public Goods Game Applications Asymmetric Information The dark colored chapters are “core” chapters—they should probably be covered in every intermediate microeconomics course. The light-colored chapters 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 XXII 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 material 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 the material so that it is quite easy to put it pretty much wherever you desire. Similarly, the material on public goods can be introduced 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 the approach of economic analysis. Changes for the Eight Edition In this edition I have added several new examples involving events, in- cluding copyright extension, asset price bubbles, counterparty risk, value at risk, and carbon taxes. I have continued to oﬀer examples drawn from Silicon Valley ﬁrms such as Apple, eBay, Google, Yahoo and others. I dis- cuss topics such as the complementarity between the iPod and iTunes, the positive feedback associated with companies such as Facebook, and the ad auction models used by Google, Microsoft, and Yahoo. I believe that these are fresh and interesting examples of economics in action. I’ve also added an extended discussion of mechanism design issues, in- cluding two-sided matching markets and the Vickrey-Clarke-Groves mech- anisms. This ﬁeld, which was once primarily theoretical in nature, has now taken on considerable practical importance. The Test Bank and Workbook The workbook, Workouts in Intermediate Microeconomics, is an integral part of the course. It contains hundreds of ﬁll-in-the-blank exercises that lead the students through the steps of actually applying the 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 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 PREFACE XXIII 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 number 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 material in the textbook. For information on these and other ancillaries, please visit the homepage for the book at http://www.wwnorton.com/varian. The Production of the Book The entire book was typeset by the author using TEX, the wonderful type- setting system designed by Donald Knuth. I worked on a Linux system and using GNU emacs for editing, rcs for version control and the TEXLive 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. 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 and Debra Holt. John provided many comments, suggestions, and exercises based on early 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. 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- XXIV PREFACE 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 detailed comments and suggestions about how to improve the second edition. In preparing the third edition I received useful comments from the follow- ing individuals: Doris Cheng (San Jose), Imre Csekó (Budapest), Gregory Hildebrandt (UCLA), Jamie Brown Kruse (Colorado), Richard Manning (Brigham Young), Janet Mitchell (Cornell), Charles Plourde (York Univer- 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 (Concordia University), 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). The seventh edition received reviews by Irina Khindanova (Colorado School of Mines), Istvan Konya (Boston College), Shomu Banerjee (Georgia Tech) Andrew Helms (University of Georgia), Marc Melitz (Harvard Uni- versity), Andrew Chatterjea (Cornell University), and Cheng-Zhong Qin (UC Santa Barbara). Finally, I received helpful comments on the eighth edition from Kevin Balsam (Hunter College), Clive Belﬁeld (Queens College, CUNY), Jeﬀrey Miron (Harvard University), Babu Nahata (University of Louisville), and Scott J. Savage (University of Colorado). Berkeley, California October 2009 CHAPTER 1 THE MARKET 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, it hardly seems appropriate to begin your study of economics with such material. It is 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 an example of economic analysis. In this chapter we will examine a model of a particular market, the market for apartments. Along the way we will introduce several new ideas and tools of economics. Don’t worry if it all goes by rather quickly. This chapter 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. 1.1 Constructing a Model Economics proceeds by developing models of social phenomena. By a 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 THE MARKET (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, allowing 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 apartments 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 their 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 of the 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 apartments 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 apartments 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 simple principles. The optimization principle: People try to choose the best patterns of consumption 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 may induce other changes that might “destabilize” the whole system. This kind of thing can happen... but it usually doesn’t. In the case of apartments, we typically see a fairly stable rental price from 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 might change over long periods of time. It is worth observing that the deﬁnition used for equilibrium 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, equilibrium will require that the economic agents’ actions must be consistent 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 one person who is willing to pay $500 a month to rent an apartment, then if the price for apartments were $500 a month, exactly one apartment would be rented—to the one 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 apartment 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 THE SUPPLY CURVE 5 RESERVATION PRICE 500...... 490...... 480............... Demand curve............ 1 2 3... NUMBER OF APARTMENTS The demand curve for apartments. The vertical axis mea- Figure sures the market price and the horizontal axis measures how 1.1 many apartments will be rented at each price. 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 The Supply Curve 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 will consider 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) RESERVATION PRICE Demand curve NUMBER OF APARTMENTS Figure Demand curve for apartments with many demanders. 1.2 Because of the large number of demanders, the jumps between prices will be small, and the demand curve will have the con- ventional smooth shape. 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 frame of 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. MARKET EQUILIBRIUM 7 RESERVATION PRICE Supply S NUMBER OF APARTMENTS Short-run supply curve. The supply of apartments is ﬁxed Figure in the short run. 1.3 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 least p∗ 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 equilibrium: no 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) RESERVATION PRICE Supply p* Demand S NUMBER OF APARTMENTS Figure Equilibrium in the apartment market. The equilibrium 1.4 price, p∗ , is determined by the intersection of the supply and demand curves. 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∗ there are too 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 their apartments 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. COMPARATIVE STATICS 9 1.6 Comparative Statics 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” equilibria without 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. RESERVATION PRICE Old New supply supply Old p* New p* Demand S S' NUMBER OF APARTMENTS Increasing the supply of apartments. As the supply of Figure apartments increases, the equilibrium price decreases. 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 THE MARKET (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. This situation 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. RESERVATION PRICE New Old supply supply p* Old demand New demand S S' NUMBER OF APARTMENTS Figure Eﬀect of creating condominiums. If demand and supply 1.6 both shift left by the same amount the equilibrium price is un- changed. OTHER WAYS TO ALLOCATE APARTMENTS 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’ve considered 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 apartments but 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 change—there 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 the tax 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 Ways to 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 Discriminating Monopolist 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 as a 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 will get 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 as the 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 Ordinary 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 OTHER WAYS TO ALLOCATE APARTMENTS 13 height of the box is the price p 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 Supply pˆ Demand ˆ D(p) S NUMBER OF APARTMENTS Revenue box. The revenue received by the monopolist is just Figure the price times the quantity, which can be interpreted as the 1.7 area of 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 price p̂. In this case the monopolist will ﬁnd it in his interest not 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. Rent Control 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 pmax. We suppose that the price pmax 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 pmax 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 rented to diﬀerent people. 1.8 Which Way Is Best? We’ve now described four possible ways of allocating apartments to people: The competitive market. A discriminating monopolist. An ordinary monopolist. Rent control. These are four diﬀerent economic institutions 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 apartments? 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 apartment 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 allocating 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 we examine 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 involved? 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.1 We start with the following deﬁnition: if we can ﬁnd a way to make some people 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 called Pareto 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 against it. 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. Some people who really wanted to live close in 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 he feels is worth $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 1 Pareto eﬃciency is named after the nineteenth-century economist and sociologist Vilfredo Pareto (1848–1923) who was one of the ﬁrst to examine the implications of this idea. 16 THE MARKET (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 are exhausted. The resulting allocation must be Pareto eﬃcient. If not, there would be some trade that would make two people better oﬀ without hurting anyone else—but this would contradict the assumption that all voluntary trades had been carried out. An alloca- tion in which all voluntary trades have been carried out is a Pareto eﬃcient allocation. 1.10 Comparing Ways to Allocate Apartments The trading process we’ve described above is so general that you wouldn’t think that anything much could be said about its outcome. But there is one very interesting point that can be made. Let us ask who will end up with apartments in an allocation where all of the gains from trade have been exhausted. To see the answer, just note that anyone who has an apartment in the inner ring must have a higher reservation price than anyone who has an apartment in the outer ring—otherwise, they could make a trade and make both people better oﬀ. Thus if there are S apartments to be rented, then the S people with the highest reservation prices end up getting apartments in the inner ring. This allocation is Pareto eﬃcient—anything else is not, since any other assignment of apartments to people would allow for some trade that would make at least two of the people better oﬀ without hurting anyone else. Let us try to apply this criterion of Pareto eﬃciency to the outcomes of the various resource allocation devices mentioned above. Let’s start with the market mechanism. It is easy to see that the market mechanism assigns the people with the S highest reservation prices to the inner ring—namely, those people who are willing to pay more than the equilibrium price, p∗ , for their apartments. Thus there are no further gains from trade to be had once the apartments have been rented in a competitive market. The outcome of the competitive market is Pareto eﬃcient. What about the discriminating monopolist? Is that arrangement Pareto eﬃcient? To answer this question, simply observe that the discriminat- ing monopolist assigns apartments to exactly the same people who receive apartments in the competitive market. Under each system everyone who is willing to pay more than p∗ for an apartment gets an apartment. Thus the discriminating monopolist generates a Pareto eﬃcient outcome as well. EQUILIBRIUM IN THE LONG RUN 17 Although both the competitive market and the discriminating monop- olist generate Pareto eﬃcient outcomes in the sense that there will be no further trades desired, they can result in quite diﬀerent distributions of income. Certainly the consumers are much worse oﬀ under the discrimi- nating monopolist than under the competitive market, and the landlord(s) are much better oﬀ. In general, Pareto eﬃciency doesn’t have much to say about distribution of the gains from trade. It is only concerned with the eﬃciency of the trade: whether all of the possible trades have been made. What about the ordinary monopolist who is constrained to charge just one price? It turns out that this situation is not Pareto eﬃcient. All we have to do to verify this is to note that, since all the apartments will not in general be rented by the monopolist, he can increase his proﬁts by renting an apartment to someone who doesn’t have one at any positive price. There is some price at which both the monopolist and the renter must be better oﬀ. As long as the monopolist doesn’t change the price that anybody else pays, the other renters are just as well oﬀ as they were before. Thus we have found a Pareto improvement—a way to make two parties better oﬀ without making anyone else worse oﬀ. The ﬁnal case is that of rent control. This also turns out not to be Pareto eﬃcient. The argument here rests on the fact that an arbitrary assignment of renters to apartments will generally involve someone living in the inner ring (say Mr. In) who is willing to pay less for an apartment than someone living in the outer ring (say Ms. Out). Suppose that Mr. In’s reservation price is $300 and Ms. Out’s reservation price is $500. We need to ﬁnd a Pareto improvement—a way to make Mr. In and Ms. Out better oﬀ without hurting anyone else. But there is an easy way to do this: just let Mr. In sublet his apartment to Ms. Out. It is worth $500 to Ms. Out to live close to the university, but it is only worth $300 to Mr. In. If Ms. Out pays Mr. In $400, say, and trades apartments, they will both be better oﬀ: Ms. Out will get an apartment that she values at more than $400, and Mr. In will get $400 that he values more than an inner-ring apartment. This example shows that the rent-controlled market will generally not result in a Pareto eﬃcient allocation, since there will still be some trades that could be carried out after the market has operated. As long as some people get inner-ring apartments who value them less highly than people who don’t get them, there will be gains to be had from trade. 1.11 Equilibrium in the Long Run We have analyzed the equilibrium pricing of apartments in the short run— when there is a ﬁxed supply of apartments. But in the long run the supply of apartments can change. Just as the demand curve measures the number of apartments that will be demanded at diﬀerent prices, the supply curve measures the number of apartments that will be supplied at diﬀerent prices. 18 THE MARKET (Ch. 1) The ﬁnal determination of the market price for apartments will depend on the interaction of supply and demand. And what is it that determines the supply behavior? In general, the number of new apartments that will be supplied by the private market will depend on how proﬁtable it is to provide apartments, which depends, in part, on the price that landlords can charge for apartments. In order to analyze the behavior of the apartment market in the long run, we have to examine the behavior of suppliers as well as demanders, a task we will eventually undertake. When supply is variable, we can ask questions not only about who gets the apartments, but about how many will be provided by various types of market institutions. Will a monopolist supply more or fewer apartments than a competitive market? Will rent control increase or decrease the equi- librium number of apartments? Which institutions will provide a Pareto eﬃcient number of apartments? In order to answer these and similar ques- tions we must develop more systematic and powerful tools for economic analysis. Summary 1. Economics proceeds by making models of social phenomena, which are simpliﬁed representations of reality. 2. In this task, economists are guided by the optimization principle, which states that people typically try to choose what’s best for them, and by the equilibrium principle, which says that prices will adjust until demand and supply are equal. 3. The demand curve measures how much people wish to demand at each price, and the supply curve measures how much people wish to supply at each price. An equilibrium price is one where the amount demanded equals the amount supplied. 4. The study of how the equilibrium price and quantity change when the underlying conditions change is known as comparative statics. 5. An economic situation is Pareto eﬃcient if there is no way to make some group of people better oﬀ without making some other group of people worse oﬀ. The concept of Pareto eﬃciency can be used to evaluate diﬀerent ways of allocating resources. REVIEW QUESTIONS 19 REVIEW QUESTIONS 1. Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. What would the demand curve look like? 2. In the above example, what would the equilibrium price be if there were 24 apartments to rent? What if there were 26 apartments to rent? What if there were 25 apartments to rent? 3. If people have diﬀerent reservation prices, why does the market demand curve slope down? 4. In the text we assumed that the condominium purchasers came from the inner-ring people—people who were already renting apartments. What would happen to the price of inner-ring apartments if all of the condo- minium purchasers were outer-ring people—the people who were not cur- rently renting apartments in the inner ring? 5. Suppose now that the condominium purchasers were all inner-ring peo- ple, but that each condominium was constructed from two apartments. What would happen to the price of apartments? 6. What do you suppose the eﬀect of a tax would be on the number of apartments that would be built in the long run? 7. Suppose the demand curve is D(p) = 100 − 2p. What price would the monopolist set if he had 60 apartments? How many would he rent? What price would he set if he had 40 apartments? How many would he rent? 8. If our model of rent control allowed for unrestricted subletting, who would end up getting apartments in the inner circle? Would the outcome be Pareto eﬃcient? CHAPTER 2 BUDGET CONSTRAINT The economic theory of the consumer is very simple: economists assume that consumers choose the best bundle of goods they can aﬀord. To give content to this theory, we have to describe more precisely what we mean by “best” and what we mean by “can aﬀord.” In this chapter we will examine how to describe what a consumer can aﬀord; the next chapter will focus on the concept of how the consumer determines what is best. We will then be able to undertake a detailed study of the implications of this simple model of consumer behavior. 2.1 The Budget Constraint We begin by examining the concept of the budget constraint. Suppose that there is some set of goods from which the consumer can choose. In real life there are many goods to consume, but for our purposes it is conve- nient to consider only the case of two goods, since we can then depict the consumer’s choice behavior graphically. We will indicate the consumer’s consumption bundle by (x1 , x2 ). This is simply a list of two numbers that tells us how much the consumer is choos- ing to consume of good 1, x1 , and how much the consumer is choosing to TWO GOODS ARE OFTEN ENOUGH 21 consume of good 2, x2. Sometimes it is convenient to denote the consumer’s bundle by a single symbol like X, where X is simply an abbreviation for the list of two numbers (x1 , x2 ). We suppose that we can observe the prices of the two goods, (p1 , p2 ), and the amount of money the consumer has to spend, m. Then the budget constraint of the consumer can be written as p1 x1 + p2 x2 ≤ m. (2.1) Here p1 x1 is the amount of money the consumer is spending on good 1, and p2 x2 is the amount of money the consumer is spending on good 2. The budget constraint of the consumer requires that the amount of money spent on the two goods be no more than the total amount the consumer has to spend. The consumer’s aﬀordable consumption bundles are those that don’t cost any more than m. We call this set of aﬀordable consumption bundles at prices (p1 , p2 ) and income m the budget set of the consumer. 2.2 Two Goods Are Often Enough The two-good assumption is more general than you might think at ﬁrst, since we can often interpret one of the goods as representing everything else the consumer might want to consume. For example, if we are interested in studying a consumer’s demand for milk, we might let x1 measure his or her consumption of milk in quarts per month. We can then let x2 stand for everything else the consumer might want to consume. When we adopt this interpretation, it is convenient to think of good 2 as being the dollars that the consumer can use to spend on other goods. Under this interpretation the price of good 2 will automatically be 1, since the price of one dollar is one dollar. Thus the budget constraint will take the form p1 x1 + x2 ≤ m. (2.2) This expression simply says that the amount of money spent on good 1, p1 x1 , plus the amount of money spent on all other goods, x2 , must be no more than the total amount of money the consumer has to spend, m. We say that good 2 represents a composite good that stands for ev- erything else that the consumer might want to consume other than good 1. Such a composite good is invariably measured in dollars to be spent on goods other than good 1. As far as the algebraic form of the budget constraint is concerned, equation (2.2) is just a special case of the formula given in equation (2.1), with p2 = 1, so everything that we have to say about the budget constraint in general will hold under the composite-good interpretation. 22 BUDGET CONSTRAINT (Ch. 2) 2.3 Properties of the Budget Set The budget line is the set of bundles that cost exactly m: p1 x1 + p2 x2 = m. (2.3) These are the bundles of goods that just exhaust the consumer’s income. The budget set is depicted in Figure 2.1. The heavy line is the budget line—the bundles that cost exactly m—and the bundles below this line are those that cost strictly less than m. x2 Vertical intercept = m/p 2 Budget line; slope = – p1 /p2 Budget set Horizontal intercept = m/p1 x1 Figure The budget set. The budget set consists of all bundles that 2.1 are aﬀordable at the given prices and income. We can rearrange the budget line in equation (2.3) to give us the formula m p1 x2 = − x1. (2.4) p2 p2 This is the formula for a straight line with a vertical intercept of m/p2 and a slope of −p1 /p2. The formula tells us how many units of good 2 the consumer needs to consume in order to just satisfy the budget constraint if she is consuming x1 units of good 1. PROPERTIES OF THE BUDGET SET 23 Here is an easy way to draw a budget line given prices (p1 , p2 ) and income m. Just ask yourself how much of good 2 the consumer could buy if she spent all of her money on good 2. The answer is, of course, m/p2. Then ask how much of good 1 the consumer could buy if she spent all of her money on good 1. The answer is m/p1. Thus the horizontal and vertical intercepts measure how much the consumer could get if she spent all of her money on goods 1 and 2, respectively. In order to depict the budget line just plot these two points on the appropriate axes of the graph and connect them with a straight line. The slope of the budget line has a nice economic interpretation. It mea- sures the rate at which the market is willing to “substitute” good 1 for good 2. Suppose for example that the consumer is going to increase her consumption of good 1 by Δx1.1 How much will her consumption of good 2 have to change in order to satisfy her budget constraint? Let us use Δx2 to indicate her change in the consumption of good 2. Now note that if she satisﬁes her budget constraint before and after making the change she must satisfy p1 x1 + p2 x2 = m and p1 (x1 + Δx1 ) + p2 (x2 + Δx2 ) = m. Subtracting the ﬁrst equation from the second gives p1 Δx1 + p2 Δx2 = 0. This says that the total value of the change in her consumption must be zero. Solving for Δx2 /Δx1 , the rate at which good 2 can be substituted for good 1 while still satisfying the budget constraint, gives Δx2 p1 =−. Δx1 p2 This is just the slope of the budget line. The negative sign is there since Δx1 and Δx2 must always have opposite signs. If you consume more of good 1, you have to consume less of good 2 and vice versa if you continue to satisfy the budget constraint. Economists sometimes say that the slope of the budget line measures the opportunity cost of consuming good 1. In order to consume more of good 1 you have to give up some consumption of good 2. Giving up the opportunity to consume good 2 is the true economic cost of more good 1 consumption; and that cost is measured by the slope of the budget line. 1 The Greek letter Δ, delta, is pronounced “del-ta.” The notation Δx1 denotes the change in good 1. For more on changes and rates of changes, see the Mathematical Appendix. 24 BUDGET CONSTRAINT (Ch. 2) 2.4 How the Budget Line Changes When prices and incomes change, the set of goods that a consumer can aﬀord changes as well. How do these changes aﬀect the budget set? Let us ﬁrst consider changes in income. It is easy to see from equation (2.4) that an increase in income will increase the vertical intercept and not aﬀect the slope of the line. Thus an increase in income will result in a par- allel shift outward of the budget line as in Figure 2.2. Similarly, a decrease in income will cause a parallel shift inward. x2 m’/p2 Budget lines m/p2 Slope = –p1/p 2 m/p1 m’/p1 x1 Figure Increasing income. An increase in income causes a parallel 2.2 shift outward of the budget line. What about changes in prices? Let us ﬁrst consider increasing price 1 while holding price 2 and income ﬁxed. According to equation (2.4), increasing p1 will not change the vertical intercept, but it will make the budget line steeper since p1 /p2 will become larger. Another way to see how the budget line changes is to use the trick de- scribed earlier for drawing the budget line. If you are spending all of your money on good 2, then increasing the price of good 1 doesn’t change the maximum amount of good 2 you could buy—thus the vertical inter- cept of the budget line doesn’t change. But if you are spending all of your money on good 1, and good 1 becomes more expensive, then your HOW THE BUDGET LINE CHANGES 25 consumption of good 1 must decrease. Thus the horizontal intercept of the budget line must shift inward, resulting in the tilt depicted in Fig- ure 2.3. x2 m/p2 Budget lines Slope = –p'1 /p2 Slope = –p1 /p2 m/p'1 m/p1 x1 Increasing price. If good 1 becomes more expensive, the Figure budget line becomes steeper. 2.3 What happens to the budget line when we change the prices of good 1 and good 2 at the same time? Suppose for example that we double the prices of both goods 1 and 2. In this case both the horizontal and vertical intercepts shift inward by a factor of one-half, and therefore the budget line shifts inward by one-half as well. Multiplying both prices by two is just like dividing income by 2. We can also see this algebraically. Suppose our original budget line is p1 x1 + p2 x2 = m. Now suppose that both prices become t times as large. Multiplying both prices by t yields tp1 x1 + tp2 x2 = m. But this equation is the same as m p1 x1 + p2 x2 =. t Thus multiplying both prices by a constant amount t is just like dividing income by the same constant t. It follows that if we multiply both prices 26 BUDGET CONSTRAINT (Ch. 2) by t and we multiply income by t, then the budget line won’t change at all. We can also consider price and income changes together. What happens if both prices go up and income goes down? Think about what happens to the horizontal and vertical intercepts. If m decreases and p1 and p2 both increase, then the intercepts m/p1 and m/p2 must both decrease. This means that the budget line will shift inward. What about the slope of the budget line? If price 2 increases more than price 1, so that −p1 /p2 decreases (in absolute value), then the budget line will be ﬂatter; if price 2 increases less than price 1, the budget line will be steeper. 2.5 The Numeraire The budget line is deﬁned by two prices and one income, but one of these variables is redundant. We could peg one of the prices, or the income, to some ﬁxed value, and adjust the other variables so as to describe exactly the same budget set. Thus the budget line p1 x1 + p2 x2 = m is exactly the same budget line as p1 m x1 + x2 = p2 p2 or p1 p2 x1 + x2 = 1, m m since the ﬁrst budget line results from dividing everything by p2 , and the second budget line results from dividing everything by m. In the ﬁrst case, we have pegged p2 = 1, and in the second case, we have pegged m = 1. Pegging the price of one of the goods or income to 1 and adjusting the other price and income appropriately doesn’t change the budget set at all. When we set one of the prices to 1, as we did above, we often refer to that price as the numeraire price. The numeraire price is the price relative to which we are measuring the other price and income. It will occasionally be convenient to think of one of the goods as being a numeraire good, since there will then be one less price to worry about. 2.6 Taxes, Subsidies, and Rationing Economic policy often uses tools that aﬀect a consumer’s budget constraint, such as taxes. For example, if the government imposes a quantity tax, this means that the consumer has to pay a certain amount to the government TAXES, SUBSIDIES, AND RATIONING 27 for each unit of the good he purchases. In the U.S., for example, we pay about 15 cents a gallon as a federal gasoline tax. How does a quantity tax aﬀect the budget line of a consumer? From the viewpoint of the consumer the tax is just like a higher price. Thus a quantity tax of t dollars per unit of good 1 simply changes the price of good 1 from p1 to p1 + t. As we’ve seen above, this implies that the budget line must get steeper. Another kind of tax is a value tax. As the name implies this is a tax on the value—the price—of a good, rather than the quantity purchased of a good. A value tax is usually expressed in percentage terms. Most states in the U.S. have sales taxes. If the sales tax is 6 percent, then a good that is priced at $1 will actually sell for $1.06. (Value taxes are also known as ad valorem taxes.) If good 1 has a price of p1 but is subject to a sales tax at rate τ , then the actual price facing the consumer is (1 + τ )p1.2 The consumer has to pay p1 to the supplier and τ p1 to the government for each unit of the good so the total cost of the good to the consumer is (1 + τ )p1. A subsidy is the opposite of a tax. In the case of a quantity subsidy, the government gives an amount to the consumer that depends on the amount of the good purchased. If, for example, the consumption of milk were subsidized, the government would pay some amount of money to each consumer of milk depending on the amount that consumer purchased. If the subsidy is s dollars per unit of consumption of good 1, then from the viewpoint of the consumer, the price of good 1 would be p1 − s. This would therefore make the budget line ﬂatter. Similarly an ad valorem subsidy is a subsidy based on the price of the good being subsidized. If the government gives you back $1 for every $2 you donate to charity, then your donations to charity are being subsidized at a rate of 50 percent. In general, if the price of good 1 is p1 and good 1 is subject to an ad valorem subsidy at rate σ, then the actual price of good 1 facing the consumer is (1 − σ)p1.3 You can see that taxes and subsidies aﬀect prices in exactly the same way except for the algebraic sign: a tax increases the price to the consumer, and a subsidy decreases it. Another kind of tax or subsidy that the government might use is a lump- sum tax or subsidy. In the case of a tax, this means that the government takes away some ﬁxed amount of money, regardless of the individual’s be- havior. Thus a lump-sum tax means that the budget line of a consumer will shift inward because his money income has been reduced. Similarly, a lump-sum subsidy means that the budget line will shift outward. Quantity taxes and value taxes tilt the budget line one way or the other depending 2 The Greek letter τ , tau, rhymes with “wow.” 3 The Greek letter σ is pronounced “sig-ma.” 28 BUDGET CONSTRAINT (Ch. 2) on which good is being taxed, but a lump-sum tax shifts the budget line inward. Governments also sometimes impose rationing constraints. This means that the level of consumption of some good is ﬁxed to be no larger than some amount. For example, during World War II the U.S. government rationed certain foods like butter and meat. Suppose, for example, that good 1 were rationed so that no more than x1 could be consumed by a given consumer. Then the budget set of the consumer would look like that depicted in Figure 2.4: it would be the old budget set with a piece lopped oﬀ. The lopped-oﬀ piece consists of all the consumption bundles that are aﬀordable but have x1 > x1. x2 Budget line Budget set x1 x1 Figure Budget set with rationing. If good 1 is rationed, the section 2.4 of the budget set beyond the rationed quantity will be lopped oﬀ. Sometimes taxes, subsidies, and rationing are combined. For example, we could consider a situation where a consumer could consume good 1 at a price of p1 up to some level x1 , and then had to pay a tax t on all consumption in excess of x1. The budget set for this consumer is depicted in Figure 2.5. Here the budget line has a slope of −p1 /p2 to the left of x1 , and a slope of −(p1 + t)/p2 to the right of x1. TAXES, SUBSIDIES, AND RATIONING 29 x2 Budget lin

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