ECON 533 & ECON 602 Quiz 2, November 15, 2020 Profesor: Manuel S. Santos Fall 2020 PLEASE SUBMIT BEFORE NOVEMBER 22. PLEASE, DO NOT COMMUNICATE WITH YOUR CLASSMATES. You can answer 5 out of 8 short questions, and 2 problems. Grad students must answer 5 short questions (including VI-VIII), and two problems (including problem 3). If you answer six short questions, then one short question counts as bonus. Same for problem 3. 1. QUESTION I: Can you write down a CES production function? Which parameter determines the (constant) elasticity of substitution? And the labor income share? Which assumptions would you need to make in the evolution of wages and rental rates in order to replicate the declining US labor income share? 2. QUESTION II: Suppose that we have increasing returns to scale. Would the cost function be concave or convex in output? Would the marginal cost be increasing or decreasing? Would the optimization problem be well defined? 3. QUESTION III: In some textbooks we are told that tuitive. How would you explain this? @y @w = @L . @p This looks counterin- 4. QUESTION IV: What does it mean third-degree price discrimination? Would you provide some examples? 5. QUESTION V: Please, discuss. Does it make sense for Zara to have these short selling cycles? How Zara grew into the World’s Largest Retailer. ”When you went to Gucci or Chanel in October, you knew the chances were good that clothes would still be there in February,”BUT ”With Zara, you know that if you don’t buy it, right then and there, within 11 days the entire stock will change. You buy it now or never. And because the prices are so low, you buy it now.” 6. QUESTION VI: Could you write down the first-order condition of the prototypical moral hazard model (hidden e↵ort) as a function of the likelihood ratio? How would you interpret this condition to provide optimal incentives for rewarding e↵ort? 7. QUESTION VII In the adverse selection model discussed in class, we encountered the following condition: ✓L C(0, ✓L ) ✓H C(t̂, ✓L ). Please, explain this condition. Moreover, how does this condition get translated in an insurance market with two types of consumers (the bad type and the good type). Hint: Mas-Colell, 13.D.2. 1 8. QUESTION VIII In our corruption paper, is Equation (5) an IR constraint or an IC constraint? Explain the meaning of this constraint (is it a moral hazard model?). Would you suggest any changes to this constraint? 9. PROBLEM 1: A monopolist (AT &T ) is facing the following demand schedule P = 24 3Q. That is, Q = 0 implies P = 24, then Q = 1 implies P = 21, and Q = 2 implies P = 18, and so one. Fixed costs will be neglected in this analysis. The marginal cost is constant and equal to 6 for every unit produced. Determine: (i) The quantity produced corresponding to the amount of maximum profit. (ii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC =6 under both Cournot and Bertrand Competition. (iii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=7 under Bertrand Competition. (iv) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=5 under Bertrand Competition. 10. PROBLEM 2: Spotify o↵ers a hassle-free (no-commercials) program. Here, at UM, a professor would be willing to subscribe for a monthly free of $30, and a student would be willing to subscribe for $10. There is a second program in which commercials take ten percent of the time. The company will get one-dollar revenue for running these commercials in all cases. However, the disutility of the commercials to each student would be $2, and to a professor would be $8.00. Assume that half of the population are professors and half are students, and Spotify is committed to serve both markets. A. (Market segmentation) Compute the optimal price(s) for each type in the case that Spotify has access to the UM records and is able to tell who is a professor and a student. B. (Hidden Types). Compute optimal price(s) in the case that Spotify has no access to UM records, and cannot identify types. C. (Hidden Types). Assume linear preferences and linear revenues. An undergrad student from ECO 533 has suggested to Spotify to change the second program so that commercials should take 20 percent of the time. Again redo part B, assuming that in the second program commercials take 20 percent of the time. D. (Hidden Types) Actually, our student goes further and claims to have computed the optimal percentage amount of advertising for the second program under the linearity assumption on preferences and commercial revenues. Following part B, are you able to compute the optimal amount of advertising for Spotify serving UM? 11. PROBLEM 3: This is Mas-Collel, 13.C.6. Let us assume the following condition: pG ⇧ (1 + r) > pB ⇧ (1 + r) > 0. Now, following this problem in the book: (i) Find the level of Ri (i = 1, 2) in a separating equilibrium. (ii) Find the level of R in a pooling equilibrium. 2 (iii) How a separating equilibrium will look like in case that the bank can also o↵er a new contract in which the entrepreneur is required to contribute a fraction x of the one dollar initial outlay. Assume that the entrepreneur can get this money at an interest rate ⇢ slightly higher than r. (Else, assume that the entrepreneur has the cash.) 3 ECON 533 & ECON 602 Quiz 2, November 15, 2020 Profesor: Manuel S. Santos Fall 2020 PLEASE SUBMIT BEFORE NOVEMBER 22. PLEASE, DO NOT COMMUNICATE WITH YOUR CLASSMATES. You can answer 5 out of 8 short questions, and 2 problems. Grad students must answer 5 short questions (including VI-VIII), and two problems (including problem 3). If you answer six short questions, then one short question counts as bonus. Same for problem 3. 1. QUESTION I: Can you write down a CES production function? Which parameter determines the (constant) elasticity of substitution? And the labor income share? Which assumptions would you need to make in the evolution of wages and rental rates in order to replicate the declining US labor income share? 2. QUESTION II: Suppose that we have increasing returns to scale. Would the cost function be concave or convex in output? Would the marginal cost be increasing or decreasing? Would the optimization problem be well defined? 3. QUESTION III: In some textbooks we are told that tuitive. How would you explain this? @y @w = @L . @p This looks counterin- 4. QUESTION IV: What does it mean third-degree price discrimination? Would you provide some examples? 5. QUESTION V: Please, discuss. Does it make sense for Zara to have these short selling cycles? How Zara grew into the World’s Largest Retailer. ”When you went to Gucci or Chanel in October, you knew the chances were good that clothes would still be there in February,”BUT ”With Zara, you know that if you don’t buy it, right then and there, within 11 days the entire stock will change. You buy it now or never. And because the prices are so low, you buy it now.” 6. QUESTION VI: Could you write down the first-order condition of the prototypical moral hazard model (hidden e↵ort) as a function of the likelihood ratio? How would you interpret this condition to provide optimal incentives for rewarding e↵ort? 7. QUESTION VII In the adverse selection model discussed in class, we encountered the following condition: ✓L C(0, ✓L ) ✓H C(t̂, ✓L ). Please, explain this condition. Moreover, how does this condition get translated in an insurance market with two types of consumers (the bad type and the good type). Hint: Mas-Colell, 13.D.2. 1 8. QUESTION VIII In our corruption paper, is Equation (5) an IR constraint or an IC constraint? Explain the meaning of this constraint (is it a moral hazard model?). Would you suggest any changes to this constraint? 9. PROBLEM 1: A monopolist (AT &T ) is facing the following demand schedule P = 24 3Q. That is, Q = 0 implies P = 24, then Q = 1 implies P = 21, and Q = 2 implies P = 18, and so one. Fixed costs will be neglected in this analysis. The marginal cost is constant and equal to 6 for every unit produced. Determine: (i) The quantity produced corresponding to the amount of maximum profit. (ii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC =6 under both Cournot and Bertrand Competition. (iii) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=7 under Bertrand Competition. (iv) Equilibrium price if a new competitor, Vodafone, enters the market with a MC=5 under Bertrand Competition. 10. PROBLEM 2: Spotify o↵ers a hassle-free (no-commercials) program. Here, at UM, a professor would be willing to subscribe for a monthly free of $30, and a student would be willing to subscribe for $10. There is a second program in which commercials take ten percent of the time. The company will get one-dollar revenue for running these commercials in all cases. However, the disutility of the commercials to each student would be $2, and to a professor would be $8.00. Assume that half of the population are professors and half are students, and Spotify is committed to serve both markets. A. (Market segmentation) Compute the optimal price(s) for each type in the case that Spotify has access to the UM records and is able to tell who is a professor and a student. B. (Hidden Types). Compute optimal price(s) in the case that Spotify has no access to UM records, and cannot identify types. C. (Hidden Types). Assume linear preferences and linear revenues. An undergrad student from ECO 533 has suggested to Spotify to change the second program so that commercials should take 20 percent of the time. Again redo part B, assuming that in the second program commercials take 20 percent of the time. D. (Hidden Types) Actually, our student goes further and claims to have computed the optimal percentage amount of advertising for the second program under the linearity assumption on preferences and commercial revenues. Following part B, are you able to compute the optimal amount of advertising for Spotify serving UM? 11. PROBLEM 3: This is Mas-Collel, 13.C.6. Let us assume the following condition: pG ⇧ (1 + r) > pB ⇧ (1 + r) > 0. Now, following this problem in the book: (i) Find the level of Ri (i = 1, 2) in a separating equilibrium. (ii) Find the level of R in a pooling equilibrium. 2 (iii) How a separating equilibrium will look like in case that the bank can also o↵er a new contract in which the entrepreneur is required to contribute a fraction x of the one dollar initial outlay. Assume that the entrepreneur can get this money at an interest rate ⇢ slightly higher than r. (Else, assume that the entrepreneur has the cash.) 3 QUIZ 2 Question 2: 1. Increasing returns to scale infers that the cost function is Convex. 2. The marginal cost is increasing. 3. The optimization problem will be defined that variable factor like labor is not fully utilized in increasing returns to scale. Question 4: Third degree price discrimination occurs when a company charges different prices to different groups of consumers. For example, theatres divide their costumers into seniors, adults, and children, and charge them different prices for the same movie. Question 5: Zara makes money by having these short selling cycles. It also helps Zara to clear out all its stock. Luxuries like Gucci and Chanel takes time to clear out their stock. We do not see Gucci and Chanel put “BIG SALE “mark on their windows. And because the price of Zara is lower than Gucci and Chanel, they are easier to clear out stock. This is due to the downward sloping demand curve; Customers will buy things when the price of a product is low. And when the price of a product is high, their willingness to buy will decrease. In this case, prices of luxuries like Gucci and Chanel are high, so the quantity demand for their product is respectively low. Zara, however, set its price respectively low, so the quantity demanded is high. Hence, Zara grew into the world’s largest retailer. MICROECONOMIC THEORY Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Microeconomic Theory Basic Principles and Extensions ELEVENTH EDITION WALTER NICHOLSON Amherst College CHRISTOPHER SNYDER Dartmouth College Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Microeconomic Theory: Basic Principles and Extensions, Eleventh Edition Walter Nicholson, Christopher Snyder VP/Editorial Director: Jack W. Calhoun Publisher: Joe Sabatino Sr. Acquisitions Editor: Steve Scoble Sr. Developmental Editor: Susanna C. Smart Marketing Manager: Nathan Anderson Sr. Content Project Manager: Cliff Kallemeyn Media Editor: Sharon Morgan Sr. Frontlist Buyer: Kevin Kluck Sr. Marketing Communications Manager: Sarah Greber ª 2012, 2008 South-Western, Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. 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For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com All graphs and figures owned by Cengage Learning. ª 2010 Cengage Learning. Printed in the United States of America 1 2 3 4 5 6 7 15 14 13 12 11 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. To Beth, Sarah, David, Sophia, Abby, Nate, and Christopher To Maura Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. About the authors Walter Nicholson is the Ward H. Patton Professor of Economics at Amherst College. He received a B.A. in mathematics from Williams College and a Ph.D. in economics from the Massachusetts Institute of Technology (MIT). Professor Nicholson’s primary research interests are in the econometric analyses of labor market problems, including welfare, unemployment, and the impact of international trade. For many years, he has been Senior Fellow at Mathematica, Inc. and has served as an advisor to the U.S. and Canadian governments. He and his wife, Susan, live in Naples, Florida, and Amherst, Massachusetts. Christopher M. Snyder is a Professor of Economics at Dartmouth College. He received his B.A. in economics and mathematics from Fordham University and his Ph.D. in economics from MIT. He is Research Associate in the National Bureau of Economic Research, a member of the Industrial Organization Society board, and Associate Editor of the International Journal of Industrial Organization and Review of Industrial Organization. His research covers various theoretical and empirical topics in industrial organization, contract theory, and law and economics. Professor Snyder and his wife Maura Doyle (who also teaches economics at Dartmouth) live within walking distance of campus in Hanover, New Hampshire, with their three school-aged daughters. Professors Nicholson and Snyder are also the authors of Intermediate Microeconomics and Its Application (Cengage Learning, 2010). vii Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Brief Contents Preface PART ONE xix Introduction CHAPTER 1 CHAPTER 2 PART TWO CHAPTER 4 CHAPTER 5 CHAPTER 6 THREE CHAPTER 8 PART CHAPTER 10 CHAPTER 11 PART CHAPTER 13 SIX CHAPTER 15 PART CHAPTER 17 EIGHT The Partial Equilibrium Competitive Model General Equilibrium and Welfare 457 Monopoly 501 Imperfect Competition Pricing in Input Markets CHAPTER 16 PART Production Functions 303 Cost Functions 333 Profit Maximization 371 409 Market Power 499 CHAPTER 14 SEVEN 301 Competitive Markets 407 CHAPTER 12 PART Uncertainty 209 Game Theory 251 Production and Supply CHAPTER 9 FIVE Preferences and Utility 89 Utility Maximization and Choice 117 Income and Substitution Effects 145 Demand Relationships among Goods 187 Uncertainty and Strategy 207 CHAPTER 7 FOUR 21 Choice and Demand 87 CHAPTER 3 PART 1 Economic Models 3 Mathematics for Microeconomics CHAPTER 19 579 Labor Markets 581 Capital and Time 607 Market Failure CHAPTER 18 531 639 Asymmetric Information 641 Externalities and Public Goods 685 Brief Answers to Queries 717 Solutions to Odd-Numbered Problems 727 Glossary of Frequently Used Terms 739 Index 747 ix Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Contents Preface ……………………………………………………………………………………………………………………………… xix PART ONE Introduction CHAPTER 1 Economic Models …………………………………………………………………………………………………….. 3 Theoretical Models 3 Verification of Economic Models 4 General Features of Economic Models 5 Development of the Economic Theory of Value 9 Modern Developments 17 Summary 18 Suggestions for Further Reading 19 CHAPTER 2 Mathematics for Microeconomics………………………………………………………………………….. 21 Maximization of a Function of One Variable 21 Functions of Several Variables 26 Maximization of Functions of Several Variables 33 The Envelope Theorem 35 Constrained Maximization 39 Envelope Theorem in Constrained Maximization Problems 45 Inequality Constraints 46 Second-Order Conditions and Curvature 48 Homogeneous Functions 55 Integration 58 Dynamic Optimization 63 Mathematical Statistics 67 Summary 76 Problems 77 Suggestions for Further Reading 82 Extensions: Second-Order Conditions and Matrix Algebra 83 PART TWO Choice and Demand CHAPTER 3 Preferences and Utility…………………………………………………………………………………………… 89 Axioms of Rational Choice 89 xi Copyright 2011 Cengage Learning. 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Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xii Contents Utility 90 Trades and Substitution 92 The Mathematics of Indifference Curves 99 Utility Functions for Specific Preferences 102 The Many-Good Case 106 Summary 106 Problems 107 Suggestions for Further Reading 110 Extensions: Special Preferences 112 CHAPTER 4 Utility Maximization and Choice…………………………………………………………………………… 117 An Initial Survey 118 The Two-Good Case: A Graphical Analysis 119 The n-Good Case 122 Indirect Utility Function 128 The Lump Sum Principle 129 Expenditure Minimization 131 Properties of Expenditure Functions 134 Summary 136 Problems 136 Suggestions for Further Reading 140 Extensions: Budget Shares 141 CHAPTER 5 Income and Substitution Effects …………………………………………………………………………… 145 Demand Functions 145 Changes in Income 147 Changes in a Good’s Price 149 The Individual’s Demand Curve 152 Compensated (Hicksian) Demand Curves and Functions 155 A Mathematical Development of Response to Price Changes 160 Demand Elasticities 163 Consumer Surplus 169 Revealed Preference and the Substitution Effect 174 Summary 176 Problems 177 Suggestions for Further Reading 180 Extensions: Demand Concepts and the Evaluation of Price Indices 181 CHAPTER 6 Demand Relationships among Goods……………………………………………………………………. 187 The Two-Good Case 187 Substitutes and Complements 189 Net (Hicksian) Substitutes and Complements 191 Copyright 2011 Cengage Learning. 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Contents xiii Substitutability with Many Goods 193 Composite Commodities 193 Home Production, Attributes of Goods, and Implicit Prices 197 Summary 200 Problems 200 Suggestions for Further Reading 203 Extensions: Simplifying Demand and Two-Stage Budgeting 204 PART THREE Uncertainty and Strategy CHAPTER 7 Uncertainty …………………………………………………………………………………………………………… 209 Mathematical Statistics 209 Fair Gambles and the Expected Utility Hypothesis 210 Expected Utility 211 The von Neumann–Morgenstern Theorem 212 Risk Aversion 214 Measuring Risk Aversion 217 Methods for Reducing Uncertainty and Risk 222 Insurance 222 Diversification 223 Flexibility 224 Information 231 The State-Preference Approach to Choice Under Uncertainty 232 Asymmetry of Information 238 Summary 238 Problems 239 Suggestions for Further Reading 242 Extensions: The Portfolio Problem 244 CHAPTER 8 Game Theory ………………………………………………………………………………………………………… 251 Basic Concepts 251 Prisoners’ Dilemma 252 Nash Equilibrium 254 Mixed Strategies 260 Existence of Equilibrium 265 Continuum of Actions 265 Sequential Games 268 Repeated Games 274 Incomplete Information 277 Simultaneous Bayesian Games 278 Signaling Games 282 Experimental Games 288 Copyright 2011 Cengage Learning. 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Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xiv Contents Evolutionary Games and Learning 290 Summary 290 Problems 291 Suggestions for Further Reading 295 Extensions: Existence of Nash Equilibrium PART FOUR 296 Production and Supply CHAPTER 9 Production Functions ……………………………………………………………………………………………. 303 Marginal Productivity 303 Isoquant Maps and the Rate of Technical Substitution 306 Returns to Scale 310 The Elasticity of Substitution 313 Four Simple Production Functions 316 Technical Progress 320 Summary 324 Problems 325 Suggestions for Further Reading 328 Extensions: Many-Input Production Functions 329 CHAPTER 10 Cost Functions………………………………………………………………………………………………………. 333 Definitions of Costs 333 Cost-Minimizing Input Choices 336 Cost Functions 341 Cost Functions and Shifts in Cost Curves 345 Shephard’s Lemma and the Elasticity of Substitution 355 Short-Run, Long-Run Distinction 355 Summary 362 Problems 363 Suggestions for Further Reading 366 Extensions: The Translog Cost Function 367 CHAPTER 11 Profit Maximization ………………………………………………………………………………………………. 371 The Nature and Behavior of Firms 371 Profit Maximization 373 Marginal Revenue 375 Short-Run Supply by a Price-Taking Firm 380 Profit Functions 383 Profit Maximization and Input Demand 389 Summary 395 Problems 396 Suggestions for Further Reading 400 Extensions: Boundaries of the Firm 401 Copyright 2011 Cengage Learning. 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Contents PART FIVE xv Competitive Markets CHAPTER 12 The Partial Equilibrium Competitive Model ………………………………………………………….. 409 Market Demand 409 Timing of the Supply Response 413 Pricing in the Very Short Run 413 Short-Run Price Determination 415 Shifts in Supply and Demand Curves: A Graphical Analysis 419 Mathematical Model of Market Equilibrium 422 Long-Run Analysis 425 Long-Run Equilibrium: Constant Cost Case 426 Shape of the Long-Run Supply Curve 428 Long-Run Elasticity of Supply 431 Comparative Statics Analysis of Long-Run Equilibrium 431 Producer Surplus in the Long Run 435 Economic Efficiency and Welfare Analysis 438 Price Controls and Shortages 441 Tax Incidence Analysis 442 Summary 447 Problems 447 Suggestions for Further Reading 451 Extensions: Demand Aggregation and Estimation 453 CHAPTER 13 General Equilibrium and Welfare …………………………………………………………………………. 457 Perfectly Competitive Price System 457 A Graphical Model of General Equilibrium with Two Goods 458 Comparative Statics Analysis 467 General Equilibrium Modeling and Factor Prices 469 A Mathematical Model of Exchange 471 A Mathematical Model of Production and Exchange 482 Computable General Equilibrium Models 485 Summary 489 Problems 490 Suggestions for Further Reading 494 Extensions: Computable General Equilibrium Models 495 PART SIX Market Power CHAPTER 14 Monopoly ……………………………………………………………………………………………………………… 501 Barriers to Entry 501 Copyright 2011 Cengage Learning. 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Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xvi Contents Profit Maximization and Output Choice 503 Monopoly and Resource Allocation 507 Monopoly, Product Quality, and Durability 510 Price Discrimination 513 Second-Degree Price Discrimination through Price Schedules Regulation of Monopoly 519 Dynamic Views of Monopoly 523 Summary 523 Problems 524 Suggestions for Further Reading 527 Extensions: Optimal Linear Two-Part Tariffs 528 CHAPTER 517 15 Imperfect Competition ………………………………………………………………………………………….. 531 Short-Run Decisions: Pricing and Output 531 Bertrand Model 533 Cournot Model 534 Capacity Constraints 540 Product Differentiation 541 Tacit Collusion 547 Longer-Run Decisions: Investment, Entry, and Exit 551 Strategic Entry Deterrence 557 Signaling 559 How Many Firms Enter? 562 Innovation 566 Summary 568 Problems 569 Suggestions for Further Reading 572 Extensions: Strategic Substitutes and Complements 573 PART SEVEN Pricing in Input Markets CHAPTER 16 Labor Markets ………………………………………………………………………………………………………. 581 Allocation of Time 581 A Mathematical Analysis of Labor Supply 584 Market Supply Curve for Labor 588 Labor Market Equilibrium 589 Wage Variation 591 Monopsony in the Labor Market 595 Labor Unions 598 Summary 601 Problems 601 Suggestions for Further Reading 605 Copyright 2011 Cengage Learning. 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Contents CHAPTER xvii 17 Capital and Time ………………………………………………………………………………………………….. 607 Capital and the Rate of Return 607 Determining the Rate of Return 609 The Firm’s Demand for Capital 616 Present Discounted Value Approach to Investment Decisions 618 Natural Resource Pricing 623 Summary 626 Problems 626 Suggestions for Further Reading 630 APPENDIX The Mathematics of Compound Interest ……………………………………………………………….. 631 Present Discounted Value 631 Continuous Time 633 PART EIGHT Market Failure CHAPTER 18 Asymmetric Information ……………………………………………………………………………………….. 641 Complex Contracts as a Response to Asymmetric Information 641 Principal-Agent Model 642 Hidden Actions 645 Owner-Manager Relationship 646 Moral Hazard in Insurance 650 Hidden Types 655 Nonlinear Pricing 656 Adverse Selection in Insurance 663 Market Signaling 670 Auctions 672 Summary 676 Problems 676 Suggestions for Further Reading 679 Extensions: Nonlinear Pricing with a Continuum of Types 680 CHAPTER 19 Externalities and Public Goods…………………………………………………………………………….. 685 Defining Externalities 685 Externalities and Allocative Inefficiency 687 Solutions to the Externality Problem 691 Attributes of Public Goods 694 Public Goods and Resource Allocation 696 Lindahl Pricing of Public Goods 700 Voting and Resource Allocation 703 A Simple Political Model 705 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xviii Contents Voting Mechanisms 708 Summary 710 Problems 710 Suggestions for Further Reading 713 Extensions: Pollution Abatement 714 Brief Answers to Queries…………………………………………………………………………………………………717 Solutions to Odd-Numbered Problems ……………………………………………………………………………727 Glossary of Frequently Used Terms ………………………………………………………………………………… 739 Index ………………………………………………………………………………………………………………………………… 747 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Preface The 11th edition of Microeconomic Theory: Basic Principles and Extensions continues a successful collaboration between the authors starting with the 10th edition. This edition represents a significant effort to continue refining and modernizing our treatment of microeconomics. Despite the significant changes appearing in virtually every chapter, the text retains all of the elements that have made it successful for so many editions. The basic approach is to focus on building intuition about economic models while providing students with the mathematical tools needed to go further in their studies. The text also seeks to facilitate that linkage by providing many numerical examples, advanced problems, and extended discussions of empirical implementation—all of which are intended to show students how microeconomic theory is used today. New developments continue to keep the field exciting, and we hope this edition manages to capture that excitement. New to the Eleventh Edition We took a fresh look at every chapter to make sure that they continue to provide clear and up-to-date coverage of all of the topics examined. The major revisions include the following. • • • • • • • • • • Many of the topics in our introductory chapter on mathematics have been revised to conform more closely to methods usually encountered in the recent economics literature. The chapters on uncertainty and game theory have been broken out into their own separate part. This shrinks the part of the book on choice and demand to a more manageable size and emphasizes the unique nature of the strategy and uncertainty topics. The chapter on uncertainty (Chapter 7) has been extensively revised. The sections on real options and the value of information have been expanded. Applications to financial economics and the portfolio problem have been streamlined and collected in the Extensions. The treatment of game theory (Chapter 8) has been substantially streamlined, providing the same level of rigor in a third less space. A modern treatment of the literature on firms’ boundaries and objectives (The Theory of the Firm) has been added to the body of Chapter 9 and expanded on further in the Extensions. Our general equilibrium chapter (Chapter 13) has been thoroughly revised. Most notably we now use this chapter to provide students with an elementary introduction to vector notation. We have added a number of new topics to our discussion of labor markets focusing mainly on issues related to human capital and job search. Coverage of behavioral economics has been expanded, sprinkled throughout various relevant chapters. A handful of behavioral economics problems have been included. The public-good problem is rigorously analyzed using game theory (Chapter 19). Dozens of new problems have been added. xix Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xx Preface Supplements to the Text The thoroughly revised ancillaries for this edition include the following. • • The Solutions Manual and Test Bank (by the text authors). The Solutions Manual contains comments and solutions to all problems, and the test bank has been revised to include additional questions. Both are available to all adopting instructors in electronic version on the text Web site (www.cengage.com/economics/nicholson) and on the Instructor Resources CD (IRCD). PowerPoint Lecture Presentation Slides. PowerPoint slides for each chapter of the text provide a thorough set of outlines for classroom use or for students as a study aid. The slides are available from the book’s Web site (www.cengage.com/economics/ nicholson) and on the IRCD. Online Resources South-Western, a part of Cengage Learning, provides students and instructors with a set of valuable online resources that are an effective complement to this text. Each new copy of the book comes with a registration card that provides access to Economic Applications and InfoTrac College Edition. Economic Applications The purchase of this new textbook includes complimentary access to South-Western’s InfoApps (InfoTrac and Economic Applications) Web site. The Web site includes a suite of regularly updated Web features for economics students and instructors: EconNews, EconDebates, and EconData. These resources can help students deepen their understanding of economic concepts by analyzing current news stories, policy debates, and economic data. EconApps can also help instructors develop assignments, case studies, and examples based on real-world issues. EconDebates provides current coverage of economics policy debates; it includes a primer on the issues, links to background information, and commentaries. EconNews summarizes recent economics news stories and offers questions for further discussion. EconData presents current and historical economic data with accompanying commentary, analysis, and exercises. Students buying a used book can purchase access to InfoApps at www.cengagebrain.com. InfoTrac College Edition The purchase of this new textbook also comes with four months of access to InfoTrac. This powerful and searchable online database provides access to full text articles from more than a thousand different publications ranging from the popular press to scholarly journals. Instructors can search topics and select readings for students, and students can search articles and readings for homework assignments and projects. The publications cover a variety of topics and include articles that range from current events to theoretical developments. InfoTrac College Edition offers instructors and students the ability to integrate scholarship and applications of economics into the learning process. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Preface xxi Acknowledgments We are indebted to the team at Cengage and especially to Susan Smart for once again bringing her organizing and cajoling skills to this edition. The copyeditors at Cenveo Publisher Services did a great job of making sense of our messy manuscripts. Juli Cook’s text design succeeded in achieving two seemingly irreconcilable goals—making the text both compact and easy to read. Cliff Kallemeyn did a fine job of keeping the production on track; we especially appreciated the way he coordinated the copyediting and page production processes. Devanand Srinivasan supervised the actual production of pages, dealing expertly with the super-abundance of equations. We thank our colleagues at Amherst and Dartmouth College for valuable conversations and understanding. Several colleagues who used the book for their courses offered us detailed suggestions for revision. We have also benefitted from the reactions of generations of students to the use of the book in our own microeconomics classes. Over the years, Amherst students Mark Bruni, Eric Budish, Adrian Dillon, David Macoy, Tatyana Mamut, Anoop Menon, Katie Merrill, Jordan Milev, Doug Norton, and Jeff Rodman and Dartmouth students Wills Begor and Glynnis Kearny worked with us revising various chapters. Walter gives special thanks to his wife Susan; after providing much-needed support through twenty-two editions of his microeconomics texts, she is happy for the success, but wonders about his sanity. Walter’s children (Kate, David, Tory, and Paul) still seem to be living happy and productive lives despite a severe lack of microeconomic education. Perhaps this can be remedied as the next generation (Beth, Sarah, David, Sophia, Abby, Nate, and Christopher) grows older. At least he hopes they will wonder what the books dedicated to them are all about. The texts sit on a convenient shelf, awaiting this curiosity. Chris gives special thanks to his family—his wife, Maura Doyle, and their daughters, Clare, Tess, and Meg—for their patience during the revision process. Maura has extensive experience using the book in her popular microeconomics courses at Dartmouth College, and was a rich source of suggestions reflected in this revision. Perhaps our greatest debt is to instructors who adopt the text, who share a similar view of how microeconomics should be taught. We are grateful for the suggestions that teachers and students have shared with us over the years and encourage teachers and students to continue to e-mail us with any comments on the text (wenicholson@amherst.edu or Christopher.M.Snyder@dartmouth.edu). Walter Nicholson Amherst, Massachusetts Christopher Snyder Hanover New Hampshire July 2011 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Introduction PART ONE Chapter 1 Economic Models Chapter 2 Mathematics for Microeconomics This part contains two chapters. Chapter 1 examines the general philosophy of how economists build models of economic behavior. Chapter 2 then reviews some of the mathematical tools used in the construction of these models. The mathematical tools from Chapter 2 will be used throughout the remainder of this book. 1 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. CHAPTER ONE Economic Models The main goal of this book is to introduce you to the most important models that economists use to explain the behavior of consumers, firms, and markets. These models are central to the study of all areas of economics. Therefore, it is essential to understand both the need for such models and the basic framework used to develop them. The goal of this chapter is to begin this process by outlining some of the conceptual issues that determine the ways in which economists study practically every question that interests them. Theoretical Models A modern economy is a complicated entity. Thousands of firms engage in producing millions of different goods. Many millions of people work in all sorts of occupations and make decisions about which of these goods to buy. Let’s use peanuts as an example. Peanuts must be harvested at the right time and shipped to processors who turn them into peanut butter, peanut oil, peanut brittle, and numerous other peanut delicacies. These processors, in turn, must make certain that their products arrive at thousands of retail outlets in the proper quantities to meet demand. Because it would be impossible to describe the features of even these peanut markets in complete detail, economists have chosen to abstract from the complexities of the real world and develop rather simple models that capture the ‘‘essentials.’’ Just as a road map is helpful even though it does not record every house or every store, economic models of, say, the market for peanuts are also useful even though they do not record every minute feature of the peanut economy. In this book we will study the most widely used economic models. We will see that, even though these models often make heroic abstractions from the complexities of the real world, they nonetheless capture essential features that are common to all economic activities. The use of models is widespread in the physical and social sciences. In physics, the notion of a ‘‘perfect’’ vacuum or an ‘‘ideal’’ gas is an abstraction that permits scientists to study real-world phenomena in simplified settings. In chemistry, the idea of an atom or a molecule is actually a simplified model of the structure of matter. Architects use mock-up models to plan buildings. Television repairers refer to wiring diagrams to locate problems. Economists’ models perform similar functions. They provide simplified portraits of the way individuals make decisions, the way firms behave, and the way in which these two groups interact to establish markets. 3 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 4 Part 1: Introduction Verification of Economic Models Of course, not all models prove to be ‘‘good.’’ For example, the earth-centered model of planetary motion devised by Ptolemy was eventually discarded because it proved incapable of accurately explaining how the planets move around the sun. An important purpose of scientific investigation is to sort out the ‘‘bad’’ models from the ‘‘good.’’ Two general methods have been used for verifying economic models: (1) a direct approach, which seeks to establish the validity of the basic assumptions on which a model is based; and (2) an indirect approach, which attempts to confirm validity by showing that a simplified model correctly predicts real-world events. To illustrate the basic differences between the two approaches, let’s briefly examine a model that we will use extensively in later chapters of this book—the model of a firm that seeks to maximize profits. The profit-maximization model The model of a firm seeking to maximize profits is obviously a simplification of reality. It ignores the personal motivations of the firm’s managers and does not consider conflicts among them. It assumes that profits are the only relevant goal of the firm; other possible goals, such as obtaining power or prestige, are treated as unimportant. The model also assumes that the firm has sufficient information about its costs and the nature of the market to which it sells to discover its profit-maximizing options. Most real-world firms, of course, do not have this information readily available. Yet such shortcomings in the model are not necessarily serious. No model can exactly describe reality. The real question is whether this simple model has any claim to being a good one. Testing assumptions One test of the model of a profit-maximizing firm investigates its basic assumption: Do firms really seek maximum profits? Some economists have examined this question by sending questionnaires to executives, asking them to specify the goals they pursue. The results of such studies have been varied. Businesspeople often mention goals other than profits or claim they only do ‘‘the best they can’’ to increase profits given their limited information. On the other hand, most respondents also mention a strong ‘‘interest’’ in profits and express the view that profit maximization is an appropriate goal. Therefore, testing the profit-maximizing model by testing its assumptions has provided inconclusive results. Testing predictions Some economists, most notably Milton Friedman, deny that a model can be tested by inquiring into the ‘‘reality’’ of its assumptions.1 They argue that all theoretical models are based on ‘‘unrealistic’’ assumptions; the very nature of theorizing demands that we make certain abstractions. These economists conclude that the only way to determine the validity of a model is to see whether it is capable of predicting and explaining real-world events. The ultimate test of an economic model comes when it is confronted with data from the economy itself. Friedman provides an important illustration of that principle. He asks what kind of theory one should use to explain the shots expert pool players will make. He argues that the laws of velocity, momentum, and angles from theoretical physics would be a suitable 1 See M. Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953), chap. 1. For an alternative view stressing the importance of using ‘‘realistic’’ assumptions, see H. A. Simon, ‘‘Rational Decision Making in Business Organizations,’’ American Economic Review 69, no. 4 (September 1979): 493–513. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models 5 model. Pool players shoot shots as if they follow these laws. But most players asked whether they precisely understand the physical principles behind the game of pool will undoubtedly answer that they do not. Nonetheless, Friedman argues, the physical laws provide accurate predictions and therefore should be accepted as appropriate theoretical models of how experts play pool. Thus, a test of the profit-maximization model would be provided by predicting the behavior of real-world firms by assuming that these firms behave as if they were maximizing profits. (See Example 1.1 later in this chapter.) If these predictions are reasonably in accord with reality, we may accept the profit-maximization hypothesis. However, we would reject the model if real-world data seem inconsistent with it. Hence the ultimate test of any theory is its ability to predict real-world events. Importance of empirical analysis The primary concern of this book is the construction of theoretical models. But the goal of such models is always to learn something about the real world. Although the inclusion of a lengthy set of applied examples would needlessly expand an already bulky book,2 the Extensions included at the end of many chapters are intended to provide a transition between the theory presented here and the ways that theory is applied in empirical studies. General Features of Economic Models The number of economic models in current use is, of course, large. Specific assumptions used and the degree of detail provided vary greatly depending on the problem being addressed. The models used to explain the overall level of economic activity in the United States, for example, must be considerably more aggregated and complex than those that seek to interpret the pricing of Arizona strawberries. Despite this variety, practically all economic models incorporate three common elements: (1) the ceteris paribus (other things the same) assumption; (2) the supposition that economic decisionmakers seek to optimize something; and (3) a careful distinction between ‘‘positive’’ and ‘‘normative’’ questions. Because we will encounter these elements throughout this book, it may be helpful at the outset to describe the philosophy behind each of them. The ceteris paribus assumption As in most sciences, models used in economics attempt to portray relatively simple relationships. A model of the market for wheat, for example, might seek to explain wheat prices with a small number of quantifiable variables, such as wages of farmworkers, rainfall, and consumer incomes. This parsimony in model specification permits the study of wheat pricing in a simplified setting in which it is possible to understand how the specific forces operate. Although any researcher will recognize that many ‘‘outside’’ forces (e.g., presence of wheat diseases, changes in the prices of fertilizers or of tractors, or shifts in consumer attitudes about eating bread) affect the price of wheat, these other forces are held constant in the construction of the model. It is important to recognize that economists are not assuming that other factors do not affect wheat prices; rather, such other variables are assumed to be unchanged during the period of study. In this way, the effect 2 For an intermediate-level text containing an extensive set of real-world applications, see W. Nicholson and C. Snyder, Intermediate Microeconomics and Its Application, 11th ed. (Mason, OH: Thomson/Southwestern, 2010). Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 6 Part 1: Introduction of only a few forces can be studied in a simplified setting. Such ceteris paribus (other things equal) assumptions are used in all economic modeling. Use of the ceteris paribus assumption does pose some difficulties for the verification of economic models from real-world data. In other sciences, the problems may not be so severe because of the ability to conduct controlled experiments. For example, a physicist who wishes to test a model of the force of gravity probably would not do so by dropping objects from the Empire State Building. Experiments conducted in that way would be subject to too many extraneous forces (e.g., wind currents, particles in the air, variations in temperature) to permit a precise test of the theory. Rather, the physicist would conduct experiments in a laboratory, using a partial vacuum in which most other forces could be controlled or eliminated. In this way, the theory could be verified in a simple setting, without considering all the other forces that affect falling bodies in the real world. With a few notable exceptions, economists have not been able to conduct controlled experiments to test their models. Instead, they have been forced to rely on various statistical methods to control for other forces when testing their theories. Although these statistical methods are as valid in principle as the controlled experiment methods used by other scientists, in practice they raise a number of thorny issues. For that reason, the limitations and precise meaning of the ceteris paribus assumption in economics are subject to greater controversy than in the laboratory sciences. Structure of Economic Models Most of the economic models you will encounter in this book will have a mathematical structure. They will highlight the relationships between factors that affect the decisions of households and firms and the results of those decisions. Economists tend to use different names for these two types of factors (or, in mathematical terms, variables). Variables that are outside of a decision-maker’s control are called exogenous variables. Such variables are inputs into economic models. For example, in consumer theory we will usually treat individuals as price-takers. The prices of goods are determined outside of our models of consumer behavior, and we wish to study how consumers adjust to them. The results of such decisions (e.g., the quantities of each good that a consumer buys) are endogenous variables. These variables are determined within our models. This distinction is pictured schematically in Figure 1.1. Although the actual models developed by economists may be complicated, they all have this basic structure. A good way to start studying a particular model is to identify precisely how it fits into this framework. This distinction between exogenous and endogenous variables will become clearer as we explore a variety of economic models. Keeping straight which variables are determined outside a particular model and which variables are determined within a model can be confusing; therefore, we will try to remind you about this as we go along. The distinction between exogenous and endogenous variables is also helpful in understanding the way in which the ceteris paribus assumption is incorporated into economic models. In most cases we will want to study how the results of our models change when one of the exogenous variables changes. It is possible, even likely, that the change in such a single variable will change all the results calculated from the model. For example, as we will see, it is likely that the change in the price of a single good will cause an individual to change the quantities of practically every good he or she buys. Examining all such responses is precisely why economists build models. The ceteris paribus assumption is enforced by changing only one exogenous variable, holding all others constant. If we wish to study the effects of a change in the price of gasoline on a household’s purchases, we change that price in our model, but we do not change the prices of other goods (and in some cases we do not change the individual’s income either). Holding the other prices constant is what is meant by studying the ceteris paribus effect of an increase in the price of gasoline. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models FIGURE 1.1 7 Values for exogenous variables are inputs into most economic models. Model outputs (results) are values for the endogenous variables. Structure of a Typical Microeconomic Model EXOGENOUS VARIABLES Households: Prices of goods Firms: Prices of inputs and output ECONOMIC MODEL Households: Utility maximization Firms: Profit maximization ENDOGENOUS VARIABLES Households: Quantities bought Firms: Output produced, inputs hired Optimization assumptions Many economic models start from the assumption that the economic actors being studied are rationally pursuing some goal. We briefly discussed such an assumption when investigating the notion of firms maximizing profits. Example 1.1 shows how that model can be used to make testable predictions. Other examples we will encounter in this book include consumers maximizing their own well-being (utility), firms minimizing costs, and government regulators attempting to maximize public welfare. Although, as we will show, all these assumptions are unrealistic, and all have won widespread acceptance as good starting places for developing economic models. There seem to be two reasons for this acceptance. First, the optimization assumptions are useful for generating precise, solvable models, primarily because such models can draw on a variety of mathematical techniques suitable for optimization problems. Many of these techniques, together with the logic behind them, are reviewed in Chapter 2. A second reason for the popularity of optimization models concerns their apparent empirical validity. As some of our Extensions show, such models seem to be fairly good at explaining reality. In all, then, optimization models have come to occupy a prominent position in modern economic theory. EXAMPLE 1.1 Profit Maximization The profit-maximization hypothesis provides a good illustration of how optimization assumptions can be used to generate empirically testable propositions about economic behavior. Suppose that a firm can sell all the output that it wishes at a price of p per unit and that the total costs of production, C, depend on the amount produced, q. Then profits are given by profits ¼ p ¼ pq CðqÞ: (1:1) Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 8 Part 1: Introduction Maximization of profits consists of finding that value of q which maximizes the profit expression in Equation 1.1. This is a simple problem in calculus. Differentiation of Equation 1.1 and setting that derivative equal to 0 give the following first-order condition for a maximum: dp ¼ p C 0 ðqÞ ¼ 0 or dq p ¼ C 0 ðqÞ: (1:2) In words, the profit-maximizing output level (q) is found by selecting that output level for which price is equal to marginal cost, C 0 ðqÞ. This result should be familiar to you from your introductory economics course. Notice that in this derivation the price for the firm’s output is treated as a constant because the firm is a price-taker. That is, price is an exogenous variable in this model. Equation 1.2 is only the first-order condition for a maximum. Taking account of the secondorder condition can help us to derive a testable implication of this model. The second-order condition for a maximum is that at q it must be the case that d 2p ¼ C 00 ðqÞ < 0 dq 2 or C 00 ðq Þ > 0: (1:3) That is, marginal cost must be increasing at q for this to be a true point of maximum profits. Our model can now be used to ‘‘predict’’ how a firm will react to a change in price. To do so, we differentiate Equation 1.2 with respect to price (p), assuming that the firm continues to choose a profit-maximizing level of q: d½ p C 0 ðq Þ ¼ 0 dq ¼ 0: ¼ 1 C 00 ðq Þ dp dp (1:4) Rearranging terms a bit gives dq 1 ¼ 00 > 0: dp C ðq Þ (1:5) Here the final inequality again reflects the fact that marginal cost must be increasing at q if this point is to be a true maximum. This then is one of the testable propositions of the profitmaximization hypothesis—if other things do not change, a price-taking firm should respond to an increase in price by increasing output. On the other hand, if firms respond to increases in price by reducing output, there must be something wrong with our model. Although this is a simple model, it reflects the way we will proceed throughout much of this book. Specifically, the fact that the primary implication of the model is derived by calculus, and consists of showing what sign a derivative should have, is the kind of result we will see many times. Notice that in this model there is only one endogenous variable—q, the quantity the firm chooses to produce. There is also only one exogenous variable—p, the price of the product, which the firm takes as a given. Our model makes a specific prediction about how changes in this exogenous variable affect the firm’s output choice. QUERY: In general terms, how would the implications of this model be changed if the price a firm obtains for its output were a function of how much it sold? That is, how would the model work if the price-taking assumption were abandoned? Positive-normative distinction A final feature of most economic models is the attempt to differentiate carefully between ‘‘positive’’ and ‘‘normative’’ questions. Thus far we have been concerned primarily with positive economic theories. Such theories take the real world as an object to be studied, attempting to explain those economic phenomena that are observed. Positive economics seeks to determine how resources are in fact allocated in an economy. A somewhat different use of economic theory is normative analysis, taking a definite stance about what should be done. Under the heading of normative analysis, economists have a great deal to Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models 9 say about how resources should be allocated. For example, an economist engaged in positive analysis might investigate how prices are determined in the U.S. health-care economy. The economist also might want to measure the costs and benefits of devoting even more resources to health care by, for example, offering government-subsidized health insurance. But when he or she specifically advocates that such an insurance plan should be adopted, the analysis becomes normative. Some economists believe that the only proper economic analysis is positive analysis. Drawing an analogy with the physical sciences, they argue that ‘‘scientific’’ economics should concern itself only with the description (and possibly prediction) of real-world economic events. To take political positions and to plead for special interests are considered to be outside the competence of an economist acting as such. Of course, an economist, like any other citizen, is free to express his or her views on political matters. But when doing so he or she is acting as a citizen, not an economist. For other economists, however, the positive-normative distinction seems artificial. They believe that the study of economics necessarily involves the researchers’ own views about ethics, morality, and fairness. According to these economists, searching for scientific ‘‘objectivity’’ in such circumstances is hopeless. Despite some ambiguity, this book tries to adopt a positivist tone, leaving normative concerns for you to decide for yourself. Development of the Economic Theory of Value Because economic activity has been a central feature of all societies, it is surprising that these activities were not studied in any detail until fairly recently. For the most part, economic phenomena were treated as a basic aspect of human behavior that was not sufficiently interesting to deserve specific attention. It is, of course, true that individuals have always studied economic activities with a view toward making some kind of personal gain. Roman traders were not above making profits on their transactions. But investigations into the basic nature of these activities did not begin in any depth until the eighteenth century.3 Because this book is about economic theory as it stands today, rather than the history of economic thought, our discussion of the evolution of economic theory will be brief. Only one area of economic study will be examined in its historical setting: the theory of value. Early economic thoughts on value The theory of value, not surprisingly, concerns the determinants of the ‘‘value’’ of a commodity. This subject is at the center of modern microeconomic theory and is closely intertwined with the fundamental economic problem of allocating scarce resources to alternative uses. The logical place to start is with a definition of the word ‘‘value.’’ Unfortunately, the meaning of this term has not been consistent throughout the development of the subject. Today we regard value as being synonymous with the price of a commodity.4 Earlier philosopher-economists, however, made a distinction between the market price of a commodity and its value. The term value was then thought of as being, in some sense, synonymous with ‘‘importance,’’ ‘‘essentiality,’’ or (at times) ‘‘godliness.’’ Because ‘‘price’’ and ‘‘value’’ were separate concepts, they could differ, and most early economic 3 For a detailed treatment of early economic thought, see the classic work by J. A. Schumpeter, History of Economic Analysis (New York: Oxford University Press, 1954), pt. II, chaps. 1–3. 4 This is not completely true when ‘‘externalities’’ are involved, and a distinction must be made between private and social value (see Chapter 19). Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 10 Part 1: Introduction discussions centered on these divergences. For example, St. Thomas Aquinas believed value to be divinely determined. Because prices were set by humans, it was possible for the price of a commodity to differ from its value. A person accused of charging a price in excess of a good’s value was guilty of charging an ‘‘unjust’’ price. St. Thomas believed that, in most cases, the ‘‘just’’ rate of interest was zero. Any lender who demanded a payment for the use of money was charging an unjust price and could be—and sometimes was—prosecuted by church officials. The founding of modern economics During the latter part of the eighteenth century, philosophers began to take a more scientific approach to economic questions. The 1776 publication of The Wealth of Nations by Adam Smith (1723–1790) is generally considered the beginning of modern economics. In his vast, all-encompassing work, Smith laid the foundation for thinking about market forces in an ordered and systematic way. Still, Smith and his immediate successors, such as David Ricardo (1772–1823), continued to distinguish between value and price. To Smith, for example, the value of a commodity meant its ‘‘value in use,’’ whereas the price represented its ‘‘value in exchange.’’ The distinction between these two concepts was illustrated by the famous water–diamond paradox. Water, which obviously has great value in use, has little value in exchange (it has a low price); diamonds are of little practical use but have a great value in exchange. The paradox with which early economists struggled derives from the observation that some useful items have low prices whereas certain nonessential items have high prices. Labor theory of exchange value Neither Smith nor Ricardo ever satisfactorily resolved the water–diamond paradox. The concept of value in use was left for philosophers to debate, while economists turned their attention to explaining the determinants of value in exchange (i.e., to explaining relative prices). One obvious possible explanation is that exchange values of goods are determined by what it costs to produce them. Costs of production are primarily influenced by labor costs—at least this was so in the time of Smith and Ricardo—and therefore it was a short step to embrace a labor theory of value. For example, to paraphrase an example from Smith, if catching a deer takes twice the number of labor hours as catching a beaver, then one deer should exchange for two beavers. In other words, the price of a deer should be twice that of a beaver. Similarly, diamonds are relatively costly because their production requires substantial labor input, whereas water is freely available. To students with even a passing knowledge of what we now call the law of supply and demand, Smith’s and Ricardo’s explanation must seem incomplete. Did they not recognize the effects of demand on price? The answer to this question is both yes and no. They did observe periods of rapidly rising and falling relative prices and attributed such changes to demand shifts. However, they regarded these changes as abnormalities that produced only a temporary divergence of market price from labor value. Because they had not really developed a theory of value in use, they were unwilling to assign demand any more than a transient role in determining relative prices. Rather, long-run exchange values were assumed to be determined solely by labor costs of production. The marginalist revolution Between 1850 and 1880, economists became increasingly aware that to construct an adequate alternative to the labor theory of value, they had to devise a theory of value in use. During the 1870s, several economists discovered that it is not the total usefulness of a commodity that helps to determine its exchange value, but rather the usefulness of the last unit consumed. For example, water is certainly useful—it is necessary for all life. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models 11 Marshall theorized that demand and supply interact to determine the equilibrium price (p) and the quantity (q) that will be traded in the market. He concluded that it is not possible to say that either demand or supply alone determines price or therefore that either costs or usefulness to buyers alone determines exchange value. FIGURE 1.2 The Marshallian Supply–Demand Cross Price D S p* D S q* Quantity per period However, because water is relatively plentiful, consuming one more pint (ceteris paribus) has a relatively low value to people. These ‘‘marginalists’’ redefined the concept of value in use from an idea of overall usefulness to one of marginal, or incremental, usefulness— the usefulness of an additional unit of a commodity. The concept of the demand for an incremental unit of output was now contrasted with Smith’s and Ricardo’s analysis of production costs to derive a comprehensive picture of price determination.5 Marshallian supply–demand synthesis The clearest statement of these marginal principles was presented by the English economist Alfred Marshall (1842–1924) in his Principles of Economics, published in 1890. Marshall showed that demand and supply simultaneously operate to determine price. As Marshall noted, just as you cannot tell which blade of a scissors does the cutting, so too you cannot say that either demand or supply alone determines price. That analysis is illustrated by the famous Marshallian cross shown in Figure 1.2. In the diagram the quantity of a good purchased per period is shown on the horizontal axis, and its price appears on the vertical axis. The curve DD represents the quantity of the good demanded per period at each possible price. The curve is negatively sloped to reflect the marginalist principle that as quantity increases, people are willing to pay less for the last unit purchased. It is the value of this last unit that sets the price for all units purchased. The curve SS shows how (marginal) production costs increase as more output is produced. This reflects the increasing cost of producing one more unit as total output expands. In other words, the upward slope of the SS curve reflects increasing marginal costs, just as the downward slope of the DD curve reflects decreasing marginal value. The two curves intersect at p, q. This is an equilibrium point—both buyers and sellers are content with the quantity being traded and the price at which it is traded. If one of the curves should shift, the equilibrium point would shift to a new location. Thus, price and quantity are simultaneously determined by the joint operation of supply and demand. 5 Ricardo had earlier provided an important first step in marginal analysis in his discussion of rent. Ricardo theorized that as the production of corn increased, land of inferior quality would be used and this would cause the price of corn to increase. In his argument Ricardo recognized that it is the marginal cost—the cost of producing an additional unit—that is relevant to pricing. Notice that Ricardo implicitly held other inputs constant when discussing decreasing land productivity; that is, he used one version of the ceteris paribus assumption. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 12 Part 1: Introduction EXAMPLE 1.2 Supply–Demand Equilibrium Although graphical presentations are adequate for some purposes, economists often use algebraic representations of their models both to clarify their arguments and to make them more precise. As an elementary example, suppose we wished to study the market for peanuts and, based on the statistical analysis of historical data, concluded that the quantity of peanuts demanded each week (q, measured in bushels) depended on the price of peanuts (p, measured in dollars per bushel) according to the equation: quantity demanded ¼ qD ¼ 1,000 100p: (1:6) Because this equation for qD contains only the single independent variable p, we are implicitly holding constant all other factors that might affect the demand for peanuts. Equation 1.6 indicates that, if other things do not change, at a price of $5 per bushel people will demand 500 bushels of peanuts, whereas at a price of $4 per bushel they will demand 600 bushels. The negative coefficient for p in Equation 1.6 reflects the marginalist principle that a lower price will cause people to buy more peanuts. To complete this simple model of pricing, suppose that the quantity of peanuts supplied also depends on price: quantity supplied ¼ qS ¼ 125 þ 125p: (1:7) Here the positive coefficient of price also reflects the marginal principle that a higher price will call forth increased supply—primarily because (as we saw in Example 1.1) it permits firms to incur higher marginal costs of production without incurring losses on the additional units produced. Equilibrium price determination. Therefore, Equations 1.6 and 1.7 reflect our model of price determination in the market for peanuts. An equilibrium price can be found by setting quantity demanded equal to quantity supplied: qD ¼ qS (1:8) 1,000 100p ¼ 125 þ 125p (1:9) 225p ¼ 1,125 (1:10) p ¼ 5: (1:11) or or thus, At a price of $5 per bushel, this market is in equilibrium: At this price people want to purchase 500 bushels, and that is exactly what peanut producers are willing to supply. This equilibrium is pictured graphically as the intersection of D and S in Figure 1.3. A more general model. To illustrate how this supply–demand model might be used, let’s adopt a more general notation. Suppose now that the demand and supply functions are given by qD ¼ a þ bp and qS ¼ c þ dp (1:12) where a and c are constants that can be used to shift the demand and supply curves, respectively, and b (0) represent demanders’ and suppliers’ reactions to price. Equilibrium in this market requires qD ¼ qS or a þ bp ¼ c þ dp: (1:13) Thus, equilibrium price is given by6 p ¼ ac : db (1:14) 6 Equation 1.14 is sometimes called the ‘‘reduced form’’ for the supply–demand structural model of Equations 1.12 and 1.13. It shows that the equilibrium value for the endogenous variable p ultimately depends only on the exogenous factors in the model (a and c) and on the behavioral parameters b and d. A similar equation can be calculated for equilibrium quantity. Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models 13 FIGURE 1.31Changing Supply–Demand Equilibria The initial supply–demand equilibrium is illustrated by the intersection of D and S (p ¼ 5, q ¼ 500). When demand shifts to qD 0 ¼ 1; 450 100p ðdenoted as D 0 Þ, the equilibrium shifts to p ¼ 7, q ¼ 750. Price ($) D′ 14.5 S D 10 7 5 S 0 500 750 D D′ 1,000 1,450 Quantity per period (bushels) Notice that in our previous example a ¼ 1,000, b ¼ 100, c ¼ 125, and d ¼ 125; therefore, p ¼ 1,000 þ 125 1,125 ¼ ¼ 5: 125 þ 100 225 (1:15) With this more general formulation, however, we can pose questions about how the equilibrium price might change if either the demand or supply curve shifted. For example, differentiation of Equation 1.14 shows that dp 1 ¼ > 0; da db dp 1 ¼ < 0: dc db (1:16) That is, an increase in demand (an increase in a) increases equilibrium price, whereas an increase in supply (an increase in c) reduces price. This is exactly what a graphical analysis of supply and demand curves would show. For example, Figure 1.3 shows that when the constant term, a, in the demand equation increases to 1,450, equilibrium price increases to p ¼ 7 [¼ (1,450 þ 125)/225]. QUERY: How might you use Equation 1.16 to ‘‘predict’’ how each unit increase in the exogenous constant a affects the endogenous variable p? Does this equation correctly predict the increase in p when the constant a increases from 1,000 to 1,450? Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 14 Part 1: Introduction Paradox resolved Marshall’s model resolves the water–diamond paradox. Prices reflect both the marginal evaluation that demanders place on goods and the marginal costs of producing the goods. Viewed in this way, there is no paradox. Water is low in price because it has both a low marginal value and a low marginal cost of production. On the other hand, diamonds are high in price because they have both a high marginal value (because people are willing to pay quite a bit for one more) and a high marginal cost of production. This basic model of supply and demand lies behind much of the analysis presented in this book. General equilibrium models Although the Marshallian model is an extremely useful and versatile tool, it is a partial equilibrium model, looking at only one market at a time. For some questions, this narrowing of perspective gives valuable insights and analytical simplicity. For other, broader questions, such a narrow viewpoint may prevent the discovery of important relationships among markets. To answer more general questions we must have a model of the whole economy that suitably mirrors the connections among various markets and economic agents. The French economist Leon Walras (1831–1910), building on a long Continental tradition in such analysis, created the basis for modern investigations into those broad questions. His method of representing the economy by a large number of simultaneous equations forms the basis for understanding the interrelationships implicit in general equilibrium analysis. Walras recognized that one cannot talk about a single market in isolation; what is needed is a model that permits the effects of a change in one market to be followed through other markets. For example, suppose that the demand for peanuts were to increase. This would cause the price of peanuts to increase. Marshallian analysis would seek to understand the size of this increase by looking at conditions of supply and demand in the peanut market. General equilibrium analysis would look not only at that market but also at repercussions in other markets. An increase in the price of peanuts would increase costs for peanut butter makers, which would, in turn, affect the supply curve for peanut butter. Similarly, the increasing price of peanuts might mean higher land prices for peanut farmers, which would affect the demand curves for all products that they buy. The demand curves for automobiles, furniture, and trips to Europe would all shift out, and that might create additional incomes for the providers of those products. Consequently, the effects of the initial increase in demand for peanuts eventually would spread throughout the economy. General equilibrium analysis attempts to develop models that permit us to examine such effects in a simplified setting. Several models of this type are described in Chapter 13. Production possibility frontier Here we briefly introduce some general equilibrium ideas by using another graph you should remember from introductory economics—the production possibility frontier. This graph shows the various amounts of two goods that an economy can produce using its available resources during some period (say, one week). Because the production possibility frontier shows two goods, rather than the single good in Marshall’s model, it is used as a basic building block for general equilibrium models. Figure 1.4 shows the production possibility frontier for two goods: food and clothing. The graph illustrates the supply of these goods by showing the combinations that can be produced with this economy’s resources. For example, 10 pounds of food and 3 units of clothing could be produced, or 4 pounds of food and 12 units of clothing. Many other combinations of food and clothing could also be produced. The production possibility frontier shows all of them. Combinations of food and clothing outside the frontier cannot Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Chapter 1: Economic Models FIGURE 1.4 Production Possibility Frontier 15 The production possibility frontier shows the different combinations of two goods that can be produced from a certain amount of scarce resources. It also shows the opportunity cost of producing more of one good as the amount of the other good that cannot then be produced. The opportunity cost at two different levels of clothing production can be seen by comparing points A and B. Quantity of food per week Opportunity cost of clothing = 12 pound of food A 10 9.5 Opportunity cost of clothing = 2 pounds of food B 4 2 0 3 4 12 13 Quantity of clothing per week be produced because not enough resources are available. The production possibility frontier reminds us of the basic economic fact that resources are scarce—there are not enough resources available to produce all we might want of every good. This scarcity means that we must choose how much of each good to produce. Figure 1.4 makes clear that each choice has its costs. For example, if this economy produces 10 pounds of food and 3 units of clothing at point A, producing 1 more unit of clothing would ‘‘cost’’ ½ pound of food—increasing the output of clothing by 1 unit means the production of food would have to decrease by ½ pound. Thus, the opportunity cost of 1 unit of clothing at point A is ½ pound of food. On the other hand, if the economy initially produces 4 pounds of food and 12 units of clothing at point B, it would cost 2 pounds of food to produce 1 more unit of clothing. The opportunity cost of 1 more unit of clothing at point B has increased to 2 pounds of food. Because more units of clothing are produced at point B than at point A, both Ricardo’s and Marshall’s ideas of increasing incremental costs suggest that the opportunity cost of an additional unit of clothing will be higher at point B than at point A. This effect is shown by Figure 1.4. The production possibility frontier provides two general equilibrium insights that are not clear in Marshall’s supply and demand model of a single market. First, the graph shows that producing more of one good means producing less of another good because resources are scarce. Economists often (perhaps too often!) use the expression ‘‘there is no such thing as a free lunch’’ to explain that every economic action has opportunity costs. Second, the production possibility frontier shows that opportunity costs depend on how much of each good is produced. The frontier is like a supply curve for two goods: It Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 16 Part 1: Introduction shows the opportunity cost of producing more of one good as the decrease in the amount of the second good. Therefore, the production possibility frontier is a particularly useful tool for studying several markets at the same time. EXAMPLE 1.3 The Production Possibility Frontier and Economic Inefficiency General equilibrium models are good tools for evaluating the efficiency of various economic arrangements. As we will see in Chapter 13, such models have been used to assess a wide variety of policies such as trade agreements, tax structures, and environmental regulations. In this simple example, we explore the idea of efficiency in its most elementary form. Suppose that an economy produces two goods, x and y, using labor as the only input. The production function for good x is x ¼ lx0:5 (where lx is the quantity of labor used in x production), and the production function for good y is y ¼ 2ly0:5 . Total labor available is constrained by lx þ ly 200. Construction of the production possibility frontier in this economy is extremely simple: lx þ ly ¼ x2 þ 0:25y2 200 (1:17) where the equality holds exactly if the economy is to be producing as much as possible (which, after all, is why it is called a ‘‘frontier’’). Equation 1.17 shows that the frontier here has the shape of a quarter ellipse—its concavity derives from the diminishing returns exhibited by each production function. Opportunity cost. Assuming this economy is on the frontier, the opportunity cost of good y in terms of good x can be derived by solving for y as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1:18) y2 ¼ 800 4×2 or y ¼ 800 4×2 ¼ ½800 4×2 0:5 And then differentiating this expression: dy 4x ¼ 0:5½800 4×2 0:5 ð8xÞ ¼ : dx y (1:19) Suppose, for example, labor is equally allocated between the two goods. Then x ¼ 10, y ¼ 20, and dy/dx ¼ 4(10)/20 ¼ 2. With this allocation of labor, each unit increase in x output would require a reduction in y of 2 units. This can be verified by considering a slightly different allocation, lx ¼ 101 and ly ¼ 99. Now production is x ¼ 10.05 and y ¼ 19.9. Moving to this alternative allocation would have Dy ð19:9 20Þ 0:1 ¼ ¼ ¼ 2, Dx ð10:05 10Þ 0:05 which is precisely what was derived from the calculus approach. Concavity. Equation 1.19 clearly illustrates the concavity of the production possibility frontier. The slope of the frontier becomes steeper (more negative) as x output increases and y output decreas
