This page intentionally left blank MICROECONOMIC THEORY 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 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 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 For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Sr Rights Specialist: Deanna Ettinger Production Service: Cenveo Publisher Services Sr Art Director: Michelle Kunkler Internal Designer: Juli Cook/Plan-It Publishing Cover Designer: Red Hangar Design LLC Cover Image: ª Jason Reed/Getty Images Library of Congress Control Number: 2011928483 ISBN-13: 978-111-1-52553-8 ISBN-10: 1-111-52553-6 South-Western 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd 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 15 14 13 12 11 To Beth, Sarah, David, Sophia, Abby, Nate, and Christopher To Maura This page intentionally left blank 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 This page intentionally left blank 744 Glossary of Frequently Used Terms Q Quasi-concave Function A function for which the set of all points for which f (X) > k is convex concave [that is, U ðWÞ > 0; U 00 ðWÞ < 0] Absolute risk aversion is measured by rWị ẳ U 00 Wị=U Wị Relative risk aversion is measured by R rrWị ẳ Rate of Product Transformation (RPT ) The rate at which one output can be traded for another in the productive process while holding the total quantities of inputs constant The RPT is the absolute value of the slope of the production possibility frontier Rate of Return The rate at which present goods can be transformed into future goods For example, a oneperiod rate of return of 10 percent implies that forgoing unit of output this period will yield 1.10 units of output next period Rate of Technical Substitution (RTS ) The rate at which one input may be traded off against another in the productive process while holding output constant The RTS is the absolute value of the slope of an isoquant  dk RTS ¼ À  : dl q¼q0 Real Option An option arising in a setting outside of financial markets Rent Payments to a factor of production that are in excess of that amount necessary to keep it in its current employment Rental Rate The cost of hiring one machine for one hour Denoted by v in the text Rent-Seeking Activities Economic agents engage in rent-seeking activities when they utilize the political process to generate economic rents that would not ordinarily occur in market transactions Returns to Scale A way of classifying production functions that records how output responds to proportional increases in all inputs If a proportional increase in all inputs causes output to increase by a smaller proportion, the production function is said to exhibit decreasing returns to scale If output increases by a greater proportion than the inputs, the production function exhibits increasing returns Constant returns to scale is the middle ground where both inputs and outputs increase by the same proportions Mathematically, if f mk; mlị ẳ mk f k; lị; k > implies increasing returns, k = constant returns, and k < decreasing returns Risk Aversion Unwillingness to accept fair bets Arises when an individual’s utility of wealth function is S ÀWU 00 ðWÞ : U ðWÞ Second-Order Conditions Mathematical conditions required to ensure that points for which first-order conditions are satisfied are indeed true maximum or true minimum points These conditions are satisfied by functions that obey certain convexity assumptions Second Theorem of Welfare Economics Any Pareto optimal allocation can be attained as a Walrasian equilibrium by suitable transfers of initial endowments Shephard’s Lemma Application of the envelope theorem, which shows that a consumer’s compensated demand functions and a firm’s (constant output) input demand functions can be derived from partial differentiation of expenditure functions or total cost functions, respectively Shifting of a Tax Market response to the imposition of a tax that causes the incidence of the tax to be on some economic agent other than the one who actually pays the tax Short Run, Long Run Distinction A conceptual distinction made in the theory of production that differentiates between a period of time over which some inputs are regarded as being fixed and a longer period in which all inputs can be varied by the producer Signaling Actions taken by individuals in markets characterized by hidden types in an effort to identify their true type Slutsky Equation A mathematical representation of the substitution and income effects of a price change on utility-maximizing choices: @x=@px ¼ @x=@px jUẳU X@x=@Iị: Social Welfare Function A hypothetical device that records societal views about equity among individuals Subgame-Perfect Equilibrium A strategy profile ðsÃ1 ; sÃ2 ; ; sÃn Þ that constitutes a Nash equilibrium for every proper subgame Substitutes (Gross) Two goods such that if the price of one increases, more of the other good will be Glossary of Frequently Used Terms demanded That is x and y are gross substitutes if @x=@py > See also Complements; Slutsky Equation Substitutes (Net) Two goods such that if the price of one increases, more of the other good will be demanded if utility is held constant That is, x and y are net substitutes if U Utility Function A mathematical conceptualization of the way in which individuals rank alternative bundles of commodities If there are only two goods, x and y, utility is denoted by utility ¼ U(x, y) @x=@py jU¼U– > 0: Net substitutability is symmetric in that V Substitution Effects Variable Costs Costs that change in response to changes in the level of output being produced by a firm This is in contrast to fixed costs, which not change Sunk Cost An expenditure on an investment that cannot be reversed and has no resale value von Neumann–Morgenstern Utility A ranking of outcomes in uncertain situations such that individuals choose among these outcomes on the basis of their expected utility values @x=@py jU¼U– ¼ @y=@px jU¼U– : See also Complements; Slutsky Equation See Income and Substitution Effects; Output and Substitution Effects; Slutsky Equation 745 Supply Function For a profit-maximizing firm, a function that shows quantity supplied (q) as a function of output price (P) and input prices (v, w): q ¼ q(P, v, w) W Wage The cost of hiring one worker for one hour Denoted by w in the text Supply Response Increases in production prompted by changing demand conditions and market prices Usually a distinction is made between short-run and longrun supply responses Walrasian Equilibrium T Walrasian Price Adjustment Tacit Collusion Choice of cooperative (monopoly) strategies without explicit collusion Total Cost Function The relationship between (minimized) total costs, output, and input prices C ¼ C(v, w, q) An allocation of resources and an associated price vector such that quantity demanded equals quantity supplied in all markets at these prices (assuming all parties act as price-takers) The assumption that markets are cleared through price adjustments in response to excess demand or supply Z Zero-Sum Game A game in which winnings for one player are losses for the other player This page intentionally left blank Index Author names are in italics; glossary terms are in boldface A AC See Average cost function (AC) Addiction, 112–113 Adverse selection, 222, 663–669 competitive insurance market and, 665–669 first-best contract, 663 second-best contract, 663–665 Agents asymmetric information and, 642 defined, 643 principal-agent model, 642–645, 720 Aggregation Cournot, 166–167 Engel, 166 of goods, 194, 204–205 AIDS (almost ideal demand system), 142–143, 184 Aizcorbe, Ana M., 182 Alcoa, entry deterrence by, 557–558 Aleskerov, Fuad, 112 Allocation of time, 581–584 graphical analysis, 583–584 income and substitution effects of change in real wage rate, 583 two-good model, 581–582 utility maximization, 582–583 Almost ideal demand system (AIDS), 142–143, 184 Altruism, 113, 117–118, 687 Anderson, E., 404 Annuities, 632 Antiderivatives calculating, 59–60 defined, 58 Antitrust laws Alcoa, 558 explicit cartels and, 547 Standard Oil Company, 561 Appropriability effect, 563–564 Aquinas, St Thomas, 10 Assumptions of nonsatiation, 120 testing, See also Ceteris paribus assumption Asymmetric information, 238, 641–676 adverse selection in insurance, 663–669 auctions, 672–675 complex contracts as response to, 641–642 gross definitions, 190–191 hidden actions, 645 hidden types, 655–656 market signaling, 670–672 moral hazard in insurance, 650–655 nonlinear pricing, 656–663, 680–682 owner-manager relationship, 646–650 principal-agent model, 642–645 Atkeson, Andrew, 330 Attributes model, 198–199 Attributes of goods See Household production models Auctions, 672–675 Automobiles flexibility in fuel usage, 224–225, 228–230 tied sales, 529 used-car market, signaling in, 671–672 Average cost (AC), 341–342 defined, 341 graphical analysis of, 343–345 properties of, 348–349 Average physical productivity, 305–306 Average revenue curve, 378–379 Axioms of rational choice, 89–90 B Backward induction, 273–274 Bairam, E., 330 Barriers to entry, 501–503 creation of, 502–503 legal, 502 oligopolies and, 562–563 technical, 501–502 Battle of the Sexes backward induction in, 273–274 expected payoffs in, 261 extensive form for, 269–270 formal definitions, 260 mixed strategies in, 262–263 Nash equilibrium in, 257–260, 270–271 subgame-perfect equilibrium, 271–273 Bayesian games, 277–282 Bayesian-Nash equilibrium, 278–282, 285–288 defined, 280 games of incomplete information, 280 Tragedy of the Commons, 281–282 Bayes’ rule, 277, 284–285 Becker, Gary, 113, 277 Behrman, Jere R., 141 Beliefs of players, 283–285 posterior, 283–285 prior, 283–285 Benefit-cost ratio, 41–42 Benefits, mandated, 590 Bentham, Jeremy, 90 Bernat, G A., 496 Bernoulli, Daniel, 210–212 Bertrand, J., 533 Bertrand game, 265, 531–534, 540 Cournot game versus, 540 differentiated products, 542–546, 574 feedback effect, 565–566 Nash equilibrium of, 533–534 natural-spring duopoly in, 536–537 tacit collusion in, 548–549 Bertrand paradox, 534 Best response 747 748 Index Cournot model, 537 defined, 254 imperfect competition, 573 payoffs in, 255–257 Tragedy of the Commons, 267 Beta coefficients, 247 Binomial distribution, 69 expected values of, 71–72 variances and standard deviations for, 73 Black, Duncan, 704–705 Blackorby, Charles, 204 Bolton, P., 680 Bonds, 632–633 Borjas, G J., 331 Brander, J A., 576 Brouwer’s theorem, 297, 475 Brown, D K., 495 Buckley, P A., 368 Budget constraints attributes model, 198–199 mathematical model of exchange, 472, 483–484 in two-good case, 119 Budget shares, 126–128, 141–143 almost ideal demand system, 142–143 CES utility, 142 linear expenditure system, 141–142 variability of, 141 Burniaux, J M., 496 Business-stealing effect, 563–564 C Calculus, fundamental theorem of, 61 Capacity constraints, 540–541 Capital, 607–626 accumulation of, 607–608 capitalization of rents, 437 costs, 333–334 demand for, 616–618 energy substitutability and, 330 natural resource pricing, 623–626 present discounted value approach, 618–623 rate of return, 609–616 time and, 631–636 Capital asset pricing model (CAPM), 247 CARA (constant absolute risk aversion) function, 219, 244–245 Cardinal properties, 57–58 Cartels, 531–532 antitrust laws and, 547 natural-spring duopoly, 536–537 CDF (cumulative distribution function), 71 Central limit theorem, 70 CEOs (chief executive officers), 372 Certainty equivalent, 216 CES utility, 104–105, 319–320, 330 budget shares and, 126–128, 142 cost functions, 346–347 demand elasticities and, 168–169 labor supply, 587–588 Ceteris paribus assumption, 5–6 partial derivatives and, 27 in utility-maximizing choices, 90–91 CGE models See Computable general equilibrium (CGE) models Chain rule, 25, 30–32 Chance nodes, 278 Change in demand, 410 Change of variable, 59 Changes in income, 147–148 Chief executive officers (CEOs), 372 China, changing demands for food in, 183–184 Choice, 112–113 individual, portfolio problem, 245–247 rational, axioms of, 89–90 special preferences, 112–113 See also State-preference model; Utility Clarke, E., 709 Clarke mechanism, 709 Classification of long-run supply curves, 430–431 Closed shops, 598 CO2 reduction strategies, 496 Coase, Ronald, 401, 513, 693 Coase theorem, 693–694 Cobb-Douglas production function, 318–319 cost functions, 346 envelope relations and, 360–361 shifting, 351–352 Solow growth model, 329–330 technical progress in, 323–324 Cobb-Douglas utility, 102–103, 183 corner solutions, 125–128 labor supply and, 586–587 Commitment versus flexibility, 551–552 Comparative statistics analysis, 422 changes in input costs, 433–435 in general equilibrium model, 467–469 industry structure, 432 shifts in demand, 432–433 Compensated cross-price elasticity of demand, 165 Compensated demand curves, 155–159 compensating variation and, 170 defined, 157 relationship between compensated/ uncompensated curves, 158–159 relationship to uncompensated curves, 160–163 Shephard’s lemma, 157–158 Compensated demand functions, 157, 159–160 Compensated own-price elasticity of demand, 165 Compensating variation (CV), 170 Compensating wage differentials, 591–594 Competition allocative inefficiency and, 689–690 failure of competitive market, 697–698 for innovation, 567–568 perfect, 415, 426, 720 See also Competitive insurance market; Imperfect competition Competitive insurance market adverse selection and, 665–669 equilibrium with hidden types, 668 equilibrium with perfect information, 667 moral hazard and, 654–655 signaling in, 670 See also Insurance Competitive price system, 457–458 behavioral assumptions, 458 law of one price, 457 Complements, 189–191 asymmetry of gross definitions, 190–191 gross, 190 imperfect competition, 573–576 net, 191–192 perfect, 103–104 Completeness and preferences, 89 Composite commodities, 193–196 generalizations and limitations, 194–196 housing costs as, 195–196 theorem, 194 two-stage budgeting and, 204–205 Compound interest, mathematics of, 631–636 Computable general equilibrium (CGE) models, 485–489, 495 economic insights from, 487–489 solving, 486 structure of, 486 Computers and empirical analysis, 18 Concave functions, 51, 53–54, 83–84 Concavity of production possibility frontier, 464–465 quasi-concave functions, 53–55 Condorcet, M de, 704 Consols (perpetuities), 624–625, 632 Constant absolute risk aversion (CARA) function, 219, 244–245 Constant cost industry, 426–428 defined, 430 infinitely elastic supply, 427–428 initial equilibrium, 426–427 responses to increase in demand, 427 Constant elasticity, 379–380 Constant elasticity of substitution (CES) function See CES utility Constant relative risk aversion, 220 Constant relative risk aversion (CRRA) function, 221 Constant returns to scale, 311 Constant risk aversion, 219–220 Constrained maximization, 39–45, 84–85 duality, 42–45 envelope theorem in, 45–46 first-order conditions and, 40 formal problem, 39–40 Lagrange multiplier method, 39, 41–42 optimal fences and, 43–45 second-order conditions and, 52–53 Index Consumer price index (CPI), 181–184 Consumer search, 546–547 Consumer surplus, 169–174 consumer welfare and expenditure function, 169–170 defined, 173 overview, 170–172 using compensated demand curve to show CV, 170 welfare changes and Marshallian demand curve, 172–174 Consumer theory, relationship of firm to, 372–373 Consumption convexity and balance in, 96–99 of goods, utility from, 91 See also Indifference curves Contingent commodities fair markets for, 234 prices of, 233–234 states of world and, 233 Contingent input demand, 354–355 cost-minimizing input choices, 338 Shephard’s lemma and, 353–355 Continuity partial equilibrium competitive model, 453 preferences and, 89–90 Continuous actions, games with, 298 Continuous random variables, 67–68 Continuous time, 633–636 continuous growth, 634 duration, 636 payment streams, 635 Continuum of actions, 265–268 Contour lines, 34, 112 Contract curves, 463–464, 477–481 Contracts, 641–642 asymmetric information, 641–642 first-best, 643, 651–652, 660, 666 second-best, 643–644, 652–654, 666–667 value of, 642 Controlled experiments, Convex functions, 83–84 Convex indifference curves, 95–96, 97, 100–101 Convexity, 96–99 Corn Laws debate, 470–471 Correspondences, functions versus, 296–297 Cost-benefit analysis, 231 Cost curves per-unit, 361–362 shifts in, 345–355 See also Cost functions Cost functions, 333–363 average and marginal, 341–342, 343–345 cost-minimizing input choices, 336–341 definitions of costs, 333–335 graphical analysis of total costs, 342–343 homogeneity, 347 input prices and, 347–348 Shephard’s lemma and elasticity of substitution, 355 shifts in cost curves and, 345–355 short-run, long-run distinction, 355–362 translog, 367–368 Cost industry decreasing, 429–430 increasing, 428–429 Cost minimization illustration of process, 340–341 principle of, 338 relationship between profit maximization and, 335 Cournot, Antoine, 166, 534 Cournot aggregation, 166–167 Cournot equilibrium, 554 Cournot game, 265–266, 534–540 feedback effect, 565–566 imperfect competition, 574 long-run equilibrium and, 564–565 Nash equilibrium of Cournot game, 535–538 natural-spring duopoly, 536–537 prices versus quantities, 540 tacit collusion in, 550–551 varying number of firms and, 539–540 Covariance, 74–76 CPI (consumer price index), 181–184 Cross-partial derivatives, 50 Cross-price effects asymmetry in, 190–191 net substitutes and complements, 192 profit maximization and input demand, 392–393 Slutsky decomposition, 188–189 Cross-price elasticity of demand, 163 Cross-productivity effects, 309–310 CRRA (constant relative risk aversion) function, 221 Cumulative distribution function (CDF), 71 CV (compensating variation), 170, 716 D Deadweight loss, 444–445 Deaton, Angus, 143 Decrease in price, graphical analysis of, 149 Decreasing cost industry, 430 Decreasing returns to scale, 312–313 Definite integrals defined, 60 differentiating, 62–63 Delay, option value of, 230 Demand See Supply and demand Demand aggregation and estimation, 453–455 Demand curves defined, 152 demand functions and, 154–155 importance of shape of supply curve, 421–422 importance to supply curves, 420–421 individual, 152–155 shifts in, 154, 421 749 uncompensated, 158–159 See also Compensated demand curves Demand elasticities, 163–169 compensated price elasticities, 165 Marshallian, 163–164 price elasticity and total spending, 164 price elasticity of demand, 164 relationships among, 165–169 Demand functions, 145–147 demand curves and, 154–155 indirect utility function, 128 mathematical model of exchange, 472–473 Demand relationships among goods, 187–200 attributes of goods, 197–200 composite commodities, 193–196 home production, 197–200 implicit prices, 197–200 net substitutes and complements, 191–192 overview, 187 simplifying demand and two-stage budgeting, 204–205 substitutability with many goods, 193 substitutes and complements, 189–191 two-good case, 187–189 Derivatives cross-partial, 50 defined, 22 homogeneity and, 56 partial, 26–30 rules for finding, 24–25 second, 23–24 value of at point, 22–23 Deterring entry See Entry deterrence/ accommodation Dewatripont, M., 680 Diamond, Peter, 546 Dictator game, 289 Diewert, W Erwin, 205 Differentiated products See Product differentiation Diminishing marginal productivity See Marginal physical product (MP) Diminishing marginal rate of substitution See Marginal rate of substitution (MRS) Diminishing returns, 462–463 Diminishing RTS See Rate of technical substitution (RTS) Direct approach, Discount factor, 275–277, 547–550 Discrete random variables, 67–68 Discrimination, price See Price discrimination Disequilibrium behavior, 442 Dissipation effect, 567 Diversification, 223–224 Dominant strategies defined, 257 Nash equilibrium, 257, 265 Doucouliagos, H., 368 Dual expenditure-minimization problem, 132 750 Index Duality, 42–45 Duffield, James A., 112 Durability of goods, 512 Dutch MIMIC model, 495 Dynamic optimization, 63–66 maximum principle, 64–66 optimal control problem, 63–64 Dynamic views of monopoly, 523 E Economic costs, 334–335 defined, 334 Economic efficiency concept of, 17 welfare analysis and, 438–441 Economic goods, in utility functions, 92 Economic models, 3–18 ceteris paribus assumption, 5–6 economic theory of value, 9–17 modern developments in, 17–18 optimization assumptions, 7–8 positive-normative distinction, 8–9 structure of economic models, 6–7 theoretical models, verification of, 4–5 Economic profits, 374 Edgeworth, Francis Y., 17 Edgeworth box diagram, 459, 460 Efficiency allocative inefficiency, 687–690 concept of, 17 efficient allocations, 460–461, 688–689 Pareto efficient allocation, 476 welfare analysis and, 438–441 Elasticity general definition of, 28–29 interpretation in mathematical model of market equilibrium, 423–424 marginal revenue and, 377–378 of substitution, 313–315, 355 of supply, 431 Elasticity of demand compensated cross-price, 165 compensated own-price, 165 cross-price, 163 monopolies and, 509–510 price, 163–164 Elasticity of substitution, 104, 350 defined, 314 graphic description of, 314–315 See also CES utility Empirical analysis computers and, 18 importance of, Empirical estimates, 431 Endogenous variables, 6–7 Energy capital and, 330 homothetic functions and, 205 Engel, Ernst, 141 Engel aggregation, 166 Engel’s law, 141 Entrepreneurial service costs, 334 Entry conditions See Entry deterrence/ accommodation Entry deterrence/accommodation barriers to entry, 501–503 entry-deterrence model, 559–560 imperfect competition, 562–566, 576 in sequential game, 574–575 strategic entry deterrence, 557–559 Envelope theorem, 35–39 Cobb–Douglas cost functions and, 360–361 in constrained maximization problems, 45–46 direct, time-consuming approach, 36–37 envelope shortcut, 37 many-variable case, 37–39 profit function, 385 Shephard’s lemma and, 353 specific example of, 35–36 Environmental externalities, 702–703 Equilibrium Bayesian-Nash, 278–282, 285–288 computable, 485–489, 495 existence of, 265 median voter, 706 separating, 286–287, 561 subgame-perfect, 271–273, 721 Walrasian, 473, 484–485 See also General equilibrium; Nash equilibrium; Partial equilibrium model Equilibrium path, 271 Equilibrium point, 11 Equilibrium price defined, 418 determination of, 418–419, 465–467 of future goods, 613, 614 supply-demand equilibrium, 12 Equilibrium rate of return, 614 Euler’s theorem, 56, 193 Evolutionary games and learning, 290 Exact price indices, 183–184 Exchange, mathematical model of, 471–482 demand functions and homogeneity, 472–473 equilibrium and Walras’ law, 473–474 existence of equilibrium in exchange model, 474–475 first theorem of welfare economics, 476–478 second theorem of welfare economics, 478–481 social welfare functions, 481–482 utility, initial endowments, and budget constraints, 472 vector notation, 471–472 Exchange economy, 479–481 Exchange value, labor theory of, 10 Exclusive goods, 695 Exogenous variables, 6–7 Expansion path, 338–340 Expected utility, 210–214 Expected value, 70–72, 209 Expenditure functions, 169–170 defined, 132–133 properties of, 134–135 substitution bias and, 182 Expenditure minimization, 131–134 Experimental games, 288–289 Dictator game, 289 Prisoners’ Dilemma, 288–289 Ultimatum game, 289 Exponential distribution, 70 expected values of random variables, 72 variances and standard deviations, 73 Extensive form games of incomplete information, 279 of sequential games, 269–270 Externalities, 685–710 allocative inefficiency and, 687–690 defined, 686, 718 defining, 685–687 graphic analysis of, 691 solutions to externality problem, 691–694 F Factor intensities, 463–464 Factor prices, 470–471 Fair bets, 214–216 Fair gambles, 210–211 Fair markets for contingent goods, 234 Fama, E F., 247 Farmland reserve pricing, 529 Feedback effect, 565–566 Feenstra, Robert C., 183 Financial option contracts, 225 Finitely repeated games, 274–275, 547 Firms, 371–373 complicating factors, 371–372 expansion path, cost-minimizing input choices, 338–341 in oligopoly setting, 562–566 profit maximization, 401–404 relationship to consumer theory, 372–373 simple model of, 371 First-best contracts, 643, 660 adverse selection and, 663 monopoly insurers, 666 moral hazard and, 651–652 nonlinear pricing, 680 principal-agent model, 643–645 First-best nonlinear pricing, 657–659 First-degree price discrimination, 514–515 First-mover advantage, 552–555 First-order conditions, 123–124 Lagrange multiplier method, 40 for maximum, 23, 33–34, 120–121 First theorem of welfare economics, 476–478 defined, 477 Edgeworth box diagram, 478 Fisher Body, 372, 401–404 Index Fixed costs short-run, 356 sunk costs versus, 552 Fixed point, 297 Fixed-proportions production function, 316–318, 345–346 Fixed supply, allocating, 65–67 Flexibility, 224–231 commitment versus, 551–552 computing option value, 227–230 implications for cost–benefit analysis, 231 model of real options, 225–227 number of options, 227 option value of delay, 230 types of options, 224–225 Folk theorem for infinitely repeated games, 275–277, 547–548 Foundations of Economic Analysis (Samuelson), 17 Friedman, Milton, Fudenberg, D., 296, 575 Full-information case, 646–647 Functional form and elasticity, 28–29 Fundamental theorem of calculus, 61 Fuss, M., 367 Future goods, 609–610, 614 G Game theory, 251–291 basic concepts, 251–252 continuum of actions, 265–268 evolutionary games and learning, 290 existence of equilibrium, 265, 296–298 experimental games, 288–289 incomplete information, 277–278 mixed strategies, 260–265 Nash equilibrium, 254–260 payoffs, 252 players, 252 Prisoners’ Dilemma, 252–254 repeated games, 274–277 sequential games, 268–274 signaling games, 282–288 simultaneous Bayesian games, 278–282 strategies, 252 Garcia, S., 368 Gaussian (Normal) distribution, 70, 72–74 Gelauff, G M M., 495 General equilibrium, 457–489 comparative statistics analysis, 467–469 mathematical model of exchange, 471–482 mathematical model of production and exchange, 482–485 modeling and factor prices, 469–471 perfectly competitive price system, 457–458 with two goods, 458–467 General equilibrium model, 14, 469–471, 692–693 computable, 485–489 simple, 487–488 welfare and, 495–496 General Motors (GM), 372, 401–404 Giffen, Robert, 152 Giffen’s paradox, 151–152 Glicksberg, I L., 298 GM (General Motors), 372, 401–404 Goods changes in price of, 149–153 demand relationships among, 187–200, 204–205 durability of, 512 exclusive, 695 fair markets for contingent, 234 future, 609–610, 614 inferior, 147–148, 150–151 information as, 231–232 nonrival, 695 normal, 147–148 See also Demand relationships among goods; Public goods Gorman, W M., 453 Gould, Brain W., 184 Government procurement, 496 Graaflund, J J., 495 Grim strategy, 276 Gross complements, 188, 190 Gross definitions, asymmetry of, 190–191 Grossman, Michael, 113 Grossman, Sanford, 401 Gross substitutes, 188, 190 Groves, T., 708 Groves mechanism, 708–709 Growth accounting, 322–324 Gruber, Jonathan, 113 H Habits and addiction, 113 Hanley, N., 714 Hanson, K., 496 Harsanyi, John, 278 Hart, Oliver, 401 Hausman, Jerry, 182–183 Hayashi, Fumio, 141 Hessian matrix, 83–84 Heterogeneous demand, 512–513 Hicks, John, 192–194 Hicksian demand curves, 155–159 relationship between compensated and uncompensated, 158–159 Shephard’s lemma, 157–158 Hicksian demand functions See Demand functions Hicksian substitutes and complements, 191–192 Hicks’ second law of demand, 193 Hidden actions, 643, 645, 647–650 Hidden types, 643, 655–656, 668, 680 Hoffmann, S., 496 Hold-up problem, 403 Homogeneity of demand, 146–147, 165–166 expenditure functions, 134 751 income aggregation and, 453 mathematical model of exchange, 472–473 profit functions, 384 Homogeneous functions, 55–58 derivatives and, 56 Euler’s theorem, 56 homothetic functions, 56–58 Homothetic functions, 56–58, 205, 312–313 Homothetic preferences, 105 Hone, P., 368 Hotelling, Harold, 385, 544 Hotelling’s beach model, 544–546 Hotelling’s lemma, 385 Household production models, 197–200 corner solutions, 199–200 illustrating budget constraints, 198–199 linear attributes model, 198 overview, 197–198 Housing costs, as composite commodity, 195–196 Human capital, 591 Hybrid equilibria, 286, 288 I Immigration, 331 Imperfect competition, 531–568 Bertrand model, 533–534 capacity constraints, 540–541 Cournot model, 534–540 entry of firms, 562–566 innovation, 566–568 longer-run decisions, 551–557 pricing and output, 531–532 product differentiation, 541–547 signaling, 559–562 strategic entry deterrence, 557–559 strategic substitutes and complements, 573–576 tacit collusion, 547–551 Implicit (shadow) prices, 197–200 Implicit functions, 32–33 Income, changes in, 147–148 Income aggregation, 453 Income effects, 145–177 consumer surplus, 169–174 demand concepts and evaluation of price indices, 181–184 demand curves and functions, 145–147, 153–159 demand elasticities, 163–169 income changes, 147–148 price changes, 149–153, 160–163 real wage rate changes, 583 two-good case, 187–188 See also Substitution effects Income elasticity of demand, 163 Incomplete-information games, 277–280 Increasing cost industry, 430 Increasing returns to scale, 311–313 752 Index Independent variables, 32 Indifference curve maps, 94–95, 102 Indifference curves convexity of, 95–96, 100–101 defined, 93 maps, 94–95, 102 mathematics of, 99–101 and transitivity, 95 two-good case, 187 utility maximization in attributes model, 199–200 Indirect approach, Indirect utility function, 128–129 Individual demand curves, 153–155 Industry structure, 432 Inequality constraints, 46–48 complementary slackness, 47–48 slack variables, 46–47 solution using Lagrange multipliers, 47 two-variable example, 46 Inferior goods, 147–148, 150–151 Inferior inputs, 339 Infinitely elastic long-run supply, 427–428 Infinitely repeated games, 275–277, 547–551 Information, 231–232 in economic models, 18 as good, 231–232 quantifying value of, 232 See also Asymmetric information Initial endowments, 472 Innovation, 566–568 competition for, 567–568 monopoly on, 566–567 Input costs changes in, 433–435 industry structure and, 434–435 Input demand decomposing into substitution and output components, 394–395 profit maximization and, 388–395 Input demand functions, 390 Inputs contingent demand for, and Shephard’s lemma, 353–355 substitution, 349, 350 supply, and long-run producer surplus, 437–438 See also Cost minimization; Labor markets Insurance adverse selection, 222, 663–669 asymmetric information, 642 competitive theft, 654–655 moral hazard, 650–655 precaution against car theft, 653–654 premiums, 217–218 risk aversion and, 216–217 in state-preference model, 235–236 willingness to pay for, 216–217 See also Competitive insurance market Integration, 58–60 antiderivatives, 58–60 definite integrals, 60 differentiating definite integral, 62–63 fundamental theorem of calculus, 61 by parts, 59 Interest rates, 614–616 Interfirm externalities, 686 Inverse elasticity rule, 504 Investments, 552, 618–623 diversification, 223–224 portfolio problem, 244–247 theory of, 618 Isoquant maps, 306–310 constant returns-to-scale production function, 312 elasticity of substitution, 315 importance of cross-productivity effects, 309–310 input inferiority, 339 rate of technical substitution, 307–309 simple production functions, 317 technical progress, 321 Isoquants, defined, 306 See also Isoquant maps; Rate of technical substitution (RTS) J Jackman, Patrick C., 182 Jensen, M., 247 Jensen’s inequality, 216, 225 Job-market signaling, 283–284 hybrid equilibrium in, 288 pooling equilibrium in, 287 separating equilibrium in, 286–287 Jorgenson, Dale W., 205 K Kakutani’s fixed point theorem, 297 Kehoe, Patrick J., 142, 330 Kehoe, Timothy J., 142 Koszegi, Botond, 113 Kuhn-Tucker conditions, 48 Kwoka, J E., 529 L Labor costs, 333 mandated benefits, 590 productivity, 304–305 Labor markets, 581–601 allocation of time, 581–584 equilibrium in, 589–590 labor unions, 598–601 market supply curve for labor, 588–589 mathematical analysis of labor supply, 584–588 monopsony in labor market, 595–597 wage variation, 591–595 Labor supply, 584–588 dual statement of problem, 585 Slutsky equation of labor supply, 585–588 Labor theory of exchange value, 10 Labor unions, 598–601 bargaining model, 600–601 modeling, 599–600 Lagrangian multiplier as benefit–cost ratio, 41–42 interpreting, 41 method for, 39 in n-good utility maximization, 124 solution using, 47 Lancaster, K.J., 198 Latzko, D., 368 Law of one price, 457 Leading principal minors, 83 Learning games, 290 Legal barriers to entry, 502 Lemons, market for, 671–672 Leontief, Wassily, 320 Leontief production functions, 319–320, 330 Lerner, Abba, 378 Lerner index, 378 LES (linear expenditure system), 141–142 Lewbel, Arthur, 205 Lightning calculations, 117 Limitations and composite commodities, 197–200 Lindahl, Erik, 700 Lindahl equilibrium, 700–703 local public goods, 702–703 shortcomings of, 701–702 Linear attributes model, 198 Linear expenditure system (LES), 141–142 Linear pricing, 656 Linear production function, 316 Local public goods, 702–703 Locay, L., 529 Long run See Short-run, long-run distinction Long-run analysis elasticity of supply, 431 long-run equilibrium, 425–428, 431–435 overview, 425 producer surplus in, 435–438 shape of supply curve, 428–431 Long-run competitive equilibrium, 425 Long-run cost curves, 358–361 Long-run elasticity of supply, 431 Long-run equilibrium comparative statistics analysis of, 431–435 conditions for, 425 constant cost case, 426–428 Cournot model, 564–565 in oligopoly, 563–565 Long-run producer surplus, 438–441 Long-run supply curves, 427–428 Lump sum principle, 129–131 M MacBeth, J., 247 Majority rule, 703–704 Index Malthus, Thomas, 304 Many-good case, 106 Marginal benefit, 41 Marginal costs (MC), 341–342, 343–345, 348–349 defined, 341 graphical analysis of, 343–344 pricing, 519–520 Marginal expense (ME), 596 Marginalism, 10–11, 373 Marginal physical product (MP), 304 Marginal productivity, 303–306 average physical productivity, 305–306 diminishing, 305–306 marginal physical product, 304 rate of technical substitution, 308 Marginal rate of substitution (MRS) defined, 93 indifference curves, 99–100 with many goods, 106 Marginal revenue (MR), 375–380 curves, 378–380 defined, 374 and elasticity, 377–378 from linear demand functions, 377 price–marginal cost markup, 378 Marginal revenue product (MRP), 389 Marginal utility (MU), 99–100, 124, 215–218, 244 Market basket index, 181–182 Market demand, 409–413 defined, 412 elasticity of market demand, 413 generalizations, 411–412 market demand curve, 409–410 shifts in, 411 shifts in market demand curve, 410–411 simplified notation, 412 Market period, 413 Markets meaning of, 541–542 reaction to shift in demand, 419 rental rates, 616–617 separation, third-degree price discrimination through, 515–517 tools for studying, 18 Market supply curve, 415–416, 588–589 Marshall, Alfred, 11, 409 Marshallian demand, 163–164, 172–174, 182–183 Marshallian substitutes and complements, 190 Marshallian supply-demand synthesis, 11–14 Masten, S E., 404 Matrix algebra constrained maxima, 84–85 quasi-concavity, 85 Maximal punishment principle for crime, 277 Maximization, 84 of one variable, 21–25 of several variables, 33–35 Maximum principle, 64–66 MC See Marginal costs (MC) McFadden, D., 367 ME (marginal expense), 596 Meade, J., 686 Median voter theorem, 705–708 median voter equilibrium, 706 optimality of median voter result, 706–708 overview, 704–705 MES (minimum efficient scale), 345 Mexico, NAFTA and, 142, 495 Microsoft, 567 Milliman, S R., 715 Minimization of costs, 335, 338, 340–341 of expenditures, 131–134 Minimum efficient scale (MES), 345 Mixed strategies, 260–265 computing mixed-strategy equilibria, 263–265 formal definitions, 261–262 Modern economics, founding of, 10 Monjardet, Bernard, 112 Monopolies, 501–524 allocational effects of, 508 barriers to entry, 501–503 coffee shop example, 662–663 defined, 501 distributional effects of, 508 dynamic views of, 523 on innovation, 566–567 linear two-part tariffs, 528–529 natural, 501 price determination for, 503 price discrimination, 513–519 product quality and durability, 510–513 profit maximization and output choice, 503–507 regulation of, 519–523 resource allocation and, 507–510 simple demand curves, 507 welfare losses and elasticity, 509–510 Monopoly output, 503–504, 506 Monopoly rents, 505 Monopsonies, 595–597 Monotonic transformations, 56–58 Monteverde, K., 404 Moore, John, 401 Moral hazard, 222, 650–655 competitive insurance market, 654–655 defined, 651 first-best insurance contract, 651–652 mathematical model, 651 second-best insurance contract, 652–654 Morgenstern, Oscar, 212 Morishima, M., 350 Morishima elasticities, 350 Most-favored customer program, 575–576 MP (marginal physical product), 304 MR See Marginal revenue (MR) 753 MRP (marginal revenue product), 389 MRS See Marginal rate of substitution (MRS) MU (marginal utility), 99–100, 124, 215–218, 244 Muellbauer, John, 143 Murphy, Kevin M., 113 Multivariable Calculus, 26–35 calculating partial derivatives, 26–27 chain rule with many variables, 30–32 elasticity, 28–29 first-order conditions for maximum, 33–34 implicit functions, 32–33 partial derivatives, 26–30 second-order conditions, 34–35 Young’s theorem, 30 Mutual funds, 247 N NAFTA (North American Free Trade Agreement), 142, 495 Nash, John, 254, 296 Nash bargaining, 402 Nash equilibrium, 254–260 in Battle of the Sexes, 257–260 of Bertrand game, 533–534 of Cournot game, 535–538 defined, 255 dominant strategies, 257 existence of, 296–298 formal definition, 254–255 imperfect competition, 573 inefficiency of, 698–700 in Prisoners’ Dilemma, 254–255 in sequential games, 270–271 underlining best-response payoffs, 255–257 Natural monopolies, 501, 519–520 Natural resource pricing, 623–626 decrease in prices, 624–625 profit-maximizing pricing and output, 623–625 renewable resources, 626 social optimality, 625 substitution, 625–626 Natural-spring duopoly, 536–539 deterring entry, 557–558 Stackelberg model, 553–555 Natural-spring oligopoly, 539–540 Negative definite, 83–84 Negative externalities, 268 Nested production functions, 330 Net complements, 191–192, 716 Net substitutes, 191–192, 721 New goods bias, 182–183 n-good case, 122–128 corner solutions, 124–128 first-order conditions, 123 implications of first-order conditions, 123–124 interpreting Lagrange multiplier, 124 Nicoletti, G., 496 754 Index n-input case elasticity of substitution, 314–315 returns to scale, 313 Nominal interest rates, 614–616 Nondepreciating machines, 617 Nonexclusive goods, 694–695 Nonhomothetic preferences, 105 Nonlinear pricing, 656–663 with continuum of types, 680–682 first-best case, 657–659 mathematical model, 657 second-best case, 659–663 Nonoptimality of short-run costs, 356–367 Nonrival goods, 695 Nonuniqueness of utility measures, 90 Normal (Gaussian) distribution, 70, 72–74 Normal form for Battle of the Sexes, 257 for Prisoners’ Dilemma, 252 Normal goods, 147–148 Normative analysis, 8–9 North American Free Trade Agreement (NAFTA), 142, 495 O Oczkowski, E., 142 Oi, Walter, 518 Oligopolies, 531–568 Bertrand model, 533–534 capacity constraints, 540–541 Cournot model, 534–540 defined, 531 entry of firms, 562–566 innovation, 566–568 longer-run decisions, 551–557 pricing and output, 531–532 product differentiation, 541–547 signaling, 559–562 strategic entry deterrence, 557–559 strategic substitutes and complements, 573–576 tacit collusion, 547–551 See also Cournot game Oliviera-Martins, J., 496 Opportunity cost doctrine, 15, 464–465 Optimal control problem, 63–64 Optimality of median voter result, 706–708 Optimization assumptions, 7–8 dynamic, 63–66 Ordinal properties, 57–58 Output choice, 374 Output effects principle of, 393 profit maximization and input demand, 391–392, 393 Outputs imperfect competition, 531–532 monopolies and, 503–504, 506 profit-maximizing, for natural resources, 623–625 Owner-manager relationship, 646–650 comparison to standard model of firm, 650 full-information case, 646–647 hidden-action case, 647–650 Ownership of machines, 617–618 P Paradox of voting, 704 Pareto, Vilfredo, 17, 476 Pareto efficient allocation, 476 Pareto superiority, 528–529 Partial derivatives calculating, 26–27 ceteris paribus assumption and, 27 defined, 26 second-order, 29 units of measurement and, 27–28 Partial equilibrium model, 14, 409–447 comparative statistics analysis, 431–435 demand aggregation and estimation, 453–455 economic efficiency and welfare analysis, 438–441 long-run analysis, 425 long-run elasticity of supply, 431 long-run equilibrium, 426–428 market demand, 409–413 mathematical model of market equilibrium, 422–424 price controls and shortages, 441–442 pricing in very short run, 413–415 producer surplus in long run, 435–438 shape of long-run supply curve, 428–431 shifts in supply and demand curves, 419–422 short-run price determination, 415–419 tax incidence analysis, 442–446 timing of supply response, 413 Payoffs, 252 in Battle of the Sexes, 261 in best response, 255–257 in Rock, Paper, Scissors game, 259–260 PDF See Probability density function (PDF) PDV See Present discounted value (PDV) Perfect Bayesian equilibrium, 285 Perfect competition, 457–458 behavioral assumptions, 458 defined, 415 law of one price, 457 long-run equilibrium, 426 Perfect complements, 103–104 Perfect price discrimination, 514–515 Perfect substitutes, 103 Perpetual rate of return, 608 Perpetuities (consols), 624–625, 632 Per-unit cost curves, 361–362 Philip, N E., 142 Pigou, A C., 691 Pigovian taxes, 691–693, 703 Players, 252, 278, 283–285 Point-slope formula, 33 Political support for trade policies, 471 Pollution abatement of, 714–715 CO2 reduction strategies, 496 emission taxes in the United Kingdom, 714 pollution rights, 693 Pontryagin, L S., 64 Pooling equilibrium, 286, 561 in competitive insurance market, 668 in job-market signaling game, 287 Portfolio problem, 244–247 CARA utility, 244–245 individual choices, 245–247 many risky assets, 245 mutual funds, 247 one risky asset, 244 optimal portfolios, 245 studies of CAPM, 247 Positive analysis, Positive definite, 83–84 Positive-normative distinction, 8–9 Posterior beliefs, 283–285 Pratt, J W., 217, 220 Pratt’s risk aversion measure, 217–219 Predatory pricing, 561–562 Predictions, testing, 4–5 Preferences, 89–107 axioms of rational choice, 89–90 many-good case, 106 mathematics of indifference curves, 99–101 overview, 89 trades and substitution, 92–99 utility, 90–92 utility functions for specific, 102–105 Present discounted value (PDV), 631–633 annuities and perpetuities, 632 bonds, 632–633 investment decisions, 618–623 Price controls and shortages, 441–442 disequilibrium behavior, 442 welfare evaluation, 442 Price discrimination, 513–517 defined, 513 perfect, 514–515 second-degree, 517–519 third-degree, 515–517 Price dispersion, 546–547 Price elasticity, 163, 164 Price–marginal cost markup, 378 Prices of contingent commodities, 233–234 of future goods, 609, 614 imperfect competition, 531–532 implicit, 197–200 law of one, 457 predatory, 561–562 response to changes in, 160–163 in short-run analysis, 415–419 versus value, 9–10 Index in very short run, 413–415 welfare effects of, 172–174 See also Bertrand game; Consumer surplus; Equilibrium price; Expenditure functions; Natural resource pricing; Nonlinear pricing; Price discrimination Price schedules, 517–519 Price takers, 376, 380–384 Primont, Daniel, 204 Prince, R., 715 Principal-agent relationship, 642–645 Principles of Economics (Marshall), 11 Prior beliefs, 283–285 Prisoners’ Dilemma, 252–254 experiments with, 288–289 finitely repeated games, 274–275 infinitely repeated games, 276 Nash equilibrium in, 255 normal form, 252 thinking strategically about, 252–254 variation of, 259 Private information See Asymmetric information Probability density function (PDF) defined, 68, 209 examples of, 68–70 random variables, 67 Producer surplus defined, 387, 435 in long run, 435–438 in short run, 386–389 Product differentiation, 541–547 Bertrand competition with, 542–546 Bertrand model, 574 consumer search and price dispersion, 546–547 Hotelling’s beach model, 544–546 meaning of ‘‘market,’’ 541–542 toothpaste as a differentiated product, 543–544 Production and exchange, mathematical model of, 482–485 budget constraints and Walras’ law, 483–484 Walrasian equilibrium, 484 Welfare economics in Walrasian model with production, 484–485 Production externalities, 689–690 Production functions, 302–324, 329–331 CES, 319–320, 330 Cobb–Douglas, 318–319, 329–330 defined, 303 elasticity of substitution, 313–315 fixed proportions, 316–318 generalized Leontief, 330 isoquant maps and rate of technical substitution, 306–310 linear, 316 marginal productivity, 303–306 nested, 330 returns to scale, 310–313 technical progress, 320–324 translog, 331 two-input, 305–306 Production possibility frontier, 14–17, 461–462 concavity of, 464–465 defined, 461 implicit functions and, 32–33 Profit functions, 384–389 envelope results, 385 properties of, 384–385 short-run, 386–389 Profit maximization, 371–396 boundaries of firm, 401–404 cost minimization and, 335 decisions, 380–381 finding derivatives and, 25 functions of variable, 49 graphical analysis, 375 input demand and, 388–395 marginalism and, 373 marginal revenue and, 375–380 by monopolies, 503–507 nature and behavior of firms, 371–373 optimization assumptions and, 7–8 output choice and, 374 overview, principle of, 374 profit functions, 384–389 second-order conditions and, 375 short-run supply by price-taking firm, 380–384 testing assumptions of, testing predictions of, 4–5 Profits, 374 monopolies, 504–505 See also Profit functions; Profit maximization Proper subgames, 271–273 Properties of expenditure functions, 134–135 Property rights, 402–403 Public goods attributes of, 694–696 defined, 696 derivation of the demand for, 698 environmental externalities and production of, 702–703 externalities, 687 Lindahl pricing of, 700–703 resource allocation and, 696–700 Roommates’ dilemma, 699–701 simple political model, 705–708 voting and resource allocation, 703–705 voting mechanisms, 708–709 Puppy dog strategy, 555–556, 558–559, 573 Pure inflation, 146 Pure strategies, 259–260 Q Quality choice models and, 112–113 of products, 511–512 755 Quantifying value of information, 232 Quantitative size of shifts in cost curves, 350–351 Quasi-concave function, 53–55 concave functions and, 53–54 convex indifference curves, 100 Quasi-concavity, 85 R Random variables continuous, 67–68 defined, 209 discrete, 67–68 expected value of, 209 and probability density functions, 67 variance and standard deviation of, 209 Rate of product transformation (RPT), 461–462 Rate of return demand for future goods, 610 effects of changes in, 612–613 equilibrium, 614 interest rates, 614–616 overview, 607–609 price of future goods and, 609 regulation of, 521–522 supply of future goods, 613–614 utility maximization, 611–612 Rate of technical substitution (RTS) defined, 307 diminishing, 308–309 importance of cross-productivity effects, 309–310 marginal productivities and, 308 reasons for diminishing, 308–309 Rational choice, axioms of, 89–90 Real interest rates, 614–616 Real option theory, 225–227 Reinsdorf, Marshall B., 183 Relative risk aversion, 220–221 Renewable resources, 626 Rent capitalization of, 437 monopoly, 505 Ricardian, 436–437 Rental rates, 616–617 Repeated games, 274–277 finitely, 274–275, 547 infinitely, 275–277, 547–551 Replacement effect, 567 Resource allocation monopoly and, 507–510 public goods and, 696–700 Returns to scale, 310–313 constant, 311 defined, 310 homothetic production functions, 312–313 n-input case, 313 Revealed preference theory, 174–176 graphical approach, 175 negativity of substitution effect, 175–176 756 Index Ricardian rent, 436–437 Ricardo, David, 10, 436 Risk aversion, 214–217 constant, 219–220 constant relative, 221 defined, 216 fair bets and, 214–216 insurance and, 216–217 measuring, 217–221 state-preference approach to choice, 234–235 See also Uncertainty Risk premiums, 237–238 Robinson, S., 496 Rock, Paper, Scissors game, 259–260 Rockefeller, John D., 561 Rodriguez, A., 529 Roy’s identity, 182–183 RPT (rate of product transformation), 461–462, 720–721 RTS See Rate of technical substitution (RTS) Russell, R Robert, 204 S SAC (short-run average total cost function), 358, 361–362 St Petersburg paradox, 210–212 Samuelson, Paul, 17, 174 Scarf, Herbert, 486 Scharfstein, D S., 247 Schmalensee, R., 715 Schmittlein, D C., 404 Schumpeter, J A., 523 Second-best contracts adverse selection, 663–665 monopoly insurer, 666–667 moral hazard, 652–654 nonlinear pricing, 680–681 principal-agent model, 643–644 Second-best nonlinear pricing, 659–663 Second-degree price discrimination, 517–519 Second derivatives, 23–24 Second-order conditions, 23, 375, 390 concave and convex functions, 51, 83–84 constrained maxima, 84–85 curvature and, 48–55 for maximum, 84, 121–122 quasi-concavity, 85 several variables, 34–35 Second-order partial derivatives, 29–30 Second-party preferences, 113 Second theorem of welfare economics, 478–481 Selfishness, 117–118 Selten, Reinhard, 275 Separating equilibrium, 286–287, 561 Sequential Battle of the Sexes game, 268–269 Sequential games, 268–274 backward induction, 273–274 Battle of the Sexes, 268–269 extensive form, 269–270 Nash equilibria, 270–271 subgame-perfect equilibrium, 271–273 Shadow (implicit) prices, 197–200 Sharpe, W F., 245 Shephard, R W., 157 Shephard’s lemma, 157–158 contingent demand for inputs and, 353–355 defined, 721 elasticity of substitution and, 355 net substitutes and complements, 192 Shogren, J F., 714 Short run, long run distinction, 355–362 fixed and variable costs, 356 graphs of per-unit cost curves, 361–362 nonoptimality of, 356–367 relationship between long-run cost curves and, 358–361 short-run marginal and average costs, 358 total costs, 356 Short-run analysis, 355–362 fixed and variable costs, 356 graphs of per-unit cost curves, 361–362 nonoptimality of, 356–367 price determination, 415–419 producer surplus in, 388–395 relationship between long-run cost curves and, 358–361 short-run marginal and average costs, 358 total costs, 356 Short-run average total cost function (SAC), 358, 361–362 Short-run fixed costs, 356 Short-run marginal cost function (SMC), 358, 361–362 Short-run market supply function, 416–417 Short-run supply curve, 381–384, 416 Short-run supply elasticity, 416 Short-run variable costs, 356 Shutdown decision, 381–384 Signaling, 559–562, 670–672 in competitive insurance markets, 670 entry-deterrence model, 559–560 market for lemons, 671–672 pooling equilibrium, 561 predatory pricing, 561–562 separating equilibrium, 561 Signaling games, 278, 282–288 Bayes’ rule, 284–285 job-market signaling, 283–284 perfect Bayesian equilibrium, 285–288 Simplexes, 297 Simultaneous games, 278–282 Bayesian–Nash equilibrium, 278–282 player types and beliefs, 278 sequential games versus, 268–272 Single-input case, 390–391 Single-peaked preferences, 704–705 Single-period rate of return, 608 Single variable calculus, 21–25 derivatives, 22 first-order condition for maximum, 23 rules for finding derivatives, 24–25 second derivatives, 23–24 second-order conditions and curvature, 23, 48–49 value of derivative at point, 22–23 Slesnick, Daniel T., 205 Slutsky, Eugen, 161 Slutsky equation, 161–163 for cross-price effects, 188–189 of labor supply, 585–588 two-good case, 187–188 SMC (short-run marginal cost function), 358, 361–362 Smith, Adam, 10, 118, 310, 476 Smith, John Maynard, 290 Smith, R B W., 529 Smith, Vernon, 288 Social optimality, 625 Social welfare function, 481–482 Solow, R M., 322–323, 329 Solow growth model, 329–330 Specialized inputs, 463 Special preferences, 112–113 habits and addiction, 113 quality, 112–113 second-party preferences, 113 threshold effects, 112 Spence, Michael, 282 Spencer, B J., 576 Stackelberg, H von, 552 Stackelberg model, 552–555 Stage games, 274–276 Standard deviation, 72–74 State-preference model, 232–238 contingent commodities, 233 fair markets for contingent goods, 234 graphic analysis of, 235–236 insurance in, 235–236 prices of contingent commodities, 233–234 risk aversion in, 234–235, 237–238 states of world and contingent commodities, 233 utility analysis, 233 States of the world, 233 Stein, J., 247 Stigler, George J., 113 Stock options, 224–225 Stocks, 61–62 Stoker, Thomas M., 205 Stone–Geary utility function, 142 Strategic entry deterrence, 557–559 Strategies, 252 dominant, 257, 265, 717 grim, 276 mixed, 260–265, 719 portfolio problem, 244–247 in Prisoners’ Dilemma, 252–254 puppy dog and top dog, 555–556, 558–559, 573 Index pure, 259–260 trigger, 274–276 Strictly mixed strategies, 260 Subgame-perfect equilibrium, 271–273 Subramanian, S., 496 Substitutes, 189–191 asymmetry of gross definitions, 190–191 elasticity of, Shephard’s lemma and, 355 gross, 190 imperfect competition, 573–576 with many goods, 193 of natural resources, 625–626 net, 191–192 perfect, 103 See also Trades and substitution Substitution bias expenditure functions and, 182 market basket index, 182 Substitution effects, 149–151, 161, 392 consumer surplus, 169–174 demand concepts and evaluation of price indices, 181–184 demand curves and functions, 153–159 demand elasticities, 163–169 demand functions, 145–147 impact on demand elasticities, 167–169 negativity of, 175–176 net substitutes and complements, 192 price changes, 149–153, 160–163 principle of, 393 profit maximization and input demand, 391, 393 real wage rate changes, 583 revealed preference and, 174–176 two-good case, 187–188 See also Income effects Sunk costs, 552 Sun Tzu, 225 Supply and demand, 112–113 equilibrium, 12–13, 458–459 shifts in, 432–433 special preferences, 112–113 synthesis, 11–14 Supply curve importance of shape of demand curve, 420–421 importance to demand curves, 421–422 long-run, 428–431 monopoly, 506–507 reasons for shifts in, 420 Supply elasticity, 416–417 elasticity of, 431 Supply function, 382–383, 385, 388, 395, 415–417 Supply response, 413 Swan, Peter, 512 Swan’s independence assumption, 512 T Tacit collusion, 547–551 in Bertrand model, 548–549 in Cournot model, 550–551 in finitely repeated games, 547 in infinitely repeated games, 547–551 Tariffs, two-part, 518–519, 528–529 Taxation environmental, 714 excess burden of, 445–446, 488–489 in general equilibrium model, 495, 692–693 Pigovian, 691–693, 703 voting for redistributive, 707–708 Tax incidence analysis, 442–446 deadweight loss and elasticity, 444–445 effects on attributes of transactions, 446 mathematical model of tax incidence, 443 transaction costs, 445–446 welfare analysis, 443–444 Taylor’s series, 80, 218 Technical barriers to entry, 501–502 Technical progress, 320–324 in Cobb–Douglas production function, 323–324 effects on production, 467 growth accounting, 322–324 measuring, 321 Teece, D J., 404 Testing assumptions, predictions, 4–5 Theil, H., 454 Theoretical models, Theory of Games and Economic Behavior, The (von Neumann and Morgenstern), 212 Third-best outcome, 643–645 Third-degree price discrimination, 515–517 Thomas, A., 368 Threshold effects, 112 Tied sales, 529 Time allocation of, 581–584 capital and, 631–636 inconsistency, 512–513 Timing of supply response, 413 Tirole, J., 296, 575 Tobin, J., 245 Top dog strategy, 555–556, 558–559, 573 Total cost function, 341 Trade general equilibrium models, 495 imperfect competition, 576 political support for, 471 prices, 470–471 Trades and substitution, 92–99 convexity, 95–99 indifference curve map, 94–95 marginal rate of substitution, 92–94 transitivity, 95 Tragedy of the Commons, 266–268, 281–282 Transaction costs, 403–404, 445–446 Transitivity 757 indifference curves and, 95 preferences and, 89 Translog cost function applications of, 368 many-input, 368 with two inputs, 367 Translog production function, 331 Trigger strategies, 274–276 Tucker, A W., 252 Two-good model allocation of time, 581–582 demand relationships among goods, 187–189 Two-good utility maximization, 119–122 budget constraint, 119 corner solutions, 122–129 first-order conditions for maximum, 120–121 second-order conditions for maximum, 121–122 Two-input case, 391 Two-part pricing, 656 Two-part tariffs, 518–519, 528–529 Two-stage budgeting homothetic functions and energy demand, 205 relation to composition commodity theorem, 204–205 theory of, 204 Two-tier pricing systems, 520–521 Typology of public goods, 695–696 U Ultimatum game, 289 Uncertainty, 209–239 asymmetry of information, 238 diversification, 223–224 in economic models, 18 expected utility hypothesis, 210–212 fair gambles, 210–211 flexibility, 224–231 information as a good, 231–232 insurance, 222 mathematical statistics, 209 measuring risk aversion, 217–221 methods for reducing risk and, 222 portfolio problem, 244–247 risk aversion, 214–217 state-preference approach to choice under, 232–238 von Neumann–Morgenstern theorem, 212–214 Uncompensated demand curves, 158–159 Uniform distribution, 69–70, 72–73 Used-car market, signaling in, 671–672 Utility, 90–92 arguments of functions, 91–92 ceteris paribus assumption, 90–91 from consumption of goods, 91 defined, 92 economic goods, 92 externalities in, 686–687 758 Index functions for specific preferences, 102–105 mathematical model of exchange, 472 maximization, 582–583, 611–612 nonuniqueness of measures, 90 See also CES utility; Cobb-Douglas utility; Indifference curves; Preferences Utility maximization, 117–136 altruism and selfishness, 117–118 in attributes model, 198–199 budget shares and, 141–143 expenditure minimization, 131–134 graphical analysis of two-good case, 119–122 indirect utility function, 128–129 individual’s intertemporal, 610–612 initial survey, 118 labor supply, 582 and lightning calculations, 117 lump sum principle, 129–131 n-good case, 122–128 properties of expenditure functions, 134–135 See also Demand relationships among goods; Income effects; Substitution effects V Value early economic thoughts on, 9–10 economic theory of, 9–17 labor theory of exchange, 10 of options, 227–230 Value and Capital (Hicks), 193–194 Value in exchange concept, 10 Value in use concept, 10 Variable costs, 356 Variables change of variable, 59 endogenous, 6–7 exogenous, 6–7 independent, 32 independent, implicit functions and, 32 random, 67–68, 209 Variance, 72–74, 209 Vector notation, 471–472 Vedenov, Dmitry V., 112 Verification of economic models, 4–5 importance of empirical analysis, profit-maximization model, testing assumptions, testing predictions, 4–5 Vickery, William, 672 Villarreal, Hector J., 184 von Neumann, John, 212 von Neumann-Morgenstern theorem, 212–214 expected utility maximization, 213–214 utility index, 212–213 von Neumann-Morgenstern utility, 212–214, 216, 252 Voting, 708–709 Clarke mechanism, 709 Groves mechanism, 708–709 mechanisms, generalizations of, 709 median voter theorem, 705–708 resource allocation and, 703–705 W Wages compensating differentials, 591–594 variation in, 591–595 Wales, Terrence J., 205 Walras, Leon, 14, 473–474 Walrasian price adjustment, 473, 484–485 Walras’ law equilibrium and, 473–474 mathematical model of production and exchange, 483–484 Water-diamond paradox, 10, 14 Weakly dominated strategy, 673 Wealth and risk aversion measurement, 218–220 Wealth of Nations, The (Smith), 10 Welfare analysis, 443–444 applied analysis, 440–441 economic efficiency and, 438–441 economics, 17 effects of price changes, 172–174 evaluation, price controls and shortages, 442 first theorem of welfare economics, 476–478 general equilibrium and, 495–496 general equilibrium models and, 495–496 loss computations, 440–441 monopolies and, 509–510 second theorem of welfare economics, 478–481 Westbrook, M D., 368 Wetzstein, Michael E., 112 White, B., 714 Williamson, Oliver, 401 Y Yatchew, A., 368 Young’s theorem, 30 ... 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 Microeconomic Theory Basic Principles and. .. Preferences and Utility 89 Utility Maximization and Choice 117 Income and Substitution Effects 145 Demand Relationships among Goods 187 Production and Supply CHAPTER PART 21 Uncertainty and Strategy... Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Microeconomic Theory: Basic Principles and Extensions, Eleventh Edition Walter Nicholson, Christopher Snyder VP/Editorial