MICROECONOMICSPrinciples and AnalysisFrank A. CowellSTICERD and Department of Economics London School of Economics December 2004.ii.ContentsContents List of Tables List of Figures Preface 1 Introduction 1.1 The rôle of microeconomic principles . potx

MICROECONOMICS Principles and Analysis Frank A Cowell STICERD and Department of Economics London School of Economics December 2004 ii Contents Contents iii List of Tables xiii List of Figures xv Preface xxiii Introduction 1.1 The rôle of microeconomic principles 1.2 Microeconomic models 1.2.1 Purpose 1.2.2 The economic actors 1.2.3 Motivation 1.2.4 The economic environment 1.2.5 Assumptions and axioms 1.2.6 “Testing” a model 1.3 Equilibrium analysis 1.3.1 Equilibrium and economic context 1.3.2 The comparative statics method 1.3.3 Dynamics and stability 1.4 Background to this book 1.4.1 Economics 1.4.2 Mathematics 1.5 Using the book 1.5.1 A route map 1.5.2 Some tips 1 2 2 4 5 6 6 7 The Firm 2.1 Basic setting 2.1.1 The …rm: basic ingredients 2.1.2 Properties of the production function 2.2 The optimisation problem 2.2.1 Optimisation stage 1: cost minimisation 2.2.2 The cost function 9 10 12 19 20 23 iii iv CONTENTS 2.3 2.4 2.5 2.6 2.7 2.8 2.2.3 Optimisation stage 2: choosing output 2.2.4 Assembling the solution The …rm as a “black box” 2.3.1 Demand and supply functions of the …rm 2.3.2 Comparative statics: the general case The short run The multiproduct …rm Summary Reading notes Exercises The 3.1 3.2 3.3 3.4 3.5 3.6 Firm and the Market Introduction The market supply curve Large numbers and the supply curve Interaction amongst …rms The size of the industry Price-setting 3.6.1 Simple monopoly 3.6.2 Discriminating monopolist 3.6.3 Entry fee 3.7 Product variety 3.8 Summary 3.9 Reading notes 3.10 Exercises The 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 The 5.1 5.2 5.3 25 26 27 29 31 35 39 44 44 44 49 49 50 53 55 56 58 58 60 61 62 64 64 64 Consumer Introduction The consumer’ environment s Revealed preference Preferences: axiomatic approach Consumer optimisation: …xed income 4.5.1 Cost-minimisation 4.5.2 Utility-maximisation Welfare 4.6.1 An application: price indices Summary Reading notes Exercises 69 69 70 72 75 80 82 83 87 92 93 93 94 Consumer and the Market Introduction The market and incomes Supply by households 5.3.1 Labour supply 5.3.2 Savings 99 99 100 100 103 104 CONTENTS 5.4 5.5 5.6 5.7 5.8 5.9 Household production Aggregation over goods Aggregation of consumers Summary Reading notes Exercises v 107 112 112 116 117 117 A Simple Economy 6.1 Introduction 6.2 Another look at production 6.2.1 Processes and net outputs 6.2.2 The technology 6.2.3 The production function again 6.2.4 Externalities and aggregation 6.3 The Robinson Crusoe economy 6.4 Decentralisation and trade 6.5 Summary 6.6 Reading notes 6.7 Exercises 121 121 122 122 124 128 128 129 132 139 139 139 General Equilibrium 7.1 Introduction 7.2 A more interesting economy 7.2.1 Allocations 7.2.2 Incomes 7.2.3 An illustration: the exchange economy 7.3 The logic of price-taking 7.3.1 The core of the exchange economy 7.3.2 Competitive equilibrium and the core: small economy 7.3.3 Competitive equilibrium and the core: large economy 7.4 The excess-demand approach 7.4.1 Properties of the excess demand function 7.4.2 Existence 7.4.3 Uniqueness 7.4.4 Stability 7.5 The rôle of prices 7.5.1 The equilibrium allocation 7.5.2 Decentralisation again 7.6 Summary 7.7 Reading notes 7.8 Exercises 143 143 144 145 147 147 149 151 152 152 156 157 160 162 163 166 167 167 171 172 172 vi CONTENTS Uncertainty and Risk 8.1 Introduction 8.2 Consumption and uncertainty 8.2.1 The nature of choice 8.2.2 State-space diagram 8.3 A model of preferences 8.3.1 Key axioms 8.3.2 Von-Neumann-Morgenstern utility 8.3.3 The “felicity” function 8.4 Risk aversion 8.4.1 Risk premium 8.4.2 Indices of risk aversion 8.4.3 Special cases 8.5 Lotteries and preferences 8.5.1 The probability space 8.5.2 Axiomatic approach 8.6 Trade 8.6.1 Contingent goods: competitive equilibrium 8.6.2 Financial assets 8.7 Individual optimisation 8.7.1 The attainable set 8.7.2 Components of the optimum 8.7.3 The portfolio problem 8.7.4 Insurance 8.8 Summary 8.9 Reading notes 8.10 Exercises 177 177 177 179 180 184 185 188 189 190 191 192 195 197 198 199 202 203 203 205 205 209 211 217 219 220 220 Welfare 9.1 Introduction 9.2 The constitution 9.3 Principles for social judgments: e¢ ciency 9.3.1 Private goods and the market 9.3.2 Departures from e¢ ciency 9.3.3 Externalities 9.3.4 Public goods 9.3.5 Uncertainty 9.3.6 Extending the e¢ ciency idea 9.4 Principles for social judgments: equity 9.4.1 Fairness 9.4.2 Concern for inequality 9.5 The social-welfare function 9.5.1 Welfare, national income and expenditure 9.5.2 Inequality and welfare loss 9.6 Summary 9.7 Reading notes 227 227 228 234 237 242 246 250 251 254 257 257 258 258 259 261 264 264 CONTENTS 9.8 Exercises vii 265 10 Strategic Behaviour 10.1 Introduction 10.2 Games –basic concepts 10.2.1 Players, rules and payoÔs 10.2.2 Information and Beliefs 10.2.3 Strategy 10.2.4 Representing a game 10.3 Equilibrium 10.3.1 Multiple equilibria 10.3.2 E¢ ciency 10.3.3 Existence 10.4 Application: duopoly 10.4.1 Competition in quantities 10.4.2 Competition in prices 10.5 Time 10.5.1 Games and subgames 10.5.2 Equilibrium: more on concept 10.5.3 Repeated interactions 10.6 Application: market structure 10.6.1 Market leadership 10.6.2 Market entry 10.6.3 Another look at duopoly 10.7 Uncertainty 10.7.1 A basic model 10.7.2 An application: entry again 10.7.3 Mixed strategies again 10.7.4 A “dynamic” approach 10.8 Summary 10.9 Reading notes 10.10Exercises and method 11 Information 11.1 Introduction 11.2 Hidden characteristics: adverse selection 11.2.1 Information and monopoly power 11.2.2 One customer type 11.2.3 Multiple types: Full information 11.2.4 Imperfect information 11.2.5 Adverse selection: Competition 11.2.6 Application: Insurance 11.3 Hidden characteristics: Signalling 11.3.1 Costly signals 11.3.2 Costless signals 11.4 Hidden actions 271 271 272 272 273 274 274 276 278 279 281 285 286 291 293 295 297 300 305 305 306 309 310 311 314 317 317 318 319 320 327 327 328 329 329 333 336 345 346 352 352 360 361 viii CONTENTS 11.4.1 The issue 11.4.2 Outline of the problem 11.4.3 A simpli…ed model 11.4.4 Principal-and-Agent: a richer model 11.5 Summary 11.6 Reading notes 11.7 Exercises 361 362 362 367 373 374 374 12 Design 12.1 Introduction 12.2 Social choice 12.3 Markets and manipulation 12.3.1 Markets: another look 12.3.2 Simple trading 12.3.3 Manipulation: power and misrepresentation 12.3.4 A design issue? 12.4 Mechanisms 12.4.1 Implementation 12.4.2 Direct mechanisms 12.4.3 The revelation principle 12.5 The design problem 12.6 Design: applications 12.6.1 Auctions 12.6.2 A public project 12.6.3 Contracting again 12.6.4 Taxation 12.7 Summary 12.8 Reading notes 12.9 Exercises 381 381 382 385 385 386 387 388 388 390 391 392 393 395 395 403 409 415 422 424 424 13 Government and the Individual 13.1 Introduction 13.2 Market failure? 13.3 Nonconvexities 13.3.1 Large numbers and convexity 13.3.2 Interactions and convexity 13.3.3 The infrastructure problem 13.3.4 Regulation 13.4 Externalities 13.4.1 Production externalities: the e¢ ciency problem 13.4.2 Corrective taxes 13.4.3 Production externalities: Private solutions 13.4.4 Consumption externalities 13.4.5 Externalities: assessment 13.5 Public consumption 13.5.1 Nonrivalness and e¢ ciency conditions 431 431 432 433 435 435 436 438 442 443 443 444 447 448 448 449 CONTENTS ix 13.5.2 Club goods 13.6 Public goods 13.6.1 The issue 13.6.2 Voluntary provision 13.6.3 Personalised prices? 13.6.4 Public goods: market failure and the design 13.6.5 Public goods: alternative mechanisms 13.7 Optimal allocations? 13.7.1 Optimum with lump-sum transfers 13.7.2 Second-best approaches 13.8 Conclusion: Economic Prescriptions 13.9 Reading notes 13.10Exercises problem Bibliography A Mathematics Background A.1 Introduction A.2 Sets A.2.1 Sets in Rn A.3 Functions A.3.1 Linear and a¢ ne functions A.3.2 Continuity A.3.3 Homogeneous functions A.3.4 Homothetic functions A.4 DiÔerentiation A.4.1 Function of one variable A.4.2 Function of several variables A.4.3 Function-of-a-Function Rule A.4.4 The Jacobian derivative A.4.5 The Taylor expansion A.4.6 Elasticities A.5 Mappings and systems of equations A.5.1 Fixed-point results A.5.2 Implicit functions A.6 Convexity and Concavity A.6.1 Convex sets A.6.2 Hyperplanes A.6.3 Separation results A.6.4 Convex and concave functions A.6.5 quasiconcave functions A.6.6 The Hessian property A.7 Maximisation A.7.1 The basic technique A.7.2 Constrained maximisation A.7.3 More on constrained maximisation 449 451 451 452 454 457 458 460 461 464 467 468 468 473 485 485 486 486 487 487 488 490 491 492 492 493 493 494 494 494 496 496 497 499 499 500 500 503 505 507 507 508 510 511 x CONTENTS A.7.4 Envelope theorem A.7.5 A point on notation A.8 Probability A.8.1 Statistics A.8.2 Bayes’rule A.8.3 Probability distributions: examples A.9 Reading notes 514 515 515 516 518 518 519 521 521 521 528 529 535 539 542 548 556 561 570 583 598 C Selected Proofs C.1 The …rm C.1.1 Marginal cost and the Lagrange multiplier C.1.2 Properties of the cost function (Theorem 2.2) C.1.3 Firm’ demand and supply functions (Theorem 2.4) s C.1.4 Firm’ demand and supply functions (continued) s C.1.5 Properties of pro…t function (Theorem 2.7) C.2 The consumer C.2.1 The representation theorem (Theorem 4.1) C.2.2 Existence of ordinary demand functions (Theorem 4.5) C.2.3 Quasiconvexity of the indirect utility function C.3 The consumer and the market C.3.1 Composite commodity (Theorem 5.1): C.3.2 The representative consumer (Theorem 5.2): C.4 A simple economy C.4.1 Decentralisation (Theorem 6.2) C.5 General equilibrium C.5.1 Competitive equilibrium and the core (Theorem 7.1) C.5.2 Existence of competitive equilibrium (Theorem 7.4) C.5.3 Uniqueness of competitive equilibrium (Theorem 7.5) C.5.4 Valuation in general equilibrium (Theorem 7.6) C.6 Uncertainty and risk C.6.1 Risk-taking and wealth (Theorem 8.7) 607 607 607 608 611 612 613 614 614 615 615 616 616 616 617 617 617 617 618 619 619 620 620 B Answers to Footnote Questions B.1 Introduction B.2 The …rm B.3 The …rm and the market B.4 The consumer B.5 The consumer and the market B.6 A simple economy B.7 General equilibrium B.8 Uncertainty and risk B.9 Welfare B.10 Strategic behaviour B.11 Information B.12 Design B.13 Government and individual 630 APPENDIX C SELECTED PROOFS Using (C.103) and integrating (C.97),the utility that an agent gets if is therefore Z Z Z d (x) N ( )= dx = ( (x)) dx = [F (x)] dx dx At the optimum ( )= ( ( )) P ( ( )) So, P ( ), the expected equilibrium payment by a participating agent with taste is : P ( ( )) = ( ) = ( ) Z [F ( )] N N [F (x)] dx (C.104) The expected revenue to seller is given by N times the expected value of (C.104) Z Z Z N N [F ( )] f ( )d N [F (x)] dx f ( ) d N = N = N = N C.9.2 Z N 1 Z Z F ( ) dF ( ) d f( ) d F( ) f( ) ( )f ( )d ( )f ( )d N Z [1 F ( )] ( )d The Clark-Groves mechanism (Theorem 12.7) The payment rule (12.32) can be written P h p1 ; p2 ; ::: = p1 ; p2 ; ::: zh h h + max ;0 (C.105) where is determined by (12.31) and h is given by (12.30) Given (12.21), (12.22) and income y h the utility of agent h is then given by h (x1 ) + xh = = h h ( ) + yh zh Ph h = p1 ; p2 ; :::; ph ; ::: = p1 ; p2 ; :::; ph ; ::: max h "n h X k=1 There are two cases to consider h zh + pk ; + yh h zk + max h ph h # ; + yh max h ; + yh C.9 DESIGN Suppose 631 h zh + h 0, then declaring ph = nh X pk h implies z k=1 so that = 1; declaring ph > h will not improve on this outcome; declaring ph < h may result in = which will reduce utility Suppose h zh + h < Declaring ph = nh X h implies pk < z k=1 and declaring ph < h will not improve on this outcome; declaring ph > may result in = which will reduce utility h Therefore declaring ph = h is a weakly dominant strategy Finally notice that the problem remains essentially unchanged if the term h max h ; in (C.105) is replaced by h [p] where h ( ) is an arbitrary h function and [p] is the list of announced valuations p1 ; p2 ; ::: with the hth component deleted, as in (10.1) Index Additivity, 124 …rst price, 397 second price, 398, 399, 401 Adverse selection, 328, 338, 346 and public projects, 409 and competition, 345 in insurance market, 346, 349, 350 Average cost, 25, 26 and equilibrium of …rm, 26 monopoly model, 342, 343 and externalities, 528 A¢ ne transformation, see function, a¢ ne, see function, a¢ ne, see funcand optimum …rm size, 527 tion, a¢ ne and returns to scale, 25, 30, 525 Agency cost, 362, 378 short-run, 36 Agent, 362 Average revenue, 59 Aggregability, 116 Axioms, 2, Aggregation , see also individual axioms by name over consumers, 112, 236 consumer theory, 73, 75, 77, 94, 124– 127, 139 over goods, 112 production, 124 Akerlof, G A., 374, 376 Allais, M., 220, 221 Allocation, 145, 152, 228, 259, 260, 386 Backwards induction, 297, 323 competitive, 146, 150, 151 Bagnoli, M., 468 core, 153, 154 Baron, D., 428, 468 Barsky, R.B., 197 e¢ cient, 235, 237, 239, 240, 245 Bator, F.M., 468 under uncertainty, 251, 253 equilibrium, 146, 148, 152, 155, 166, Battle of the sexes, 276, 280, 562 172, 240 Bayes’rule, 317, 518 fair, 257, 258 Bayesian equilibrium, 314, 317 market, 145 Nash, 313, 314, 317, 390, 395, 402, 423 Ambiguity, 187 perfect, 318, 328, 358, 373 Andreoni, J., 468 Bazerman, S.H., 396 Argmax function, 277, 515 Arrow, K.J., 172, 220, 229, 264, 374, Becker, G.S., 117 Belief, 273, 274, 312, 314, 318, 356 620 reasonable, 359, 360, 579 Atkinson, A.B., 265, 466 Attainable set, 108– 110, 131, 132, 135, Bell, D.E., 221 137, 138, 168, 235, 541, 542 Benoit, J.-P., 424 Auction, 395, 402, 424 Berck, P., 520 design issues, 401 Bergstrom, B., 468 632 INDEX 633 Common knowledge, 273, 312, 320, 328, 337, 350 Commons, 442 Compact set, 158, 487 Comparative statics, 5, 28, 31, 32, 35, 83, 101, 132 Compensating variation, 89, 92, 96, 97, 257, 330, 405, 406, 408, 409, 625 Competitive equilibrium, 143, 147, 148, 154, 156, 237, 240, 242, 243, 436, 560, 618 and e¢ icency, 240, 242 and fairness, 258 and the core, 152, 155, 156, 240 and the market mechanism, 386 existence, 160, 162 stability, 163, 165 uniqueness, 162 Complementary slackness, 513 Completeness, 75 Composite commodity theorem, 112, 616 Concave transformation, 194, 264 Concavity, 505 Cartel, see Collusion Conditional expectation, 314 Cartesian product, 486, 626, 627 Condorcet winner, 231 Certainty equivalent, 183, 191 Consequence, 179 Chamberlin, E.H., 64 Constitution, 228, 229, 382 Cheap talk, 374 Consumer sovereignty, 69, 383 Cheating, 341, 394, 457 Consumer’ surplus, 61, 90, 332, 427 s Chiang, A.C., 519 Contingent goods, 180, 181, 185, 190, Chicken game, 280, 321 203, 219, 254, 314 Chiselling, 289, 457 and Pareto e¢ ciency, 253 Cho, I.-K , 374 Continuity, 76, 162, 183, 488, 489, 505, Clark-Groves mechanism, 424, 458, 630 548, 615 Clarke, E.H., 424 and demand for inputs, 29 Closed set, 76, 487 and supply, 51 Clubs, 449 of preferences, 160 Coalition, 150, 151, 155, 545, 546 Contour, 505 Coase, R.H., 468 Contract, 225, 332, 362 Cobb-Douglas function, 94 full-information, 334, 336, 348 Collusion, 288, 309 insurance, 348 in auction, 399, 587 pooling, 338 Commitment device, 567 second-best, 340, 342, 343, 412 Commodity space, 70, 78 separating, 339 Bertrand, J., 320 Best response, 277 Better-than set, 81, 135, 168, 434 Binary relation, 486 Binmore, K., 403 Black’ theorem, 232, 622 s Black, D., 264 Bliss point, 79, 152, 531 Blocking, 150, 151, 153– 155, 617 Blume, L., 468, 520 Boadway, R.W., 264 Boiteux, M., 468 Bonds, 207, 210– 212, 214, 216 Border, K., 520 Bowen, H., 424 Broome, J., 471 Brouwer’ …xed-point theorem, 496, 618 s Bruce, N., 264 Buchanan, J.M., 468 Budget constraint, 71, 80, 83, 84, 100, 234, 531, 533, 543 and shadow prices, 133 intertemporal, 105 634 take-it-or-leave-it, 332, 336, 340, 343 Contract curve, 149, 152, 154, 543 and e¢ ciency, 253 and the core, 154, 240 under uncertainty, 203 Convexi…cation, 138, 172, 557 Convexity, 13, 18, 29, 75, 136, 168, 170, 240, 433, 463, 499, 520, 531, 541, 542, 557, 598 and aggregation, 129, 170, 435 and continuity of response function, 29 and large numbers argument, 169, 170, 435 and returns to scale, 434 and the separation result, 135 and trade, 138 Nonconvexity and allocation problems, 433, 435 Nonconvexity and the infrastructure problem, 436 strict, 28, 499 Cook, P., 94 Coordination, 628 Core, the, 151– 154, 171 and competitive equilibrium, 152, 155, 156, 240 Corner solution, 23, 512, 522, 532 Cornes, R., 468 Correspondence, 30, 282, 487 Cost function, 23, 27 and decomposition of demand, 32 and externalities, 246 and returns to scale, 524 consumer, 82, 85 and aggregation, 616 and CV, EV, 89 and indirect utility, 88, 89 and measurement of waste, 244 and price indices, 92 example, 39 optimal output, 25 properties, 24, 533 short-run, 36, 37 properties, 38 INDEX subadditive, 64 Cost minimisation, 9, 20, 21, 25, 27, 136, 609 and cost function, 23 and the consumer, 81, 83 in short run, 36 Cost-bene…t analysis, 257 Cost-of-living index, see Price index Cournot competition, 286 Cournot, A., 320 Crawford, V., 374 Credibility, 298, 317 Credit rationing, 378 CV, see Compensating variation d’ Aspremont, C., 468 Dasgupta, P., 424 de Borda voting, 233 de la Fuente, A., 505, 520 Deaton, A.S., 93, 117, 220 Debreu, G., 94, 172, 615 Decentralisation, 132– 136, 138, 139, 166– 168, 170– 172, 434 Decisive population subset, 621 Decomposition formula goods prices, 85, 101 input prices, 32, 33, 87 Demand, 87 aggregation of, 114 and factor supply, 101 and indirect utility, 260 and materials balance, 146 and the Slutsky equation, 85 and theory of …rm, 93 compensated, 83, 85, 89, 90, 244 elasticity, 58, 466 excess, see Excess demand for inputs, 29, 32, 35 conditional, 23, 25, 39 short-run, 36, 38 function, 30 inverse demand curve, 58 market, 50, 56, 57 and marginal revenue, 59 ordinary, 84, 90 INDEX 635 Design, 329, 334, 344, 356, 369, 381, ex-post, 253 382, 385, 387– 398, 401, 403, technical, 10, 22, 43, 239, 598 409– 417, 420, 454 under uncertainty, 251 Elasticity, 58, 104, 244, 466, 494– 496, and social choice, 382 529 public goods, 457 cross, 496 Determinant, 488, 499 of substitution, 15, 521 Dictatorship, 229, 384, 385, 393, 394, Ellsberg, D., 220, 222 622 Endowment point, 148, 151, 152 DiÔerentiation Function-of-a-function rule, 493, 526,Engel curve, 116 English auction, see Auction, second 532 price partial diÔerential, 492, 493, 507 Entry deterrence, 306 total diÔerential, 493 Entry fee, 61, 329, 331, 332, 335, 336 Disappointment, 185, 221 Discontinuities and equilibrium, 51, 160, Envelope theorem, 514, 524 Envy, 257 162 Equal ignorance principle, 259 Distortion in second-best, 343, 373 Equilibrium, 5, 313, 318, 319 Distribution function, 515 Bayesian, 314 Divisibility, 13, 124, 126, 127, 170 in mixed strategies, 285 Dixit, A.K., 64, 319, 324, 520 Nash, 278, 281, 319 Dominant strategy, 278, 280, 391, 563 pooling, 349, 350, 359 Doomsday machine, see Commitment separating, 350, 352, 356, 376, 577, device 578 Duopoly, 285– 289, 291, 305, 309 Subgame perfect, 297 Bertrand model, 291 Equity collusion, 288 as concern for inequality, 258 Cournot model, 286 as fairness, 257 leader-follower, 305 Equivalent variation, 89, 92, 330, 462 Dupuit, J., 94 Dutch auction, see Auction, …rst price ex ante judgments, 179 Excess demand, 156, 165 Dynamics, 6, 163 and existence of equilibrium, 160 Eads, G., 39 and materials balance, 156, 618 Edgeworth box, 148, 162, 365, 374 and stability of equilibrium, 164 Edgeworth, F.Y., 172 and uniqueness of equilibrium, 163 Education properties of, 156, 157 as investment, 141 Exchange economy, 147, 162, 173, 240, as signal, 354 265, 544 E¢ ciency, 234, 235, 237– 239 Excludability, 113, 236, 250, 448, 449, and competitive equilibrium, 240, 451 242 Expansion path, 16, 18 characterisation, 246, 249, 250, 432 Expectation, 219, 224, 253, 517 implementation problem, 246, 432, Expenditure function, see Cost func442, 449, 451, 452 tion Pareto, 235, 240, 246, 251, 252, Externality, 55, 56, 248, 442, 443, 467 258, 437, 557 consumption, 249, 250, 447 636 INDEX rules of play, 272 internalisation, 444, 446 strategy, 274 production, 140, 238, 246, 247, 443, 444, 560 Gardner, R., 319 Geiss, C., 220 Fairness, 257, 258, 265, 561 General equilibrium, see Competitive and competitive equilibrium, 258 equilibrium Farrell, J., 468 Gerard-Varet, L.-A., 468 Farrell, M.J., 172 Gibbard, A., 424 Fee schedule, 329 Gibbard-Satterthwaite theorem, 393, 424 Felicity function, 188– 194 Gibbons, R., 319 and risk aversion, 194 GiÔen good, 87, 116, 534 Financial assets, 203, 207 Goods Firm, 7, excludable, 236 multi-product, 39, 122 pure private, 236– 238 production function, see Producpure public, 236, 250, 251, 403, tion function 424, 454, 457, 458 pro…t maximisationion, see Pro…t rival, 236 maximisation Gradstein, M., 471 First-best contract, see Full-information Graph, 488 contract Greed, 78, 181 First-mover advantage, 305 Green, J., 424, 520 First-order conditions, 21, 22, 31, 42, Groves, T., 424, 468 61, 83, 85, 214, 238– 240, 246, Hahn, F.H., 172 250, 508, 509, 511, 512 Hammond, P.J., 424 Fishburn, P.C., 94 Harberger, A.C., 265 Fixed cost, 36, 435, 527, 542 Harris, M., 424 sunk, 307, 568 Harsanyi, J., 265, 319 Fixed point, 284, 496, 618 Heller, W.P., 520 FOC, see First-order conditions Folk theorem, 304, 309, 320, 454, 603, Hessian matrix, 507 Hessian property, 613 628 Hicks, J.R., 94, 265 Free disposal, 124 Hidden actions, see Principal-and-Agent Free-riding, 454 Hidden characteristics model, see AdFriedman, J., 320 verse selection, Signalling Friedman, M., 220 Hidden information, 366 Fudenberg, D., 320, 321 HoÔman-Jứrgensen, J., 520 Full-information contract, 335, 348 Holmstrửm, B., 374 Function, 548 Homogeneous, 16, 25, 30, 82, 85, 147, a¢ ne, 187, 195, 200, 487 158, 490, 491 linear, 81, 85, 117, 487 Homothetic, 15, 46, 96, 111, 211, 491 Fuss, M., 44 Hotelling’ lemma, 43 s Games Hotelling, H., 44, 468 in extensive form, 274 Household, 7, 69– 73, 82– 84, 99– 101, in strategic form, 274 107– 109, 111, 113– 116, 121, repeated, 300 143– 146, 205, 210, 227, 230, INDEX 637 234, 236, 237, 239, 240, 243, adding-up property, 534 250, 257, 258, 260, 261, 462, and aggregation over consumers, 467, 538, 546, 560, 616 116, 163, 616 and consumer welfare measures, 92, income, 147 330 production, see Household producand endogenous incomes, 101 tion inferior goods, 87 supply to market, 102 Income taxation, 415– 417, 420, 422 welfare, 261 Household production, 107, 108, 131, Independence, 185, 229 of irrelevant alternatives, 229, 232– 132, 210 234, 621 and economy attainable set, 132 s IndiÔerence curve, 77, 78, 436 and …nancial assets, 210 and contract curve, 149, 240, 543 Houthakker, H.S., 94 and reservation utility, 151 Hurwicz, L., 424 and risk-aversion, 183 Hyperplane, 168, 500, 617 concave-contoured, 79, 80, 86, 534 separating, supporting, 135, 502, under uncertainty, 181, 189 503 Industrial organisation, 305, 306, 309, Implementation, 390, 392 315, 324 Nash equilibrium, 394, 458 Inequality, 258, 261, 262, 264, 265 truthful, 391 Inferior good, 87 weak, 390 Information, 273, 327, 385 Implicit function theorem, 499, 613 common knowledge, 273 Impossibility theorem, 229, 384, 424, incomplete, imperfect, 311, 328 620 perfect, 295, 300 Incentive-compatibility constraint, 340– Information set, 273, 567 343, 351, 366, 367, 414, 420, Infrastructure, 436 574, 581 Input-requirement set, 12, 13, 18, 23, Income, 73 28, 29, 521 and “adding-up” constraint, 85 Inputs, 10, 12 and CV,EV, 89, 90 and isocost, 21 and indirect utility, 87 and marginal product, 19 and lump-sum transfers, 255 and returns to scale, 16 and property distribution, 147 demand for, 29 and shadow prices, 133 essential, 13 distribution, 258, 262, 264 inferior, 32 optimal, 460, 462 MRTS, 13 endogenous, 100, 101, 103, 147 Insurance, 207, 208, 217– 219, 346 equally-distributed equivalent, 263 adverse selection, 346, 349, 350 exogenous, 80, 113, 243 Internalisation, 444 lifetime, 105 Intuitive criterion, 359, 360, 579 national, 261 Irreversibility, 124 Income distribution, 114, 116, 262, 268, Isocost, 21, 28, 525 462, 605 Isopro…t, 41, 133, 288 Income eÔect, 87, 101, 103, 104, 162, contour (duopoly), 287, 305, 322, 534, 572, 574 565 638 Isoquant, 15, 18, 75 as set boundary, 12 homothetic, 15 shape, 13 Jacobian matrix, 494 Jensen’ inequality, 517, 550 s Juster, F.T , 197 INDEX Loomes, G., 221 Lottery, 197– 199, 201 as mechanism for providing public good, 459 Lump-sum transfers, 242, 254, 268, 461, 462 Machina, M.J., 220, 553 Macho-Stadler, I, 374, 378 Kakutani’ …xed-point theorem, 497 s Magat, W.A., 469 Kaldor, N., 265 Mailath, G.J., 320 Keenan, D.C., 265 Manipulability, 385 Kimball, M.S., 197 Manipulation, 457 Kinks, 13, 29, 80, 525 Mapping, 487 Marginal cost, 25, 32 Kleiber, C., 520 and average cost, 25, 26 Klemperer, P., 403, 424, 426 and equilibrium of …rm, 26, 27 Koopmans, T.C., 139 and equilibrium of monopolist, 60 Kotz, S., 520 and externalities, 56, 528 Kreps, D.M., 319, 374 and Lagrange multiplier, 25 Kuhn-Tucker conditions, 512 short-run, 37, 527 l’ Hôpital’ rule, 267, 492 s Marginal …rm, 57, 64 Labour supply, 103, 119, 410, 416 Marginal product, 19, 27 LaÔont, J J., 374 Marginal rate of substitution, 80, 106 LaÔont, J.-J., 424, 468 and e ciency, 134, 239, 240, 250, Lagrange multiplier, 21, 22, 88, 237, 437 238, 534 Marginal rate of technical substitution, and marginal cost, 25 13, 15, 16, 22, 41, 521 Lagrangean function, 19, 21, 42, 82, and e¢ ciency, 22 83, 101, 238, 251, 510, 541 Marginal rate of transformation, 40, 41, Lagrangean multiplier, 510 43 Lancaster, K., 117 Marginal revenue, 59 Laspeyres index, 93 Market, 3, 6, 7, 9, 28 Ledyard, J., 468 and …rm’ responses, 35 s Lemons model, 376 and price-taking …rms, 49, 52, 53, Lexicographic ordering, 77, 531 55– 57 Lichtenstein, S., 184 and the consumer, 70 Lifetime income, 105 as a mechanism, 386 Likelihood ratio, 367 competitive, 11 Limit, 489 pseudo, 444– 447, 470 Lindahl solution, 454 Market entry, 57, 306, 315 Lindahl, E., 468 Market failure, 245, 431, 432, 442, 448 Linear Expenditure System, 95, 466 public goods, 451, 452 Lipman, P., 468 Marschak, J., 553 Local public good, 468 Martimort, D., 374 Maskin, E., 320, 424 Loeb, M., 424, 469 INDEX Masquerading, 338, 339, 341, 343, 349, 351, 385, 414, 440, 574, 591, 594 Materials balance condition, 130, 146, 147, 156, 238, 559, 619 Matrix, 487 Hessian, 507 Jacobian, 494, 498 Maximisation, see Optimisation McFaddden, D., 44 Meade, J.E., 468 Mean, see Expectation Mechanism, 389 direct-revelation, 391, 415 Median, 516 Menezes, C., 220 Message, 352, 354, 391 Minimax, 279, 301– 303, 310 Mirrlees, J.A., 374, 424 Mixed strategy, see Strategy,mixed Monopolistic competition, 62 Monopoly, 50, 58, 62, 345, 545 , see also Entry fee and duopoly, 288 and information, 329 and market entry, 306 and rent seeking, 268 and waste, 244, 268, 439, 598 discriminating, 60 natural, 64, 97, 439 regulated, 66, 97, 440, 442 Monopsony, 345 Monotonicity, 384, 385, 395, 583 Moral hazard, 208, 361 Morgan, J., 468 Morgenstern, O., 220 Moulin, H., 267 MRS, see Marginal rate of substitution MRT, see Marginal rate of transformation MRTS, see Marginal rate of technical substitution Muellbauer, J., 93, 117, 220 Multipart tariÔ, 344 Mussa, M., 375 Myerson, R.B., 319, 424, 428, 468 639 Nash equilibrium, 278– 281, 319, 627 and e¢ ciency, 280 existence, 285 method of solution, 278 Nash, J.F., 319 National income, 261 Nationalisation, 439 Natural monopoly, 64, 97, 439 Nature, 272, 273, 311 Negative-semidenite matrix, 33 partial diÔerential, 507 Neighbourhood, 488 Net output, 39, 42– 44, 122– 128, 131, 132, 134, 139, 146, 156, 237, 238, 527, 543 No free lunch, 124 No-distortion-at-the-top principle, 343, 375, 414, 415, 420, 422, 427, 594 Node, 274, 276 Non-convexity, see Convexity Numộraire, 105 OÔer curve, 102, 146, 152, 162, 544 and Excess demand function, 546 Oi, W., 61 Oligopoly, 285 Bertrand model, 291, 292 collusion, 288 Cournot model, 286, 288, 289, 309, 310, 321, 322, 453 leadership model, 305 Open set, see Closed set Optimisation, 11, 72, 81, 84, 93, 101, 130, 131, 238, 260, 262, 463, 507, 510, 520, 521 and output choice, 25 and separation result, 136, 138 by consumers, 80, 85, 87 dual approach, 81 by …rms, 9, 11, 19, 26, 27, 134, 145 by monopolist, 58 constrained, 510– 512 cost minimisation, 20 social-welfare, 462 Order statistic, 403, 426, 517 640 Osborne, M.J., 319 Ostaszewski, A., 520 Output, 10 net, see Net output Output eÔect, 32 87 34, Over-insurance, 208 Overtime, 104, 536, 575 Paasche index, 93 Palfrey, T.R., 468 Pareto e¢ ciency, see E¢ ciency Pareto Pareto superiority, 234, 254, 255, 270, 403, 599 potential, 255, 257, 265, 406 Participation constraint, 331, 332, 334, 341, 342, 364– 367, 369, 371, 412, 413 Perez-Castrillo, D., 374, 378 Perfect Bayesian equilibrium, 318, 328 Pigou, A.C., 64, 468 Pivotal agent, 409 PLUM principle, 259 Plurality voting, 233 Pooling, 219, 338, 339, 349, 350 contract, 339 equilibrium, 349, 350, 359 of risks, 219 Portfolio choice, 206 Pratt, J.W., 220 Preference, 80, 144, 155, 168, 227, 230, 231, 237, 257, 258, 529, 531 “representative citizen” 436 , and price indices, 92 and social welfare, 228 and utility function, 77 axioms, 75, 77, 78, 80 relation, 75 revealed, see Revealed preference single-peaked, 232, 622 under uncertainty axioms, 185, 187 Preference reversal, 184 Price, 10 contingent goods, 203 input price ratio, 22 set by …rm, 58 INDEX shadow, 134, 135, 168, 240, 248, 250, 433, 437, 542, 617 Price index, 92, 93 Principal-and-Agent hidden action, 361, 362, 367, 370, 374 simpli…ed model, 362 hidden characteristics, 410 Prisoner’ Dilemma, 280, 563 s in repeated game, 301, 310, 568 Prisoner-of-War camp, see Exchange economy Private goods, 113, 114, 146, 236– 238, 467 Probability, 197– 199, 202, 210, 212, 214, 216, 269, 515, 516, 518, 520, 553, 561 conditional, 312, 518 distribution, 515 subjective, 189, 253, 269 Product diÔerentiation, 52, 62 Production function, 10, 12, 16, 19, 25, 29, 128, 144 and externalities, 246 and general equilibrium, 162 CES, 46 multi-product, 122 short run, 38 smoothness, 37 Production set, see Technology set Production-possibility set, 131, 140, 470, 541 Pro…le of preferences, 228, 229, 383, 392, 620 of strategies, 276, 278, 297 Pro…t function, 43, 44 Pro…t maximisation, 9, 11, 25, 27, 42, 59, 72, 134 and competitive equilibrium, 145 and decentralisation, 135 and e¢ ciency, 240 and industry size, 57 and trade, 137 comparative statics, 31, 35 Pro…ts, 11, 62, 133, 145, 436, 525, 529 INDEX 641 Regulation, 438– 440, 442 Rent seeking, 268 Reny, P.J , 424 Replication, 54, 153, 155, 170 Representative consumer theorem, 116, 616 Repullo, R., 424 Response function, 510, 511, 514 Returns to scale, 16, 18, 126, 127 and externalities, 434, 435 and the cost function, 25, 30 Revealed likelihood, 186 Revealed preference, 72, 75 strong axiom, 75 weak axiom, 73, 116, 163, 165, 171, 547 Revelation principle, 392, 402, 424 Revenue equivalence, 402, 628 Ricketts, M., 374 Risk, 549 and inequality, 262 Risk aversion, 188, 194, 263 absolute, 192, 195 Quality, 375 and inequality, 265 Quantity discount, 84, 344, 532, 574 relative, 193, 196 Quasi-…xed factor, 35 Risk premium, 191, 192, 194, 220, 262, Quasi-monopolist, 62, 64 263 Quasi-transitivity, 230, 556 Rivalness, 113, 146, 236, 250, 251, 448, Quasiconcave, 79, 81, 162, 183, 190, 449, 451 285, 505– 507, 513 Robinson Crusoe, 129– 135, 137, 139, Quasiconvex, 88, 615 143, 144, 147, 167, 170, 171, 433, 438 Radford, D., 148 Rosen, S., 375 Ramsey, F.P., 468 Rosenthal, H., 468 Random variable, 515 Ross, S.A., 374 as a move by “Nature” 272, 311 Rothschild, M., 220, 374 , Randomisation, 202, 284, 285, 315, 567 Roy’ identity, 88, 261, 466, 561, 606 s coordinated, 301, 321, 628 Roy, R., 94 Rasmusen, E., 319 Rubinstein, A., 323 Rational choice, 73, 156, 274, 280, 320 Rationality, see Rational choice Salanie, B., 374, 424 Reaction function, 5, 286 Samuelson, L., 320 public-goods game, 453 Samuelson, P.A., 44, 94, 264 Real line, 486 Samuelson, W.F., 396 Rectangular distribution, 426, 519 Sandler, T., 468 Regret, 185, 221 Sandmo, A., 269 and costs, 59 and decentralisation, 136 and entry, 57 and household income, 147 and national income, 262 and net outputs, 132 maximisation, see Pro…t maximisation Property distribution, 148, 149, 151, 152, 166, 167, 171, 240, 262, 462 Prospect, 179– 181, 183, 185, 186, 189, 194, 263 Pseudo market, 444– 447, 470 Public goods, 236, 250, 251, 264, 403, 424, 451– 454, 457– 459, 470 demand for, 457 e¢ ciency conditions, 251 Lindahl solution, 456 lottery …nance, 459 money-back guarantee, 459 provision point, 459 642 Satterthwaite, M.A., 424 Savage, L.J., 220 Savings, 69, 104 Scarf, H., 172 Schmalensee, R., 64 Schweizer, U., 172 Scitovsky, T., 265 Screening, 338, see also Adverse selection Second-best, 461 contract, 340, 342, 343, 412, 419 taxation, 464 Securities, see Financial assets Self selection, 336 Sel…shness, Separating equilibrium, 350, 352, 356, 376, 577, 578 Separation results, 500 Sequence, 488 Shadow price, 133– 135, 168, 240, 248, 250, 433, 437, 542, 617 Shapiro, M., 197 Shephard’ lemma, 24, 31, 32, 34, 43, s 89, 244 Shephard, R.W., 44 Shirking, 363 Short run, 11, 35– 39, 83, 255, 526, 37, 527, 532 Signalling, 352, 374 Simon, C.P , 520 Single-crossing condition, 333, 347, 354, 374, 411, 576, 591 Single-peakedness, 231, 232, 556, 622 Skeath, S., 319 Slesnick, D.T., 265 Slovic, P., 184 Slutsky equation, 85, 466, 533, 534 modi…ed, 101 own-price, 87 Snow, A., 265 Sobel, J., 374 Social choice, 382 Social choice function, 382, 383, 583 dictatorial, 384 manipulable, 385, 393 INDEX Social states, 227– 231, 233, 234, 254, 257, 259, 392, 556, 557 accessible, 255, 256 e¢ cient, 234 multidimensional, 232 Social welfare, 227, 259, 260, 262, 436, 538 and the constitution, 228 function, 258, 260– 263, 417, 418, 461, 462, 467, 468, 561, 605 Spanos, A, 520 Spence, A.M., 324, 374 Ståhl, I., 323 Stackelberg model, see Duopoly, leaderfollower Stage game, 300 Starrett, D.M., 468 State-irrelevance, 185 States-of-the-world, 178, 180, 186, 187, 219 Stationary point, 508 Statistic, 516 Stiglitz, J.E., 64, 220, 374, 466 Stone, J.R.N., 95, 466 Strøm, A., 520 Strategy, 274 correlated mixed, 321 dominant, 278, 280, 391, 563 in Bayesian game, 311 mixed, 284, 285, 317, 320, 321 pro…le, 277 pure, 283 Strategy set, 277, 285, 313, 389, 626 Stubblebine, C., 468 Subgame, 295 Subgame-perfect equilibrium, 297, 298, 300, 304– 306, 308, 310, 318 repeated games, 304, 309, 324, 325 Subjective probabilities, 189, 253, 561 Subscription price, 455 Substitution eÔect, 32 87, 104, 244 34, own-price, 37, 87, 534 Sugden, R., 221 Sundaram, R.K., 520 Sunk cost, 307, 568 Supply, 26 INDEX 643 and equilibrium, 146 Townsend, R.M., 424 and excess demand, 156 Transformation curve, 40, 47, 139 and externalities, 436 Transitivity, 75, 181, 228, 230, 548 by households, 100– 102 Tressler, J., 220 example, 104 Trigger strategy, 303, 304, 324, 325, elasticity, 244 567, 628 function, 30, 31, 60 Truth telling, 391 of competitive …rm, 29, 525 Tullock, G., 268 of industry, 51, 53, 156 Two-part tariÔ, 61, 329, 332 eÔect of externalities, 56 Type, 311, 312, 314, 329, 333, 334, eÔect of large numbers, 54 336– 338, 353, 354, 356 long-run, 57 and identity, 314 of public goods, 449 in Bayesian game, 311, 312, 314, Support theorem, 240, 242, 245, 433, 337, 338, 353, 354, 356 434, 623 under uncertainty, 253 Uncertainty, 259, 274, 319 Sutton, J., 323 Universality, 229, 621 Suzumura, K., 94 Upper hemicontinuity, 489 Sydsæter, K., 520 Utility, 77, 78, 80, 135, 144, 162, 185, 219, 231, 534, 556, 598 Tatonnement, 164 -possibility set, 235 Tax and accessibility, 256 corrective, 444, 448 and consumer cost, 89 optimal income, 415– 417, 420, 422, and CV,EV, 90 424 and e¢ ciency, 234, 238, 240, 251, Tax-compliance game, 321 560 Taylor expansion, 494 and externalities, 249, 250, 521 Technique, 12, 13, 15, 27, 107, 108, and fairness, 257 111, 125, 126, 132 and income distribution, 462 Technology, 10, 38, 72, 124, 125, 130, and social welfare, 228, 259, 260 144, 237, 260 cardinal, 188– 194 and externalities, 246 and risk aversion, 194 and feasibility, 128, 130, 136, 235, expected, 187– 192, 200, 214, 253, 238 263, 313, 369, 548 convex, 240 and social welfare, 262 interactions, 55 in dual approach, 81– 136 83, Technology set, 124, 125, 128– 130, 135, in primal approach, 83, 84, 92, 101, 168, 170, 240, 434, 541 136, 147 Threats, 298 indirect, 88, 89, 615 Tiebout, C.M., 468 intertemporal, 106, 222, 302 Time preference, 106, 302 quadratic, 196, 222 Time, timing, 35, 104, 179, 205, 293, quasiconcave, 79, 162, 183, 190 309, 319, 328, 338 reservation, 151, 279 in games, 293 Tipping mechanism, 408, 409 von Neumann Morgenstern, see exTirole, J., 320, 321, 468 pected 644 Varian, H.R., 265, 468 Variance, 192, 517 Vega-Redondo, F., 319 Vickrey, W., 264, 265, 424 von Neumann, J., 220 von Stackelberg, H., 320 Voting, 231– 233, 265, 266, 424, 557, 622 Wage schedule, 362, 366, 369, 371 Walras’ Law, 157, 159, 165, 546, 547, 619 Walras, L., 172 WARP, see Revealed preference, weak axiom Welfare and utility, 89 of individual consumer, 69, 89, 90, 93 social, see Social welfare Willig, R.D., 94 Winner’ curse, 426 s INDEX .. . xx LIST OF FIGURES B .1 0 B .1 1 B .1 2 B .1 3 B .1 4 B .1 5 B .1 6 B .1 7 B .1 8 B .1 9 B.20 B. 21 B.22 B.23 B.24 B.25 B.26 B.27 B.28 B.29 B.30 B. 31 B.32 B.33 B.34 B.35 B.36 B.37 B.38 B.39 B.40 B. 41 B.42 B.43 B.4 4.. . 17 9 18 0 18 1 18 2 18 2 18 3 18 4 18 6 18 8 19 0 19 1 19 3 19 4 19 5 19 6 19 7 19 8 19 9 200 2 01 204 206 208 209 210 212 213 215 215 217 218 9 .1 9.2 9.3 9.4 9.5 9.6 Alf, Bill, Charlie and the Bomb .. . List of Figures 2 .1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2 .1 0 2 .1 1 2 .1 2 2 .1 3 2 .1 4 2 .1 5 2 .1 6 2 .1 7 2 .1 8 Input requirement sets for four diÔerent technologies Marginal rate of technical