CONTENTS
PREFACE
1 Technology
Measurement of inputs and outputs 1 Specification of technology 2
Example: Input requzrement set Example: Isoquant Example: Shortrun
productzon posszbzlztzes set Example: Pt-oductzon functzon Example:
Transformatzon functzon Example: Cobb-Douglas technology Example:
Leontzef technology Activity analysis 5 Monotonic technologies
6 Convex technologies 7 Regular technologies 9 Parametric representations
of technology 10 The technical rate of substitution 11
Example: TRS for a Cobb-Douglas technology The elasticity of substitution
13 Example: The elastzczty of substztutzon for the Cobb-Douglas
productzon functzon Returns to scale 14 Example: Returns to scale
and the Cobb-Douglas technology Homogeneous and homothetic technologies
17 Example: The CES productzon functzon Exercises 21
2 Profit Maximization .
Profit maximization 25 Difficulties 28 Example: The profit functzon
for Cobb-Douglas technology Properties of demand and supply functions
31 Comparative statics using the first-order conditions 32 Comparative
statics using algebra 35 Recoverability 36 Exercises 39
VI CONTENTS
3 Profit Function
Properties of the profit function 40 Example: The eflects of price
stabilization Supply and demand functions from the profit function 43
The envelope theorem 45 Comparative statics using the profit function
46 Example: The LeChatelier principle Exercises 48
4 Cost Minimization
Calculus analysis of cost minimization 49 More on second-order conditions
52 Difficulties 53 Example: Cost function for the Cobb-Douglas
technology Example: The cost function for the CES technology Example:
The cost function for the Leontief technology Example: The cost
function for the linear technology Conditional factor demand functions
58 Algebraic approach to cost minimization 61 Exercises 63
5 Cost Function ..I
Average and marginal costs 64 Example: The short-run Cobb-Douglas
cost functions Example: Constant returns to scale and the cost function
The geometry of costs 67 Example: The Cobb-Douglas cost curves
Long-run and short-run cost curves 70 Factor prices and cost functions
71 The envelope theorem for constrained optimization 75 Example:
Marginal cost revisited Comparative statics using the cost function 76
Exercises 77
6 Duality
Duality 82 Sufficient conditions for cost functions 84 Demand functions
86 Example: Applying the duality mapping Example: Constant
returns to scale and the cost function Example: Elasticity of scale and
the cost function Geometry of duality 89 Example: Production functions,
cost functions, and conditional factor demands The uses of duality
91 Exercises 93
CONTENTS VII
7 Utility Maximization
Consumer preferences n,9431 .: Example: The existence of a utility function
Example: The marginal rate of substitution Consumer behavior 98 Indirect
utility 102 Some important identities 105 The money metric
utility functions 108 Example: The Cobb-Douglas utzlity function
L
Example: The CES utility function Appendix 113 Exercises 114
8 Choice
Comparative statics 116 Example: Excise and income taxes The Slutsky
equation 119 Example: The Cobb-Douglas Slutsky equation Prop
erties of demand functions 122 Comparative statics using the first-order
conditions 123 The integrability problem 125 Example: Integrabilzty
wzth two goods Example: Integrability with several goods Duality
in consumption 129 Example: Solving for the direct utility function
Revealed preference 131 Sufficient conditions for maximization 133
Comparative statics using revealed preference 135 The discrete version
of the Slutsky equation 137 Recoverability 138 Exercises 140
9 Demand
Endowments in the budget constraint 144 Labor supply Homothetic
utility functions 146 Aggregating across goods 147 Hicksian separability
The two-good model Functional separability Aggregating
across consumers 152 Inverse demand functions 155 Continuity of
demand functions 158 Exercises 157
10 Consumers' Surplus
Compensating and equivalent variations 160 Consumer's surplus 163 ,
Quasilinear utility 164 Quasilinear utility and money metric utility
166 Consumer's surplus as an approximation 167 Aggregation 168
Nonparametric bounds 170 Exercises 171
Wf . CONTENTS
11 Uncertainty
Lotteries 172 Expected utility 173 Uniqueness of the expected utility
function 175 Other notations for expected utility 176 Risk aversion
177 Example: The demand for insurance Global risk aversion 181
Example: Comparative statics of a simple portfolio problem Example:
Asset pricing Relative risk aversion 188 Example: Mean-variance
utility State dependent utility 190 Subjective probability theory 190
Example: The Allais paradox and the Ellsberg paradox The Allais paradox
The Ellsberg paradox Exercises 194 I
. r t
12 Econometrics
The optimization hypothesis 198 Nonparametric testing for maximizing
behavior 199 Parametric tests of maximizing behavior 200 Imposing
optimization restrictions 201 Goodness-of-fit for optimizing models
201 Structural models and reduced form models 202 Estimating
technological relationships 204 Estimating factor demands 207 More
complex technologies 207 Choice of functional form 209 Example:
The Diewert cost function Example: The translog cost function Estimating
consumer demands 210 Demand functions for a single good
Multiple equations Example: Linear expenditure system Example:
Almost Ideal Demand System Summary 213
13 Cornpetltive Markets
The competitive firm 215 The profit maximization problem 216 The
industry supply function 218 Example: Different cost functions Example:
Identical cost functions Market equilibrium 219 Example:
Identical firms Entry 220 Example: Entry and long-run equilibrium
Welfare economics 221 Welfare analysis 222 Several consumers 224
Pareto efficiency 225 Efficiency and welfare 226 The discrete good
model 227 Taxes and subsidies 228 Exercises 230
CONTENTS IX
14 Monopoly -I L
Special cases 236 Comparative statics 236 Welfare and output 238
Quality choice 239 Price discrimination 241 First-degree price discrimination
243 Second-degree price discrimination 244 Example:
A graphical treatment Third-degree price discrimination 248 Welfare
effects Exercises 253
15 Came Theory
Description of a game 260 Example: Matching pennies Example:
The Pmsoner's Dzlemma Example: Cournot duopoly Example: Bertrand
duopoly Economic modeling of strategic choices 263 Solution concepts
264 Nash equilibrium 265 Example: Calculatzng a Nash equilibmum
Interpretation of mixed strategies 268 Repeated games 269 Example:
Maintaining a cartel Refinements of Nash equilibrium 271 Dominant
strategies 272 Elimination of dominated strategies 272 Sequential
games 273 Example: A szmple bargaining model Repeated games
and subgame perfection 278 Games with incomplete information 279
Example: A sealed-bid auction Discussion of Bayes-Nash equilibrium 281
Exercises 282
16 Oligopoly
Cournot equilibrium 285 Stability of the system Comparative statics
288 Several firms 289 Welfare . Bertrand equilibrium 291
_- Example: A model of sales Complements and substitutes 294 Quantity
leadership 295 Price leadership 298 Classification and choice of
models 301 Conjectural variations 302 Collusion 303 Repeated
oligopoly games 305 Sequential games 307 Limit pricing 308 Exercises
310
17 Exchange
Agents and goods 314 Walrasian equilibrium 315 Graphical analysis
316 Existence of Walrasian equilibria 317 Existence of an equilibrium
319 Example: The Cobb-Douglas Economy The first theorem of
welfare economics 323 The second welfare theorem 326 A revealed
preference argument a Pareto efficiency and calculus 329 Welfare maximization
333 Exercises 336
18 Production
Firm behavior 338 Difficulties 340 Consumer behavior 341 Labor
supply Dzstnbutzon of profits Aggregate demand 342 Existence
of an equilibrium 344 Welfare properties of equilibrium 345 A
revealed preference argument a Welfare analysis in a productive economy
348 Graphical treatment 349 Example: The Cobb-Douglas constant
returns economy Example: A decreasing-returns-to-scale economy The
Nonsubstitution Theorem 354 Industry structure in general equilibrium
356 Exercises 357
19 Time
Intertemporal preferences 358 Intertemporal optimization with two periods
359 Intertemporal optimization with several periods 361 Example:
Loganthrnic utzlity General equilibrium over time 363 Infinity
General equilibrium over states of nature 365 Exercises 366
20 Asset Markets
Equilibrium with certainty 368 Equilibrium with uncertainty 369
Notation 370 The Capital Asset Pricing Model 371 The Arbitrage
Pricing Theory 376 Two factors a Asset-speczfic nsk a Expected
utility 379 Example: Expected utzlity and the APT Complete markets
382 Pure arbitrage 383 Appendix 385 Exercises 386
CONTENTS XI
21 Equilibrium Analysis
The core of an exchange economy 387 Convexity and size 393 Uniqueness
of equilibrium 394 Gross substitutes . Index analysis . General
equilibrium dynamics 398 Tatonnement processes 398 Nontatonnement
processes 401 Exercises 402
22 Welfare
The compensation criterion 404 Welfare functions 409 Optimal taxation
410 Exercises 413
23 Public goods
Efficient provision of a discrete public good 415 Private provision of a
discrete public good 417 Voting for a discrete public good 417 Efficient
provision of a continuous public good 418 Example: Solving for
the efficient provision of a public good Private provision of a continuous
public good 420 Example: Solving for Nash equilibrium provzsion Voting
424 Example: Quasilinear utility and voting Lindahl allocations
425 Demand revealing mechanisms 426 Demand revealing mechanisms
with a continuous good 429 Exercises 430
24 Externalities
An example of a production externality 433 Solutions to the externalities
problem 433 Pigovian taxes * Missing markets . Property
rights The compensation mechanism 436 Efficiency conditions in the
presence of externalities 438 Exercises 439
XI1 CONTENTS
25 Information
The principal-agent problem 441 Full information: monopoly solution
442 Full information: competitive solution 444 Hidden action: monopoly
solution 445 Agent's action can be observed o Analysis of the
optimal incentive scheme Example: Comparative statics Example:
Principal-agent model with mean-variance utility Hidden actions: competitive
market 455 Example: Moral hazard in insurance markets Hidden
information: monopoly 457 Market equilibrium: hidden information
464 Example: An algebraic example Adverse selection 466 The
lemons market and adverse selection 468 Signaling 469 Educational
signaling 470 Exercises 471
26 Mathematics
Linear algebra 473 Definite and semidefinite matrices 475 Tests for
definite matrices Cramer's rule 477 Analysis 477 Calculus 478
Higher-order derivatives Gradients and tangent planes 480 Limits
481 Homogeneous functions 481 Affine functions 482 Convex sets
482 Separating hyperplanes 483 Partial differential equations 483
Dynamical systems 484 Random variables 485
27 Optimization
Single variable optimization 487 First-order and second-order conditions
Example: First- and second-order conditions. Concavity
The envelope theorem Example: The value function Example: The
envelope theorem Comparative statics Example: Comparative statics
for a particular problem Multivariate maximization 493 First- and
second-order conditions Comparative statics Example: Comparative
statics Convexity and concavity Quasiconcave and quasiconvex
functions Constrained maximization 497 An alternative second-order
condition 498 How to remember the second-order conditions The
envelope theorem Constrained maximization with inequality constraints
503 Setting up Kuhn-Tucker problems 504 Existence and continuity
of a maximum 506
References l A1 Answers to Odd-Numbered Exercises l A9 Index 1 A37