1 Theory of Demand 1
1.1 A Direct Approach to Demand Theory 1
1.2 Demand Theory without Transitivity 13
1.3 The Classical Theory 15
1.4 The Method of Revealed Preference 22
1.5 Market Demand Functions 25
Appendixes
A. Continuity of mx p 33
B. Negative Semide?niteness of mij p 34
C. Euler’s Theorem for f p 35
D. Quasi-linear Preferences 35
E. The Law of Demand and Risk Aversion 36
F. The Strong Axiom of Revealed Preference38
G. Group Demand Functions 40
2Ta ? tonnement Stability of Equilibrium 45
2.1 Excess Demand Functions 45
2.2 Market Equilibrium 50
2.3 Matrices with Quasi-dominant Diagonals50
2.4 The Process of Ta ? tonnement 52
2.5 Local Stability of the Ta ? tonnement54
2.6 Ta ? tonnement with Expectations 64
2.7 An Economy of Firms 69
2.8 An Economy of Activities 77
2.9 Ta ? tonnment with Trading 82
2.10 Global Stability with GrossSubstitutes 89
3 Leontief Models of Production 109
3.1 The Simple Leontief Model 109
3.2 A Simple Leontief Model of Growth 114
3.3 The Simple Model with VariableCoe‰cients 118
3.4 Nonsubstitution with Capital Stocks 122
3.5 Current Prices and Interest Rates 129
Appendix
Continuity of mA s 129
4 Comparative Statics 133
4.1 The Local Theory of Comparative Statics133
4.2 The Morishima Case 140
4.3 Global Comparative Statics 143
4.4 Comparative Statics for the IndividualAgent 145
4.5 Comparative Statics and Supermodularity150
Appendixes
A. Local Uniqueness of Equilibrium 153
B. Jacobi’s Theorem 157
C. Negative De?niteness under Constraint158
D. Maximization under Constraint 161
E. Matrices Whose Roots Have Negative RealParts 163
5 Pareto Optimality and the Core 165
5.1 Pareto Optimum and CompetitiveEquilibrium 165
5.2 Competitive Equilibrium and the Core171
5.3 Nonemptiness of the Core 181
5.4 The Existence of CompetitiveEquilibrium 183
6 Existence and Uniqueness of CompetitiveEquilibrium 189
6.1 Existence in an Economy of Activities189
6.2 Existence in an Economy of Firms 197
6.3 Interiority and Irreducibility 207
6.4 Existence of Competitive Equilibriumwith an
In?nite Commodity Space 214
6.5 Uniqueness of Equilibrium 229
Appendix
7 Competitive Equilibrium over Time 239
7.1 The von Neumann Model 240
7.2 Turnpike Theorems for the von NeumannModel 244
7.3 A Generalized Ramsey Growth Model 248
7.4 Turnpike Theorems over an In?niteHorizon 255
7.5 The Generalized Ramsey Model withDiscounting 259
7.6 A Turnpike Theorem for theQuasi-stationary
Model 264
7.7 The Turnpike in Competitive Equilibrium272
Appendix
A Leontief Model with Capital Coe‰cients asa von
Neumann Model
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