Mathematical Economics: Twenty Papers of Gerard Debreu

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Cambridge University Press, 31. 10. 1986 - Počet stran: 250
These twenty papers were selected by the author. The book includes a major introduction by Werner Hildenbrand, who assesses Professor Debreu's contribution to economic theory and explains the part played by these papers in the development of the subject.
 

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The coefficient of resource utilization
30
2 Basic mathematical concepts
33
4 Optimum and loss defined in the satisfaction space
35
5 Optimum and loss defined in the commodity space
36
7 Historical note
39
8 The discontinuous case
40
9 The coefficient of resource utilization 𝞺
41
10 Definitions of the economic loss
43
3 Independent factors of the action set
125
References
131
New concepts and techniques for equilibrium analysis
133
2 Lemmata
136
3 Proof of the theorem
140
4 Equilibrium and quasiequilibrium
146
References
149
A limit theorem on the core of an economy
151

11 Minimax interpretation of 𝞺
44
12 Isomorphism with the theory of statistical decision functions
45
References
48
A social equilibrium existence theorem
50
1 Topological concepts
51
2 Equilibrium points
52
3 Saddle points and MinMax operator
55
4 Historical note
56
References
57
A classical taxsubsidy problem
59
1 The economic system
60
2 The coefficient of resource utilization 𝞺
61
3 First and second differentials of 𝞺
62
4 A general expression of the economic loss
64
5 Application to the taxsubsidy case
66
References
67
Existence of an equilibrium for a competitive economy
68
1 Statement of the first existence theorem for a competitive equilibrium
70
2 A lemma on abstract economies
77
3 Proof of Theorem I
79
4 Statement of the second existence theorem for a competitive equilibrium
85
5 Proof of Theorem II
88
6 Historical note
94
References
96
Valuation equilibrium and Pareto optimum
98
1 The economic system
99
2 Valuation equilibrium
100
5 A Pareto optimum is a valuation equilibrium
101
6 The free disposal assumption
104
Representation of a preference ordering by a numerical function
105
2 Two representation lemmas
106
3 Two representation theorems
108
References
110
Market equilibrium
111
Appendix
113
Economics under uncertainty
115
Topological methods in cardinal utility theory
120
1 Stochastic objects of choice
121
2 Stochastic act of choice
123
2 The core in a pure exchange economy
153
3 The core as the number of consumers becomes infinite
156
4 The core in a productive economy
159
5 Generalizations
161
References
162
Continuity properties of Paretian utility
163
2 Proof of the theorem
164
3 Continuity properties of the representation
168
4 An example
171
Neighboring economic agents
173
References
178
Economies with a finite set of equilibria
179
References
185
Smooth preferences
186
2 Discreteness of E𝒢
187
3 Continuity of E
189
References
199
a corrigendum
201
References
202
Excess demand functions
203
1 Proof of the theorem
204
2 Appendix
208
3 Proof of the proposition
209
The rate of convergence of the core of an economy
210
Proof of the theorem
212
References
216
Four aspects of the mathematical theory of economic equilibrium
217
2 The computation of economic equilibria
221
3 Regular differentiable economies
224
4 The core of a large economy
226
References
230
The application to economics of differential topology and global analysis regular differentiable economies
232
References
239
Least concave utility functions
242
2 Existence of a least concave representation
243
3 Proof of the theorem
245
References
250
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Strana 26 - Now the reason for this sterility of the Walrasian system is largely, I believe, that he did not go on to work out the laws of change for his system of General Equilibrium. He could tell what conditions must be satisfied by the prices established with given resources and given preferences ; but he did not explain what would happen if tastes or resources changed."1...
Strana 239 - Y. Balasko, Some Results on Uniqueness and on Stability of Equilibrium in General Equilibrium Theory, J.
Strana 1 - Alles, was Gegenstand des wissenschaftlichen Denkens überhaupt sein kann, verfällt, sobald es zur Bildung einer Theorie reif ist, der axiomatischen Methode und damit mittelbar der Mathematik.
Strana 2 - ... have a passionate hatred of abstraction, chiefly, I think, because of its intellectual difficulty; but as they do not wish to give this reason, they invent all sorts of others that sound grand. They say that all reality is concrete, and that in making abstractions we are leaving out the essential. They say that all abstraction is falsification, and that as soon as you have left out any aspect of something actual you have exposed yourself to the risk of fallacy in arguing from its remaining aspects...
Strana 17 - In every problem of economic theory certain variables (quantities, prices, etc.) are designated as unknowns, in whose determination we are interested. Their values emerge as a solution of a specified set of relationships imposed upon the unknowns by assumption or hypothesis.

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