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" Topological Methods in Walrasian Economics "
by Egbert Dierker.
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BL
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752214
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b572173
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| Main Entry
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by Egbert Dierker.
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Topological Methods in Walrasian Economics\ by Egbert Dierker.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1974
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| Series Statement
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Lecture Notes in Economics and Mathematical Systems, Mathematical Economics, 92.
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| ISBN
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3540066225
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: 3642658008
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: 9783540066224
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: 9783642658006
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| Contents
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1. The Economic Framework --; 2. Introduction to the Mathematics --; 3. Differentiable Manifolds and Mappings, Tangents, Vectorfields --; 4. Regular Equilibria. A First Approach --; 5. Scarf's Example --; 6. Excess Demand Functions --; 7. Debreu's Theorem on the Finiteness of the Number of Equilibria of an Economy --; 8. Continuity of the Walras Correspondence for C° Demand Functions --; 9. Density of Transversal Intersection --; 10. Regular Economies --; 11. Stability Questions and the Number of Equilibria --; 12. Large Economies --; Some Standard Notation --; References.
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| Abstract
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In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econoƯ mics at the university of Bonn, w. Germany1~ The economists, howƯ ever, had a mathematical background well above the average " Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand funcƯ tions [see Debreu (1972)] and regular economies based on agents with smooth preferences are not presented here " Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise " It is only a minor restriction, at present, that functional anaƯ lysis is not used " But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting " Economic knowledge is not required, but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) " Although the formulation of our economic problem uses a map between Euclidean spaces only, we shall also consider ma- folds " Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds " (Under differentiability assumpƯ tions, for instance, the graph of the equilibrium set corresponƯ.
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Economics.
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Egbert Dierker
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