عنوان

Topological Methods in Walrasian Economics

(Number (ISBN

3540066225

(Number (ISBN

3642658008

(Number (ISBN

9783540066224

(Number (ISBN

9783642658006

Number

b572173

Title Proper

Topological Methods in Walrasian Economics

General Material Designation

[Book]

First Statement of Responsibility

by Egbert Dierker.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1974

Series Title

Lecture Notes in Economics and Mathematical Systems, Mathematical Economics, 92.

Text of Note

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.

Text of Note

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.

Economics.

by Egbert Dierker.

Egbert Dierker

Electronic name

[Book]

Y