Topological Methods in Walrasian Economics

1. Front Matter

   Pages N1-V

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2. The Economic Framework

   • Egbert Dierker

   Pages 3-14

3. Introduction to the Mathematics

   • Egbert Dierker

   Pages 15-24

4. Differentiable Manifolds and Mappings, Tangents, Vectorfields

   • Egbert Dierker

   Pages 25-39

5. Regular Equilibria. A First Approach

   • Egbert Dierker

   Pages 40-46

6. Scarf’s Example

   • Egbert Dierker

   Pages 47-55

7. Excess Demand Functions

   • Egbert Dierker

   Pages 56-66

8. Debreu’s Theorem on the Finiteness of the Number of Equilibria of an Economy

   • Egbert Dierker

   Pages 67-72

9. Continuity of the Walras Correspondence for C° Demand Functions

   • Egbert Dierker

   Pages 73-88

10. Density of Transversal Intersection

    • Egbert Dierker

    Pages 89-95

11. Regular Economies

    • Egbert Dierker

    Pages 96-103

12. Stability Questions and the Number of Equilibria

    • Egbert Dierker

    Pages 104-116

13. Large Economies

    • Egbert Dierker

    Pages 117-125

14. Back Matter

    Pages 126-133

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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 econo­ mics at the university of Bonn , w.Germany1~ The economists , how­ 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 func­ 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 ana­ 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 assump­ tions , for instance , the graph of the equilibrium set correspon­

• agents
• economics
• economy
• equilibrium
• general equilibrium
• general equilibrium theory
• linear optimization
• mathematics

• Wirtschaftstheoretische Abteilung, Inst, für Gesellschafts- und Wirtschaftswissenschaften, Bonn, Germany

  Egbert Dierker

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