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Topological Methods in Walrasian Economics

  • Book
  • © 1974

Overview

Authors:
  1. Egbert Dierker

    1. Wirtschaftstheoretische Abteilung, Inst, für Gesellschafts- und Wirtschaftswissenschaften, Bonn, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 92)

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Table of contents (12 chapters)

  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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About this book

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

Authors and Affiliations

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

    Egbert Dierker

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