# Topological Methods in Walrasian Economics

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

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

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

- DOI https://doi.org/10.1007/978-3-642-65800-6
- Copyright Information Springer-Verlag Berlin Heidelberg 1974
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-06622-4
- Online ISBN 978-3-642-65800-6
- Series Print ISSN 0075-8442
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