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Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium

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  • Maćkowiak, Piotr

Abstract

The primary goal of the paper is to deliver a simple proof of equivalence between Brouwer’s fixed point theorem and the existence of equilibrium in a simple exchange model with monotonic consumers. To achieve this end, we discuss some equivalent formulations of Brouwer’s theorem and prove additional ones, that are ’approximating’ in character or seem to be better suited for economic applications than the standard results.

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File URL: http://mpra.ub.uni-muenchen.de/42461/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42461.

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Date of creation: 2011
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Handle: RePEc:pra:mprapa:42461

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Keywords: existence of equilibrium; Brouwer’s fixed point; simple exchange model;

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  1. Kam-Chau Wong, 1997. "Excess demand functions, equilibrium prices, and existence of equilibrium," Economic Theory, Springer, vol. 10(1), pages 39-54.
  2. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
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