Munich Personal RePEc Archive

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

Maćkowiak, Piotr (2011): Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium. Published in: Quantitative Methods in Economics 2012, (M. Matłoka, ed.), Poznań University of Economics Press, ISBN: 978-83-7417-703-0 (2012): pp. 164-171.

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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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