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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.

Suggested Citation

  • Maćkowiak, Piotr, 2011. "Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium," MPRA Paper 42461, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42461
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    File URL: https://mpra.ub.uni-muenchen.de/42461/1/MPRA_paper_42461.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Tijs, S.H. & Torre, A. & Brânzei, R., 2001. "Approximate Fixed Point Theorems," Other publications TiSEM e13a067a-56df-417a-b030-f, Tilburg University, School of Economics and Management.
    3. Tijs, S.H. & Torre, A. & Brânzei, R., 2001. "Approximate Fixed Point Theorems," Discussion Paper 2001-55, Tilburg University, Center for Economic Research.
    4. Kam-Chau Wong, 1997. "Excess demand functions, equilibrium prices, and existence of equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 39-54.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    existence of equilibrium; Brouwer’s fixed point; simple exchange model;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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