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The existence of equilibrium in a simple exchange model

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  • Maćkowiak, Piotr

Abstract

This paper gives a new proof of the existence of equilibrium in a simple model of an exchange economy. We first formulate and prove a simple combinatorial lemma and then we use it to prove the existence of equilibrium. The combinatorial lemma allows us to derive an algorithm for the computation of equilibria. Though the existence theorem is formulated for functions defined on open simplices it is equivalent to the Brouwer fixed point theorem.

Suggested Citation

  • Maćkowiak, Piotr, 2013. "The existence of equilibrium in a simple exchange model," MPRA Paper 46764, University Library of Munich, Germany, revised Apr 2013.
    • Handle: RePEc:pra:mprapa:46764
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    File URL: https://mpra.ub.uni-muenchen.de/46764/1/MPRA_paper_46764.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. Mackowiak, Piotr, 2010. "The existence of equilibrium without fixed-point arguments," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1194-1199, November.
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    Cited by:

    1. Le, Thanh & Le Van, Cuong & Pham, Ngoc-Sang & Sağlam, Çağrı, 2020. "Direct Proofs of the Existence of Equilibrium, the Gale-Nikaido-Debreu Lemma and the Fixed Point Theorems using Sperner’s Lemma," MPRA Paper 110933, University Library of Munich, Germany, revised 28 Oct 2020.

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    More about this item

    Keywords

    Simple exchange model; equilibrium existence; zero of a function; fixed point; computation of equilibria; simplicial methods;
    All these keywords.

    JEL classification:

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

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