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The existence of equilibrium in a simple exchange model


  • Maćkowiak, Piotr


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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    References listed on IDEAS

    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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    More about this item


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

    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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