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The existence of equilibrium without fixed-point arguments

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  • Mackowiak, Piotr

Abstract

Abstract This paper gives a proof of the existence of general equilibrium without the use of a fixed point theorem. Unlike other results of this type, the conditions we use do not imply that the set of equilibrium prices is convex. We use an assumption on the excess demand correspondence that is related to, but weaker than, the weak axiom of revealed preference (WARP). The proof is carried out for compact and convex valued upper hemicontinuous excess demand correspondences satisfying this WARP-related condition and some other standard conditions. We also provide an algorithm for finding equilibrium prices.

Suggested Citation

  • Mackowiak, Piotr, 2010. "The existence of equilibrium without fixed-point arguments," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1194-1199, November.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1194-1199
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    References listed on IDEAS

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    1. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 337-343, February.
    2. Joseph Greenberg, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, Oxford University Press, vol. 91(3), pages 513-516.
    3. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Rosa Barbolla & Luis C. Corchón, 1989. "An Elementary Proof of the Existence of a Competitive Equilibrium in a Special Case," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 385-389.
    6. Frayssé, Jean, 2009. "A simple proof of the existence of an equilibrium when the weak axiom holds," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 767-769, December.
    7. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.
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    Cited by:

    1. Ruscitti, Francesco, 2012. "On the boundary behavior of the excess demand function," Research in Economics, Elsevier, vol. 66(4), pages 371-374.
    2. Maćkowiak, Piotr, 2013. "The existence of equilibrium in a simple exchange model," MPRA Paper 46764, University Library of Munich, Germany, revised Apr 2013.

    More about this item

    Keywords

    Existence of economic equilibrium The weak axiom of revealed preference Excess demand correspondence Distribution economies Law of demand;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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