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A simple proof of the existence of an equilibrium when the weak axiom holds

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  • Frayssé, Jean

Abstract

An elementary proof of the existence of a competitive equilibrium is given for economies where the weak axiom holds. It is shown by an induction argument on the number of goods that the problem is reduced to the question of the existence of an equilibrium in a two-good economy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:11:p:767-769
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    References listed on IDEAS

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    1. Joseph Greenberg, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(3), pages 513-516.
    2. 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.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. 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, President and Fellows of Harvard College, vol. 104(2), pages 385-389.
    5. Fraysse, J., 1997. "An Elementary Proof of the Existence of a Competitive Equilibrium in Some SPecial Classes of Economies," Papers 97.479, Toulouse - GREMAQ.
    6. Dana, Rose-Anne, 1993. "Existence, uniqueness and determinacy of Arrow-Debreu equilibria in finance models," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 563-579.
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    Cited by:

    1. Mackowiak, Piotr, 2010. "The existence of equilibrium without fixed-point arguments," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1194-1199, November.
    2. Gourdel, Pascal & Le Van, Cuong & Pham, Ngoc-Sang & Tran Viet, Cuong, 2023. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems," MPRA Paper 116541, University Library of Munich, Germany.
    3. Ruscitti, Francesco, 2012. "On the boundary behavior of the excess demand function," Research in Economics, Elsevier, vol. 66(4), pages 371-374.

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