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Abraham Wald's equilibrium existence proof reconsidered

Author

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  • Reinhard John

    (Wirtschaftstheoretische Abteilung II, UniversitÄt Bonn, Adenauerallee 24-42, D-53113 Bonn, GERMANY)

Abstract

For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution.

Suggested Citation

  • Reinhard John, 1999. "Abraham Wald's equilibrium existence proof reconsidered," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 417-428.
    • Handle: RePEc:spr:joecth:v:13:y:1999:i:2:p:417-428
    Note: Received: July 22, 1997; revised version: December 11, 1997
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    Citations

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    Cited by:

    1. Pascal Gourdel & Cuong Le Van & Ngoc-Sang Pham & Cuong Tran Viet, 2023. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems," Working Papers hal-04008394, HAL.
    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. Marco Sahm, 2017. "Risk aversion and prudence in contests," Economics Bulletin, AccessEcon, vol. 37(2), pages 1122-1132.
    4. Móczár, József, 2006. "Arrow-Debreu-modell és a Kornai-kritika harminc év után [The Arrow-Debreu Model and Kornai s critique, thirty years after]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 175-194.
    5. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, December.
    6. Jozsef Moczar, 2017. "Arrow-Debreu Model versus Kornai-critique," Athens Journal of Business & Economics, Athens Institute for Education and Research (ATINER), vol. 3(2), pages 143-170, April.
    7. Simone Tonin, 2018. "Existence of Equilibrium Prices: A Pedagogical Proof," Papers 1808.03129, arXiv.org, revised Sep 2018.
    8. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.

    More about this item

    Keywords

    Abraham Wald · Existence of equilibrium · Pseudomonotonicity · Variational inequality problem.;

    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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