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Abraham Wald's equilibrium existence proof reconsidered


  • Reinhard John

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


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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    References listed on IDEAS

    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December.
    7. Allais Maurice, 1990. "Cardinal Utility," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 1(2), pages 1-38, June.
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    Cited by:

    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. repec:ebl:ecbull:eb-17-00215 is not listed on IDEAS
    3. 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.

    More about this item


    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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