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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 6 (November)
Pages: 1194-1199

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Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1194-1199

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Web page: http://www.elsevier.com/locate/jmateco

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

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References

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  1. Barbolla, Rosa & Corchon, Luis C, 1989. "An Elementary Proof of the Existence of a Competitive Equilibrium in a Special Case," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 104(2), pages 385-89, May.
  2. Frayssé, Jean, 2009. "A simple proof of the existence of an equilibrium when the weak axiom holds," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 45(11), pages 767-769, December.
  3. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(3-4), pages 337-343, February.
  4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
  5. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers, University at Albany, SUNY, Department of Economics 06-07, University at Albany, SUNY, Department of Economics.
  6. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1421-1442, November.
  7. Greenberg, Joseph, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 91(3), pages 513-16, August.
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Cited by:
  1. Maćkowiak, Piotr, 2013. "The existence of equilibrium in a simple exchange model," MPRA Paper 46764, University Library of Munich, Germany, revised Apr 2013.

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