The existence of equilibrium without fixed-point arguments
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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- 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, vol. 104(2), pages 385-89, May.
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- John Quah, 2004.
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Economics Series Working Papers
2004-W07, University of Oxford, Department of Economics.
- 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.
- John K.-H. Quah, 2004. "The existence of equilibrium when excess demand obeys the weak axiom," Economics Papers 2004-W07, Economics Group, Nuffield College, University of Oxford.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
- 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.
- Greenberg, Joseph, 1977. "An Elementary Proof of the Existence of a Competitive Equilibrium with Weak Gross Substitutes," The Quarterly Journal of Economics, MIT Press, vol. 91(3), pages 513-16, August.
- John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
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