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Equilibria in reflexive Banach lattices with a continuum of agents

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  • Araujo, Aloisio
  • Martins-da-Rocha, Victor-Filipe
  • Monteiro, Paulo K.

Abstract

We consider exchange economies with a measure space of agents and for which the commodity space is a separable and reflexive Banach lattice. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini-Yannelis [27] and Podczeck [25]. In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/6273.

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Date of creation: 2004
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Publication status: Published in Economic Theory, 2004, Vol. 24, no. 3. pp. 469-492.Length: 23 pages
Handle: RePEc:dau:papers:123456789/6273

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Keywords: Competitive equilibria; Continuum of agents; Reflexive Banach lattice commodity spaces; Uniform properness;

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References

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  1. Joseph M. Ostroy & William R. Zame, 1988. "Non-Atomic Economies and the Boundaries of Perfect Competition," UCLA Economics Working Papers 502, UCLA Department of Economics.
  2. Rustichini, Aldo & Yannelis, Nicholas C., 1991. "Edgeworth's conjecture in economies with a continuum of agents and commodities," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 307-326.
  3. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
  4. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-23, September.
  5. Bernard Cornet & V. F. Martins-Da-Rocha, 2005. "Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200503, University of Kansas, Department of Economics, revised Feb 2005.
  6. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
  7. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
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Cited by:
  1. Bernard Cornet & V. F. Martins-Da-Rocha, 2005. "Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200503, University of Kansas, Department of Economics, revised Feb 2005.
  2. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
  3. Khan, M. Ali Khan, 2007. "Perfect Competition," MPRA Paper 2202, University Library of Munich, Germany.
  4. Evren, Özgür & Hüsseinov, Farhad, 2008. "Theorems on the core of an economy with infinitely many commodities and consumers," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1180-1196, December.

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