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Arbitrage and equilibrium in unbounded exchange economies with satiation

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  • Allouch, Nizar
  • Le Van, Cuong
  • Page, Frank Jr.

Abstract

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations.Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents' preferences are satiated, the absence of arbitrage is suffcient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades - that is, as long as agents' preferences satisfy weaknonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation - a condition considerably weaker than local or global nonsatiation - that makes possible this transformation.

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Bibliographic Info

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

Volume (Year): 42 (2006)
Issue (Month): 6 (September)
Pages: 661-674

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Handle: RePEc:eee:mateco:v:42:y:2006:i:6:p:661-674

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

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  1. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00086096, HAL.
  2. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 3(2), pages 131-134, July.
  3. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
  4. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(1), pages 45-57, February.
  5. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 34(4), pages 439-469, December.
  6. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922 Elsevier.
  7. Milne, Frank, 1980. "Short-Selling, Default Risk and the Existence of Equilibrium in a Securities Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 255-67, June.
  8. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00250167, HAL.
  9. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(1), pages 170-175, October.
  10. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 2(1), pages 9-15, March.
  11. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 169-193, July.
  12. Florenzano, Monigue & Le Van, Cuong, 1986. "A note on the Gale-Nikaido-Debreu lemma and the existence of general equilibrium," Economics Letters, Elsevier, Elsevier, vol. 22(2-3), pages 107-110.
  13. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, Elsevier, vol. 52(2), pages 153-162, August.
  14. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 9(1-2), pages 113-134, January.
  15. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 38(4), pages 373-391, December.
  16. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1103-23, November.
  17. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  18. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
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Citations

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Cited by:
  1. De Giorgi, Enrico & Hens, Thorsten & Rieger, Marc Oliver, 2010. "Financial market equilibria with cumulative prospect theory," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 46(5), pages 633-651, September.
  2. Martins-da-Rocha, Victor Filipe & Monteiro, Paulo Klinger, 2007. "Unbounded exchange economies with satiation: how far can we go?," Economics Working Papers (Ensaios Economicos da EPGE) 646, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  3. Won, Dong Chul & Yannelis, Nicholas C., 2011. "Equilibrium theory with satiable and non-ordered preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(2), pages 245-250, March.
  4. Won, Dong Chul & Yannelis, Nicholas C., 2008. "Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(11), pages 1266-1283, December.

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