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Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy

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  • Allouch, N.
  • Florenzano, M.

Abstract

In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in a infinite dimensional setting. We then show how these results apply to some finance models.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Papiers d'Economie Mathématique et Applications with number 2000.119.

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Length: 20 pages
Date of creation: 2000
Date of revision:
Handle: RePEc:fth:pariem:2000.119

Contact details of provider:
Postal: France; Universite de Paris I - Pantheon- Sorbonne, 12 Place de Pantheon-75005 Paris, France
Phone: + 33 44 07 81 00
Fax: + 33 1 44 07 83 01
Web page: http://cermsem.univ-paris1.fr/
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Keywords: ARBITRAGE ; MARKET ; CONSUMPTION;

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References

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  1. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
  2. Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS) 598, University of Warwick, Department of Economics.
  3. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
  4. Florenzano Monique, 1988. "Edgeworth equilibria, fuzzy core and equilibria of a production economy without ordered preferences," CEPREMAP Working Papers (Couverture Orange) 8822, CEPREMAP.
  5. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  6. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
  7. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer, vol. 1(1), pages 108-16, January.
  8. Kim, Chongmin, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 341-56, April.
  9. Brown, D.J. & Werner, J., 1992. "Arbitrage and Existence of Equilibrium in Finite Asset Markets," Papers 43, Stanford - Institute for Thoretical Economics.
  10. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  11. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
  12. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
  13. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
  14. Allouch, Nizar & Van, Cuong Le & Page Jr. Frank H., 2002. "Arbitrage, Equilibrium And Nonsatiation," The Warwick Economics Research Paper Series (TWERPS) 637, University of Warwick, Department of Economics.
  15. 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.
  16. Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, vol. 78(2), pages 321-328, February.
  17. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer, vol. 14(2), pages 297-310.
  18. 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, vol. 52(2), pages 153-162, August.
  19. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society.
  20. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152.
  21. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
  22. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
  23. Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, vol. 59(2), pages 364-384, April.
  24. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
  25. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
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Citations

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Cited by:
  1. repec:hal:journl:halshs-00085726 is not listed on IDEAS
  2. Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2005. "Linear and non-linear price decentralization," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086101, HAL.
  3. Luciano De Castro & Marialaura Pesce & Nicolas Yannelis, 2011. "Core and Equilibria under ambiguity," Discussion Papers 1534, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
  5. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 661-674, September.
  6. Wassim Daher & V. Filipe Martins-Da-Rocha & Yiannis Vailakis, 2005. "Asset market equilibrium with short-selling and differential information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00173787, HAL.
  7. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
  8. Monique Florenzano & Elena L. Del Mercato, 2006. "Edgeworth and Lindahl-Foley equilibria of a general equilibrium model with private provision of pure public goods," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085726, HAL.
  9. repec:hal:journl:halshs-00598038 is not listed on IDEAS
  10. Allouch, Nizar & Florenzano, Monique, 2013. "Edgeworth rejective core and dividends equilibria of satiated exchange economies," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 1-6.
  11. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
  12. repec:hal:journl:halshs-00173787 is not listed on IDEAS
  13. Nizar Allouch & Monique Florenzano, 2012. "Fuzzy Rejective Core of Satiated Economies with Unbounded Consumption Sets," Working Papers 690, Queen Mary, University of London, School of Economics and Finance.
  14. repec:hal:journl:halshs-00092809 is not listed on IDEAS

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