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Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy

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  • Nizar Allouch

    (Universite de Paris 1)

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 Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1901.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1901

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References

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  1. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  2. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
  3. Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 62(1), pages 101-14, January.
  4. Kim, Chongmin, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(2), pages 341-56, April.
  5. Aliprantis, C. D. & D. J. Brown & I. A. Polyrakis & J. Werner, 1996. "Portfolio Dominance and Optimality in Infinite Security Markets," Discussion Paper Serie B 383, University of Bonn, Germany.
  6. Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1996. "On the different notions of arbitrage and existence of equilibrium," CEPREMAP Working Papers (Couverture Orange) 9616, CEPREMAP.
  7. Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, Elsevier, vol. 78(2), pages 321-328, February.
  8. 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.
  9. 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.
  10. 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, Elsevier, vol. 114(2), pages 345-357, February.
  11. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
  12. Florenzano Monique, 1988. "Edgeworth equilibria, fuzzy core and equilibria of a production economy without ordered preferences," CEPREMAP Working Papers (Couverture Orange) 8822, CEPREMAP.
  13. Page, F.H.Jr. & Wooders, M.H. & Monteiro, P.K., 1999. "Inconsequential Arbitrage," The Warwick Economics Research Paper Series (TWERPS) 561, University of Warwick, Department of Economics.
  14. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 182R, Cowles Foundation for Research in Economics, Yale University.
  15. Florenzano, Monique & Deghdak, Messaoud, 1997. "Decentralizing edgeworth equilibria in economies with many commodities," CEPREMAP Working Papers (Couverture Orange) 9721, CEPREMAP.
  16. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1396, Econometric Society.
  17. 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.
  18. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152.
  19. Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(2), pages 364-384, April.
  20. 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, Springer, vol. 1(1), pages 108-16, January.
  21. 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.
  22. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
  23. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(2), pages 416-427, August.
  24. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, Elsevier, vol. 41(2), pages 392-404, April.
  25. 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.
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Citations

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Cited by:
  1. 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.
  2. Luciano Castro & Marialaura Pesce & Nicholas Yannelis, 2011. "Core and equilibria under ambiguity," Economic Theory, Springer, Springer, vol. 48(2), pages 519-548, October.
  3. Monique Florenzano & Elena Laureana Del Mercato, 2004. "Edgeworth and Lindahl-Foley equilibria of a general equilibrium model with private provision of pure public goods," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b04082, Université Panthéon-Sorbonne (Paris 1).
  4. Nizar Allouch & Monique Florenzano, 2012. "Fuzzy Rejective Core of Satiated Economies with Unbounded Consumption Sets," Working Papers, Queen Mary, University of London, School of Economics and Finance 690, Queen Mary, University of London, School of Economics and Finance.
  5. Daher, Wassim & Martins-da-Rocha, Victor-Filipe & Vailakis, Yiannis, 2007. "Asset market equilibrium with short-selling and differential information," Economics Papers from University Paris Dauphine 123456789/2967, Paris Dauphine University.
  6. 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.
  7. repec:hal:journl:halshs-00598038 is not listed on IDEAS
  8. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
  9. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b04116, Université Panthéon-Sorbonne (Paris 1).
  10. repec:hal:journl:halshs-00092809 is not listed on IDEAS
  11. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, Springer, vol. 2(1), pages 101-122, January.
  12. 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.
  13. repec:hal:journl:halshs-00173787 is not listed on IDEAS
  14. repec:hal:journl:halshs-00085726 is not listed on IDEAS

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