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Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy

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Author Info
Allouch, N.
Florenzano, M.

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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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Publisher 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

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Postal: France; Universite de Paris I - Pantheon- Sorbonne, 12 Place de Pantheon-75005 Paris, France
Web page: http://cermsem.univ-paris1.fr/
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Related research
Keywords: ARBITRAGE ; MARKET ; CONSUMPTION;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. 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. [Downloadable!] (restricted)
    Other versions:
  2. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Blackwell Publishing, vol. 62(1), pages 101-14, January. [Downloadable!] (restricted)
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  6. Florenzano, Monique & Deghdak, Messaoud, 1997. "Decentralizing edgeworth equilibria in economies with many commodities," CEPREMAP Working Papers (Couverture Orange) 9721, CEPREMAP.
  7. Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papiers d'Economie Mathématique et Applications 1999.34, Université Panthéon-Sorbonne (Paris 1).
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  8. 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. [Downloadable!] (restricted)
    Other versions:
  9. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December. [Downloadable!] (restricted)
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  10. Kim, Chongmin, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Blackwell Publishing, vol. 65(2), pages 341-56, April. [Downloadable!] (restricted)
  11. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November. [Downloadable!] (restricted)
  12. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April. [Downloadable!] (restricted)
  13. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation, Yale University. [Downloadable!]
  14. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society. [Downloadable!]
  15. 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. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
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  18. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August. [Downloadable!] (restricted)
  19. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Blackwell Publishing, vol. 56(3), pages 467-73, July. [Downloadable!] (restricted)
  20. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485. [Downloadable!] (restricted)
  21. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!] (restricted)
  2. Wassim Daher & V. Martins-da-Rocha & Yiannis Vailakis, 2007. "Asset market equilibrium with short-selling and differential information," Economic Theory, Springer, vol. 32(3), pages 425-446, September. [Downloadable!] (restricted)
    Other versions:
  3. 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_v1, HAL. [Downloadable!]
    Other versions:
  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). [Downloadable!]
  5. Wassin Daher & V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2005. "Asset market equilibrium with short-selling and differential information," Cahiers de la Maison des Sciences Economiques b05098, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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