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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 Paris I - Economie Mathematique et Applications in its series Papers 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

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  1. 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)
  2. 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)
  3. 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)
    Other versions:
  4. Florenzano, Monique & Deghdak, Messaoud, 1997. "Decentralizing edgeworth equilibria in economies with many commodities," CEPREMAP Working Papers (Couverture Orange) 9721, CEPREMAP.
  5. Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papers 1999.34, Paris I - Economie Mathematique et Applications.
    Other versions:
  6. 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:
  7. 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)
    Other versions:
  8. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November. [Downloadable!] (restricted)
  9. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation, Yale University. [Downloadable!]
  10. Monique Florenzano & Valeri Marakulin, 2000. "Production Equilibria in Vector Lattices," Econometric Society World Congress 2000 Contributed Papers 1396, Econometric Society. [Downloadable!]
  11. 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)
  12. 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)
  13. 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)
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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. 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:
  2. Nizar Allouch & Cuong Le Van & Frank H. Page, 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Post-Print halshs-00096040_v1, HAL. [Downloadable!]
  3. Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2006. "Production equilibria," Post-Print halshs-00092809_v1, HAL. [Downloadable!]
  4. 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 b04082, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
    Other versions:
  5. 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!]
  6. 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!]
  7. Monique Florenzano & Elena Del Mercato, 2006. "Edgeworth and Lindahl-Foley equilibria of a general equilibrium model with private provision of pure public goods," Post-Print halshs-00085726_v1, HAL. [Downloadable!]
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