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Unbounded exchange economies with satiation: How far can we go?

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  • Martins-da-Rocha, V. Filipe
  • Monteiro, Paulo K.

Abstract

We unify and generalize the existence results in Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55 (6), 1403-1418], Dana et al. [Dana, R.-A., Le Van, C., Magnien, F., 1999. On the different notions of arbitrage and existence of equilibrium. Journal of Economic Theory 87 (1), 169-193], Allouch et al. [Allouch, N., Le Van, C., Page Jr., F.H., 2006. Arbitrage and equilibrium in unbounded exchange economies with satiation. Journal of Mathematical Economics 42 (6), 661-674], Allouch and Le Van [Allouch, N., Le Van, C., 2008. Erratum to "Walras and dividends equilibrium with possibly satiated consumers". Journal of Mathematical Economics 45 (3-4), 320-328]. We also show that, in terms of weakening the set of assumptions, we cannot go too far.

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Bibliographic Info

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

Volume (Year): 45 (2009)
Issue (Month): 7-8 (July)
Pages: 465-478

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Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:465-478

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

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Keywords: Competitive equilibrium Unbounded action sets Satiation Individually rational utility set No-arbitrage;

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References

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  1. 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.
  2. Nizar Allouch & Cuong Le Van, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00101189, HAL.
  3. 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.
  4. Le Van, C. & Page, F.H.Jr. & Wooders, M., 2001. "Arbitrage and Equilibrium in Economies with Externalities," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 588, University of Warwick, Department of Economics.
  5. Brown,Donald & Werner,Jan, 1991. "Arbitrage and existence of equilibrium in infinite asset markets," Discussion Paper Serie A, University of Bonn, Germany 344, University of Bonn, Germany.
  6. 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.
  7. 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.
  8. Nizar Allouch & Cuong Le Van & Frank H. Page, 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00096040, HAL.
  9. 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.
  10. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1169-74, July.
  11. 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.
  12. repec:hal:journl:halshs-00241543 is not listed on IDEAS
  13. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 37(2), pages 81-94, April.
  14. 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.
  15. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  16. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, Springer, vol. 4(2), pages 183-195, March.
  17. 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. repec:hal:journl:halshs-00241543 is not listed on IDEAS
  2. 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.
  3. Sato, Norihisa, 2010. "Satiation and existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 46(4), pages 534-551, July.
  4. repec:hal:journl:halshs-00598038 is not listed on IDEAS
  5. Nizar Allouch & Cuong Le Van, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Working Papers, Development and Policies Research Center (DEPOCEN), Vietnam 08, Development and Policies Research Center (DEPOCEN), Vietnam.
  6. Nizar Allouch & Monique Florenzano, 2011. "Satiated economies with unbounded consumption sets : fuzzy core and equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00598038, HAL.
  7. Allouch, Nizar & Florenzano, Monique, 2013. "Edgeworth rejective core and dividends equilibria of satiated exchange economies," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 49(1), pages 1-6.
  8. 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.
  9. 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.

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