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Inconsequential Arbitrage

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  • Page, F.H.Jr.
  • Wooders, M.H.
  • Monteiro, P.K.

Abstract

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, we prove that inconsequential arbitrage is sufficient for existence of equilibrium. With a slightly stronger condition of local nonsatiation than required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that the existence of a pareto-optimal allocation implies inconsequential arbitrage, implying that inconsequential arbitrage is necessary and sufficient for existence of an equilibrium.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp561.pdf
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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 561.

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Length: 36 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:wrk:warwec:561

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Keywords: ARBITRAGE ; ALLOCATIONS ; EQUILIBRIUM;

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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. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922 Elsevier.
  3. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 31(1), pages 170-175, October.
  4. Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 101-14, January.
  5. Chichilnisky, G., 1996. "A Topological Invariant for Competitive Markets," Discussion Papers 1996_16, Columbia University, Department of Economics.
  6. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
  7. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
  8. 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.
  9. Frank H. Page Jr. & (**), Myrna H. Wooders & Paulo K. Monteiro, 1999. "Arbitrage and global cones: Another counterexample," Social Choice and Welfare, Springer, vol. 16(2), pages 337-346.
  10. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  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, vol. 52(2), pages 153-162, August.
  12. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  13. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
  14. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  15. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-23, November.
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