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Generic Determinacy of Equilibria with Local Substitution

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  • Frank Riedel

    (University of California, Berkeley)

Abstract

Consumption of a good at one point in time is a substitute for consumption of the same good an instant earlier or later. Utility functions which conform to this fact must necessarily be non-time separable, as Hindy, Huang, and Kreps show. When agents' utility functions are non-time separable in the required way, the price space consists of semimartingales with an absolutely continuous compensator. In general, this space is not closed under taking pointwise maxima, that is, it is not a lattice. Therefore, neither the Mas-Colell/Richard existence theorem nor the determinacy theorem by Shannon/Zame apply. In a paper with Peter Bank, existence is established for such intertemporal economies; here, I show that generically, the number of equilibria is finite and that equilibrium allocations depend continuously on endowments. The notion of genericity is (finite) prevalence as developed by Anderson/Zame.

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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0303001.

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Length: 15 pages
Date of creation: 19 Mar 2003
Date of revision:
Handle: RePEc:wpa:wuwpge:0303001

Note: 15 pages, Acrobat .pdf
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  1. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
  2. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
  3. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
  4. Frank Riedel & Peter Bank, 2001. "Existence and structure of stochastic equilibria with intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 487-509.
  5. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
  6. Aliprantis, Charalambos D., 1997. "On the Mas-Colell-Richard Equilibrium Theorem," Journal of Economic Theory, Elsevier, vol. 74(2), pages 414-424, June.
  7. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
  8. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  9. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-97, November.
  10. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
  11. Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
  12. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  13. G. Constantinides, 1990. "Habit formation: a resolution of the equity premium puzzle," Levine's Working Paper Archive 1397, David K. Levine.
  14. Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
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