Generic Determinacy of Equilibria with Local Substitution
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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- Chris Shannon & William R. Zame, 2002.
"Quadratic Concavity and Determinacy of Equilibrium,"
Econometric Society, vol. 70(2), pages 631-662, March.
- Chris Shannon and William R. Zame., 1999. "Quadratic Concavity and Determinacy of Equilibrium," Economics Working Papers E99-271, University of California at Berkeley.
- Shannon, Chris & Zame, William R., 1999. "Quadratic Concavity and Determinacy of Equilibrium," Department of Economics, Working Paper Series qt3fv586x6, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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- Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
- 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.
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- Aliprantis, Charalambos D., 1997. "On the Mas-Colell-Richard Equilibrium Theorem," Journal of Economic Theory, Elsevier, vol. 74(2), pages 414-424, June.
- 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.
- Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
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