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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.

Suggested Citation

  • Frank Riedel, 2003. "Generic Determinacy of Equilibria with Local Substitution," GE, Growth, Math methods 0303001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:0303001
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    References listed on IDEAS

    as
    1. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    2. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
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    4. 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.
    5. Frank Riedel & Peter Bank, 2001. "Existence and structure of stochastic equilibria with intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 487-509.
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    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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