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 agentsâ€™ 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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