Determinacy of Competitive Equilibria in Economies with Many Commodities

Posted: 25 Sep 1999

See all articles by Chris Shannon

Chris Shannon

University of California, Berkeley - Department of Economics

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Abstract

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. This paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. This paper also defines two notions of concavity, called uniform concavity and weighted uniform concavity, which generalize standard finite-dimensional notions of differential concavity to an infinite-dimensional setting by prohibiting goods from becoming perfect substitutes asymptotically. For the case of economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, results in this paper show that equilibria are generically determinate as long as utility functions and production sets are uniformly concave or weighted uniformly concave.

JEL Classification: D51, C62, D90

Suggested Citation

Shannon, Chris, Determinacy of Competitive Equilibria in Economies with Many Commodities. Economic Theory, Vol. 14, Iss. 1, July 1999. Available at SSRN: https://ssrn.com/abstract=176550

Chris Shannon (Contact Author)

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

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