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Determinacy of Equilibria in Dynamic Models with Finitely Many Consumers

Working Paper 400 | Published October 1, 1988

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Authors

David K. Levine Visiting Scholar
Timothy J. Kehoe Consultant, University of Minnesota, and National Bureau of Economic Research
Determinacy of Equilibria in Dynamic Models with Finitely Many Consumers

Abstract

We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite dimensional fixed point problem stated in terms of prices and commodities into a finite dimensional Negishi problem involving individual weights in a social value function. By adding a set of artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time zero factor endowments and derivatives of the social value function.




Published in: _Journal of Economic Theory_ (Vol. 50, Iss. 1, February 1990, pp. 1-21), https://doi.org/10.1016/0022-0531(90)90082-U. An updated version was published as: [Staff Report 118](https://doi.org/10.21034/sr.118)