Staff Report 118

Determinacy of Equilibria in Dynamic Models With Finitely Many Consumers

Timothy J. Kehoe | Consultant
David K. Levine | Visiting Scholar
Paul M. Romer

Published March 1, 1989

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 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, No. 1, February 1990, pp. 1-21)

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