Indeterminacy of Equilibrium in Dynamic Models with Externalities

Michele Boldrin and Aldo Rustichini

No 955R, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: In this paper we study the indeterminacy of equilibria in infinite horizon capital accumulation models with technological externalities. Our investigation encompasses both models with bounded and unbounded accumulation paths, and models with one and two sectors of production. Under reasonable assumptions we find that equilibria are locally unique in the one sector economies, at least as long as cycles are not present and trajectories are therefore monotone. On the other hand we show (by means of an example) that persistent oscillations are possible when the external effect is particularly strong and capital accumulation is bounded. In this case indeterminacy maybe present as we are unable to rule out the eexistence of a continuum of equilibria converging to the cycle. The situation is different in economies with two sectors of production. Here it is very easy to construct analytical examples where a positive external effect induces a two dimensional manifold of equilibria converging to the same steady state (in the bounded case) or to the same constant growth rate (in the unbounded case), For the latter we also point out that the dynamic behavior of these equilibria is quite complicated and that persistent fluctuations in their growth rates are possible.

Date: 1991-05
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