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The Existence of Ramsey Equilibrium

Robert A. Becker
John H. Boyd III
Ciprian Foias

Abstract

We demonstrate existence of a perfect foresight equilibrium under borrowing constraints in a one-sector model with infinitely-lived heterogeneous agents. The class of admissible preferences includes, but is not limited to, recursive preferences. Existence is proven using a tatonnement argument under appropriate conditions on preferences and technology. A new measure of discounting, the norm of marginal impatience, is used to determine which technologies are admissible. Depending on the norm of marginal impatience, the admissible technology may either allow for permanent growth, or have a maximum sustainable stock.