Optimal growth and recursive utility: Phase diagram analysis

The dynamics of the one-sector optimal growth model with recursive utility is analyzed through the use of a phase diagram. The steady state uniquely exists and is a saddle point. An increase in recursivity lowers both the steady-state capital and steady-state consumption. The model differs from the constant discount rate model in that a reduction in the population growth rate or a Hicks-neutral technical progress increases the steady-state consumption but not necessarily the steady-state capital.This research was supported in part by Indiana University through an Outstanding Young Faculty Award for which the author is grateful.The author is particularly indebted to Robert Becker and John Boyd for a careful reading of and detailed comments on an earlier draft, and to Frank Raymond and an anonymous referee for suggesting various expositional improvements. He is also indebted to Roy Gardner, Nori Hashimoto, and Nicolas Spulber for their suggestions.