Recursive utility and optimal capital accumulation. I. Existence

Abstract

This paper demonstrates existence of optimal capital accumulation paths when the planner's preferences are represented by a recursive objective functional. Time preference is flexible. We employ a general multiple capital good reduced-form model. Existence of optimal paths is addressed via the classical Weierstrass theorem. The topology is uniform convergence of capital stocks on compact subsets, which is equivalent to weak convergence of investment flows under our maintained hypotheses. An improved version of a lemma due to Varaiya proves compactness of the feasible set. A monotonicity argument is combined with a powerful theorem of Cesari to demonstrate upper semicontinuity. © 1989.