Recursive utility and the Ramsey problem

Abstract

This paper examines existence, continuity, and characterization of optimal paths under “recursive” preferences. Current utility is a fixed (aggregator) function of current consumption and future utility. For suitable aggregators, a useful refinement of the Contraction Mapping Theorem generates the utility function, as in Lucas and Stokey ( J. Econ. Theory 32 (1984), 139–171). A broader class of aggregators is handled via a limiting argument analogous to partial summation. The Weierstrass theorem yields the existence of optimal paths. Under somewhat more stringent conditions on the aggregator and technology, optimal paths are continuous in initial capital stocks, and are characterized by generalized Euler equations and a transversality condition.