Nonlinear Functional Analysis and Optimal Economic Growth

Abstract

A problem of existence and characterization of solutions of optimal growth models in many sector economies is studied. The social utility to he optimized is a generalized form of a preference depending additively on consumption at the different dates of the planning period. The optimization is restricted to a set of admissible growth paths defined by production-investment-consumption relations described by n system of differential equations. Sufficient conditions are given for existence of a solution in a Hilbert space of paths, without convexity assumptions on either the utilities or the technology, using techniques of nonlinear functional analysis. A characterization is given of the utilities which are continuous with respect to the Hilbert space norm. Under convexity assumptions A characterization is also given of optimal and efficient solutions by competitive prices. .