Nonlinear Functional Analysis and Optimal Economic Growth

17 Pages Posted: 24 Mar 2009

Date Written: November 15, 1977

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. .

Suggested Citation

Chichilnisky, Graciela, Nonlinear Functional Analysis and Optimal Economic Growth (November 15, 1977). Available at SSRN: https://ssrn.com/abstract=1366875 or http://dx.doi.org/10.2139/ssrn.1366875

Graciela Chichilnisky (Contact Author)

Columbia University ( email )

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