Munich Personal RePEc Archive

Nonlinear functional analysis and optimal economic growth

Chichilnisky, Graciela (1977): Nonlinear functional analysis and optimal economic growth. Published in: Journal of Mathematical Analysis and Applications , Vol. 61, No. no. 2 (15. November 1977): pp. 504-520.

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Abstract

A problem of existence and characterization of solutions of optimal growth models in many sector economies is studied The social utility to be optimized is a generalized form of a preference depending additively on consumption at the different dates of the planning period. The optimization b rattrirted to a set of admissible growth paths defined by production-investment-consumption relations described by a 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 of the technology, using techniques of nonlinear functional analysis. A characterization is given of the utilities which re continuous with respect to the Hilbert space norm. Under convexity assumptions a characteristic is also given of optimal and efficient solutions by competitive prices.

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