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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: nonlinear; optimal; growth; growth models; many sector; utility; optimization; growth paths; admissible; Hilbert; intertemporal allocations; policy; welfare; social welfare; competitive; topology; Sobolev; feasible; matrix; consumption; Lemmas
• Subjects: D - Microeconomics > D9 - Intertemporal Choice; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

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