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Nonlinear functional analysis and optimal economic growth

  • Chichilnisky, Graciela

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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File URL: http://mpra.ub.uni-muenchen.de/7990/1/MPRA_paper_7990.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7990.

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Date of creation: 1977
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Publication status: Published in Journal of Mathematical Analysis and Applications no. 2.61(1977): pp. 504-520
Handle: RePEc:pra:mprapa:7990
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