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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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
7990.
Length: Date of creation: 1977 Date of revision: Publication status: Published in Journal of Mathematical Analysis and Applications no. 2.61(1977): pp. 504-520 Handle: RePEc:pra:mprapa:7990
Find related papers by JEL classification: D9 - Microeconomics - - Intertemporal Choice and Growth C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
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