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On the existence and sensitivity analysis of optimal catital accumulation paths in continuous time, infinite horizon models

Published online by Cambridge University Press:  17 February 2009

E. Flytzanis  and
Nikolaos S. Papageorgiou
E. Flytzanis
Affiliation:
Athens School of Economics –34, Greece.
Nikolaos S. Papageorgiou
Affiliation:
University of California, Department of Mathematics, Davis, California 95616, U.S.A.
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Abstract

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In this paper we consider an infinite horizon, continuous time model of economic growth. We prove two theorems; one on the existence of optimal paths of capital accumulation and the other on the dependence of the set of optimal paths on the initial capital stock (sensitivity analysis). In the existence result the underlying technology set is nonconvex and only its “investment’ slices are convex. The proof is direct, without any use of necessary conditions. In the sensitivity analysis, the technology set is convex and so we have that the value function is concave. Then having that, we show that the set of optimal paths is an upper semicaontinuous multifunction of the initial capital stock.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 4 , April 1989 , pp. 450 - 459
Copyright
Copyright © Australian Mathematical Society 1989

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