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

Abstract

AbstractIn 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.