Acyclicity and Stability for Intertemporal Optimization Models

Abstract

This paper provides a turnpike-like theorem for multidimensional, optimal-growth models, which holds for evey level of the discount factor. It is shown that when the short-run return fu nction of the reduced-form model satisfies a certain sufficient condi tion, then the resulting dynamics is of a simple type, i.e., it must converge to some steady state. The result is obtained in two steps: f irst it is shown that dynamical systems satisfying an acyclic binary relation must be simple; second, the value function for the optimal p roblem is used to define a binary relation on the space of feasible s tates. The necessary and sufficient conditions under which the latter binary relation is acyclic are provided, and their relation to the t echnology and preferences is outlined. Copyright 1988 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.