ON THE RELATIONSHIP BETWEEN DISCOUNTING AND COMPLICATED BEHAVIOR IN DYNAMIC OPTIMIZATION MODELS

This paper explores the relationship between discounting and complicat ed behavior in dynamic optimization models. An inverse relationship be tween the discount factor of a dynamic optimization model and the topo logical entropy of the corresponding optimal policy function is establ ished. For an aggregative model, this generalizes a result obtained by Montrucchio and Sorger. The generalization makes it possible to apply directly the results developed by Block, Guckenheimer, Misiurewicz an d Young on the computation of the topological entropy of dynamical sys tems to obtain upper bounds on the discount factor necessary for the o ccurrence of topological chaos in aggregative dynamic optimization mod els. (C) 1998 Elsevier Science B.V.