An exact discount factor restriction for period-three cycles in dynamic optimization models

Abstract

This paper explores the precise extent of discounting needed to generate period-three cycles in a standard aggregative dynamic optimization framework. It is shown that there is a "universal constant", M ≡ [(√5 - 1)/2]2≈0.3819, such that (i) if an optimal program of any dynamic optimization model exhibits a period-three cycle, then the discount factor is less than M; and (ii) if the discount factor is smaller than M, then it is possible to construct a transition possibility set and a utility function such that the resulting dynamic optimization model exhibits a period-three cycle. Journal of Economic Literature Classification Numbers: C61, E32, O41. © 1996 Academic Press, Inc.