ON THE OPTIMALITY OF LIMIT-CYCLES IN DYNAMIC ECONOMIC-SYSTEMS

The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium. © 1991 Springer-Verlag.