On the application of Discrete Time Optimal Control Concepts to Economic Problems

Abstract

An extension of the use of the maximum principle to solve Discrete-time Optimal Control Problems (DTOCP), in which the state equations are in the form of general equations, rather than difference equations has been examined. Comparing the previous maximum principle to the proposed, revealed that the only difference, lies in the law of motion of the co- state variables and in particular, by applying the Bellman’s optimality principle and backward recursion, showed that the previous maximum principle is a subclass of our maximum principle. An economic problem was considered using the Timber Supply Model (TSM) 2000 to exemplify the use of the maximum principle in solving DTOCP problems. Furthermore derivations of necessary conditions which will be used to identify the optimal time paths for the variables were derived.

Keywords: maximum principle, dynamic optimization, economic models