Optimal Control of a National Economic System With Full Employment

Abstract

In this paper, we consider an optimal control problem of a national economic system with full employment in which the “Marginal Propensity to Save” and the “Profit Margin” are treated as control variables. This problem is modelled and modified on the basis of the cyclical growth theory developed by Keynes, Phillips, Bergstrom [2], The well-known Pontryagin Maximum Principle and the transversality condition [6] are then applied to obtain the optimum saving policy and profit margin following the steps of Ahmed and Yeo [1]. For illustration, a numerical example is solved using Davidon, Fletcher, Powell method with Fibonacci search technique in the last section.