A STOCHASTIC ECONOMIC GROWTH MODEL TAKING INTO ACCOUNT SOCIAL NEED

Abstract

The optimal behaviour of a stochastic macroeconomic growth model is examined. The model has two state variables: k, capital per unit of labour and z, desired consumption per unit of labour. The stochastic element is the average efficiency of capital, e, whose values over time are supposed to be the realizations of a stochastic process {et}N having a transition probability density p(et| ut-1) depending on the values of the control variable u - the rate of investment. The macroeconomic optimality criterion is considered to be the minimization of the expected deviation, over the planning horizon, of the actual consumption from the desired consumption. The paper gives sufficient conditions for the optimal control to be a monotonous bang-bang control; this behaviour is similar to that obtained for the deterministic case. The crucial assumption for monotonicity is that the growth rate of the desired consumption should not exceed the expected growth rate of capital. Comparison of monotonous and non-monotonous trajectories shows that monotonicity is important, since monotonous trajectories are “better” as concerns the average consumption, the average growth rate of consumption and the final value of capital.