Optimal government stablization in a simple multiplier-accelerator economy

This paper formulates the problem of determining the optimal stabilization policy for a simple macroeconomic model as a state-regulator problem. In the general case where the government has a finite planning horizon and where investment is generated by a flexible accelerator the optimal government policy is shown to satisfy a first order linear differential equation with variable coefficients. With an infinite horizon these coefficients become constants and upon integrating the equation the optimal government expenditure is seen to be a mixture of a proportional and an integral policy. When the simplet instantaneous accelerator is assumed the policy becomes purely proportional. In the latter part of the paper this case is extended to the situtation where various parameters characterizing the economy are stochastic. Similar control laws are obtained, although in this case the intensity of control will depend upon the noise in the system.