企業活動の最適制御

財政・金融政策の有効性について

抄録

This paper is a study of social optimal control rules of enterprise behavior in the framework of optimal control theory. In the neoclassical theory, enterprise are treated as a mere taker of the price given by the market under the principle of profit maximization. But, in the real economic world, enterprises have power to determine prices and the volume of production. Futhermore enterprise behavior must be alalyzed in the feed back system with factor markets as endogeneous variables. And, we must recognize that the real economy is typically disequilibrium.
Based on these premises, it is more proper to formulate enterprise behavior as maximizing the following utility function
J (X, p) =pX-C (X) -μ (X-D (p) ) ²
p: price, X : the volume of production,
C: cost function, D: demand function,
μ: unit penalty
In the real economy, enterprises do not maximize their utility function in the sense of global optimality, and seem to approach the true optimal point through quadratic optimization. Thus, it may be formulated by Newton method.
[Xp]=[∇²J]^-1∇J
This system of equations has a locally stable solution. But, when endogeneous factor prices, wage and interest rate, are considered, the system does not always stable solution. If the system is unstable, the feed back control using fiscal and monetary policy would be required. But negative feed back system does not always produce stable conditions. It means that sometimes discretionary fiscal and monetary policy could make the economy more unstable and produce situations such as stagflation. The system must be controled by optimal control rule. In this paper, it is shown by Pontryagin's maximization principle in linear system.
But the real economy is typically nonLinear. When the government controls the economy using a linear economic model, adjustment must be made on the nonlinear factor. It may be made by adaptive control rule.
In this paper, Model Refference Adaptive Control System Theory, which is a feed back system (optimal control) ajusted by errors between realized values and estimations by linear model, is introduced. The control of system stability theory.
Then, general control rules of enterprise activity are shown.