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.

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The relation between budgets and political factors is one of the interesting target of the analysis for the public choice studies. But growing interests now can not show clearly the evidence between them. While, inapplicability of public choice theory to Japanese own conditions would makes the analysis more difficult, it is therefore needed to make clear, because the relation in fact do function in our society, we are sure.
In this paper, we try to make clear the relation as one case between the budget size of the expenditure item “efficient land use for agriculture” and “the number of the representatives of ruling party” in every 47 prefectures.
The results of analysis show the positive relation for our presumption between them, but they are not enough to support our further assumptions.
The explanation variables here are from principal factors analysis which make equally adjusted independent components concerning about five data categories, labour, land, capital, physical environment and social environment. Furthermore, we take the power index category into independent variables. This variable playes as the political factor shows the positive relation in the process of the step-wise multi-regression.
This analysis will be expanded to the other budgets categories and other power indexes.

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[in Japanese]

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In public choice there have been many positive analyses which attempt to elucidate the supply mechanism of public goods. In many cases, central and basic model is the application of median voter model which originated from Bowen-Black's seminal work. However recently this simple demand-side model has shown its defects. These developments have paralleled with the supply-side analyses since Niskanen's incentive work.
The aims of this paper are to attempt to connect clearly supply-side factors with demand-side analysis of public goods and to examine their effects on demand mechanism, e, g, overor underexpansion of budget size. The work of this paper is divided into two parts. In the first half (chapter 2), we reexamine several studies which made an analysis of the supply amount of public good, e, g, from the viewpoint of Pareto efficiency of resource allocation, and clarify the problems involved and the limits of demand-side model. In the second half (chapter 3), we begin to criticize that usual studies have not accurately distinguished supply amount of public goods (G) from budget level (E) and for that reason we introduce, so to speak, public good supply function, i, e. G=f (E) by which we would represent the structure of supply side. We analyze what effects are had on demand mechanism and grope for the possibility of a model joining demand side with supply side.
In conclusion, first we may find that the inclusion of public good supply function could improve the former studies using median voter model. Second, it could be indicated that individual misperception of supply process of public goods, e, g, about the parameters representing public good supply function, brings about the bias against individual demand behavior, and eventually the decision of budget level. This should be also regarded as an interpretation for arguments about fiscal illusion. Therefore, it is suggested that individual information about supply-side mechanism as well as behavioral analysis of them, i, e, the analysis of productive efficiency of public sector, are very important in connection with efficiency of budget size.

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