我国鉄鋼業における企業行動の研究 : 投資函数の測定のために

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The ultimate purpose of this study is to get an investment function in the most autonomous form. So far, a great many trials have been made to measure the investment functions with the tool of regression analysis, in which gross investment is taken as a dependent variable, and many factors which are guessed at to influence the investment are taken as independent variables. The factors which determine investment, however, are so complicated that it might be safely said that the limit of these trials has been revealed. In this study, the mechanism to determine investment is treated as one part which belongs to the whole mechanism determining all predictive activities of a firm. On this ground, the gain function of firm's behavior is analyzed. The investment function is reduced as one of the gain maximizing solutions expressed by "exogenous" variables. The other solutions are the fund demand functions and so on. Therefore, it is the central problem. in this study to measure the gain function of firms. Then, I will outline the theoretical model and methods of estimations. A firm determines not only the value of investment but also of mary other "endogenous" variables, say, the amount of raised funds, the expenditure for current production and so on. Among these variables a certain identical relation exists, if we look at it from the view poirt of the relation between accommodation and expenditure of fund. We can get this relation from a balance sheet, a statement of profit and loss, and a table of net profit distribution. It becomes (1)[numerical formula] The ultimate purpose of this study is to get an investment function in the most autonomous form. So far, a great many trials have been made to measure the investment functions with the tool of regression analysis, in which gross investment is taken as a dependent variable, and many factors which are guessed at to influence the investment are taken as independent variables. The factors which determine investment, however, are so complicated that it might be safely said fchat the limit of these trials has been revealed. In this study, the mechanism to determine investment is treated as one part which belongs to the whole mechanism determining all predictive activities of a firm. On this ground, the gain function of firm's behavior is analyzed. The investment function is reduced as one of the gain maximizing solutions expressed by "exogenous" variables. The other solutions are the fund demand functions and so on. Therefore, it is the central problem. in this study to measure the gain function of firms. Then, I will outline the theoretical model and methods of estimations. A firm determines not only the value of investment but also of mary other "endogenous" variables, say, the amount of raised funds, the expenditure for current production and so on. Among these variables a certain identical relation exists, if we look at it from the view poirt of the relation between accommodation and expenditure of fund. We can get this relation from a balance sheet, a statement of profit and loss, and a table of net profit distribution. It becomes (1) C+I=yi+--+y≫ + yia, where C denotes the expenditure for current production (net of depreciation cost), I gross investment for capital equipment, y_1,・・・・・・, y_m increments (or decrements) of various debt balances from the previous period and t_<13> receipts from sales. Of course, many other variables considered not important are omitted in this identity. A firm will determine the values of its endogenous variables so as to maximize its gain Λ, being subject to the relation (1). Our hypothesis on the gain function is as follows, (2) [numerical formula] A firm will determine the values of its endogenous variables so as to maximize its gain Λ, being subject to the relation (1). Our hypothesis on the gain function is as follows, (2) A = n-￡l, where II stands for the present values of "gross" profit which is expected to be gained from (money) capital invested during one unit of time (the term "gross" is used here to show that this profit contains interest cost) and Ω represents the appraised money term value of psychological resistance which the firm may feel when employing that amount of capital during one unit of time. II can be divided into two kinds of gross profit, profit from the capital invested into the productive operation, II_1 and profit from the capital invested into the capital assets, II_2. If we show explicitly the endogenous variables which are considered to influence II_1, II_2 and Ω, (3) [numerical formula] where Y_1, ,Y_m are the debt balances of various types of funds (including capital stock) Therefore [numerical formula] Here μ and v denote the average time lengthes for whithdrawal of money expensed in the forms of C and I respectively. The μ and v have to be taken into consideration in this way because II was defined as the gross profit per unit time. The conditional equations for equilibrium in which Λ is maximized subject to (1) are (4) [numerical formula] If a firm behaves according to the gain maximization hypothesis defined above, (4) must hold at any periods. So if any one expression of these equations (4) is known in its value, it means that the values of the other expressions are known at the same time. In this sense, let us examine the value of[numerical formula] If we neglect general administrative expense, distribution cost and corporation tax,[numerical formula] becomes (5) where y^^～_<13> is sale-proceeds which the firm expects to obtain expending the current cost C, X the physical quantity of sales, P its price, q the physical quantity of inputs and s its price. The marginal productivity (dX)/(dq) can be calculated from "operating production function," which is the technological relation between output X and input q operating: the given equipment. In this paper we adopted two alternative methods in order to get the value s/P・(dq)/(dX). One way is to take the slope of the line connecting: two points, namely, the point (C_t, y^^～_<13,i,t> and the point (C_<t-1>,y^^～_<13,t-1>), in the space of (C,.y^^～_<13>) as the approximate value of s/P・(dq)/(dX). But in this case price change must be taken into account (the change of capital equipments was assumed to be negligible). This price modification was done by the following formula. (6) [numerical formula] The other method is to estimate the operating production functions directly. Generally speaking, they can not be estimated without data of the capital assets, the measurement of which is notoriously difficult. Fortunately the data of productive capacity are available in the iron and steel industry, and we assume that the productive capacity Q is this output level corresponding to the operating degree which produces the maximum value of q/X. We specified the operating production function by and using the above assumption about the productive capacity we could estimate the values of two parameters α and β at each period of each firm. (dq)/(dX) is given by αβ・sinβq. Then, using the values of [numerical formula] estimated by the atove procedures, we sought the factors affecting v/μ・(dI)/(dII_2) and μ・(θY_i)/(θΩ) (i==1, ・・・・・・, m) by the regression analysis. In other words, we tried to estimate the shape of the marginal gross profit schedule of investment-and of the marginal fund resistance schedules. They are the partial derivative functions of Λ. All of these estimations were carried out by time series analysis for each firm fin Japanese iron and steel industry. The results of these regression analyses can not be stated here because of limited space.
慶應義塾大学の論文
1960-12-25

著者

岩田暁一
慶應義塾大学商学部

我国鉄鋼業における企業行動の研究 : 投資函数の測定のために

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