This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Economic Analysis of Environmental Problems Volume Author/Editor: Edwin S. Mills, ed. Volume Publisher: NBER Volume ISBN: 0-87014-267-4 Volume URL: http://www.nber.org/books/mill75-1 Publication Date: 1975 Chapter Title: Optimum Investment in Social Overhead Capital Chapter Author: Hirofumi Uzawa Chapter URL: http://www.nber.org/chapters/c2831 Chapter pages in book: (p. 9 - 26) Optimum Investment in Social Overhead Capital Hiro/umi Uzawa, University of Tokyo Introduction In most industrialized countries, the "environment" has come to play a significant role in recent years both in the process of resource allocation and in the determination of real income distribution. This is primarily due to the fact that, in these countries, the environment has become scarce relative to those resources which may be piivately appropriated and ef- ficiently allocated through the market mechanism. There is no inherent mechanism in a decentralized market economy whereby the scarcity of so- cial resources may be effectively restored. In decentralized economies, most research has been concerned with regulating the use of the environment; few researchers have analyzed the effects the accumulation of the environ- nient may have upon the pattern of resource allocation and income dis- tribution in general. In order to analyze the role played by the environment in the processes of resource allocation and income distribution, it may be convenient to introduce a broader concept of 'social overhead capital," of which the environment may be regarded as an important component. Social over- head capital is defined as those resources which are not privately ap- 1)ropriated, either for technological reasons or for social and institutional reasons, and which may be used by the members of the society [ice of charge or with nominal charges. Social overhead capital may be collec- tively produced by the society, as in the case of social capital such as roads, bridges, sewage systems, and ports, or it may be simply endowed in the society as in the case of natural capital such as air, water, etc. Thus all scarce resources may be classified into two categories; private means of production and social overhead capital. In a decentralized mar- 9 10 HIROFUMIUZAWA o ket economy, private means of production are allocated through the mar- sod ket mechanism, resulting in an efficient allocation of given amounts of a scarce resources, but the management of social overhead capital has to be delegated to a certain social institution. sis Such social institutions in charge of social overhead capital are con- cerned with two functions. First, they have to devise regulatory measures in order to see to it that the given stock of social overhead capital may be efficiently allocated among the members of the society and effectively sen utilized by each member. Second, they are concerned with the construc- tion of social overhead capital by using private anti social means of pro. {6] cluction in such a way that the resulting pattern of resource allocation and income distribution is optimum from the social point of view. In in this paper, I should first like to discuss the criteria by which social institu- tions in charge of social overhead capital allocate scarce resources in order to attain a dynamic pattern of resource allocation which is optimum from the social point of view. Next I should like to analyze the problem of what sort of criteria one has to impose upon the behavior of social institutions which are in charge of the management and construction of such social overhead capital. It will in particular be shown that, if the effect of social overhead capital is neutral in the sense precisely defined below, then the of dynamically optimum pattern of accumulation of social overhead capital th may result when the use of the services from such a social overhead capital ov is priced according to its marginal social cost and an interest subsidy is given to the extent to which the market (real) rate of interest differs from ovf the social rate of discount. a T m Social Overhead Capital ki p Before I proceed with the main discussion, I should like to present a le general framework in which some of the more crucial aspects of social w overhead capital may be detailed. The services provided by social over- head capital are usually analyzed in terms of Samuelsonian pul)lic goo(Is, as introduced in Samuelson's now classical papers [2, 3]. However, most thi of the familiar examples of social overhead capital such as highways, air, etc., do not satisfy the definition of public goods. There are two as- pects of the services provided by social overhead capital with which I am particularly concerned. The first aspect is related to the choice made by each member of the society of the level at which he uses the services; the U Samuelsonian concept of pure public goods excludes such a possibility. p For most services provided by social overhead capital, the members of the o OPTIMUM INVESTMENT IN SOCIAL OVERHEAD CAPITAL 11 society have, within a significant range, freedom in determining the of amounts of the services they use. be The second aspect which has been neglected in the Samuelsonian analy. • sisis related to the phenomenon of congestion. For most over- head capital, the capacity of overhead capital is generally limited and the effectiveness of a Certain amount of the services to be derived from be thegiven stock of overhead capital is affected by the amounts of the same services other members of the society are using. The concept of social overhead which has been introduced in Uzawa [6] may take care of these two aspects which are characteristic of most services provided by the government as public goods. The basic approach Iii in Uzawa [6] may be briefly outlined as follows. u. All the means of production are classified into two categories; private er means of production and social overhead capital. Private means of pro- in duction, simply referred to as private capital, may be privately appro- at priated and each member of the society may dispose of private capital us which he possesses in such a way that his utility or profit is maximized. On al the other hand, social overhead capital, simply referred to as social cap- al ital or overhead capital, may not be privately appropriated and the use of the services derived from overhead capital may be regulated either by al the government or by a social institution to which the management of a! overhead capital is delegated. is In the following discussion, it is assumed that both private capital and m overhead capital are respectively composed of homogeneous quantities, and that the output produced by various production units is identical. The main propositions obtained in this paper may be extended, without much difficulty, to the general situation where there may exist several kinds of overhead capital as well as private capital. Is is also assumed that private capital is a variable factor of production in the sense that it costs a less to shift its usage from one line to another. Again, the analysis may, al with slight modifications, be extended to the general situation where some private capital goods are fixed factors of production, involving significant adjustment costs either in the process of accumulation or in the shift in st their allocation. r, The effects of social overhead capital upon the productive process are formulated in terms of the short-run production function which sum- marizes production processes of each producing unit. Namely, the output producedby a typical production unitis assumed to depend upon the amount of the services of social overhead capital as well as that of Y. private capital. Let and be respectively the amount of the services Le of private and social capital used by producing unit f3, and let X and V 12 HIROFUMI UZAWA fl be respectively the total amount of the services of social capital being (Usi utilized and the stock of social capital existing at each moment of time. If and stand for the typical consuming unit and producing unit, respectively, then x (I) The production function for producing unitmay be written as: spel = X, V). (2) The dependence of the production function upon X and V indicates that the phenomenon of congestion occurs with respect to the use of the serv- ices of social overhead capital. The effect of congestion may be brought out by the assumptions: it1 0. (3) The Samuelsonian case of pure public goods may be regarded as the limit- LeC ing case where the production function F$ is independent of XB and X. The standard ploperties concerning the piocluction function are as- sumed for the present case. In particular, it will be asstirnecl that the marginal rates of substitution between various factors are diminishing and that the production processes are subject to constant returns to scale. Namely, the production function given by (2) is concave with respect to X, and V, and it is linear homogeneous with respect to all of its if variables. Furthermore, it is assumed that private capital and social capital are complementary in the sense that the increase in the use of the services of social capital shifts the schedule of the marginal product of private capital upward; namely, > 0. (4) he Social overhead capital may be defined neutral, when the negative el[ect pl due to the increase in the aggregate level of the use of the services of over- head capital is precisely counterbalanced by the corresponding increase be in the stock of social overhead capital.