p The pure theory of public expenditure was first expounded in a consistent form in the 1950s in three articles by 112 Professor Samuelson.  [112•1  In the subsequent period the pure theory of public expenditure gained wide renown in Western economic and financial literature; it is part and parcel of courses on the theory of public finance.  [112•2 

p The “pure theory of public expenditure" fully preserves the category of governmental services but emphasises the specific forms of the consumption of these services. For this a special theoretical construction is introduced, the concept of the “public good”. The main feature, distinguishing a public good from a private one, is that consumption of a public good by a member of society does not entail any harm for other persons, the scale of their consumption remaining unchanged.

p It is not difficult to see that when a good possesses such properties all usual principles of commercial activity simply lose their meaning. Let us, for example, turn to the usual technique of the microeconomic theory, a comparison of the marginal rates of substitution in the production of goods. In elementary models of perfect competition it is assumed that in the production of a given assortment of goods an equilibrium and simultaneously an optimal use of resources is achieved at that point where the marginal rate of substitution of any pair of resources in the production of any pair of goods is equal.  [112•3  But as soon as a public good is included, the conditions of equilibrium essentially change: 113 the marginal rates of substitution of private resources in the production of private goods, as before, must be equal to the marginal rates of substitution of private resources in the production of public goods. But substitution between the public and private resources is regulated by entirely different interrelations. Let us assume, however, that these conditions are met. Then a more general question arises, namely, the criteria for the choice between public and private goods, and, together with this, the distribution of private goods among members of society. It can be demonstrated that there is a set of solutions which satisfy the criterion of optimality usually employed in microeconomic models (the Pareto criterion).  [113•1  To choose from this abundance of alternative decisions the best one, it is necessary to introduce into the model a macroeconomic choice function or, following the terminology accepted in Western economic literature, the “social welfare function”. The entire presentation of this problem in essence differs little from the presentation of other problems in the welfare theory—the ensuring of maximum utility of public goods with a simultaneous minimising of the burden of tax payments.

p The usual market operations in this system are inadequate even for achieving the Pareto optimum. As soon as public goods are introduced into the model the former mechanism of marginal analysis and equalisation of marginal rates of substitution is undermined.

In ordinary models supply of an additional good presupposes some cost of its production. In a model which includes a public good everything is different: as long as such a good is already produced the increase in the number of its consumers is not linked theoretically with any additional expenditures and so the marginal costs, and consequently, the prices may be equal to zero. Therefore, even some of those authors who energetically defend the principles of private enterprise and the “sovereignty” of individual needs, note that the efficient management requires other, non-market, methods of satisfying the individual needs 114 in goods possessing the properties of a public good. This, in turn, may give rise to the necessity of government financial activity.

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 [112•1]   Paul A. Samuelson, “The Pure Theory of Public Expenditure”, Review of Economics and Statistics, Vol. XXXVI, No. 4, November 1954, pp. 387–89; Paul A. Samuelson, “Diagrammatic Exposition of a Theory of Public Expenditure”, Review of Economics and Statistics, Vol. XXXVII, No. 4, November 1955, pp. 350–56; Paul A. Samuelson, “Aspects of Public Expenditure Theories”, Review of Economics and Statistics, Vol. XL, No. 4, November 1958, pp. 332–38; and also Paul A. Samuelson, “Pure Theory of Public Expenditure and Taxation”, Public Economics. An Analysis of Public Production and Consumption and Their Relations to the Private Sectors. Proceedings of a Conference Held by the International Economic Association, London, 1969, pp. 98–123.

 [112•2]   See, for example, Richard A. Musgrave, The Theory of Public Finance. A Study in Public Economy, pp. 61–89.

 [112•3]   For a description of such models and conditions for the achievement of an equilibrium see Samuel Karlin, Mathematical Methods and Theory in Games, Programming and Economics, Addison-Wesley Publishing Co., Inc., Palo Alto, Mass., London, 1959.

 [113•1]   A detailed exposition of these problems in a formalised way can be found in Paul Samuelson’s latest work mentioned above which was issued in 1969.