Efficiency in the Optimum Supply of Public Goods

Abstract

WHEN THE GOVERNMENT'S production of public goods is financed by distortionary taxes, the conventional optimality rule of equality between the sum of marginal rates of substitution and the marginal rate of transformation (Samuelson [13]) has to be modified so as to take account of the excess-burden created by the means of finance. The importance of this modification has already been recognized by Pigou [10], and has recently been treated formally by Atkinson and Stern [1]. These authors have examined the question of whether the optimum output levels of public goods financed by distortionary taxation are larger or smaller than their levels in the full optimum with lump-sum taxation. One expects intuitively that with distortionary taxation the conventional rule will overestimate the net benefits of public goods, but it has been shown that dependence of private consumption, and hence of tax revenue, on the supply of public goods, may reverse the intuitive conclusion. In general, varying the supply of a public good will vary the demand for private goods (or the supply of factors), thereby varying government revenues. There is thus a fundamental interdependence between decisions about the relative quantities supplied of various public goods and the structure of taxation used to finance these goods. As a consequence, in general the marginal rate of substitution between two public goods is not equal at the optimum to their marginal rate of transformation (the ratio of producer prices). In this paper we are concerned with the following question: in an economy