Distortionary Taxes and the Provision of Public Goods

Economists have long been concerned with finding an efficient level of public expenditure. The classic statement of the problem was given by Paul Samuelson (1954). An optimal level of expenditure is where the sum of the marginal rates of substitution between the public good and a reference good equals the marginal rate of transformation between the public good and the reference good (?MRS = MRT). However, Samuelson's formula assumes that all of the revenue needed to finance public goods can be raised with lump-sum taxes. Since this is not generally possible, the formula must be modified to account for the distortionary effects of the tax system. An appropriate modification is to multiply the cost side of the equation by a term that is commonly called the marginal cost of public funds (MCF). In the case of Samuelson's formula, where government is entirely financed with lump-sum taxes, the MCF would be exactly 1.0. In the traditional view of economists, distortionary taxes cause the MCF to be greater than one, thus raising the cost of providing public goods. In this paper, we discuss some cases where the MCF may be less than one. We will illustrate this possibility using numerical examples for labor taxes.