Distortionary Taxes and the Provision of Public Goods

Abstract

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). He measured the marginal benefits of a pure public good by the sum of the marginal rates of substitution between the public good and a reference private good (ΣMRS). In effect, the amount of the reference private good that people would be willing to give up in exchange for the public good provides a yardstick for measuring the satisfaction provided by the public good. Samuelson then measured the marginal cost of the project by the marginal rate of transformation (MRT) between the public good and the reference private good. An optimal level of expenditure is where ΣMRS = MRT. For the cost-benefit analysis of a particular public project, this condition implies that the sum of the marginal benefits to all consumers should be compared to the marginal cost of the project.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). The MCF is defined, in terms of the reference private good, as the cost to consumers per unit of revenue. Since the MRT is the revenue cost per unit of public good, multiplication yields the cost to

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