The Relationship between the Marginal Cost of Public Funds and Marginal Excess Burden

Abstract

A large literature has recently developed which attempts to measure the marginal cost (shadow price) of public funds.' The motivation for much of this literature is the recognition that many of the tax instruments used by governments generate substantial amounts of excess burden (deadweight loss). Jerry A. Hausman (1981), for example, estimates that for an average prime-aged American male with a wage of ten dollars in 1975 the excess burden generated by the federal income tax was over fifty percent of the revenue raised from taxing that individual. One might suspect that such large excess burden estimates would require a change in the way government project costs are calculated in benefit-cost analysis. If the revenue required to finance a project is raised through distortionary taxation, then intuition would suggest that the excess burden generated by the increase in tax rates needed to finance the project should be incorporated into the cost of the project. However, this analysis is not entirely consistent with the theoretical literature on the optimal provision of public goods which are financed by distortionary taxation. When distortionary taxes are used to finance public goods, and the level of public good provision does not affect consumption of the taxed goods, the standard Samuelsonian rule which equates the sum (over consumers) of the marginal rates of substitution between a private good and a public good with the marginal rate of transformation between the two goods must be modified to account for the marginal effect of increases in tax rates on the revenue raised from the existing taxes.2 The intuition behind this result is that we need to correct for indirect leakages from existing government revenue sources when considering an incremental expenditure. If the increase in tax rates needed to finance the project causes a reduction in the revenue raised by the current tax structure, then we need to account for this loss in calculating the cost of the project. It is important to note that this result concerns the values of uncompensated demand elasticities. An example first provided by Atkinson and Stern (1974) illustrates this point. Consider a world where the only tax is on labor earnings, and incremental expenditure on the public good does not affect the demand for leisure. In this case, the marginal rate of transformation will overstate the cost of the public good as long as the uncompensated wage elasticity of labor supply is negative. This is because an increase in the tax rate causes an increase in labor supply, leading to an indirect increase in government revenue. From the excess burden perspective described earlier, this example is very puzzling. It is well known that even if the uncompensated own price elasticity of a good is zero, a tax on that good can still result in a large deadweight loss. We instead need the compensated elasticity to be zero to ensure that there will be no excess burden. However, the *Department of Economics, University of California, Davis, CA 95616. This paper is based on chapter two of my dissertation at the University of Wisconsin-Madison. I wish to thank the members of my dissertation committee, Martin David, Robert Haveman (chair), and Arthur Goldberger, for very helpful advice and comments. I have also benefited from comments by Don Fullerton and Bruce Hamilton. An anonymous referee provided unusually helpful comments and corrected an error in the figure. 1Don Fullerton (1989) provides a recent survey and analysis of this literature. 2This is shown by Anthony Atkinson and Nicholas H. Stern (1974) and David E. Wildasin (1979). The effect of provision of the public good on consumption of the taxed goods must also generally be taken into account.

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