The Marginal Cost of Public Funds is One

This paper develops a Mirrlees (1971) framework with heterogeneous agents to analyze optimal redistributive taxes, optimal provision of public goods and the marginal cost of public funds (MCF). Standard MCF measures are shown to suffer from three defects: i) The MCF for the (non-individualized) lump-sum tax is generally not equal to one. ii) The MCF for distortionary taxes is not directly related to the marginal excess burden. iii) MCF measures for both lump-sum and distortionary taxes are highly sensitive to the choice of the untaxed numéraire good. These problems are caused by using the private rather than the social marginal value of private income to calculate the MCF, and disappear by using the social marginal value of private income. Moreover, by allowing for redistributional concerns, the marginal excess burden of distortionary taxes equals the marginal distributional gain at the optimal tax system. MCF therefore equals one, both for lump-sum and distortionary taxes, and the modified Samuelson rule should not be corrected for the marginal cost of public funds.