A Pigovian Rule for the Optimum Provision of Public Goods
NBER Working Paper No. 1681
The integrated treatant of optimal taxation and public expenditure presented here is based on the dual relationship between the prices of private goods and the quantities of public goods. In this paper we derive analogues of Roy's identity and the Slutsky equation for the case of public goods. The optimal provision of public goods and the level of taxation are shown to be dual problems.The conditions for optimum public good provision can be expressed as a ndification of the Samuelson conditions with extra terms representing (a) the distortionary effect of taxes on the willingness to pay for the public good, and (b) distributional effects.The former captures Pigou's notion of the indirect daniage caused by the need to finance public expenditure out of distortionary taxes, and we call this the "Pigou term". In certain cases a very simple benefit-cost ratio for public projects emerges that is equivalent to measuring benefits as if they were taxed.
Published: Journal of Public Economics, vol. 30, no.3, pp 273-291. 1986.