Optimal tax theory: A synthesis

Necessary conditions for optimal taxation are derived (i) when taxes are constrained to be linear, (ii) when the form of taxation is unconstrained, (iii) when some commodities are subject to nonlinear taxation, the remainder to proportional taxation. Among the results obtained are several that help to determine upon which commodities the tax system ought to bear most heavily. In particular, a criterion for the effect of commodity taxes in the presence of an optimal income tax is found. The paper concludes with a general principle of simple form for optimal economic policies of all kinds.