Ever since Corlett and Hague (1953), it has been understood that it tends to be optimal on
second-best grounds to (relatively) tax complements to leisure and subsidize substitutes because
doing so helps to offset the distorting effect of taxation on labor supply. Yet in the context of
simultaneous optimization of a nonlinear income tax and commodity taxes, Atkinson and Stiglitz
(1976) claim to have demonstrated the opposite, that goods complementary with leisure should “face lower tax rates, whereas substitutes face higher tax rates.” Derivations in leading texts on
optimal taxation seem to yield opposing conclusions regarding the sign of optimal deviation of
commodity taxes from uniformity. It is demonstrated that the optimality of relatively taxing
leisure complements is indeed correct, and conflicting results are explained.