On the sign of the optimum marginal income tax

This paper studies a central aspect of optimal income taxation as modelled in Mirrlees' original paper on the topic (identical leisure/consumption preferences, qualitatively homogeneous "skills" in production), namely, whether given concave utilitarianism alone the optimal marginal income tax will be non-negative. A well-known positive answer to this question (in weak inequality form) was given in the said paper which, however, we show requires additive separability of individual utility (in the ordinal and cardinal senses). Our main result here is to derive the required (strict) positivity of the marginal tax under weak conditions, slightly wider than noninferiority of consumption and leisure, with preferences otherwise arbitrary.