On the Sign of the Optimal Marginal Income Tax

A well-known result of Mirrlees (1971 ; proposition 3) says that the optimal marginal rate of income tax is non-negative throughout the scale, for the model he considers and given only a mild regularity condition on preferences. That is, the burden of taxation unambiguously increases with earnings. This result is very useful. The model to which it applies is admittedly special (identical leisure / consumption preferences), but it is reassuring to know that no further specialisation of assumptions is required to reach such a basic conclusion ; incentive effects from taxation will never turn the desired pattern of redistribution on its head, at any level of income. The above result, as we shall see, is indeed a property of income taxes rather than generally, but its proof in Mirrlees (1971) implicitly adopts a very special case, namely additive separability of preferences, which is only later in the same paper explicitly adopted and discussed. Our purpose here is to derive a rather more general set of conditions that ensure the required non-negativity, or in fact strict positivity, of marginal tax at all interior levels of income ; these essentially amount to non-inferiority of leisure, apart from the above-mentioned regularity condition on preferences used by Mirrlees, assumption A.1 as below. The central result of the paper is theorem 1 at the close of section 4, whose derivation is based on other results, some with separate interest, obtained earlier on in the paper.