The conflict between equity and efficiency considerations in income taxation is a familiar problem, but no general rules that take both of these considerations into account have yet been established. On the basis of a concrete model, a variety of examples has been recently analyzed and calculated by Mirrlees [2]. In these examples, the optimal income tax schedule appears to be progressive with a negative tax at low incomes. The optimal marginal tax rate is approximately constant in the vicinity of 60 per cent. It is not known, however, how sensitive these results are with respect to various assumptions of the model. In Mirrlees' model, individuals are assumed to maximize identical utility functions that depend on consumption and labour. The return to labour is assumed to depend partly on an innate skill factor associated with each individual. Through individual decisions, the distribution of skill in the population generates distributions of labour, consumption, and utility. Income taxation is then introduced in order to improve income distribution and social welfare, defined as the sum of individual utilities.3 In this paper we use the above model to prove the following result: if the supply of labour in the economy is a non-decreasing function of the net wage rate then, among linear tax functions, the optimal tax schedule provides a positive lump-sum at zero income, and the optimal marginal tax rate is bounded above by a fraction that decreases with the minimum elasticity of the labour supply.4 It may be noted that this result does not depend on any assumption about the form of the individual utility functions or on the underlying distribution of ability in the population.