The Problem of Optimum Income Taxation: A Remark on Its Monotonicity Constraint

We apply a generalized version of Brito and Oakland's (1977) approach to deal with monotonicity constraints in the nonlinear taxation problem of Mirrlees (1971) . This allows removing some analytical weaknesses in the derivation of the necessary conditions that characterize the optimal income tax, impossible to handle with the type of variation used for the proof in Mirrlees (1969) . The qualitative properties of the tax are thus restored provided the candidate consumption functions are restricted to be twice differentiable, except on countably many points, with no corners near the intervals where they show a strictly concave shape.