Note on the shape of the optimum income tax schedule

We consider the class of two-bracket, piecewise linear tax schedules [Sheshinski (1971, 1972)] and provide sufficient conditions for the optimum income tax schedule to have positive marginal rates and to be strictly convex. Calculations yield optimum tax rates between 20 and 35 percent and moderate rate progression. The Max-min optimum has higher tax rates, but not necessarily more rate progression, than the utilitarian optimum. The conditions are quite general, postulating nondecreasing income effects as the level of income increases.