The optimal two-bracket linear income tax

We investigate two-bracket piecewise linear income tax structures. In a two-class economy, Pareto-efficient tax schedules of this type feature at least one marginal tax rate equal to zero, and that the marginal tax rate may be increasing and declining. We then investigate the optimal structure of taxation when the social welfare function, utility function and distribution of abilities are characterized as in the standard optimal linear income tax problem. In all cases the second marginal tax rate is less than the first rate but progressivity, in the sense of a uniformly rising average tax rate, generally obtains.