The optimal two-bracket linear income tax

Abstract

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.

Optimal Piecewise Linear Income Taxation

“…An important result is that, contrary to the results presented by Slemrod et al . (), for currently relevant empirical wage distributions the optimal tax structures consistently show marginal rate progressivity, giving what we have called here the convex case.…”

“…There are two main papers in the theoretical literature on the continuum‐of‐types case, by Sheshinski () and Slemrod et al . (). We believe these papers leave the literature in a rather unfinished state, despite the fact that the paper by Slemrod et al .…”

“…Slemrod et al . () show that Sheshinski's proof does not hold in general because it ignores the existence of a discontinuity in the tax revenue function in the nonconvex case. They then carry out simulations which, using standard functional forms for the social welfare function, the individual utility function and the distribution of wage rates/productivities, in all cases produce the converse result—the upper‐bracket marginal tax rate is optimally always lower.…”

Optimal unemployment insurance and redistribution

“…We assume that is the virtual tax function for a worker with wage rate . In practice, a piecewise linear tax system, such as that analyzed by Slemrod, Yitzhaki, Mayshar, and Lundholm (), applies different marginal tax rates to different income ranges. Such tax structures are commonly used.…”

Taxation and Redistribution: Some Clarifications

“…Although there are assumptions under which marginal rates would tend to be rising for much of the upper-income range, in most analyses the optimal scheme features falling marginal rates at least at the very top end of the income distribution (although this need not necessarily be so except for the top individual). 25 In addition, Slemrod et al (1994), who compare an optimal flat tax (one that includes transfers) with an optimal two-bracket tax, find in their simulations that the second, higher-income bracket should have a somewhat lower marginal rate -and, indeed, this difference is greater the more weight one's social welfare function puts on equality.…”