In an earlier paper, we examined the nature of individual and collective preferences over alternative income tax schedules in the context of a simple model in which individuals respond to high tax rates by working in an untaxed "sheltered" sector of the economy. There we established the social optimality of a linear income tax among the set of tax schedules that are continuous, nondecreasing convex functions of income. Here we relax the restrictions on tax schedules, most importantly allowing schedules to have concave (decreasing marginal tax rate) as well as convex (increasing marginal tax rate) regions. In fact, we prove that a linear income tax is socially preferred to any nonlinear lower semi-continuous tax schedule
