On the shape of optimal tax schedule

Take consumers to be described by a parameter h (skill, needs, etc.) with utilities defined on N commodities, including factor supplies. Our main result is that if in the optimum each component of this consumption vector is bounded and bounded away from zero over the population, each marginal tax must be zero at both ends of the corresponding tax schedule. For the income tax case, it is also shown that if the marginal tax rate at the top of the scale is positive, one can construct another tax schedule which is strongly Pareto superior (dominating the first one at all or most income levels), requirements of information being low.