This paper addresses questions of the following nature: under what conditions does a welfare-improving reform of the existing piecewise linear income tax schedule necessitate a change in a particular agent type's marginal tax rate? Our analysis therefore addresses the sorts of questions typically debated by policy-makers, using a model of income taxation that resembles income tax systems used in practice. A locally optimal tax schedule is a special case of our tax reform analysis---the current piecewise linear income tax schedule is locally optimal if there does not exist an equilibrium-preserving and welfare-improving reform. We show that local optima involve progressive taxation, in that marginal tax rates are increasing in income. An extension of the model to include linear commodity taxation is also considered. In this case, local optima comprise positive commodity taxation and progressive income taxation.
