Are Two Tax Rates Better than One?

Should two-band income taxes be progressive given a general income distribution? Weprovide a negative answer under utilitarian and max-min welfare functions. While this resultclarifies some ambiguities in the literature, it does not rule out progressive taxes in general. Ifwe maximize total or weighted utility of the poor, as often intended by the society,progressive taxes can be justified, especially when the ‘rich’ are very rich. Under theseobjectives we obtain necessary conditions for progressive taxes, which only depend onaggregate features of income distributions. The validity of these conditions is examined usingplausible income distributions....