THE IMPOSSIBILITY OF A PROGRESSIVE TAX STRUCTURE

When households are identical in all respects other than income, a non -decreasing average tax rate is both necessary and sufficient for post -tax incomes to be always at least as equal as pre-tax incomes. This p aper investigates whether this well known result can be extended to ho useholds with different needs. A tax structure which never increases i nequality (in the Lorenz sense) is shown to be unable to discriminate between household types. If, in addition, the tax structure never redu ces the relative income of the poorest member of the neediest group of households, then the same proportional tax must be applied to all hou seholds, and redistribution is impossible either within or between gro ups of households with differing needs. A similar conclusion is reache d using conventional equivalence scale arguments, and also applies whe n the parameters of the tax schedules are determined endogenously. We discuss the significance of this impossibility result and its implicat ions for tax design. (C) 1998 Elsevier Science S.A.