Neid und Progressive Besteuerung

Abstract

There is an increasing theoretical interest in envy free equitable allocations. It seems natural to extend the literature by explicitly introducing income taxation as instrument towards elimination or reduction of envy. Such an inclusion of the income tax has not been addressed to in the recent theoretical papers on envy free allocations. We use the Foley-Varian concepts of envy as this is the most advanced theory on the topic. The use of this approach allows us in a straightforward manner to show the conditions for the achievement of envy free allocations, and to elaborate the differences between aggregate envy and social welfare. Summarizing, our main results, are as follows:

• (a) An equitable allocation can be reached by a progressive income tax if we disregard all disincentive effects of taxation on labour supply. This income tax, however, must equalize all net incomes (!). If, on the other hand, people reduce their labour supply because of taxation, it is impossible to find an income tax which guarantees equitable net income allocations for all possible distributions of individual abilities. For an a priori fixed distribution of abilities an equitable allocation can be achieved by income taxation, but only by a tax that includes all people to stop working.

• (b) Ordinal aggregate measures of envy are never changed by income taxation as long as the tax does not alter that ranking of individuals which underlies the individual envy. This implies a general failure of ordinal envy measures as it is typically one of the axioms of income taxation not to change individual rankings.

• (c) Minimizing cardinal aggregate measures of envy is conceptually different from maximizing cardinal social welfare functions although the results might coincide. Progressivity of a linear income tax can be shown to be a sufficient condition for envy minimization if the individual envy and its social acceptance follow particular patterns.