Perverse Income Redistribution

We propose to develop a framework that will yield conditions under which a rank-preserving marginal transfer from a richer individual to a poorer individual exacerbates income inequality. We will seek to show that this happens when individuals` preferences depend negatively not only on work time (costly effort) but also on relative deprivation. We plan to show rigorously that the set of preference profiles that gives rise to this perverse effect of a transfer on inequality (when inequality is measured by the Gini coefficient) is a non-empty open subset of all preference profiles. An example illustrates our research idea.

We consider a stylized production economy (an artisan economy), in which two individuals produce a single consumption good. The utility of each individual depends negatively on his work effort and on his distaste for low relative income, and positively on his consumption. By way of a constructive example we show that in such a constellation, a marginal rank-preserving transfer from a richer individual to a poorer individual can lead simultaneously to exacerbated inequality as measured by the Gini index and to a decrease of Sens (1973) measure of social welfare. We subsequently generalize the example, showing that the results of the example hold for a non-empty, open neighborhood in the space of utility functions.