We demonstrate that a rank-preserving transfer from a richer individual to a poorer individual can exacerbate income inequality (when inequality is measured by the Gini coefficient). This happens when individuals' preferences depend negatively not only on work time (effort) but also on low relative income. It is rigorously shown that the set of preference profiles that gives rise to this perverse effect of a transfer on inequality is a non-empty open subset of all preference profiles. A robust example illustrates this result.
a rank-preserving inequality-narrowing transfer the Gini coefficient low relative income relative deprivation exacerbated inequality