A note on Inequality-Preserving Distributional Changes

This note considers the problem of distributing a fixed amount of money (‘income’) among a given number of people, such that inequality (measured by either the Gini or Atkinson measure) takes a specified value. It is well known that simultaneous equations admit of many solutions where the number of variables exceeds that of equations (constraints). However, the approach examines cases where there are just one or two degrees of freedom, clarifying the resulting range of distributions. The properties of simultaneous disequalising and equalising transfers are discussed.