Modelling Inequality with a Single Parameter

Abstract

We argue that the Lorenz curve for income is well-modelled by members of the one-parameter family of functions:

$$ \left\{ {y = \left( {1 - \left( {1 - r} \right)^k } \right)^{\frac{1}{k}} } \right\} $$

. We justify this statement with data from the Luxembourg Income Study. The family of curves arises from a dynamic model of income growth, in which the parameter k has a direct economic interpretation.