On a property of Lorenz curves with monotone elasticity and its application to the study of inequality by using tax data

The Lorenz curve is the most widely used graphical tool for describing and comparing inequality of income distributions. In this paper, we show that the elasticity of this curve is an indicator of the effect, in terms of inequality, of a truncation of the income distribution. As an application, we consider tax returns as equivalent to the truncation from below of a hypothetical income distribution. Then, we replace this hypothetical distribution by the income distribution obtained from a general household survey and use the dual Lorenz curve to anticipate this effect.