The Zenga Equality curve: a new approach to measuring tax redistribution and progressivity

We adopt and extend the new Zenga inequality curve to study the degree of progressivity as well as the redistributive and re-ranking effects of a personal income tax system. Moreover, we also establish the social welfare implications of these new inequality measures and compare them with the classical approach based on the Lorenz curve and the Gini coefficient. The Zenga methodology is based on comparing the mean income of the poorest income earners with the mean income of the remaining richest part of the population. To the best of our knowledge, this approach has never been applied to study the effects produced by a personal income tax. To fill this gap in the literature, we prove that the elasticity of the Zenga uniformity curve with respect to the Lorenz curve is always greater than 1, thus recasting—within the new paradigm—the most important curves and the corresponding tax indices, such as the Reynolds–Smolensky, the Kakwani, and the Atkinson–Plotnick–Kakwani indices. We then derive three important inequalities for the newly developed measures, inspired by the well-known properties of the classical approach. Finally, we show how some information, which could remain unnoticed by the cumulative approach inherent to the Lorenz curve, is instead highlighted by the new methodology. The advantages of complementing the classic indices with the new ones are discussed through an application to the Italian tax system.