From microscopic taxation and redistribution models to macroscopic income distributions

TL;DR

This paper introduces a flexible nonlinear differential equation framework for modeling income distribution dynamics in closed societies, capturing the emergence of empirical features like Pareto tails and realistic inequality measures.

Contribution

It develops a general model that links individual interactions to collective income distribution patterns, explaining the emergence of observed empirical features.

Findings

Asymptotic distributions exhibit Pareto-like power law tails.

Lorenz curves and Gini indices match real-world income inequality data.

The model can generate various income distribution scenarios based on parameter choices.

Abstract

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution of the income distribution over the population and to explain the emergence of collective features based on the knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.