Exploiting the flexibility of a family of models for taxation and redistribution

TL;DR

This paper explores a family of nonlinear differential equation models for taxation and redistribution in closed market societies, analyzing how different parameters and behavioral heterogeneity influence income distribution over time.

Contribution

It introduces a flexible family of models for income distribution dynamics and demonstrates their ability to replicate fat tails using the k-generalized distribution.

Findings

Behavioral heterogeneity influences fat tail formation.

Different parameter choices affect long-term income distribution.

Models fit well with the k-generalized distribution.

Abstract

We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence to different parameter choices. We analyse the influence of the various choices on the long time shape of the income distribution. Several simulations suggest that behavioral heterogeneity among the individuals plays a definite role in the formation of fat tails of the asymptotic stationary distributions. This is in agreement with results found with different approaches and techniques. We also show that an excellent fit for the computational outputs of our models is provided by the k-generalized distribution introduced by G. Kaniadakis (Physica A 296 (2001) 405-425).