Microscopic Models for Welfare Measures Addressing a Reduction of Economic Inequality

TL;DR

This paper introduces a flexible micro-to-macro kinetic model to analyze how different fiscal and welfare policies impact income distribution and economic inequality, providing insights into effective inequality reduction strategies.

Contribution

The paper develops a nonlinear differential equation-based model linking individual interactions to macroeconomic income profiles, incorporating taxation and redistribution effects.

Findings

Reducing welfare for the rich can lower the Gini index more effectively than increasing upper tax rates.

Certain policies can slightly increase total tax revenue while reducing inequality.

The model demonstrates the impact of fiscal policies on long-term income distributions.

Abstract

We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential equations which involve parameters defined by probabilities. Society is described as an ensemble of individuals divided into income classes; the individuals exchange money through binary and ternary interactions, leaving the total wealth unchanged. The ternary interactions represent taxation and redistribution effects. Dynamics is investigated through computational simulations, the focus being on the effects that different fiscal policies and differently weighted welfare policies have on the long-run income distributions. The model provides a tool which may contribute to the identification of the most effective actions towards a reduction of economic inequality. We find for instance that, under certain hypotheses, the Gini index is more affected by a policy of reduction of the welfare and subsidies for the rich classes than by an increase of the upper tax rate. Such a policy also has the effect of slightly increasing the total tax revenue.