From microscopic taxation and redistribution models to macroscopic income distributions

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.

12 pages, 4 figures. Version submitted to Physica A on Feb 15, 2011

References in corpus (4)

• Kinetic Exchange Models for Income and Wealth Distributions
• A study of the personal income distribution in Australia
• The Gompertz-Pareto Income Distribution
• Gamma-distribution and wealth inequality

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• Microscopic models for the study of taxpayer audit effects
• Stochastic Evolving Differential Games Toward a Systems Theory of Behavioral Social Dynamics
• Stochastic Effects in a Discretized Kinetic Model of Economic Exchange
• Economic inequality and mobility for stochastic models with multiplicative noise
• A nonconservative kinetic framework for a closed-market society subject to shock events