Micro to macro models for income distribution in the absence and in the presence of tax evasion

Abstract

We investigate the effect of tax evasion on the income distribution and the inequality index of a society through a kinetic model described by a set of nonlinear ordinary differential equations. The model allows to compute the global outcome of binary and multiple microscopic interactions between individuals. When evasion occurs, both individuals involved in a binary interaction take advantage of it, while the rest of the society is deprived of a part of the planned redistribution. In general, the effect of evasion on the income distribution is to decrease the population of the middle classes and increase that of the poor and rich classes. We study the dependence of the Gini index on several parameters (mainly taxation rates and evasion rates), also in the case when the evasion rate increases proportionally to a taxation rate which is perceived by citizens as unfair. Finally, we evaluate the relative probability of class advancement of individuals due to direct interactions and welfare provisions, and some typical temporal rates of convergence of the income distribution to its equilibrium state.

21 pages, 9 figures. Submitted to Appl. Math. Comput

Cited by in corpus (7)

• Economic inequality and mobility in kinetic models for social sciences
• Microscopic Models for Welfare Measures Addressing a Reduction of Economic Inequality
• Common Origin of Power-law Tails in Income Distributions and Relativistic Gases
• A nonconservative kinetic model under the action of an external force field for modeling the medical treatment of autoimmune response
• Microscopic models for the study of taxpayer audit effects
• Stochastic Effects in a Discretized Kinetic Model of Economic Exchange
• Economic inequality and mobility for stochastic models with multiplicative noise