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We investigate the effect of tax evasion on the income distribution and theinequality index of a society through a kinetic model described by a set ofnonlinear ordinary differential equations. The model allows to compute theglobal outcome of binary and multiple microscopic interactions betweenindividuals. When evasion occurs, both individuals involved in a binaryinteraction take advantage of it, while the rest of the society is deprived ofa part of the planned redistribution. In general, the effect of evasion on theincome distribution is to decrease the population of the middle classes andincrease that of the poor and rich classes. We study the dependence of the Giniindex on several parameters (mainly taxation rates and evasion rates), also inthe case when the evasion rate increases proportionally to a taxation ratewhich is perceived by citizens as unfair. Finally, we evaluate the relativeprobability of class advancement of individuals due to direct interactions andwelfare provisions, and some typical temporal rates of convergence of theincome distribution to its equilibrium state.

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