  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.
