Abstract
A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the audited taxpayer fraction and of the penalties imposed to noncompliant individuals. A complex systems perspective is adopted: society is considered as a system composed by a large number of heterogeneous individuals. These are divided into income classes and may as well have different tax evasion behaviors. The variation in time of the number of individuals in each class is described by a system of nonlinear differential equations of the kinetic discretized Boltzmann type involving transition probabilities. A priori, one could think that audits and fines should have a positive effect on the reduction of economic inequality and correspondingly of the Gini index G. According to our model, however, such effect is rather small. In contrast, the effect on the increase of the tax revenue may be significant.