Modelling taxation and redistribution: A discrete active particle kinetic approach

Exchange Models for the Emergence of Income Distribution and Economic Inequality

“…Issues like redistribution through means-tested welfare policies, the impact of tax evasion on the income distribution and the effects of taxpayer audits have been treated in [12][13][14][15][16]. In all these cases simulations show that after a sufficiently long time the solution (x 1 (t), ..., x n (t)) of the equations reaches an equilibrium state which depends on the total income and on the interaction parameters, but not on the initial distribution.…”

“…In the traditional literature, ODEs are typically associated with macroscopic phenomena, and accordingly, models are often described by only one or a few equations. In contrast, the model we are proposing, first developed in [12] and then variously extended and exploited e.g. in [13][14][15][16] to deal with different specific questions, is formulated by means of systems of several differential equations.…”

“…In particular, these expressions contain parameters which can be variously tuned and represent encounter frequencies, saving propensities, average incomes, tax rates, and also tax evasion rates. In any case, the C hk j and T hk j [ ] are constructed in such a way that the vector (x 1 (t), ..., x n (t)) (suitably normalized) is a discretized probability density function at time t. We point out that in the cases studied in [12][13][14][15][16], as also here, the total wealth is assumed to remain constant in time. Growth or variation of the wealth, however, can be considered as well and are in fact the object of ongoing investigation.…”

“…The binary interactions provide a stylized representation of the payments producing income (the payment of an employer to a worker, of a patient to a physician, of a client to a lawyer and so on); the ternary interactions represent the effects of taxation and redistribution, processes which do not involve only the pair of directly interacting individuals (see [12] for the description of the mechanism). The differential equations which express the model are as many as the classes, distinguished by their average income.…”

“…In the basic version, it takes the form [12][13][14][15][16], also depending on the different questions therein tackled. In particular, these expressions contain parameters which can be variously tuned and represent encounter frequencies, saving propensities, average incomes, tax rates, and also tax evasion rates.…”