Microscopic models for welfare measures addressing a reduction of economic inequality

Abstract

We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential equations which involve parameters defined by probabilities. Society is described as an ensemble of individuals divided into income classes; the individuals exchange money through binary and ternary interactions, leaving the total wealth unchanged. The ternary interactions represent taxation and redistribution effects. Dynamics is investigated through computational simulations, the focus being on the effects that different fiscal policies and differently weighted welfare policies have on the long-run income distributions. The model provides a tool which may contribute to the identification of the most effective actions toward a reduction of economic inequality. We find for instance that, under certain hypotheses, the Gini index is more affected by a policy of reduction of the welfare and subsidies for the rich classes than by an increase of the upper tax rate. Such a policy also has the effect of slightly increasing the total tax revenue.

Uncertainty dynamics in a model of economic inequality

“…Besides, the urge to identify possible mechanisms for the formation of such collective phenomenon prompted the formulation of related models within an enlarged scientific community (see e.g. [4][5][6][7][8][9]). …”

“…For example, the model proposed in [8] (see also [10]) by two of the present authors is expressed by a system of nonlinear differential equations describing the evolution in time of the income distribution. Specific trading rules which characterize the behavior of individuals of different income classes together with the existence of a taxation and a welfare system are postulated.…”

“…[8] is that of uncertainty. In almost all walks of life, the presence of chance is unavoidable, at least to some extent.…”

“…[8]: in other words, the 'deterministic' component of the present model is simpler (and so was that of the models in [11] and [12]). We limit ourselves to consider the occurrence of a wealth of monetary exchanges between individuals and to this we now add the effect of additive and multiplicative stochastic terms.…”

“…We limit ourselves to consider the occurrence of a wealth of monetary exchanges between individuals and to this we now add the effect of additive and multiplicative stochastic terms. Another difference with the approach developed in [8,11,12] is the following. Whereas the variables in these papers describe the fractions of individuals belonging to different income classes, the variables here are the incomes of the classes.…”