Kinetic models of conservative economies with wealth redistribution

Abstract

We introduce and discuss kinetic models for wealth distribution in a simple market economy, which are able to reproduce the salient features of the wealth distribution by including taxes to each trading process and redistributing the collected money among the population according to a given criterion. Our analysis gives a theoretical basis to some recent research that analyzed discrete simplified models for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. It is shown that in general the redistribution is able to modify the Pareto index, and that this modification can be quantified in terms of the redistribution operator.

Kinetic models for optimal control of wealth inequalities

“…The CPT model with taxation and redistribution has been proposed in [6]. There, taxation was acting on interactions (21) to take away a percentage δ of the trade wealth, to give…”

Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

“…Opinion formation is an important ground of application of mathematics to the modeling of social sciences, hence several valuable papers have been devoted to this topic, for example [12,50,70,89,90,131] have developed interesting models based on kinetic theory methods. These methods have also been applied to modeling financial markets [61,62].…”

Wealth distribution in presence of debts: A Fokker–Planck description

“…It was obtained by one of the present authors with Cordier and Pareschi [16] via an asymptotic procedure applied to a Boltzmann-type kinetic model for binary trading in presence of risks. Also, the same equation with a modified drift term appears when considering suitable asymptotics of Boltzmann-type equations for binary trading in presence of taxation [7], in the case in which taxation is described by the redistribution operator introduced in [8]. Systems of Fokker-Planck equations of type (1.2) have been considered in [20] to model wealth distribution in different countries which are coupled by mixed trading.…”