Issue
EPL
Volume 88, Number 1, October 2009
Article Number 10007
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/88/10007
Published online 23 October 2009
EPL, 88 (2009) 10007
DOI: 10.1209/0295-5075/88/10007

Wealth redistribution in conservative linear kinetic models

G. Toscani

Dipartimento di Matematica, Università degli studi di Pavia - 27100 Pavia, Italy, EU

giuseppe.toscani@unipv.it

received 28 July 2009; accepted in final form 25 September 2009; published October 2009
published online 23 October 2009

Abstract
We introduce and discuss kinetic models for wealth distribution which include both taxation and uniform redistribution. The evolution of the continuous density of wealth obeys a linear Boltzmann equation where the background density represents the action of an external subject on the taxation mechanism. The case in which the mean wealth is conserved is analyzed in full details, by recovering the analytical form of the steady states. These states are probability distributions of convergent random series of a special structure, called perpetuities. Among others, Gibbs distribution appears as steady state in case of total taxation and uniform redistribution.

PACS
05.20.Dd - Kinetic theory.
89.65.Gh - Economics; econophysics, financial markets, business and management.
02.50.-r - Probability theory, stochastic processes, and statistics.

© EPLA 2009