| Issue |
EPL
Volume 88, Number 1, October 2009
|
|
|---|---|---|
| Article Number | 10007 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/88/10007 | |
| Published online | 23 October 2009 | |
Wealth redistribution in conservative linear kinetic models
Dipartimento di Matematica, Università degli studi di Pavia - 27100 Pavia, Italy, EU
Corresponding author: giuseppe.toscani@unipv.it
Received:
28
July
2009
Accepted:
25
September
2009
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
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