Communications in Mathematical Sciences

Volume 7 (2009)

Number 4

Kinetic models of conservative economies with wealth redistribution

Pages: 901 – 916



Marzia Bisi

Giampiero Spiga

Giuseppe Toscani


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.


Wealth and income distributions; kinetic models; Boltzmann equation; taxation and redistribution

2010 Mathematics Subject Classification

35B40, 82C40, 91B60

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