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Kinetic and Related Models (KRM)
 

Analysis of a model for wealth redistribution

Pages: 1 - 27, Volume 1, Issue 1, March 2008      doi:10.3934/krm.2008.1.1

 
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Daniel Matthes - Department of Mathematics at the University of Pavia, via Ferrata 1, 27100 Pavia, Italy (email)
Giuseppe Toscani - Department of Mathematics at the University of Pavia, via Ferrata 1, 27100 Pavia, Italy (email)

Abstract: A recent application of the kinetic theory for many particle systems is the description of the redistribution of wealth among trading agents in a simple market economy. This paper provides an analytical investigation of the particular model with quenched saving propensities, which has been introduced by Chakrabarti, Chatterjee and Manna [11]. We prove uniqueness and dynamical stability of the stationary solution to the underlying Boltzmann equation, and provide estimates on the rate of equilibration. As one main result, we obtain that realistic steady wealth distributions with Pareto tail are only algebraically stable in this framework.

Keywords:  Econophysics, Boltzmann equation, Pareto distribution.
Mathematics Subject Classification:  Primary: 35B40, 91B60; Secondary: 82C40.

Received: November 2007;      Revised: November 2007;      Available Online: February 2008.