Kinetic Equations modelling Wealth Redistribution: A comparison of Approaches
AbstractKinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply e.g. to the market model with risky investments [S. Cordier, L. Pareschi and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [B.K. Chakrabarti, A. Chatterjee and S.S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.
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Bibliographic InfoPaper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 08-03.
Length: 16 pages
Date of creation: 09 Jul 2008
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-08-06 (All new papers)
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- G. Toscani & C. Brugna & S. Demichelis, 2012. "Kinetic models for the trading of goods," Papers 1208.6305, arXiv.org.
- Bertotti, Maria Letizia & Modanese, Giovanni, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3782-3793.
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