Kinetic equations modelling wealth redistribution: a comparison of approaches

Kinetic 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 [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.