EXPONENTIAL AND ALGEBRAIC RELAXATION IN KINETIC MODELS FOR WEALTH DISTRIBUTION

Two classes of kinetic models for wealth distribution in simple market economies are compared in view of their speed of relaxation towards stationarity in a Wasserstein metric. We prove fast (exponential) convergence for a model with risky investments introduced by Cordier, Pareschi and Toscani,⁷ and slow (algebraic) convergence for the model with quenched saving propensities of Chakrabarti, Chatterjee and Manna.³ Numerical experiments confirm the analytic results.