Hydrodynamics from kinetic models of conservative economies

Abstract

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The collision operator used here is the Fokker–Planck operator introduced by J.P. Bouchaud and M. Mezard [Wealth condensation in a simple model of economy, Physica A 282 (2000) 536–545], which has been recently obtained in a suitable asymptotic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [S. Cordier, L. Pareschi, G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys. 120 (2005) 253–277]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.