On a kinetic model for a simple market economy

Stéphane Cordier (), Lorenzo Pareschi () and Giuseppe Toscani ()
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Stéphane Cordier: MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique
Lorenzo Pareschi: Center for Modelling Computing and Statistics, c/o Department of Economy, Institutions and Territory - UniFE - Università degli Studi di Ferrara = University of Ferrara
Giuseppe Toscani: UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia] - UNIPV - Università degli Studi di Pavia [Italia] = University of Pavia [Italy] = Université de Pavie [Italie]

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Abstract: In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.

Keywords: Econophysics; Boltzmann equation; wealth and income distributions; Fokker Planck model; Monte Carlo simulations; Pareto distribution (search for similar items in EconPapers)
Date: 2004-12-21
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