On a Kinetic Model for a Simple Market Economy

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.

[1]  Victor M. Yakovenko,et al.  Statistical mechanics of money , 2000 .

[2]  B. Mandelbrot.  THE PARETO-LEVY LAW AND THE DISTRIBUTION OF INCOME* , 1960 .

[3]  Sorin Solomon,et al.  STOCHASTIC LOTKA-VOLTERRA SYSTEMS OF COMPETING AUTO-CATALYTIC AGENTS LEAD GENERICALLY TO TRUNCATED PARETO POWER WEALTH DISTRIBUTION, TRUNCATED LEVY DISTRIBUTION OF MARKET RETURNS, CLUSTERED VOLATILITY, BOOMS AND CRACHES * , 1998, cond-mat/9803367.

[4]  Bikas K. Chakrabarti,et al.  Statistical mechanics of money: how saving propensity affects its distribution , 2000, cond-mat/0004256.

[5]  Giuseppe Toscani,et al.  One-dimensional kinetic models of granular flows , 2000 .

[6]  V. Plerou,et al.  A theory of power-law distributions in financial market fluctuations , 2003, Nature.

[7]  Anirban Chakraborti,et al.  DISTRIBUTIONS OF MONEY IN MODEL MARKETS OF ECONOMY , 2002 .

[8]  S. Redner,et al.  Wealth distributions in asset exchange models , 1998, 1006.4595.

[9]  Ricardo Brito,et al.  High-energy tails for inelastic Maxwell models , 2002 .

[10]  Andrea Puglisi,et al.  KINETICS MODELS OF INELASTIC GASES , 2002 .

[11]  Sean McNamara,et al.  Kinetics of a one‐dimensional granular medium in the quasielastic limit , 1993 .

[12]  Irene M. Gamba,et al.  On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions , 2000 .

[13]  Axel Klar,et al.  A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model , 1996 .

[14]  M. H. Ernst,et al.  Extension of Haff's cooling law in granular flows , 1998 .

[15]  M. Mézard,et al.  Wealth condensation in a simple model of economy , 2000, cond-mat/0002374.

[16]  R. Illner,et al.  The mathematical theory of dilute gases , 1994 .

[17]  F. Slanina.  Inelastically scattering particles and wealth distribution in an open economy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Sorin Solomon,et al.  Theoretical analysis and simulations of the generalized Lotka-Volterra model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. H. Ernst,et al.  Scaling Solutions of Inelastic Boltzmann Equations with Over-Populated High Energy Tails , 2002 .

[20]  H. Eugene Stanley,et al.  Econophysics: Two-phase behaviour of financial markets , 2003, Nature.

[21]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .