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On a Kinetic Model for a Simple Market Economy

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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.

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Authors and Affiliations

  1. Department of Mathematics and Applications, Mathematical Physics (MAPMO)UMR 6628, University of Orléans and CNRS, 45067, Orléans, France

    Stephane Cordier

  2. Department of Mathematics, University of Ferrara, Via Machiavelli 35, I-44100, Ferrara, Italy

    Lorenzo Pareschi

  3. /o Department of Economy, Center for Modelling Computing and Statistics, Institutions and Territory, University of Ferrara, Via del Gregorio 13, I-44100, Ferrara, Italy

    Lorenzo Pareschi

  4. Department of Mathematics, University of Pavia, via Ferrata 1, 27100, Pavia, Italy

    Giuseppe Toscani

Authors
  1. Stephane Cordier
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  2. Lorenzo Pareschi
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  3. Giuseppe Toscani
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Correspondence to Stephane Cordier.

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Cordier, S., Pareschi, L. & Toscani, G. On a Kinetic Model for a Simple Market Economy. J Stat Phys 120, 253–277 (2005). https://doi.org/10.1007/s10955-005-5456-0

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  • DOI: https://doi.org/10.1007/s10955-005-5456-0

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