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On a kinetic model for a simple market economy

Author

Listed:
  • 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 = University of Pavia)

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.

Suggested Citation

  • Stéphane Cordier & Lorenzo Pareschi & Giuseppe Toscani, 2004. "On a kinetic model for a simple market economy," Working Papers hal-00003648, HAL.
    • Handle: RePEc:hal:wpaper:hal-00003648
    Note: View the original document on HAL open archive server: https://hal.science/hal-00003648
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