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The Kinetics of Wealth and the Origin of the Pareto Law


  • Bruce M. Boghosian


An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy changes due to interactions with other molecules. We pursue this analogy and derive a Boltzmann equation for the time evolution of the wealth distribution of a population of agents for the so-called Yard-Sale Model of wealth exchange. We examine the solutions to this equation by a combination of analytical and numerical methods, and investigate its long-time limit. We study an important limit of this equation for small transaction sizes, and derive a partial integrodifferential equation governing the evolution of the wealth distribution in a closed economy. We then describe how this model may be extended to include features such as inflation, production and taxation. In particular, we show that the model with taxation is capable of explaining the basic features of the Pareto law, namely a lower cutoff to the wealth density at small values of wealth, and approximate power-law behavior at large values of wealth.

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  • Bruce M. Boghosian, 2012. "The Kinetics of Wealth and the Origin of the Pareto Law," Papers 1212.6300,, revised Aug 2013.
  • Handle: RePEc:arx:papers:1212.6300

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    References listed on IDEAS

    1. Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "Asymptotics and Duality for the Davis and Norman Problem," Papers 1010.0627,, revised Aug 2011.
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    7. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    8. S. Sethi & H. M. Soner & Q. Zhang & H. Jiang, 1992. "Turnpike Sets and Their Analysis in Stochastic Production Planning Problems," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 932-950, November.
    9. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    10. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131,, revised Jun 2013.
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