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The Kinetics of Wealth and the Origin of the Pareto Law

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  • Bruce M. Boghosian
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    Abstract

    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 production, inflation, and taxation.

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    File URL: http://arxiv.org/pdf/1212.6300
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    Paper provided by arXiv.org in its series Papers with number 1212.6300.

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    Date of creation: Dec 2012
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    Handle: RePEc:arx:papers:1212.6300

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    Web page: http://arxiv.org/

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