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Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law

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  • Bruce M. Boghosian

Abstract

The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B.M. Boghosian, "Kinetics of Wealth and the Pareto Law," {\it Phys. Rev. E} {\bf 89} (2014) 042804], it was shown that this results in a Fokker-Planck equation governing the distribution of wealth. With the addition of a mechanism for wealth redistribution, it was further shown that this model results in stationary wealth distributions that are very similar in form to Pareto's well known law. In this paper, a much simpler derivation of that Fokker-Planck equation is presented.

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  • Bruce M. Boghosian, 2014. "Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law," Papers 1407.6851, arXiv.org.
    • Handle: RePEc:arx:papers:1407.6851
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    Cited by:

    1. Aktaev, Nurken E. & Bannova, K.A., 2022. "Mathematical modeling of probability distribution of money by means of potential formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    2. Chorro, Christophe, 2016. "A simple probabilistic approach of the Yard-Sale model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 35-40.
    3. Boghosian, Bruce M. & Devitt-Lee, Adrian & Johnson, Merek & Li, Jie & Marcq, Jeremy A. & Wang, Hongyan, 2017. "Oligarchy as a phase transition: The effect of wealth-attained advantage in a Fokker–Planck description of asset exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 15-37.
    4. Li, Jie & Boghosian, Bruce M. & Li, Chengli, 2019. "The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 423-442.
    5. Max Greenberg & H. Oliver Gao, 2024. "Twenty-five years of random asset exchange modeling," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-27, June.
    6. David W. Cohen & Bruce M. Boghosian, 2023. "Bounding the approach to oligarchy in a variant of the yard-sale model," Papers 2310.16098, arXiv.org, revised Apr 2024.
    7. Christoph Borgers & Claude Greengard, 2023. "A new probabilistic analysis of the yard-sale model," Papers 2308.01485, arXiv.org.
    8. Lima, Hugo & Vieira, Allan R. & Anteneodo, Celia, 2022. "Nonlinear redistribution of wealth from a stochastic approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    9. Sam L. Polk & Bruce M. Boghosian, 2020. "The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality," Papers 2006.15008, arXiv.org, revised Oct 2021.

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