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Distributions Of Money In Model Markets Of Economy

Author

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  • ANIRBAN CHAKRABORTI

    (Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700 064, India)

Abstract

We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing with locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-period, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.

Suggested Citation

  • Anirban Chakraborti, 2002. "Distributions Of Money In Model Markets Of Economy," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(10), pages 1315-1321.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:10:n:s0129183102003905
    DOI: 10.1142/S0129183102003905
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    Citations

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    Cited by:

    1. Arnab Chatterjee & Bikas K Chakrabarti, 2005. "Ideal-Gas Like Markets: Effect of Savings," Papers physics/0507136, arXiv.org, revised Jul 2005.
    2. Chorro, Christophe, 2016. "A simple probabilistic approach of the Yard-Sale model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 35-40.
    3. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    4. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-31.
    5. Takeshi Kato & Yoshinori Hiroi, 2021. "Wealth disparities and economic flow: Assessment using an asset exchange model with the surplus stock of the wealthy," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-16, November.
    6. Takeshi Kato, 2022. "Wealth Redistribution and Mutual Aid: Comparison using Equivalent/Nonequivalent Exchange Models of Econophysics," Papers 2301.00091, arXiv.org.
    7. Christoph Borgers & Claude Greengard, 2023. "A new probabilistic analysis of the yard-sale model," Papers 2308.01485, arXiv.org.
    8. 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.
    9. Bagatella-Flores, N. & Rodríguez-Achach, M. & Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2015. "Wealth distribution of simple exchange models coupled with extremal dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 168-175.
    10. Neñer, Julian & Laguna, María Fabiana, 2021. "Optimal risk in wealth exchange models: Agent dynamics from a microscopic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    11. 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.
    12. N. Bagatella-Flores & M. Rodriguez-Achach & H. F. Coronel-Brizio & A. R. Hernandez-Montoya, 2014. "Wealth distribution of simple exchange models coupled with extremal dynamics," Papers 1407.7153, arXiv.org.
    13. Bouleau, Nicolas & Chorro, Christophe, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 379-395.
    14. Takeshi Kato, 2022. "Islamic and capitalist economies: Comparison using econophysics models of wealth exchange and redistribution," Papers 2206.05443, arXiv.org, revised Sep 2022.
    15. Adams Vallejos & Ignacio Ormazabal & Felix A. Borotto & Hernan F. Astudillo, 2018. "A new $\kappa$-deformed parametric model for the size distribution of wealth," Papers 1805.06929, arXiv.org.
    16. Patriarca, Marco & Chakraborti, Anirban & Germano, Guido, 2006. "Influence of saving propensity on the power-law tail of the wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 723-736.
    17. KOBAYASHI, Kenta & 小林, 健太 & TAKAOKA, Koichiro & 高岡, 浩一郎, 2016. "Some Asymptotic Results for the Yard-Sale Model of Asset Exchange," Working Paper Series G-1-17, Hitotsubashi University Center for Financial Research.
    18. Düring, Bertram & Matthes, Daniel & Toscani, Giuseppe, 2008. "A Boltzmann-type approach to the formation of wealth distribution curves," CoFE Discussion Papers 08/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    19. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01138383, HAL.
    20. Vallejos, Adams & Ormazábal, Ignacio & Borotto, Félix A. & Astudillo, Hernán F., 2019. "A new κ-deformed parametric model for the size distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 819-829.
    21. 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.
    22. Takeshi Kato & Yasuyuki Kudo & Hiroyuki Mizuno & Yoshinori Hiroi, 2020. "Regional Inequality Simulations Based on Asset Exchange Models with Exchange Range and Local Support Bias," Papers 2002.09272, arXiv.org, revised Jul 2020.
    23. Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Post-Print hal-01138383, HAL.
    24. Li, Jie & Boghosian, Bruce M., 2018. "Duality in an asset exchange model for wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 154-165.

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