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An analogy of the size distribution of business firms with Bose–Einstein statistics

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  • Hernández-Pérez, R.
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    Abstract

    We approach the size distribution of business firms by proposing an analogy of the firms’ ranking with a boson gas, identifying the annual revenue of the firms with energy. We found that Bose–Einstein statistics fits very well to the empirical cumulative distribution function for the firms’ ranking for different countries. The fitted values for the temperature-like parameter are compared between countries and with an index of economic development, and we found that our results support the hypothesis that the temperature of the economy can be associated with the level of economic development of a country. Moreover, for most of the countries the value obtained for the fugacity-like parameter is close to 1, suggesting that the analogy could correspond to a photon gas in which the number of particles is not conserved; this is indeed the case for real-world firms’ dynamics, where new firms arrive in the economy and other firms disappear, either by merging with others or through bankruptcy.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110004541
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 389 (2010)
    Issue (Month): 18 ()
    Pages: 3837-3843

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    Handle: RePEc:eee:phsmap:v:389:y:2010:i:18:p:3837-3843

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Firms’ size distribution; Bose–Einstein statistics;

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    1. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    2. Okuyama, K & Takayasu, M & Takayasu, H, 1999. "Zipf's law in income distribution of companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 125-131.
    3. Cirillo, Pasquale, 2010. "An analysis of the size distribution of Italian firms by age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 459-466.
    4. F. Clementi & T. Di Matteo & M. Gallegati & G. Kaniadakis, 2007. "The k-generalized distribution: A new descriptive model for the size distribution of incomes," Papers 0710.3645, arXiv.org, revised Jan 2008.
    5. Hernández-Pérez, R. & Angulo-Brown, F. & Tun, Dionisio, 2006. "Company size distribution for developing countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 607-618.
    6. Ramsden, J.J. & Kiss-Haypál, Gy., 2000. "Company size distribution in different countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 220-227.
    7. D'Hulst, R. & Rodgers, G.J., 2001. "Business size distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 328-333.
    8. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    9. Gaffeo, Edoardo & Gallegati, Mauro & Palestrini, Antonio, 2003. "On the size distribution of firms: additional evidence from the G7 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 117-123.
    10. Zhang, Jianhua & Chen, Qinghua & Wang, Yougui, 2009. "Zipf distribution in top Chinese firms and an economic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2020-2024.
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