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Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics

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  • Anindya S. Chakrabarti
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    Abstract

    We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. Our ultimate goal is to reproduce the well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide some exact results on the distributions. Our model easily reproduces the power law. The fluctuations in the growth rate falls with increasing size following a power law (with an exponent 1 whereas the data suggests that the exponent is around 1/6). However, the distribution of the difference of the firm-size in this model has Laplace distribution whereas the real data suggests that the difference of the log sizes has the same distribution.

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    File URL: http://arxiv.org/pdf/1112.2168
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    Paper provided by arXiv.org in its series Papers with number 1112.2168.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.2168

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    1. S. V. Buldyrev & L. A. N. Amaral & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: II. Modeling of company growth," Papers cond-mat/9702085, arXiv.org.
    2. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2009. "Microeconomics of the ideal gas like market models," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 388(19), pages 4151-4158.
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    9. A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 60(2), pages 135-149, November.
    10. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, Elsevier, vol. 49(4), pages 453-457, October.
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    13. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
    14. Repetowicz, Przemysław & Hutzler, Stefan & Richmond, Peter, 2005. "Dynamics of money and income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 356(2), pages 641-654.
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    16. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 87(5), pages 972-90, October.
    17. Ishikawa, Atushi, 2005. "Pareto law and Pareto index in the income distribution of Japanese companies," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 349(3), pages 597-608.
    18. L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
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