Bimodality in the firm size distributions: a kinetic exchange model approach

Regular Article


Firm growth process in the developing economies is known to produce divergence in their growth path giving rise to bimodality in the size distribution. Similar bimodality has been observed in wealth distribution as well. Here, we introduce a modified kinetic exchange model which can reproduce such features. In particular, we will show numerically that a nonlinear retention rate (or savings propensity) causes this bimodality. This model can accommodate binary trading as well as the whole system-side trading thus making it more suitable to explain the non-standard features of wealth distribution as well as firm size distribution.


Statistical and Nonlinear Physics 


  1. 1.
    R. Axtell, Science 293, 1818 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    H. Aoyama, Y. Fujiwara, Y. Ikeda, H. Iyetomi, W. Souma, Econophysics and Companies: Statistical life and death in complex business networks (Cambridge University Press, New York, 2010)Google Scholar
  3. 3.
    Y. Lee, L.A.N. Amaral, D. Canning, M. Meyer, H.E. Stanley, Phys. Rev. Lett. 81, 3275 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    H. Aoyama, W. Souma, Y. Fujiwara, Physica A 324, 352 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    A. Ishikawa, Physica A 349, 597 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Fujiwara, C.D. Guilmi, H. Aoyama, M. Gallegatti, W. Souma, Physica A 335, 197 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    A. Ishikawa, Physica A 363, 367 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Ijiri, H. Simon, Skew Distributions and the Size of Business Firms (North Holland Pub., Amsterdam, 1977)Google Scholar
  9. 9.
    B. Podobnik, D. Horvatic, F. Pammolli, F. Wang, H.E. Stanley, I. Grosse, Phys. Rev. E 77, 056102 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    B. Podobnik, D. Horvatic, A. Petersen, B. Urosevic, H.E. Stanley, Proc. Natl. Acad. Sci. 107, 18325 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    T. Mizuno, M. Takayasu, H. Takayasu, Physica A 332, 403 (2004)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    M. Riccaboni, F. Pammolli, S.V. Buldyrev, L. Ponta, H.E. Stanley, Proc. Natl. Acad. Sci. 105, 19595 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    M.H.R. Stanley, L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Mass, M.A. Salinger, H.E. Stanley, Nature 379, 804 (1996)ADSCrossRefGoogle Scholar
  14. 14.
    M.H.R. Stanley, L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Mass, M.A. Salinger, H.E. Stanley, J. Phys. I 7, 621 (1997)Google Scholar
  15. 15.
    S.V. Buldyrev, L.A.N. Amaral, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley, M.H.R. Stanley, J. Phys. I 7, 635 (1997)CrossRefGoogle Scholar
  16. 16.
    J.R. Tybout, J. Econ. Lit. 38, 11 (2000)CrossRefGoogle Scholar
  17. 17.
    A. Chatterjee, B.K. Chakrabarti, Eur. Phys. J. B 60, 135 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    A. Chakrabarti, Physica A 391, 6039 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    M. Kozak, Micro, small and medium enterprises: a collection of published data, published by IFC, database/msme_database.htm
  20. 20.
    J.C. Ferrero, The monomodal, polymodal, equilibrium and nonequilibrium distribution of money in Econophysics of wealth Distribution, edited by Chatterjee et al. (Springer-Verlag, Milan, 2005)Google Scholar
  21. 21.
    R. Lawrence, Brookings Rev. 3, 3 (1984)CrossRefGoogle Scholar
  22. 22.
    D. Quah, Econ. J. 106, 1045 (1996)CrossRefGoogle Scholar
  23. 23.
    X. Sala-i-martin, Quart. J. Econ. 121, 351 (2006)CrossRefGoogle Scholar
  24. 24.
    V. Yakovenko, J.B. Rosser, Rev. Mod. Phys. 81, 1703 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    J.A. Hartigan, P.M. Hartigan, Ann. Statist. 13, 70 (1985)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    A. Kar Gupta, Models of wealth distribution- a perspective in Econophysics and Sociophysics, edited by Chakrabarti et al. (Wiley-VCH, Berlin, 2006)Google Scholar
  27. 27.
    A. Chakraborti, B.K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000)ADSCrossRefGoogle Scholar
  28. 28.
    E. Rossi-hansberg, M. Wright, Am. Econ. Rev. 97, 1639 (2007)CrossRefGoogle Scholar
  29. 29.
    C. Arellano, Y. Bai, J. Zhang, J. Monetary Econ. 59, 533 (2012)CrossRefGoogle Scholar
  30. 30.
    H. Aoyama, Y. Fujiwara, W. Souma, Physica A 344, 117 (2004)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Economics Department, Boston UniversityBostonUSA

Personalised recommendations