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On size and growth of business firms


  • De Fabritiis, G.
  • Pammolli, F.
  • Riccaboni, M.


We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e., the increase of the number of new elementary business units and their size growth. We find a power-law relationship between size and the variance of growth rates for both firms and products, with an exponent between −0.17 and −0.15, with a remarkable stability upon aggregation. We then introduce a simple and general model of proportional growth for both the number of firm independent constituent units and their size, which conveys a good representation of the empirical evidences. This general and plausible generative process can account for the observed scaling in a wide variety of economic and industrial systems. Our findings contribute to shed light on the mechanisms that sustain economic growth in terms of the relationships between the size of economic entities and the number and size distribution of their elementary components.

Suggested Citation

  • De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
  • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:38-44 DOI: 10.1016/S0378-4371(03)00043-8

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    References listed on IDEAS

    1. Stephen Hymer & Peter Pashigian, 1962. "Firm Size and Rate of Growth," Journal of Political Economy, University of Chicago Press, vol. 70, pages 556-556.
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    Cited by:

    1. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
    2. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    3. Wright, Ian, 2005. "The social architecture of capitalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 589-620.
    4. Kaldasch, Joachim, 2015. "The Product Life Cycle of Durable Goods," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 1-17.
    5. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    6. Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728,, revised Jan 2014.
    7. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348,, revised Dec 2009.
    8. Murat ATAN & Emre BOZDAĞ, 2011. "Avrupa Karbonatlı İçecekler Piyasasında Firma Büyüklüğü Ve Büyüklük Genişleme Oranı İlişkisi," Ekonomik Yaklasim, Ekonomik Yaklasim Association, vol. 22(80), pages 19-38.
    9. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2011. "Innovation and Corporate Dynamics: A Theoretical Framework," DISA Working Papers 2011/08, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
    10. Fabio Pammolli & Dongfeng Fu & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence," Papers physics/0609011,
    11. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    12. repec:eee:phsmap:v:481:y:2017:i:c:p:265-275 is not listed on IDEAS
    13. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    14. Marco Bee & Massimo Riccaboni & Stefano Schiavo, 2011. "Pareto versus lognormal: a maximum entropy test," Department of Economics Working Papers 1102, Department of Economics, University of Trento, Italia.
    15. Kaldasch, Joachim, 2011. "Evolutionary model of an anonymous consumer durable market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2692-2715.
    16. Kaldasch, Joachim, 2012. "Evolutionäre Diffusion und der Produktlebenszyklus von Gebrauchsgütern," EconStor Preprints 59748, ZBW - German National Library of Economics.
    17. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    18. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    19. Buldyrev, Sergey V. & Pammolli, Fabio & Riccaboni, Massimo & Yamasaki, Kazuko & Fu, Dongfeng & Matia, Kaushik & Stanley, H. Eugene, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," MPRA Paper 15980, University Library of Munich, Germany.
    20. Kaldasch, Joachim, 2012. "Evolutionary model of the growth and size of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3751-3769.
    21. Masanao Aoki, 2006. "Long-run Behavior of Macroeconomic Models with Heterogeneous Agents: Asymptotic Behavior of One- and Two-Parameter Poisson-Dirichlet Distributions," CIRJE F-Series CIRJE-F-425, CIRJE, Faculty of Economics, University of Tokyo.
    22. Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
    23. Macuchova, Zuzana & Rudholm, Niklas & Tang, Aili, 2014. "Firm growth in the Swedish energy sector: Will large firms become even more dominant?," HUI Working Papers 104, HUI Research.

    More about this item


    Firm growth; Power laws; Gibrat's law; Economic growth; Pharmaceutical industry;

    JEL classification:

    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance
    • L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology; Plastics
    • D39 - Microeconomics - - Distribution - - - Other


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