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Zipf's law and maximum sustainable growth

Author

Listed:
  • Yannick Malevergne

    (EM - EMLyon Business School)

  • Alex Saichev
  • Didier Sornette

Abstract

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective growth rate of incumbent firms (which includes their possible demise) and the growth rate of investments in entrant firms. Under the additional assumption that firms do not consume more resources than available, we show that Zipf's law is the signature that firms grow at the maximum reachable long-term rate.

Suggested Citation

  • Yannick Malevergne & Alex Saichev & Didier Sornette, 2013. "Zipf's law and maximum sustainable growth," Post-Print hal-02313060, HAL.
    • Handle: RePEc:hal:journl:hal-02313060
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    Citations

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    Cited by:

    1. Vandermarliere, B. & Ryckebusch, J. & Schoors, K. & Cauwels, P. & Sornette, D., 2017. "Discrete hierarchy of sizes and performances in the exchange-traded fund universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 111-123.
    2. Di Guilmi, Corrado & Fujiwara, Yoshi, 2025. "Does the supply network shape the firm size distribution? The Japanese case," Economic Modelling, Elsevier, vol. 152(C).
    3. Toda, Alexis Akira, 2016. "Zipf's Law: A Microfoundation," MPRA Paper 78985, University Library of Munich, Germany.
    4. Anindya S. Chakrabarti, 2017. "Scale-free distribution as an economic invariant: a theoretical approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 1-26, April.
    5. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    6. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    7. Yu Zhang & Claudio Tessone, 2024. "Bitcoin Transaction Behavior Modeling Based on Balance Data," Papers 2409.10407, arXiv.org.
    8. Ke Wu & Spencer Wheatley & Didier Sornette, 2018. "Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisations," Papers 1803.03088, arXiv.org, revised May 2018.
    9. Christian Schluter & Mark Trede, 2019. "Size distributions reconsidered," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 695-710, July.
    10. Jo~ao Pedro Jerico & Franc{c}ois P. Landes & Matteo Marsili & Isaac P'erez Castillo & Valerio Volpati, 2016. "When does inequality freeze an economy?," Papers 1602.07300, arXiv.org, revised Apr 2016.
    11. Didier Sornette & Thomas Maillart & Giacomo Ghezzi, 2014. "How Much Is the Whole Really More than the Sum of Its Parts? 1 ⊞ 1 = 2.5: Superlinear Productivity in Collective Group Actions," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-15, August.
    12. Charles I. Jones & Jihee Kim, 2018. "A Schumpeterian Model of Top Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 1785-1826.
    13. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.
    14. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    15. Gregor Semieniuk & Ellis Scharfenaker, 2014. "A Bayesian Latent Variable Mixture Model for Filtering Firm Profit Rate," SCEPA working paper series. 2014-1, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    16. Davide Fiaschi & Imre Kondor & Matteo Marsili & Valerio Volpati, 2014. "The Interrupted Power Law and the Size of Shadow Banking," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    17. Edouard Ribes, 2018. "Growth patterns of US professional services firms," Working Papers hal-01762381, HAL.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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