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Zipf's law and maximum sustainable growth

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  • Malevergne, Y.
  • Saichev, A.
  • Sornette, D.

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

  • Malevergne, Y. & Saichev, A. & Sornette, D., 2013. "Zipf's law and maximum sustainable growth," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1195-1212.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:6:p:1195-1212
    DOI: 10.1016/j.jedc.2013.02.004
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    1. 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.
    2. 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.
    3. repec:spr:jeicoo:v:12:y:2017:i:1:d:10.1007_s11403-015-0148-6 is not listed on IDEAS
    4. Charles I. Jones & Jihee Kim, 2014. "A Schumpeterian Model of Top Income Inequality," NBER Working Papers 20637, National Bureau of Economic Research, Inc.
    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. Gregor Semieniuk & Ellis Scharfenaker, 2014. "A Bayesian Latent Variable Mixture Model for Filtering Firm Profit Rate," SCEPA working paper series. SCEPA's main areas of research are macroeconomic policy, inequality and poverty, and globalization. 2014-1, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    8. Davide Fiaschi & Imre Kondor & Matteo Marsili & Valerio Volpati, 2013. "The Interrupted Power Law and The Size of Shadow Banking," Papers 1309.2130, arXiv.org, revised Apr 2014.
    9. 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.
    10. Edouard Ribes, 2018. "Growth patterns of US professional services firms," Working Papers hal-01762381, HAL.

    More about this item

    Keywords

    Firm growth; Gibrat's law; Zipf's law;

    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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