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Zipf's law and maximum sustainable growth

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  • Y. Malevergne
  • A. Saichev
  • D. 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. Remarkably, Zipf's law is the signature of the long-term optimal allocation of resources that ensures the maximum sustainable growth rate of an economy.

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Paper provided by arXiv.org in its series Papers with number 1012.0199.

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Date of creation: Dec 2010
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Handle: RePEc:arx:papers:1012.0199

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Cited by:
  1. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.

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