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Analytical Derivation of Power Laws in Firm Size Variables from Gibrat’s Law and Quasi-inversion Symmetry: A Geomorphological Approach

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Author Info

  • Atushi Ishikawa

    (Department of Informatics and Business, Faculty of Business Administration and Information Science, Kanazawa Gakuin University)

  • Shouji Fujimoto

    (Department of Informatics and Business, Faculty of Business Administration and Information Science, Kanazawa Gakuin University)

  • Takayuki Mizuno

    (National Institute of Informatics.)

  • Tsutomu Watanabe

    (Graduate School of Economics, University of Tokyo)

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    Abstract

    We start from Gibrat’s law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L.We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

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    Bibliographic Info

    Paper provided by University of Tokyo, Graduate School of Economics in its series UTokyo Price Project Working Paper Series with number 019.

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    Length: 22 pages
    Date of creation: Jan 2014
    Date of revision:
    Handle: RePEc:upd:utppwp:019

    Contact details of provider:
    Postal: University of Tokyo 702 Faculty of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan
    Phone: +81-3-3812-2111
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    Web page: http://www.e.u-tokyo.ac.jp/
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    Keywords: econophysics; power law; Gibrat’s law;

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