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

Atushi Ishikawa, Shouji Fujimoto, Takayuki Mizuno and Tsutomu Watanabe
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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

No 19, UTokyo Price Project Working Paper Series from University of Tokyo, Graduate School of Economics

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.

Keywords: econophysics; power law; Gibrat’s law (search for similar items in EconPapers)
Pages: 22 pages
Date: 2014-01
New Economics Papers: this item is included in nep-bec, nep-com, nep-ind, nep-net and nep-tid
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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