A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

Sergey V. Buldyrev, Fabio Pammolli (), Massimo Riccaboni (), Kazuko Yamasaki, Dongfeng Fu, Kaushik Matia and H. Eugene Stanley

MPRA Paper from University Library of Munich, Germany

Abstract: We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent φ = 2+b/(1−b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.

Keywords: firm growth; size distribution; Gibrat law; Zipf law (search for similar items in EconPapers)
JEL-codes: D21 D39 E17 L00 L16 L25 L60 L65 O47 (search for similar items in EconPapers)
Date: 2006-08-31
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Published in The European Physical Journal B 2.57(2007): pp. 131-138

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Working Paper: A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment (2006)
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