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

The European Physical Journal B, Vol. 57, No. 2, pp. 131-138

Posted: 26 Nov 2007 Last revised: 24 Dec 2007

See all articles by Sergey Buldyrev

Sergey Buldyrev

Yeshiva University - Department of Physics

Fabio Pammolli

Polytechnic University of Milan - Department of Management, Economics and Industrial Engineering; CERM Foundation

Massimo Riccaboni

KU Leuven - Department of Managerial Economics, Strategy, and Innovation; IMT Institute for Advanced Studies

Kazuko Yamasaki

Tokyo University of Information Sciences

H. Eugene Stanley

Boston University - Center for Polymer Studies

Dongfeng Fu

Boston University - Department of Physics

Kaushik Matia

Boston University - Department of Physics

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.

Suggested Citation

Buldyrev, Sergey and Pammolli, Fabio and Riccaboni, Massimo and Yamasaki, Kazuko and Stanley, H. Eugene and Fu, Dongfeng and Matia, Kaushik, A Generalized Preferential Attachment Model for Business Firms Growth Rates, II: Mathematical Treatment. Available at SSRN: https://ssrn.com/abstract=1032597

Sergey Buldyrev

Yeshiva University - Department of Physics ( email )

500 West, 185th Street
New York, NY 10033
United States

Fabio Pammolli (Contact Author)

Polytechnic University of Milan - Department of Management, Economics and Industrial Engineering ( email )

Via Lambruschini 4C - building 26/A
Milano, 20156
Italy

CERM Foundation ( email )

Via Fiorentina, 1
Siena, Siena 53100
Italy

HOME PAGE: http://www.cermlab.it

Massimo Riccaboni

KU Leuven - Department of Managerial Economics, Strategy, and Innovation ( email )

Naamsestraat 69 bus 3500
Leuven, 3000
Belgium

IMT Institute for Advanced Studies ( email )

Complesso San Micheletto
Lucca, 55100
Italy

Kazuko Yamasaki

Tokyo University of Information Sciences ( email )

Tokyo
Japan

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

Dongfeng Fu

Boston University - Department of Physics ( email )

590 Commonwealth Avenue
Boston, MA 02215
United States

Kaushik Matia

Boston University - Department of Physics ( email )

590 Commonwealth Avenue
Boston, MA 02215
United States

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