A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment
AbstractWe 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 $\phi=2+b/(1-b)$ 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 $\zeta=3$. 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number physics/0609020.
Date of creation: Sep 2006
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- Buldyrev, Sergey V. & Pammolli, Fabio & Riccaboni, Massimo & Yamasaki, Kazuko & Fu, Dongfeng & Matia, Kaushik & Stanley, H. Eugene, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," MPRA Paper 15980, University Library of Munich, Germany.
- L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance
- D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
- O47 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Measurement of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
- D39 - Microeconomics - - Distribution - - - Other
- L00 - Industrial Organization - - General - - - General
- L60 - Industrial Organization - - Industry Studies: Manufacturing - - - General
- L - Industrial Organization
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