Buldyrev, Sergey V. and Pammolli, Fabio and Riccaboni, Massimo and Yamasaki, Kazuko and Fu, Dongfeng and Matia, Kaushik and Stanley, H. Eugene (2006): A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment. Published in: The European Physical Journal B , Vol. 57, No. 2 (May 2007): pp. 131138.

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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 socioeconomic 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 powerlaw tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the sizevariance relationship of the firm growth rates.
Item Type:  MPRA Paper 

Original Title:  A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment 
Language:  English 
Keywords:  firm growth, size distribution, Gibrat law, Zipf law 
Subjects:  L  Industrial Organization > L2  Firm Objectives, Organization, and Behavior > L25  Firm Performance: Size, Diversification, and Scope D  Microeconomics > D2  Production and Organizations > D21  Firm Behavior: Theory O  Economic Development, Innovation, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity > O47  Empirical Studies of Economic Growth ; Aggregate Productivity ; CrossCountry Output Convergence D  Microeconomics > D3  Distribution > D39  Other L  Industrial Organization > L0  General > L00  General L  Industrial Organization > L6  Industry Studies: Manufacturing > L60  General L  Industrial Organization > L6  Industry Studies: Manufacturing > L65  Chemicals ; Rubber ; Drugs ; Biotechnology L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L16  Industrial Organization and Macroeconomics: Industrial Structure and Structural Change ; Industrial Price Indices E  Macroeconomics and Monetary Economics > E1  General Aggregative Models > E17  Forecasting and Simulation: Models and Applications 
Item ID:  15980 
Depositing User:  Laknori 
Date Deposited:  01 Jul 2009 09:17 
Last Modified:  23 Oct 2016 04:49 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/15980 