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 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15980.
Date of creation: 31 Aug 2006
Date of revision:
Publication status: Published in The European Physical Journal B 2.57(2007): pp. 131-138
firm growth; size distribution; Gibrat law; Zipf law;
Other versions of this item:
- S. V. Buldyrev & F. Pammolli & M. Riccaboni & K. Yamasaki & D. Fu & K. Matia & H. E. Stanley, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," Papers physics/0609020, arXiv.org.
- 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
- L65 - Industrial Organization - - Industry Studies: Manufacturing - - - Chemicals; Rubber; Drugs; Biotechnology
- L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure
- E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
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