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.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
15980.
Length: Date of creation: 31 Aug 2006 Date of revision: Publication status: Published in The European Physical Journal B 2.57(2007): pp. 131-138 Handle: RePEc:pra:mprapa:15980
Find related papers by JEL classification: L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance D21 - Microeconomics - - Production and Organizations - - - Firm Behavior 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
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