A generalized preferential attachment model for business firms growth rates

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. PACS. 89.75.Fb Structures and organization in complex systems – 89.65.Gh Economics; econophysics, financial markets, business and management