A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

@misc{citeulike:884100, 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 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.}, author = {Buldyrev, S. V. and Pammolli, F. and Riccaboni, M. and Yamasaki, K. and Fu, D. and Matia, K. and Stanley, H. E. }, citeulike-article-id = {884100}, eprint = {physics/0609020}, keywords = {firms, growth, rates}, month = {Sep}, posted-at = {2006-10-05 00:03:19}, priority = {2}, title = {A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment}, url = {http://arxiv.org/abs/physics/0609020}, year = {2006} }

TY - ELEC ID - citeulike:884100 L3 - citeulike-article-id:884100 TI - A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment N2 - 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 $\phi=2+b/(1-b)$ 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. KW - firms KW - growth KW - rates AU - Buldyrev, SV AU - Pammolli, F AU - Riccaboni, M AU - Yamasaki, K AU - Fu, D AU - Matia, K AU - Stanley, HE PY - 2006/Sep/04/ UR - http://arxiv.org/abs/physics/0609020 ER -