Physics – Physics and Society

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2006-09-04

Physics

Physics and Society

19 pages 6 figures Applications of Physics in Financial Analysis, APFA5

Scientific paper

10.1140/epjb/e2007-00165-8

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.

**Buldyrev Sergey V.**

Physics – Condensed Matter – Soft Condensed Matter

Scientist

**Fu Dongfeng**

Physics – Physics and Society

Scientist

**Matia Kaushik**

Physics – Physics and Society

Scientist

**Pammolli Fabio**

Physics – Physics and Society

Scientist

**Riccaboni Massimo**

Physics – Physics and Society

Scientist

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