Non-Gibrat's law in the middle scale region

Author Info

• Masashi Tomoyose
• Shouji Fujimoto
• Atushi Ishikawa
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Abstract

By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the equation which gives the Pareto index $\mu$ in TST model. Moreover, we extend the model modifying the stochastic coefficient under a Non-Gibrat's law. In this model, the detailed balance is also numerically observed. The resultant pdf is power-law in the large scale Gibrat's law region, and is the log-normal distribution in the middle scale Non-Gibrat's one. These are accurately confirmed in the numerical simulation.

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File URL: http://arxiv.org/pdf/0809.3060

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Paper provided by arXiv.org in its series Papers with number 0809.3060.

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Handle: RePEc:arx:papers:0809.3060

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1. Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
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Cited by:
1. Ishikawa, Atushi, 2008. "Power-Law and Log-Normal Distributions in Firm Size Displacement Data," Economics Discussion Papers 2008-45, Kiel Institute for the World Economy.

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