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# Non-Gibrat's law in the middle scale region

## Author

Listed:
• Masashi Tomoyose
• Shouji Fujimoto
• Atushi Ishikawa

## 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.

## Suggested Citation

• Masashi Tomoyose & Shouji Fujimoto & Atushi Ishikawa, 2008. "Non-Gibrat's law in the middle scale region," Papers 0809.3060, arXiv.org.
• Handle: RePEc:arx:papers:0809.3060
as

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

## References listed on IDEAS

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1. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
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## Citations

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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 (IfW).

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