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Kinematics and dynamics of Pareto–Zipf's law and Gibrat's law

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  • Aoyama, Hideaki
  • Fujiwara, Yoshi
  • Souma, Wataru

Abstract

We discuss Pareto–Zipf's law and Gibrat's law found in the high-end regions of personal income, company's income, and various measures of company size. The fact that these phenomenological laws coexist in wide range of data suggests some deep mathematical relations between them. In this paper we find just such relationships under the law of detailed-balance. This sets a basis for perturbative treatment of the economic change.

Suggested Citation

  • Aoyama, Hideaki & Fujiwara, Yoshi & Souma, Wataru, 2004. "Kinematics and dynamics of Pareto–Zipf's law and Gibrat's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 117-121.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:117-121
    DOI: 10.1016/j.physa.2004.06.099
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    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.
    2. Fujiwara, Yoshi & Souma, Wataru & Aoyama, Hideaki & Kaizoji, Taisei & Aoki, Masanao, 2003. "Growth and fluctuations of personal income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 598-604.
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    1. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.
    2. Ikeda, Yuichi & Aoyama, Hideaki & Iyetomi, Hiroshi & Fujiwara, Yoshi & Souma, Wataru & Kaizoji, Taisei, 2007. "Response of firm agent network to exogenous shock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 138-148.
    3. Kočišová, J. & Horváth, D. & Brutovský, B., 2009. "The efficiency of individual optimization in the conditions of competitive growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3585-3592.
    4. Chakrabarti, Anindya S., 2012. "Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6039-6050.
    5. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
    6. Anindya S. Chakrabarti, 2013. "Bimodality in the firm size distributions: a kinetic exchange model approach," Papers 1302.3818, arXiv.org, revised May 2013.

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