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Equilibrium Distribution of Labor Productivity: A Theoretical Model

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  • Hideaki Aoyama
  • Hiroshi Iyetomi
  • Hiroshi Yoshikawa

Abstract

We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors on the basis of an exhaustive dataset in Japan. The theoretical formula succeeds in explaining the two distinctive observational facts in a unified way, that is, a Boltzmann distribution with negative temperature on low-to-medium productivity side and a decreasing part in a power-law form on high productivity side.

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  • Hideaki Aoyama & Hiroshi Iyetomi & Hiroshi Yoshikawa, 2012. "Equilibrium Distribution of Labor Productivity: A Theoretical Model," Papers 1205.2470, arXiv.org.
    • Handle: RePEc:arx:papers:1205.2470
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    References listed on IDEAS

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    8. Hideaki Aoyama & Hiroshi Yoshikawa & Hiroshi Iyetomi & Yoshi Fujiwara, 2010. "Productivity dispersion: facts, theory, and implications," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 5(1), pages 27-54, June.
    9. Fujiwara, Yoshi & Iyetomi, Hiroshi & Ikeda, Yuichi & Souma, Wataru, 2009. "Distribution of Labour Productivity in Japan over the Period 1996-2006," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-14.
    10. Ikeda, Yuichi & Fujiwara, Yoshi & Aoyama, Hideaki & Iyetomi, Hiroshi & Souma, Wataru, 2009. "Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-17.
    11. Hideaki Aoyama & Yoshi Fujiwara & Yuichi Ikeda & Hiroshi Iyetomi & Wataru Souma, 2009. "Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors," Papers 0901.1500, arXiv.org.
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