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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. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hideaki Aoyama & Hiroshi Iyetomi & Hiroshi Yoshikawa, 2015. "Equilibrium distribution of labor productivity: a theoretical model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 57-66, April.
    • Handle: RePEc:spr:jeicoo:v:10:y:2015:i:1:p:57-66
    DOI: 10.1007/s11403-013-0118-9
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    References listed on IDEAS

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    5. Scalas, Enrico & Garibaldi, Ubaldo, 2009. "A Dynamic Probabilistic Version of the Aoki-Yoshikawa Sectoral Productivity Model," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-10.
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    9. 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.
    10. 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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    1. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2021. "Why does production function take the Cobb–Douglas form?," Evolutionary and Institutional Economics Review, Springer, vol. 18(1), pages 79-102, April.

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    More about this item

    Keywords

    Labor productivity; Equilibrium; Detailed balance ; Firm theory; C02; E20; O40;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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