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A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs

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  • Arnaud Dupuy

Abstract

In very different fields of economics, economic inference and policy evaluation require economists to parametrize a production function that links measures of input factors to measures of output. While doing so, strong assumptions are implicitly made about microeconomic variables governing the shape of the aggregate production function. In this paper, I develop an assignment model that provides a microeconomic foundation for aggregate production functions. The shape of the production function depends crucially on the distribution of workers and jobs and the type of technological changes depends crucially on the evolution of these distributions. Sufficient and necessary conditions are provided for the production function to be of the Constant Ratio of Elasticities of Substitution form, a form nesting the broadly used Constant Elasticity of Substitution form. This model provides a way to evaluate how stringent assumptions about the type of production function or technological change are by comparing the implied distribution of jobs and its evolution over time to observations of the distribution of jobs and its evolution over time.
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  • Arnaud Dupuy, 2012. "A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs," Economica, London School of Economics and Political Science, vol. 79(315), pages 534-556, July.
    • Handle: RePEc:bla:econom:v:79:y:2012:i:315:p:534-556
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    References listed on IDEAS

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    1. Teulings, Coen N, 1995. "The Wage Distribution in a Model of the Assignment of Skills to Jobs," Journal of Political Economy, University of Chicago Press, vol. 103(2), pages 280-315, April.
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    Cited by:

    1. Vallizadeh E. & Muysken J. & Ziesemer T.H.W., 2015. "Offshoring of medium-skill jobs, polarization, and productivity effect: Implications for wages and low-skill unemployment," MERIT Working Papers 2015-004, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    2. Lex Borghans & Bas ter Weel, 2008. "Understanding the Technology of Computer Technology Diffusion: Explaining Computer Adoption Patterns and Implications for the Wage Structure," Journal of Income Distribution, Ad libros publications inc., vol. 17(3-4), pages 37-70, September.
    3. Maciej Albinowski & Joanna Franaszek, 2024. "Minimum Hours Constraints: The Role of Organizational Culture," IBS Working Papers 01/2024, Instytut Badan Strukturalnych.
    4. Schultheiss, Tobias & Pfister, Curdin & Gnehm, Ann-Sophie & Backes-Gellner, Uschi, 2023. "Education expansion and high-skill job opportunities for workers: Does a rising tide lift all boats?," Labour Economics, Elsevier, vol. 82(C).
    5. HIRAGUCHI Ryoji, 2015. "On the Stochastic Macro-equilibrium and a Microfoundation for the Production Function," Discussion papers 15040, Research Institute of Economy, Trade and Industry (RIETI).
    6. Michael Knoblach & Fabian Stöckl, 2020. "What Determines The Elasticity Of Substitution Between Capital And Labor? A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 847-875, September.
    7. Andres Gomez-Lievano & Vladislav Vysotsky & Jose Lobo, 2018. "Artificial Increasing Returns to Scale and the Problem of Sampling from Lognormals," Papers 1807.09424, arXiv.org, revised Jul 2020.
    8. Mangin, Sephorah, 2017. "A theory of production, matching, and distribution," Journal of Economic Theory, Elsevier, vol. 172(C), pages 376-409.
    9. Stephen J. DeCanio, 2022. "Simple efficiency-distribution models of production, with an application to robotics," SN Business & Economics, Springer, vol. 2(8), pages 1-16, August.
    10. Arnaud Dupuy, 2008. "The Assignment of Workers to Tasks, Wage Distribution, and Technical Change: A Critical Review," Journal of Income Distribution, Ad libros publications inc., vol. 17(3-4), pages 12-36, September.
    11. Dohmen, T.J. & Falk, A. & Huffman, D. & Marklein, F. & Sunde, U., 2008. "Biased probability judgment: representative evidence for pervasiveness and economic outcomes," ROA Research Memorandum 009, Maastricht University, Research Centre for Education and the Labour Market (ROA).
    12. Lex Borghans & Bas ter Weel, 2008. "Understanding the Technology of Computer Technology Diffusion: Explaining Computer Adoption Patterns and Implications for the Wage Structure," Journal of Income Distribution, Ad libros publications inc., vol. 17(3-4), pages 37-70, September.
    13. DeCanio, Stephen J., 2016. "Robots and humans – complements or substitutes?," Journal of Macroeconomics, Elsevier, vol. 49(C), pages 280-291.
    14. Vladimir Matveenko, 2013. "Resources, Institutions And Technologies: Game Modeling Of Dual Relations," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 9(3), pages 7-28.

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    More about this item

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • D3 - Microeconomics - - Distribution
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs
    • O3 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights

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