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A microfoundation for normalized CES production functions with factor-augmenting technical change

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Abstract

We derive the aggregate normalized CES production function from idea-based microfoundations where firms are allowed to choose their capital- and labor-augmenting technology optimally from a menu of available technologies. This menu is in turn augmented through factor-specific R&D. The considered model yields a number of interesting results. First, normalization of the production function can be maintained simultaneously at the local and at the aggregate level, greatly facilitating interpretation of the aggregate production function’s parameters in terms of the underlying idea distributions. Second, in line with earlier findings, if capital- and labor-augmenting ideas are independently Weibull-distributed then the aggregate production function is CES; if they are independently Pareto-distributed, then it is Cobb–Douglas. Third, by disentangling technology choice by firms from R&D output, one can draw a clearcut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Fourth, it is argued that the Weibull distribution should be a good approximation of the true unit factor productivity distribution (and thus the CES should be a good approximation of the true aggregate production function) if a “technology” is in fact an assembly of a large number of complementary components. This argument is illustrated with a novel, tractable model of directed (factor-specific) R&D. Finally, it is shown that all our results carry forward to the general case of n-input production functions.

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  • Jakub Growiec, 2011. "A microfoundation for normalized CES production functions with factor-augmenting technical change," NBP Working Papers 98, Narodowy Bank Polski, Economic Research Department.
  • Handle: RePEc:nbp:nbpmis:98
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    Cited by:

    1. repec:kap:jeczfn:v:124:y:2018:i:3:d:10.1007_s00712-017-0567-z is not listed on IDEAS
    2. Miguel A. Leon-Ledesma & Mathan Satchi, 2015. "Appropriate Technology and Balanced Growth," Studies in Economics 1614, School of Economics, University of Kent, revised Nov 2016.
    3. repec:eee:dyncon:v:87:y:2018:i:c:p:74-93 is not listed on IDEAS
    4. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    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. Mangin, Sephorah, 2017. "A theory of production, matching, and distribution," Journal of Economic Theory, Elsevier, vol. 172(C), pages 376-409.
    7. Jakub Growiec & Jakub Muck, 2015. "Isoelastic Elasticity of Substitution Production Functions," Discussion Papers 15-13, University of Copenhagen. Department of Economics.
    8. Growiec, Jakub, 2015. "On the modeling of size distributions when technologies are complex," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 1-8.
    9. repec:spr:weltar:v:154:y:2018:i:1:d:10.1007_s10290-017-0295-z is not listed on IDEAS
    10. Marco Bee & Stefano Schiavo, 2018. "Powerless: gains from trade when firm productivity is not Pareto distributed," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 154(1), pages 15-45, February.
    11. Growiec, Jakub, 2013. "Factor-augmenting technology choice and monopolistic competition," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 86-94.
    12. Zhu, Yanyuan & Feng, Xiao, 2014. "China's national production function since 1997: A reinvestigation," Working Papers in Economics 2014,2, Bundeswehr University Munich, Economic Research Group.
    13. Miguel A. Leon-Ledesma & Mathan Satchi, 2015. "Appropriate Technology and the Labour Share," Studies in Economics 1505, School of Economics, University of Kent, revised Nov 2016.
    14. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.

    More about this item

    Keywords

    CES production function; normalization; Weibull distribution; direction of technical change; directed R&D; optimal technology choice;

    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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