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A Microfoundation for Normalized CES Production Functions with Factor-Augmenting Technical Change

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  • Jakub Growiec

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 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 clear-cut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Finally, 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.

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Bibliographic Info

Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c016_013.

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Length: 21 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:deg:conpap:c016_013

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

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  1. Nakamura, Hideki, 2009. "Micro-foundation for a constant elasticity of substitution production function through mechanization," Journal of Macroeconomics, Elsevier, Elsevier, vol. 31(3), pages 464-472, September.
  2. Miguel A. Leon-Ledesma & Mathan Satchi, 2011. "The Choice of CES Production Techniques and Balanced Growth," Studies in Economics, Department of Economics, University of Kent 1113, Department of Economics, University of Kent.
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  6. Jakub Growiec, 2012. "Factor-Augmenting Technology Choice and Monopolistic Competition," DEGIT Conference Papers, DEGIT, Dynamics, Economic Growth, and International Trade c017_038, DEGIT, Dynamics, Economic Growth, and International Trade.
  7. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, MIT Press, vol. 1(1), pages 1-37, 03.
  8. Jakub Growiec, 2007. "Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth," Economic Theory, Springer, Springer, vol. 31(3), pages 489-499, June.
  9. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, American Economic Association, vol. 89(2), pages 129-132, May.
  10. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 26(5), pages 769-799, December.
  11. Mihaela Pintea & Peter Thompson, 2005. "Technological Complexity and Economic Growth," Working Papers 0502, Florida International University, Department of Economics.
  12. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 114(3), pages 739-767, August.
  13. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, Elsevier, vol. 101(1), pages 87-90, October.
  14. Growiec, Jakub, 2006. "A New Class of Production Functions and an Argument Against Purely Labor-Augmenting Technical Change," MPRA Paper 7069, University Library of Munich, Germany.
  15. León-Ledesma, Miguel A. & McAdam, Peter & Willman, Alpo, 2009. "Identifying the elasticity of substitution with biased technical change," Working Paper Series, European Central Bank 1001, European Central Bank.
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  17. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  18. Caselli, Francesco & Coleman II, Wilbur John, 2000. "The World Technology Frontier," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2584, C.E.P.R. Discussion Papers.
  19. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1389-1420, November.
  20. Charles I. Jones, 2011. "Intermediate Goods and Weak Links in the Theory of Economic Development," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 1-28, April.
  21. Daron Acemoglu & Veronica Guerrieri, 2008. "Capital Deepening and Nonbalanced Economic Growth," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 116(3), pages 467-498, 06.
  22. de La Grandville, Olivier, 1989. "Erratum [In Quest of the Slutsky Diamond]," American Economic Review, American Economic Association, American Economic Association, vol. 79(5), pages 1307, December.
  23. Olivier de La Grandville & Rainer Klump, 2000. "Economic Growth and the Elasticity of Substitution: Two Theorems and Some Suggestions," American Economic Review, American Economic Association, American Economic Association, vol. 90(1), pages 282-291, March.
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Cited by:
  1. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 26(5), pages 769-799, December.
  2. Jakub Growiec, 2013. "On the modeling of size distributions when technologies are complex," EcoMod2013 5611, EcoMod.
  3. Jakub Growiec, 2012. "Factor-Augmenting Technology Choice and Monopolistic Competition," DEGIT Conference Papers, DEGIT, Dynamics, Economic Growth, and International Trade c017_038, DEGIT, Dynamics, Economic Growth, and International Trade.

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