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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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References

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  1. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor-augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502.
  2. Miguel A. Le�n-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-57, September.
  3. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2011. "The normalized CES production function: theory and empirics," Working Paper Series 1294, European Central Bank.
  4. Klump, Rainer & Preissler, Harald, 2000. " CES Production Functions and Economic Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 102(1), pages 41-56, March.
  5. Daron Acemoglu, 2007. "Equilibrium Bias of Technology," Econometrica, Econometric Society, vol. 75(5), pages 1371-1409, 09.
  6. Jakub Growiec, 2005. "Beyond the Linearity Critique: The Knife-Edge Assumption of Steady State Growth," GE, Growth, Math methods 0505003, EconWPA, revised 23 Jun 2005.
  7. Daron Acemoglu & Veronica Guerrieri, 2006. "Capital Deepening and Non-Balanced Economic Growth," NBER Working Papers 12475, National Bureau of Economic Research, Inc.
  8. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, 03.
  9. Palivos, Theodore & Karagiannis, Giannis, 2010. "The Elasticity Of Substitution As An Engine Of Growth," Macroeconomic Dynamics, Cambridge University Press, vol. 14(05), pages 617-628, November.
  10. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
  11. Mihaela Iulia Pintea & Peter Thompson, 2007. "Technological Complexity and Economic Growth," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 276-293, April.
  12. Jakub Growiec, 2012. "Factor-Augmenting Technology Choice and Monopolistic Competition," DEGIT Conference Papers c017_038, DEGIT, Dynamics, Economic Growth, and International Trade.
  13. Francesco Caselli & Wilbur John Coleman II, 2006. "The World Technology Frontier," American Economic Review, American Economic Association, vol. 96(3), pages 499-522, June.
  14. de La Grandville, Olivier, 1989. "Erratum [In Quest of the Slutsky Diamond]," American Economic Review, American Economic Association, vol. 79(5), pages 1307, December.
  15. Kremer, Michael, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 551-75, August.
  16. de La Grandville, Olivier, 1989. "In Quest of the Slutsky Diamond," American Economic Review, American Economic Association, vol. 79(3), pages 468-81, June.
  17. Nakamura, Hideki, 2009. "Micro-foundation for a constant elasticity of substitution production function through mechanization," Journal of Macroeconomics, Elsevier, vol. 31(3), pages 464-472, September.
  18. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  19. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
  20. Miguel A. Leon-Ledesma & Mathan Satchi, 2011. "The Choice of CES Production Techniques and Balanced Growth," Studies in Economics 1113, Department of Economics, University of Kent.
  21. 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.
  22. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
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Cited by:
  1. Growiec, Jakub, 2013. "Factor-augmenting technology choice and monopolistic competition," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 86-94.
  2. Klump, Rainer & McAdam, Peter & Willman, Alpo, 2011. "The normalized CES production function: theory and empirics," Working Paper Series 1294, European Central Bank.

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