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

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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Paper provided by Narodowy Bank Polski, Economic Research Department in its series NBP Working Papers with number 98.

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Length: 39
Date of creation: 2011
Handle: RePEc:nbp:nbpmis:98
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  16. 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.
  17. Daron Acemoglu, 2007. "Equilibrium Bias of Technology," Econometrica, Econometric Society, vol. 75(5), pages 1371-1409, September.
  18. 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.
  19. 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.
  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.
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  22. de La Grandville, Olivier, 1989. "Erratum [In Quest of the Slutsky Diamond]," American Economic Review, American Economic Association, vol. 79(5), pages 1307-1307, December.
  23. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  24. 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.
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