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The cobb-douglas function as an approximation of other functions

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  • Frédéric Reynès

    (OFCE (OFCE))

Abstract

By defining the Variable Output Elasticities Cobb-Douglas function, this article shows that a large class of production functions can be approximated by a Cobb-Douglas function with nonconstant output elasticity. Compared to standard flexible functions such as the Translog function, this framework has several advantages. It requires only the use of the first order approximation while respecting the theoretical curvature conditions of the isoquants. This greatly facilitates the deduction of linear input demands function without the need of involving the duality theorem. Moreover, it allows for a generalization of the CES function to the case where the elasticity of substitution between each pair of inputs is not necessarily the same.

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Paper provided by Sciences Po in its series Sciences Po publications with number 2011-21.

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Date of creation: Oct 2011
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Handle: RePEc:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0

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Keywords: flexible production functions; Cobb-Douglas function; CES function;

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  1. Jesus Felipe & F. Gerard Adams, 2005. ""A Theory of Production" The Estimation of the Cobb-Douglas Function: A Retrospective View," Eastern Economic Journal, Eastern Economic Association, vol. 31(3), pages 427-445, Summer.
  2. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 43-68, January.
  3. Dale W. Jorgenson, 1998. "Growth, Volume 1: Econometric General Equilibrium Modeling," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100738, December.
  4. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
  5. Perroni, C. & Rutherford, T., 1991. "Regular Flexibility of Nested CES Functions," Working Papers, Wilfrid Laurier University, Department of Economics 91145, Wilfrid Laurier University, Department of Economics.
  6. Grant, James H., 1993. "The translog approximate function : Substitution among inputs in manufacturing evaluated at sample means," Economics Letters, Elsevier, vol. 41(3), pages 235-240.
  7. Blanchard, Olivier Jean & Kiyotaki, Nobuhiro, 1987. "Monopolistic Competition and the Effects of Aggregate Demand," American Economic Review, American Economic Association, vol. 77(4), pages 647-66, September.
  8. Matthieu Lemoine & Gian Luigi Mazzi & Paola Monperrus-Veroni & Frédéric Reynes, 2010. "A new production function estimate of the euro area output gap This paper is based on a report for Eurostat: 'Real time estimation of potential output, output gap, NAIRU and Phillips curve for Euro-zo," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 29-53.
  9. Frédéric Reynes & Yasser Yeddir-Tamsamani & Gaël Callonec, 2011. "Presentation of the Three-ME model: Multi-sector Macroeconomic Model for the Evaluation of Environmental and Energy policy," Documents de Travail de l'OFCE, Observatoire Francais des Conjonctures Economiques (OFCE) 2011-10, Observatoire Francais des Conjonctures Economiques (OFCE).
  10. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.
  11. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  12. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
  13. Samuelson, Paul A, 1979. "Paul Douglas's Measurement of Production Functions and Marginal Productivities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 87(5), pages 923-39, October.
  14. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-88, September.
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