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The Cobb-Douglas function as a flexible function

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  • Frédéric Reynés

    (OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po)

Abstract

By defining the Variable Output Elasticities Cobb-Douglas function, this article shows that a large class of production functions can be written as Cobb-Douglas function with non-constant output elasticity. Compared to standard flexible functions such as the Translog function, this framework has several advantages. [1] It does not requires the use of a second order approximation. [2] This greatly facilitates the deduction of linear input demands function without the need of involving the duality theorem. [3] 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. [4] This provides a more general and more flexible framework compared to the traditional nested CES approach while facilitating the analyze of the substitution properties of nested CES functions. The case of substitutions between energy, capital and labor is provided.

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  • Frédéric Reynés, 2017. "The Cobb-Douglas function as a flexible function," Working Papers hal-03582829, HAL.
    • Handle: RePEc:hal:wpaper:hal-03582829
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03582829
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    References listed on IDEAS

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    1. Miguel A. León-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 1330-1357, September.
    2. 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.
    3. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    4. Perroni, Carlo & Rutherford, Thomas F., 1995. "Regular flexibility of nested CES functions," European Economic Review, Elsevier, vol. 39(2), pages 335-343, February.
    5. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    6. Blanchard, Olivier Jean & Kiyotaki, Nobuhiro, 1987. "Monopolistic Competition and the Effects of Aggregate Demand," American Economic Review, American Economic Association, vol. 77(4), pages 647-666, September.
    7. Yazid Dissou & Lilia Karnizova & Qian Sun, 2015. "Industry-level Econometric Estimates of Energy-Capital-Labor Substitution with a Nested CES Production Function," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 43(1), pages 107-121, March.
    8. 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 882-888, September.
    9. Dale W. Jorgenson, 1998. "Growth, Volume 1: Econometric General Equilibrium Modeling," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100738, April.
    10. van der Werf, Edwin, 2008. "Production functions for climate policy modeling: An empirical analysis," Energy Economics, Elsevier, vol. 30(6), pages 2964-2979, November.
    11. 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.
    12. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(2), pages 201-218.
    13. Thompson, Henry, 2006. "The applied theory of energy substitution in production," Energy Economics, Elsevier, vol. 28(4), pages 410-425, July.
    14. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7, March.
    15. 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.
    16. Koetse, Mark J. & de Groot, Henri L.F. & Florax, Raymond J.G.M., 2008. "Capital-energy substitution and shifts in factor demand: A meta-analysis," Energy Economics, Elsevier, vol. 30(5), pages 2236-2251, September.
    17. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    18. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 291-299.
    19. Manuel Frondel & Christoph M. Schmidt, 2002. "The Capital-Energy Controversy: An Artifact of Cost Shares?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 53-79.
    20. Roy, Joyashree & Sanstad, Alan H. & Sathaye, Jayant A. & Khaddaria, Raman, 2006. "Substitution and price elasticity estimates using inter-country pooled data in a translog cost model," Energy Economics, Elsevier, vol. 28(5-6), pages 706-719, November.
    21. Daniel McFadden, 1963. "Constant Elasticity of Substitution Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 73-83.
    22. Samuelson, Paul A, 1979. "Paul Douglas's Measurement of Production Functions and Marginal Productivities," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 923-939, October.
    23. Prywes, Menahem, 1986. "A nested CES approach to capital-energy substitution," Energy Economics, Elsevier, vol. 8(1), pages 22-28, January.
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