IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v97y2019icp11-17.html
   My bibliography  Save this article

The Cobb–Douglas function as a flexible function

Author

Listed:
  • Reynès, Frédéric

Abstract

By defining the Variable Output Elasticities Cobb–Douglas function, this article shows that a large class of production functions can be written as a 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 require 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 tractable 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.

Suggested Citation

  • Reynès, Frédéric, 2019. "The Cobb–Douglas function as a flexible function," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 11-17.
    • Handle: RePEc:eee:matsoc:v:97:y:2019:i:c:p:11-17
    DOI: 10.1016/j.mathsocsci.2018.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489618300799
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2018.10.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:hal:spmain:info:hdl:2441/11505qn4ak95irt0cafaeim81j is not listed on IDEAS
    2. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    3. 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.
    4. 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.
    5. Berndt, Ernst R & Wood, David O, 1979. "Engineering and Econometric Interpretations of Energy-Capital Complementarity," American Economic Review, American Economic Association, vol. 69(3), pages 342-354, June.
    6. Thompson, Henry, 2006. "The applied theory of energy substitution in production," Energy Economics, Elsevier, vol. 28(4), pages 410-425, July.
    7. 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.
    8. 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.
    9. 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.
    10. Gissela Landa & Frederic Raynes & Ivan Islas & François-Xavier Bellocq & Fabio Grazi, 2015. "Toward a low carbon growth in Mexico : is a double dividend possible ? A dynamic general equilibrium assessment," Documents de Travail de l'OFCE 2015-24, Observatoire Francais des Conjonctures Economiques (OFCE).
    11. 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.
    12. Perroni, Carlo & Rutherford, Thomas F., 1995. "Regular flexibility of nested CES functions," European Economic Review, Elsevier, vol. 39(2), pages 335-343, February.
    13. van der Werf, Edwin, 2008. "Production functions for climate policy modeling: An empirical analysis," Energy Economics, Elsevier, vol. 30(6), pages 2964-2979, November.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Bulavskaya, Tatyana & Reynès, Frédéric, 2018. "Job creation and economic impact of renewable energy in the Netherlands," Renewable Energy, Elsevier, vol. 119(C), pages 528-538.
    19. Prywes, Menahem, 1986. "A nested CES approach to capital-energy substitution," Energy Economics, Elsevier, vol. 8(1), pages 22-28, January.
    20. 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.
    21. 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.
    22. 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.
    23. Landa Rivera, Gissela & Reynès, Frédéric & Islas Cortes, Ivan & Bellocq, François-Xavier & Grazi, Fabio, 2016. "Towards a low carbon growth in Mexico: Is a double dividend possible? A dynamic general equilibrium assessment," Energy Policy, Elsevier, vol. 96(C), pages 314-327.
    24. 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.
    25. 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.
    26. Dale W. Jorgenson, 1998. "Growth, Volume 1: Econometric General Equilibrium Modeling," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100738, April.
    27. 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.
    28. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hal:spmain:info:hdl:2441/62drs526639gbqbrni9v9kvsv5 is not listed on IDEAS
    2. repec:spo:wpmain:info:hdl:2441/62drs526639gbqbrni9v9kvsv5 is not listed on IDEAS
    3. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," SciencePo Working papers Main hal-03403639, HAL.
    4. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," Post-Print hal-03403639, HAL.
    5. repec:spo:wpmain:info:hdl:2441/1cpd872l2j8lb968d53pu5f30q is not listed on IDEAS
    6. repec:hal:spmain:info:hdl:2441/1cpd872l2j8lb968d53pu5f30q is not listed on IDEAS
    7. Frédéric Reynés, 2017. "The Cobb-Douglas function as a flexible function," Working Papers hal-03582829, HAL.
    8. Frédéric Reynés, 2017. "The Cobb-Douglas function as a flexible function," SciencePo Working papers Main hal-03582829, HAL.
    9. Frédéric Reynès, 2017. "The Cobb-Douglas function as a flexible function. Analysing the substitution between capital, labor and energy," Documents de Travail de l'OFCE 2017-12, Observatoire Francais des Conjonctures Economiques (OFCE).
    10. Frédéric Reynès, 2011. "The cobb-douglas function as an approximation of other functions," SciencePo Working papers Main hal-01069515, HAL.
    11. repec:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    12. Frédéric Reynès, 2011. "The cobb-douglas function as an approximation of other functions," Working Papers hal-01069515, HAL.
    13. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    14. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    15. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    16. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    17. He, Yongda & Lin, Boqiang, 2019. "Heterogeneity and asymmetric effects in energy resources allocation of the manufacturing sectors in China," Energy, Elsevier, vol. 170(C), pages 1019-1035.
    18. Paul E. Brockway & Matthew K. Heun & João Santos & John R. Barrett, 2017. "Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation," Energies, MDPI, vol. 10(2), pages 1-23, February.
    19. 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.
    20. Knoblach, Michael & Rößler, Martin & Zwerschke, Patrick, 2016. "The Elasticity of Factor Substitution Between Capital and Labor in the U.S. Economy: A Meta-Regression Analysis," CEPIE Working Papers 03/16, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    21. David Clive Broadstock, 2010. "Non-linear technological progress and the substitutability of energy for capital: An application using the translog cost function," Economics Bulletin, AccessEcon, vol. 30(1), pages 84-93.
    22. Malliet, Paul & Reynès, Frédéric G., 2022. "Empirical estimates of the elasticity of substitution of a KLEM production function without nesting constraints: The case of the Variable Output Elasticity-Cobb Douglas," Conference papers 333423, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    23. Valeria Costantini & Francesco Crespi & Elena Paglialunga, 2019. "Capital–energy substitutability in manufacturing sectors: methodological and policy implications," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 9(2), pages 157-182, June.
    24. Satoshi Nakano & Kazuhiko Nishimura, 2017. "Structural propagation in a production network with restoring substitution elasticities," Papers 1701.02216, arXiv.org, revised Apr 2018.
    25. Steve Sorrell, 2014. "Energy Substitution, Technical Change and Rebound Effects," Energies, MDPI, vol. 7(5), pages 1-24, April.
    26. Anthony J. Glass & Amangeldi Kenjegaliev & Karligash Kenjegalieva, 2022. "Comparisons of deposit types and implications of the financial crisis: Evidence for U.S. banks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 641-664, January.
    27. Saunders, Harry D., 2008. "Fuel conserving (and using) production functions," Energy Economics, Elsevier, vol. 30(5), pages 2184-2235, September.
    28. Bardazzi, Rossella & Oropallo, Filippo & Pazienza, Maria Grazia, 2015. "Do manufacturing firms react to energy prices? Evidence from Italy," Energy Economics, Elsevier, vol. 49(C), pages 168-181.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:97:y:2019:i:c:p:11-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.