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Inada conditions imply that production function must be asymptotically Cobb-Douglas

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  • Barelli, Paulo
  • de Abreu Pessoa, Samuel

Abstract

We show that every twice-continuously differentiable and strictly concave function f : R+ → R+ can be bracketed between two C.E.S. functions at each open interval. In particular, for the Inada conditions to hold, a production function must be asymptotically Cobb-Douglas.
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  • Barelli, Paulo & de Abreu Pessoa, Samuel, 2003. "Inada conditions imply that production function must be asymptotically Cobb-Douglas," Economics Letters, Elsevier, vol. 81(3), pages 361-363, December.
    • Handle: RePEc:eee:ecolet:v:81:y:2003:i:3:p:361-363
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    1. Ken-ichi Inada, 1963. "On a Two-Sector Model of Economic Growth: Comments and a Generalization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 119-127.
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    Cited by:

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    2. Constantin Chilarescu, 2019. "A Production Function with Variable Elasticity of Factor Substitution," Economics Bulletin, AccessEcon, vol. 39(4), pages 2343-2360.
    3. de la Fonteijne, Marcel R., 2015. "Do Inada Conditions imply Cobb-Douglas Asymptotic Behavior or only a Elasticity of Substitution equal to one," MPRA Paper 82304, University Library of Munich, Germany.
    4. Mehdi Senouci, 2012. "Technical change in a neoclassical two-sector model of optimal growth," Working Papers halshs-00589627, HAL.
    5. repec:ebl:ecbull:v:3:y:2007:i:9:p:1-8 is not listed on IDEAS
    6. Lee E. Ohanian & Paulina Restrepo-Echavarria & Mark L. J. Wright, 2018. "Bad Investments and Missed Opportunities? Postwar Capital Flows to Asia and Latin America," American Economic Review, American Economic Association, vol. 108(12), pages 3541-3582, December.
    7. Suen, Richard M. H., 2009. "Bounding the CRRA Utility Functions," MPRA Paper 13260, University Library of Munich, Germany.
    8. Lee E. Ohanian & Paulina Restrepo-Echavarria & Mark L. J. Wright, 2013. "Bad Investments and Missed Opportunities? Capital Flows to Asia and Latin America, 1950-2007," Working Papers 2014-38, Federal Reserve Bank of St. Louis.
    9. Litina, Anastasia & Palivos, Theodore, 2010. "The Behavior Of The Saving Rate In The Neoclassical Optimal Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 14(4), pages 482-500, September.
    10. Nicol`o Cangiotti & Mattia Sensi, 2020. "Exact solutions for a Solow-Swan model with non-constant returns to scale," Papers 2008.05875, arXiv.org.
    11. Stefan baumgärtner, 2004. "The Inada Conditions for Material Resource Inputs Reconsidered," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 29(3), pages 307-322, November.
    12. Alcalá, Luis A., 2014. "On the relation between regular variation and the asymptotic elasticity of substitution," Economics Letters, Elsevier, vol. 125(1), pages 29-31.
    13. Gilberto Gonz'alez-Parra & Benito Chen-Charpentier & Abraham J. Arenas & Miguel Diaz-Rodriguez, 2015. "Mathematical modeling of physical capital using the spatial Solow model," Papers 1504.04388, arXiv.org.
    14. Jürgen Antony, 2010. "A class of changing elasticity of substitution production functions," Journal of Economics, Springer, vol. 100(2), pages 165-183, June.
    15. Richard Green & Nicholas Vasilakos, 2012. "Storing Wind for a Rainy Day: What Kind of Electricity Does Denmark Export?," The Energy Journal, , vol. 33(3), pages 1-22, July.
    16. Andrés Álvarez & Camilo Gómez & Hernando Zuleta, 2019. "Bequests, Imperfections in Factor Markets, and Long-Run Inequality: A Theoretical Assessment of Piketty," Documentos CEDE 17674, Universidad de los Andes, Facultad de Economía, CEDE.
    17. Ozkaya, Ata, 2021. "Inada conditions asymptotically transform production function into the Cobb–Douglas," Economics Letters, Elsevier, vol. 201(C).
    18. Constantin Chilarescu & Nicolas Vaneecloo, 2007. "A Stochastic Approach to the Cobb-Douglas Production Function," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    19. Mattauch, Linus & Klenert, David & Stiglitz, Joseph E. & Edenhofer, Ottmar, 2022. "Overcoming wealth inequality by capital taxes that finance public investment," Structural Change and Economic Dynamics, Elsevier, vol. 63(C), pages 383-395.
    20. Wahl, Jack E. & Broll, Udo, 2009. "Mitigation of foreign Direct investment risk and hedging," Dresden Discussion Paper Series in Economics 13/09, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    21. David I. Stern and Astrid Kander, 2012. "The Role of Energy in the Industrial Revolution and Modern Economic Growth," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    22. Shintaro Nakagawa & Masayuki Sato & Rintaro Yamaguchi, 2014. "Environment, growth, and technological change in a two-country overlapping-generations model," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 16(4), pages 397-443, October.
    23. Litina, Anastasia & Palivos, Theodore, 2008. "Do Inada conditions imply that production function must be asymptotically Cobb-Douglas? A comment," Economics Letters, Elsevier, vol. 99(3), pages 498-499, June.
    24. Serguei Kaniovski & Thomas Url & Helmut Hofer & Viola Garstenauer, 2021. "A Long-run Macroeconomic Model of the Austrian Economy (A-LMM 2.0). New Results (2021)," WIFO Studies, WIFO, number 67377.

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