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Deriving multiple-input production and utility functions from elasticities of substitution functions

Author

Listed:
  • Saad Labyad

    (University of Oxford)

  • Mehdi Senouci

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

Abstract

For each production or utility function, we can define the corresponding elasticities of substitution functions; but is the reverse true? This paper shows that yes, and that this link is fruitful. By inverting the system of partial differential equations defining the elasticities of substitution functions, we uncover an analytical formula which encompasses all production and utility functions that are admissible in Arrow-Debreu equilibria. We highlight the "Constant Elasticities of Substitution Matrix" (CESM) class of functions which, unlike the CES functions, does not assume uniform substitutability among all pairs of goods. A shortcoming of our method is that it permits only to control for local concavity while it is difficult to control for global concavity.

Suggested Citation

  • Saad Labyad & Mehdi Senouci, 2018. "Deriving multiple-input production and utility functions from elasticities of substitution functions ," Working Papers hal-01866275, HAL.
    • Handle: RePEc:hal:wpaper:hal-01866275
    Note: View the original document on HAL open archive server: https://hal.science/hal-01866275
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    References listed on IDEAS

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    1. Moysan, Gwenaël & Senouci, Mehdi, 2016. "A note on 2-input neoclassical production functions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 80-86.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. Evgeny Zhelobodko & Sergey Kokovin & Mathieu Parenti & Jacques‐François Thisse, 2012. "Monopolistic Competition: Beyond the Constant Elasticity of Substitution," Econometrica, Econometric Society, vol. 80(6), pages 2765-2784, November.
    4. 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.
    5. Growiec, Jakub & Mućk, Jakub, 2020. "Isoelastic Elasticity Of Substitution Production Functions," Macroeconomic Dynamics, Cambridge University Press, vol. 24(7), pages 1597-1634, October.
    6. Parenti, Mathieu & Ushchev, Philip & Thisse, Jacques-François, 2017. "Toward a theory of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 167(C), pages 86-115.
    7. Lawrence J. Lau, 1976. "A Note on Elasticity of Substitution Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 353-358.
    8. Moysan, Gwenaël & Senouci, Mehdi, 2016. "A note on 2-input neoclassical production functions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 80-86.
    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. 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.
    11. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    12. Revankar, Nagesh S, 1971. "A Class of Variable Elasticity of Substitution Production Functions," Econometrica, Econometric Society, vol. 39(1), pages 61-71, January.
    13. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7.
    14. Joan Robinson, 1969. "The Economics of Imperfect Competition," Palgrave Macmillan Books, Palgrave Macmillan, edition 0, number 978-1-349-15320-6.
    15. 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.
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    More about this item

    Keywords

    Production functions; Utility functions; Elasticity of substitution; Marginal productivity; Marginal utility; Factor shares;
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