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The Allen--Uzawa elasticity of substitution for nonhomogeneous production functions

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Abstract

This note proves that the representation of the Allen elasticity of substitution obtained by Uzawa for linear homogeneous functions holds true for nonhomogeneous functions. It is shown that the criticism of the Allen-Uzawa elasticity of substitution in the works of Blackorby, Primont, Russell is based on an incorrect example.

Suggested Citation

  • Elena Burmistrova & Sergey Lobanov, 2018. "The Allen--Uzawa elasticity of substitution for nonhomogeneous production functions," Papers 1802.06885, arXiv.org.
  • Handle: RePEc:arx:papers:1802.06885
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    References listed on IDEAS

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    1. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7, March.
    2. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    3. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
    4. Kusum Mundra, 2013. "Direct and dual elasticities of substitution under non-homogenous technology and nonparametric distribution," Indian Growth and Development Review, Emerald Group Publishing, vol. 6(2), pages 260 - 288, October.
    5. Charles Blackorby & R. Robert Russell, 1981. "The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and its Relationship to the Hicks and Allen Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 147-158.
    6. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, vol. 28(3), pages 203-208, December.
    7. Mario García Molina, 2005. "Capital theory and the origins of the elasticity of substitution (1932--35)," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 29(3), pages 423-437, May.
    8. 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.
    9. George C. Davis & C. Richard Shumway, 1996. "To Tell the Truth about Interpreting the Morishima Elasticity of Substitution," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 44(2), pages 173-182, July.
    10. 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.
    11. Olivier Grandville, 1997. "Curvature and the elasticity of substitution: Straightening it out," Journal of Economics, Springer, vol. 66(1), pages 23-34, February.
    12. 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.
    13. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
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