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The Morishima gross elasticity of substitution

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  • Charles Blackorby
  • Daniel Primont
  • R. Russell

Abstract

We show that the Hotelling-Lau elasticity of substitution, an extension of the Allen-Uzawa elasticity to allow for optimal output-quantity (or utility) responses to changes in factor prices, inherits all of the failings of the Allen-Uzawa elasticity identified by Blackorby and Russell [1989 AER]. An analogous extension of the Morishima elasticity of substitution to allow for output quantity changes preserves the salient properties of the original Hicksian notion of elasticity of substitution.
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  • 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.
    • Handle: RePEc:kap:jproda:v:28:y:2007:i:3:p:203-208
    DOI: 10.1007/s11123-007-0053-7
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    1. 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.
    2. Kim, H Youn, 2000. "The Antonelli versus Hicks Elasticity of Complementary and Inverse Input Demand Systems," Australian Economic Papers, Wiley Blackwell, vol. 39(2), pages 245-261, June.
    3. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    4. H. Youn Kim, 2000. "The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems," Australian Economic Papers, Wiley Blackwell, vol. 39(2), pages 245-261, June.
    5. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
    6. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    7. Paolo Bertoletti, 2001. "The Allen/Uzawa Elasticity of Substitution as a Measure of Gross input Substitutability," Rivista italiana degli economisti, Società editrice il Mulino, issue 1, pages 87-94.
    8. 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.
    9. Lau, Lawrence J., 1978. "Applications of Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 3, McMaster University Archive for the History of Economic Thought.
    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. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
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    Cited by:

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    2. Baral, Ranju & Davis, George C. & You, Wen, 2011. "Consumption time in household production: Implications for the goods-time elasticity of substitution," Economics Letters, Elsevier, vol. 112(2), pages 138-140, August.
    3. 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.
    4. Gregory G. Lubiani & Albert A. Okunade, 2013. "Production Cost Structure In Us Outpatient Physical Therapy Health Care," Health Economics, John Wiley & Sons, Ltd., vol. 22(2), pages 212-223, February.
    5. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    6. William A. Barnett & Isaac Kalonda Kanyama, 2013. "Time-varying parameters in the almost ideal demand system and the Rotterdam model: will the best specification please stand up?," Applied Economics, Taylor & Francis Journals, vol. 45(29), pages 4169-4183, October.
    7. Saumik Paul & Kunal Sen, 2023. "Construction productivity and global inequality," WIDER Working Paper Series wp-2023-135, World Institute for Development Economic Research (UNU-WIDER).
    8. Yijian He & Subhash C. Sharma, 1995. "The Morishima Elasticity of Substitution for the Profit Function," Microeconomics 9502002, University Library of Munich, Germany, revised 17 Feb 1995.
    9. Timothy Park & Johannes Sauer, 2013. "Evaluating food retailers using dual elasticities of substitution," Journal of Productivity Analysis, Springer, vol. 39(2), pages 111-122, April.
    10. Elena Burmistrova & Sergey Lobanov, 2018. "The Allen--Uzawa elasticity of substitution for nonhomogeneous production functions," Papers 1802.06885, arXiv.org.
    11. Bas Jacobs & A. Lans Bovenberg, 2011. "Optimal Taxation of Human Capital and the Earnings Function," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 957-971, December.
    12. Pant, Hom, 2015. "A generic approach to investment allocation in recursively dynamic CGE models," Conference papers 332649, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    13. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    14. Albert Okunade & Vasudeva Murthy, 2008. "Are physician and non-physician providers of outpatient mental healthcare substitutes or complements? a conceptual clarification," Health Care Management Science, Springer, vol. 11(4), pages 393-398, December.

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    More about this item

    Keywords

    Elasticity of substitution; Relative factor shares; Homotheticity; D11; D24; D33;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution

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