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Elasticities of Substitution and Complementarity: A Synthesis

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  • Paolo Bertoletti

Abstract

We derive the relationships between the net and gross elasticities of substitution and complementarity (i.e., the elasticities that refer either to the conditional or unconditional, direct or inverse demand system) in the general case of non-homothetic, variable-returns-to-scale technologies. We also show that the so-called Hicks Elasticity of Complementarity (Hicks, Oxford economic Papers 22, 289–296 (1970)) is dual to a full-fledged elasticity of gross input substitution that we call the Hotelling/Lau Elasticity of Substitution (Lau, Production Economics: A Dual Approach to Theory and Applications. Amsterdam: North-Holand (1978)). The former is, in fact, the proper elasticity of substitution in the case of the inverse, unconditional input demand. Our results should clarify some issues about the input substitutability classification. Copyright Springer Science+Business Media, Inc. 2005

Suggested Citation

  • Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
    • Handle: RePEc:kap:jproda:v:24:y:2005:i:2:p:183-196
    DOI: 10.1007/s11123-005-4703-3
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    Citations

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    Cited by:

    1. Johannes Bröcker & Till Requate, 2022. "Substitution and size effect for factor demand revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 251-265, October.
    2. 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.
    3. Paolo Bertoletti, 2016. "A Note on Consumer Surplus and the Structure of Preferences," DEM Working Papers Series 130, University of Pavia, Department of Economics and Management.
    4. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
    5. Paolo Bertoletti & Giorgio Rampa, 2011. "On Marginal Returns and Inferior Inputs," Quaderni di Dipartimento 145, University of Pavia, Department of Economics and Quantitative Methods.
    6. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
    7. Yipu Pang & Jingqi Dang & Wei Xu, . "Elasticity of Substitution, Price Effect and Sustainable Fertilizer Use: A TRANSLOG and SUR Analysis in China," Prague Economic Papers, Prague University of Economics and Business, vol. 0.
    8. Yipu Pang & Jingqi Dang & Wei Xu, 2021. "Elasticity of Substitution, Price Effect and Sustainable Fertilizer Use: A Translog and SUR Analysis in China," Prague Economic Papers, Prague University of Economics and Business, vol. 2021(2), pages 189-215.
    9. Bertoletti, Paolo, 2018. "A note on Ramsey pricing and the structure of preferences," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 45-51.
    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. Stefan Baumgaertner & Moritz A. Drupp & Martin F. Quaas, 2013. "Subsistence and substitutability in consumer preferences," Working Paper Series in Economics 290, University of Lüneburg, Institute of Economics.
    13. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    14. Stefan Baumgärtner & Moritz A. Drupp & Martin F. Quaas, 2017. "Subsistence, Substitutability and Sustainability in Consumption," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(1), pages 47-66, May.

    More about this item

    Keywords

    elasticity of substitution and complementarity; inverse demand; returns to scale; 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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