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Elasticities of substitution and complementarity

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  • David Stern

Abstract

This paper develops a classification scheme of the many different definitions of elasticities of substitution and complementarity in the production case based on duality, gross and net substitution, elasticity type, and four different basic concepts of substitution and complementarity is developed. The classic Berndt-Wood dataset is used to show how the various elasticities differ. This variation is considerable and shows that the correct elasticity should be used for the intended purpose – there is no one true elasticity of substitution. The paper also reintroduces and clarifies Pigou’s contributions to the debate on the elasticity of substitution after seventy years of obscurity in which they have not been cited.
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Suggested Citation

  • David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    • Handle: RePEc:kap:jproda:v:36:y:2011:i:1:p:79-89
    DOI: 10.1007/s11123-010-0203-1
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    16. 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.
    17. Syrquin, Moshe & Hollender, Gideon, 1982. "Elasticities of Substitution and Complementarity: The General Case," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 515-519, November.
    18. 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.
    19. Manuel Frondel & Christoph M. Schmidt, 2002. "The Capital-Energy Controversy: An Artifact of Cost Shares?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 53-79.
    20. Koetse, Mark J. & de Groot, Henri L.F. & Florax, Raymond J.G.M., 2008. "Capital-energy substitution and shifts in factor demand: A meta-analysis," Energy Economics, Elsevier, vol. 30(5), pages 2236-2251, September.
    21. Y. Mundlak, 1968. "Elasticities of Substitution and the Theory of Derived Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 225-236.
    22. 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.
    23. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    24. Thompson, Peter & Taylor, Timothy G, 1995. "The Capital-Energy Substitutability Debate: A New Look," The Review of Economics and Statistics, MIT Press, vol. 77(3), pages 565-569, August.
    25. Kim, H Youn, 1992. "The Translog Production Function and Variable Returns to Scale," The Review of Economics and Statistics, MIT Press, vol. 74(3), pages 546-552, August.
    26. Olivier Grandville, 1997. "Curvature and the elasticity of substitution: Straightening it out," Journal of Economics, Springer, vol. 66(1), pages 23-34, February.
    27. J. R. Hicks, 1936. "Distribution and Economic Progress: A Revised Version," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(1), pages 1-12.
    28. 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.
    29. Stern, David I., 2008. "Derivation of the Hicks Elasticity of Substitution from the Input Distance Function," MPRA Paper 12414, University Library of Munich, Germany.
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    More about this item

    Keywords

    Microeconomics; History of economic thought; Production; Substitution; Elasticity; B21; D12; D24;
    All these keywords.

    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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