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Elasticities of Substitution and Complementarity

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  • Stern, David I

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.

Suggested Citation

  • Stern, David I, 2008. "Elasticities of Substitution and Complementarity," MPRA Paper 12454, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:12454
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    References listed on IDEAS

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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," Review of Economic Studies, Oxford University Press, vol. 48(1), pages 147-158.
    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. 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.
    4. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, August.
    5. 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.
    6. 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.
    7. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-296, November.
    8. Olivier Grandville, 1997. "Curvature and the elasticity of substitution: Straightening it out," Journal of Economics, Springer, vol. 66(1), pages 23-34, February.
    9. Stern, David I., 2008. "Derivation of the Hicks Elasticity of Substitution from the Input Distance Function," MPRA Paper 12414, University Library of Munich, Germany.
    10. J. R. Hicks, 1936. "Distribution and Economic Progress: A Revised Version," Review of Economic Studies, Oxford University Press, vol. 4(1), pages 1-12.
    11. Berndt, Ernst R & Wood, David O, 1975. "Technology, Prices, and the Derived Demand for Energy," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 259-268, August.
    12. Peter Broer, 2004. "The Elasticities of Complementarity and Substitution," Tinbergen Institute Discussion Papers 04-101/1, Tinbergen Institute.
    13. 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.
    14. Subhash C. Sharma, 2002. "The Morishima Elasticity of Substitution for the Variable Profit Function and the Demand for Imports in the United States," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 115-135, February.
    15. 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.
    16. 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.
    17. 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.
    18. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
    19. Sato, Ryuzo & Koizumi, Tetsunori, 1973. "On the Elasticities of Substitution and Complementarity," Oxford Economic Papers, Oxford University Press, vol. 25(1), pages 44-56, March.
    20. Y. Mundlak, 1968. "Elasticities of Substitution and the Theory of Derived Demand," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 225-236.
    21. 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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    More about this item

    Keywords

    Microeconomics; history of economic thought; production; substitution; elasticity;
    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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