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Elasticities of Substitution and Complementarity

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  • David I. Stern

    () (Department of Economics, Rensselaer Polytechnic Institute, Troy NY 12180-3590, USA)

Abstract

This paper is a modern synthesis of the more than seventy years of literature on the elasticity of substitution. At times, authors, such as Mundlak, have provided syntheses of the literature but these often seem to be forgotten by later authors and particularly by applied economists. I synthesize several of these approaches with the full development of duality theory. There are many different legitimate definitions of the ES and the elasticity of complementarity (EC). None of these is the one true ES - which one is useful depends on what we wish to measure. As their value and even sign can vary dramatically, the choice of the appropriate indicator is important. I propose a classification scheme: primal vs. dual measures, gross vs. net measures, ratio, scalar and mixed elasticities, and four different basic concepts of substitution and complementarity. Additionally, the Pigou Elasticity of Complementarity is reintroduced after seventy years of obscurity and a new derivation of the basic Hicks (or direct) ES is provided. The implications for the energy-capital controversy are also briefly discussed and an empirical example shows how the various elasticities differ.

Suggested Citation

  • David I. Stern, 2004. "Elasticities of Substitution and Complementarity," Rensselaer Working Papers in Economics 0403, Rensselaer Polytechnic Institute, Department of Economics.
  • Handle: RePEc:rpi:rpiwpe:0403
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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, May.
    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. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
    10. 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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    12. Hongil Lim & C. Richard Shumway, 1997. "Technical Change and Model Specification: U.S. Agricultural Production," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(2), pages 543-554.
    13. 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.
    14. Peter Broer, 2004. "The Elasticities of Complementarity and Substitution," Tinbergen Institute Discussion Papers 04-101/1, Tinbergen Institute.
    15. Apostolakis, Bobby E., 1990. "Energy--capital substitutability/ complementarity : The dichotomy," Energy Economics, Elsevier, vol. 12(1), pages 48-58, January.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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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    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • D1 - Microeconomics - - Household Behavior
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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