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Elasticities of Substitution and Complementarity

  • Stern, David I

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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12454.

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Date of creation: 31 Dec 2008
Date of revision:
Handle: RePEc:pra:mprapa:12454
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  1. 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, 07.
  2. Syrquin, Moshe & Hollender, Gideon, 1982. "Elasticities of Substitution and Complementarity: The General Case," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 515-19, November.
  3. Stern, David I., 2008. "Derivation of the Hicks Elasticity of Substitution from the Input Distance Function," MPRA Paper 12414, University Library of Munich, Germany.
  4. Hicks, John, 1970. "Elasticity of Substitution Again: Substitutes and Complements," Oxford Economic Papers, Oxford University Press, vol. 22(3), pages 289-96, November.
  5. 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.
  6. 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 882-88, September.
  7. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
  8. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
  9. 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 565-69, August.
  10. 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.
  11. 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 245-61, June.
  12. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
  13. 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 1255-89, December.
  14. Blackorby, Charles & Primont, Daniel & Russell, R. Robert, 2007. "The Morishima Gross Elasticity of Substitution," The Warwick Economics Research Paper Series (TWERPS) 787, University of Warwick, Department of Economics.
  15. 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.
  16. 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.
  17. 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.
  18. 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 259-68, August.
  19. 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.
  20. Olivier Grandville, 1997. "Curvature and the elasticity of substitution: Straightening it out," Journal of Economics, Springer, vol. 66(1), pages 23-34, February.
  21. 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 546-52, August.
  22. Apostolakis, Bobby E., 1990. "Energy--capital substitutability/ complementarity : The dichotomy," Energy Economics, Elsevier, vol. 12(1), pages 48-58, January.
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