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Elasticities of Substitution and Complementarity: A Synthesis

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  • Paolo Bertoletti

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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

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File URL: http://hdl.handle.net/10.1007/s11123-005-4703-3
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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 24 (2005)
Issue (Month): 2 (October)
Pages: 183-196

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Handle: RePEc:kap:jproda:v:24:y:2005:i:2:p:183-196

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: elasticity of substitution and complementarity; inverse demand; returns to scale; homotheticity; D11; D24; D33;

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Cited by:
  1. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
  2. 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.
  3. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
  4. 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.
  5. David I. Stern, 2004. "Elasticities of Substitution and Complementarity," Rensselaer Working Papers in Economics 0403, Rensselaer Polytechnic Institute, Department of Economics.
  6. 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.
  7. Paolo Bertoletti & Giorgio Rampa, 2011. "On Marginal Returns and Inferior Inputs," Quaderni di Dipartimento 145, University of Pavia, Department of Economics and Quantitative Methods.

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