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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

Suggested Citation

  • Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
  • Handle: RePEc:kap:jproda:v:24:y:2005:i:2:p:183-196 DOI: 10.1007/s11123-005-4703-3
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    References listed on IDEAS

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    1. Elvira Silva & Spiro E. Stefanou, 2007. "Dynamic Efficiency Measurement: Theory and Application," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(2), pages 398-419.
    2. Jiro Nemoto & Mika Goto, 2003. "Measurement of Dynamic Efficiency in Production: An Application of Data Envelopment Analysis to Japanese Electric Utilities," Journal of Productivity Analysis, Springer, pages 191-210.
    3. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    4. Elvira Silva & Spiro Stefanou, 2003. "Nonparametric Dynamic Production Analysis and the Theory of Cost," Journal of Productivity Analysis, Springer, vol. 19(1), pages 5-32, January.
    5. Nemoto, Jiro & Goto, Mika, 1999. "Dynamic data envelopment analysis: modeling intertemporal behavior of a firm in the presence of productive inefficiencies," Economics Letters, Elsevier, vol. 64(1), pages 51-56, July.
    6. Pierre Lasserre & Pierre Ouellette, 1999. "Dynamic Factor Demands and Technology Measurement under Arbitrary Expectations," Journal of Productivity Analysis, Springer, pages 219-241.
    7. Pierre Ouellette & Stéphane Vigeant, 2000. "A General Procedure to Recover the Marginal Products of a Cost Minimizing Firm," Journal of Productivity Analysis, Springer, pages 143-162.
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    Cited by:

    1. John Gowdy & Jon D. Erickson, 2005. "The approach of ecological economics," Cambridge Journal of Economics, Oxford University Press, pages 207-222.
    2. 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.
    3. 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.
    4. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, pages 203-208.
    5. Paolo Bertoletti, 2016. "A Note on Consumer Surplus and the Structure of Preferences," DEM Working Papers Series 130, University of Pavia, Department of Economics and Management.
    6. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
    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.
    8. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, pages 79-89.
    9. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
    10. repec:kap:enreec:v:67:y:2017:i:1:d:10.1007_s10640-015-9976-z is not listed on IDEAS
    11. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, pages 79-89.

    More about this item

    Keywords

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

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution

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