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The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory

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  • Keith R. McLaren

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  • K. K. Gary Wong

Abstract

In this article we advocate more extensive use of the benefit function in specifying price-dependent or inverse demand models. In particular, we demonstrate how duality theory may be used to establish the inter-relationships between the Marshallian (or Hicksian) inverse demands and Luenberger's adjusted price functions, allowing estimable inverse demands to be derived directly from a benefit function. We also make use of a numerical inversion estimation method to rectify the "unobservability of utility problem" encountered in the empirical analysis of these inverse demands. To illustrate the usefulness of the proposed methods, we estimate two systems of inverse demands for Japanese quarterly fish consumption. Results generally indicate that the proposed methods are promising and operationally feasible so that we have opened up a wider range of empirical inverse demand specifications that can be subjected to tight theoretical restrictions.

Suggested Citation

  • Keith R. McLaren & K. K. Gary Wong, 2008. "The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory," Monash Econometrics and Business Statistics Working Papers 8/08, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2008-8
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2008/wp8-08.pdf
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    1. James Eales & Catherine Durham & Cathy R. Wessells, 1997. "Generalized Models of Japanese Demand for Fish," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(4), pages 1153-1163.
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    3. Robert H. Beach & Matthew T. Holt, 2001. "Incorporating Quadratic Scale Curves in Inverse Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(1), pages 230-245.
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    7. Hanoch, Giora, 1975. "Production and Demand Models with Direct or Indirect Implicit Additivity," Econometrica, Econometric Society, vol. 43(3), pages 395-419, May.
    8. Angus Deaton, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," Review of Economic Studies, Oxford University Press, vol. 46(3), pages 391-405.
    9. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    10. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    11. Hoanjae Park & Walter N. Thurman, 1999. "On Interpreting Inverse Demand Systems: A Primal Comparison of Scale Flexibilities and Income Elasticities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(4), pages 950-958.
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    Cited by:

    1. Hovhannisyan, Vardges & Stiegert, Kyle W. & Bozic, Marin, 2013. "On Endogeneity Of Retail Market Power In An Equilibrium Analysis: A Control Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149830, Agricultural and Applied Economics Association.
    2. Anonymous & Marchant, Mary A. & McKenzie, Andrew M. & Paudel, Krishna P., 2014. "Table of Content," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 46(02), May.
    3. Hovhannisyan, Vardges & Bozic, Marin, 2013. "A Benefit-Function Approach to Studying Market Power: An Application to the U.S. Yogurt Market," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(2), August.
    4. Chavas, Jean-Paul, 2013. "On Demand Analysis and Dynamics: A Benefit Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149683, Agricultural and Applied Economics Association.
    5. Wong, K.K. Gary, 2013. "An empirical investigation of the trade benefit function," Economics Letters, Elsevier, vol. 119(2), pages 150-153.
    6. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
    7. Jean-Michel Courtault & Bertrand Crettez & Naïla Hayek, 2008. "Complementarity and Substitutability: A Dual Approach Based on Luenberger's Benefit Function," Working Papers halshs-00447417, HAL.

    More about this item

    Keywords

    Benefit Functions; Duality Theory; Numerical Inversion Estimation Method;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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