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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.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 8/08.

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Length: 32 pages
Date of creation: Oct 2008
Date of revision:
Handle: RePEc:msh:ebswps:2008-8

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Keywords: Benefit Functions; Duality Theory; Numerical Inversion Estimation Method;

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  1. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  2. Beach, Robert H. & Holt, Matthew T., 1999. "Incorporating Quadratic Scale Curves In Inverse Demand Systems," 1999 Annual meeting, August 8-11, Nashville, TN 21579, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  3. Deaton, Angus, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," Review of Economic Studies, Wiley Blackwell, vol. 46(3), pages 391-405, July.
  4. 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.
  5. Pollak, R.A. & Wales, T.J., 1990. "The Likelihood Dominance Criterion: A New Approach To Model Selection," Working Papers 90-10, University of Washington, Department of Economics.
  6. 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.
  7. Michele Baggio & Jean-Paul Chavas, 2006. "On the Consumer Value of Environmental Diversity," Working Papers 35, University of Verona, Department of Economics.
  8. Moschini, GianCarlo & Moro, D., 1994. "Autocorrelation Specification in Singular Equation Systems," Staff General Research Papers 11134, Iowa State University, Department of Economics.
  9. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  10. Hanoch, Giora, 1975. "Production and Demand Models with Direct or Indirect Implicit Additivity," Econometrica, Econometric Society, vol. 43(3), pages 395-419, May.
  11. Holt, Matthew T., 2002. "Inverse demand systems and choice of functional form," European Economic Review, Elsevier, vol. 46(1), pages 117-142, January.
  12. Eales, James S. & Unnevehr, Laurian J., 1994. "The inverse almost ideal demand system," European Economic Review, Elsevier, vol. 38(1), pages 101-115, January.
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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. Wong, K.K. Gary, 2013. "An empirical investigation of the trade benefit function," Economics Letters, Elsevier, vol. 119(2), pages 150-153.
  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. repec:hal:wpaper:halshs-00447417 is not listed on IDEAS
  5. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
  6. 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.
  7. Anonymous & Bosch, Darrell J., 2013. "Table of contents," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 45(02), May.

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