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The Structure of Constant Elasticity Demand Models



The demand model with constant price and income elasticities has been used extensively in applied agricultural economics. This paper analyzes the structure of incomplete systems of constant elasticity demand functions. It is demonstrated that there is a duality theory for incomplete demand systems that is analogous to the duality theory for complete systems. This theory permits the recovery of that portion of the direct and indirect preferences pertaining to the goods of interest, and we can calculate exact welfare measures for changes in income and in the prices of these goods. For an incomplete system of constant elasticity demands, the Slutsky symmetry restrictions for integrability are presented and the implied structure of the direct and indirect preferences with respect to the prices and goods of interest is derived.

Suggested Citation

  • Jeffrey T. LaFrance, 1986. "The Structure of Constant Elasticity Demand Models," Monash Economics Working Papers archive-28, Monash University, Department of Economics.
  • Handle: RePEc:mos:moswps:archive-28

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    1. Lanfranco, Bruno A. & Ames, Glenn C.W. & Huang, Chung L., 2002. "Comparisons Of Hispanic Households' Demand For Meats With Other Ethnic Groups," Journal of Food Distribution Research, Food Distribution Research Society, vol. 33(01), March.
    2. Kojima, Yasutomo & Parcell, Joseph L. & Cain, Jewelwayne S., 2014. "A Demand Model of the Wholesale Vegetable Oils Market in the U.S.A," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162472, Southern Agricultural Economics Association.
    3. Buhr, Brian L., 1993. "A Quarterly Econometric Simulation Model Of The U.S. Livestock And Meat Sector," Staff Papers 13465, University of Minnesota, Department of Applied Economics.
    4. Heien, Dale, 1988. "Consumer Welfare Measures: Some Comparative Results," Northeastern Journal of Agricultural and Resource Economics, Northeastern Agricultural and Resource Economics Association, vol. 17(2), October.
    5. Lanfranco, Bruno A. & Ames, Glenn C.W. & Huang, Chung L., 2001. "Comparisons Of Hispanic Households' Demand For Meat With Other Ethnic Groups," Faculty Series 16710, University of Georgia, Department of Agricultural and Applied Economics.
    6. Jeffrey T. LaFrance & Rulon D. Pope, 2010. "Duality Theory for Variable Costs in Joint Production," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(3), pages 755-762.
    7. Coloma, German, 2009. "Estimation of Demand Systems Based on Elasticities of Substitution," Review of Applied Economics, Review of Applied Economics, vol. 5(1-2).
    8. Tey, (John) Yeong-Sheng & Shamsudin, Mad Nasir & Mohamed, Zainalabidin & Abdullah, Amin Mahir & Radam, Alias, 2008. "Demand for beef in Malaysia: Quality or Quantity?," MPRA Paper 15035, University Library of Munich, Germany.
    9. Kesavan, Thulasiram, 1988. "Monte Carlo experiments of market demand theory," ISU General Staff Papers 198801010800009854, Iowa State University, Department of Economics.
    10. Just, Richard E. & Gilligan, Daniel O., 1998. "Compensating Variation Without Apology? Willingness-To-Pay And The Failure Of Integrability," 1998 Annual meeting, August 2-5, Salt Lake City, UT 20814, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Loehman, Edna T., 1991. "Alternative Measures of Benefit for Nonmarket Goods Which are Substitutes or Complements for Market Goods," Working Papers 115913, Regional Research Project NE-165 Private Strategies, Public Policies, and Food System Performance.
    12. Jeffrey T. LaFrance, 1990. "Incomplete Demand Systems And Semilogarithmic Demand Models," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 34(2), pages 118-131, August.
    13. Phaneuf, Daniel J. & Smith, V. Kerry, 2006. "Recreation Demand Models," Handbook of Environmental Economics,in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 2, chapter 15, pages 671-761 Elsevier.
    14. Yinger, John, 2015. "Hedonic markets and sorting equilibria: Bid-function envelopes for public services and neighborhood amenities," Journal of Urban Economics, Elsevier, vol. 86(C), pages 9-25.
    15. Tongeren, Frank van & Meijl, Hans van & Surry, Yves, 2001. "Global models applied to agricultural and trade policies: a review and assessment," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 26(2), November.
    16. Terry L. Kastens & Gary W. Brester, 1996. "Model Selection and Forecasting Ability of Theory-Constrained Food Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(2), pages 301-312.
    17. Larson, Douglas M. & Lew, Daniel K. & Shaikh, Sabina L., 2002. "Estimating The Opportunity Cost Of Recreation Time In An Integrable 2-Constraint Count Demand Model," 2002 Annual meeting, July 28-31, Long Beach, CA 19600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    18. Chanyalew, Demese & Belete, Abenet, 1997. "A Statistical Analysis Of Demand For Beef, Mutton/Goat, Pork And Chicken In Kenya, 1961-1991," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 36(1), March.
    19. Eldon V. Ball & Ricardo Cavazos & Jeffrey T. LaFrance & Rulon Pope & Jesse Tack, 2010. "Aggregation and Arbitrage in Joint Production," Monash Economics Working Papers archive-22, Monash University, Department of Economics.
    20. Guijing WANG & Stanley M. FLETCHER & Dale H. CARLEY, "undated". "Determinants Of Demand For Beef: The Impact Of Fat Trimming," Department of Resource Economics Regional Research Project 95412, University of Massachusetts.


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