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A Choice Model for Packaged Goods: Dealing with Discrete Quantities and Quantity Discounts

Author

Listed:
  • Greg M. Allenby

    (Fisher College of Business, Ohio State University, 2100 Neil Avenue, Columbus, Ohio 43210)

  • Thomas S. Shively

    (Department of Management Science and Information Systems, The University of Texas at Austin, Austin, Texas 78712)

  • Sha Yang

    (Stern School of Business, 44 W. 44th Street, New York, New York 10012)

  • Mark J. Garratt

    (Strategic Modeling and Forecasting, Miller Brewing Company, 3939 W. Highland Boulevard, Milwaukee, Wisconsin 53201)

Abstract

Utility maximizing solutions to economic models of choice for goods with either discrete quantities or non-linear prices cannot always be obtained using standard first-order conditions such as Kuhn-Tucker and Roy's identity. When quantities are discrete, there is no guarantee that derivatives of the utility function are equal to derivatives of the budget constraint. Moreover, when prices are nonlinear, as in the case of quantity discounts, first-order conditions can be associated with the minimum rather than the maximum value of utility. In these cases, the utility function must be directly evaluated to determine its maximum. This evaluation can be computationally challenging when there exist many offerings and when stochastic elements are introduced into the utility function. In this paper, we provide an economic model of demand for substitute brands that is flexible, parsimonious, and easy to implement. The methodology is demonstrated with a scanner panel data set of light-beer purchases. The model is used to explore the effects of price promotions on primary and secondary demand, and the utility of product assortment.

Suggested Citation

  • Greg M. Allenby & Thomas S. Shively & Sha Yang & Mark J. Garratt, 2004. "A Choice Model for Packaged Goods: Dealing with Discrete Quantities and Quantity Discounts," Marketing Science, INFORMS, vol. 23(1), pages 95-108, June.
    • Handle: RePEc:inm:ormksc:v:23:y:2004:i:1:p:95-108
    DOI: 10.1287/mksc.1030.0022
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    References listed on IDEAS

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