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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

    as
    1. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
    2. Jeongwen Chiang, 1991. "A Simultaneous Approach to the Whether, What and How Much to Buy Questions," Marketing Science, INFORMS, vol. 10(4), pages 297-315.
    3. Peter E. Rossi & Robert E. McCulloch & Greg M. Allenby, 1996. "The Value of Purchase History Data in Target Marketing," Marketing Science, INFORMS, vol. 15(4), pages 321-340.
    4. Ruth N. Bolton, 1989. "The Relationship Between Market Characteristics and Promotional Price Elasticities," Marketing Science, INFORMS, vol. 8(2), pages 153-169.
    5. Sha Yang & Yuxin Chen & Greg Allenby, 2003. "Bayesian Analysis of Simultaneous Demand and Supply," Quantitative Marketing and Economics (QME), Springer, vol. 1(3), pages 251-275, September.
    6. Hanemann, W Michael, 1984. "Discrete-Continuous Models of Consumer Demand," Econometrica, Econometric Society, vol. 52(3), pages 541-561, May.
    7. Dipak C. Jain & Naufel J. Vilcassim, 1991. "Investigating Household Purchase Timing Decisions: A Conditional Hazard Function Approach," Marketing Science, INFORMS, vol. 10(1), pages 1-23.
    8. James H. Pedrick & Fred S. Zufryden, 1991. "Evaluating the Impact of Advertising Media Plans: A Model of Consumer Purchase Dynamics Using Single-Source Data," Marketing Science, INFORMS, vol. 10(2), pages 111-130.
    9. Greg M. Allenby, 1989. "A Unified Approach to Identifying, Estimating and Testing Demand Structures with Aggregate Scanner Data," Marketing Science, INFORMS, vol. 8(3), pages 265-280.
    10. Purushottam Papatla, 1996. "A Multiplicative Fixed-Effects Model of Consumer Choice," Marketing Science, INFORMS, vol. 15(3), pages 243-261.
    11. Pradeep K. Chintagunta, 1998. "Inertia and Variety Seeking in a Model of Brand-Purchase Timing," Marketing Science, INFORMS, vol. 17(3), pages 253-270.
    12. William R. Dillon & Sunil Gupta, 1996. "A Segment-Level Model of Category Volume and Brand Choice," Marketing Science, INFORMS, vol. 15(1), pages 38-59.
    13. Neeraj Arora & Greg M. Allenby & James L. Ginter, 1998. "A Hierarchical Bayes Model of Primary and Secondary Demand," Marketing Science, INFORMS, vol. 17(1), pages 29-44.
    14. Daniel McFadden, 1986. "The Choice Theory Approach to Market Research," Marketing Science, INFORMS, vol. 5(4), pages 275-297.
    15. Kwangpil Chang & S. Siddarth & Charles B. Weinberg, 1999. "The Impact of Heterogeneity in Purchase Timing and Price Responsiveness on Estimates of Sticker Shock Effects," Marketing Science, INFORMS, vol. 18(2), pages 178-192.
    16. Randolph E. Bucklin & James M. Lattin, 1991. "A Two-State Model of Purchase Incidence and Brand Choice," Marketing Science, INFORMS, vol. 10(1), pages 24-39.
    17. Scott A. Neslin & Caroline Henderson & John Quelch, 1985. "Consumer Promotions and the Acceleration of Product Purchases," Marketing Science, INFORMS, vol. 4(2), pages 147-165.
    18. Greg M. Allenby & Peter E. Rossi, 1991. "Quality Perceptions and Asymmetric Switching Between Brands," Marketing Science, INFORMS, vol. 10(3), pages 185-204.
    19. Tülin Erdem, 1996. "A Dynamic Analysis of Market Structure Based on Panel Data," Marketing Science, INFORMS, vol. 15(4), pages 359-378.
    20. Robert J. Dolan, 1987. "Quantity Discounts: Managerial Issues and Research Opportunities," Marketing Science, INFORMS, vol. 6(1), pages 1-22.
    21. Jorge M. Silva-Risso & Randolph E. Bucklin & Donald G. Morrison, 1999. "A Decision Support System for Planning Manufacturers' Sales Promotion Calendars," Marketing Science, INFORMS, vol. 18(3), pages 274-300.
    22. Vrinda Kadiyali & Pradeep Chintagunta & Naufel Vilcassim, 2000. "Manufacturer-Retailer Channel Interactions and Implications for Channel Power: An Empirical Investigation of Pricing in a Local Market," Marketing Science, INFORMS, vol. 19(2), pages 127-148, September.
    23. Andrew Ainslie & Peter E. Rossi, 1998. "Similarities in Choice Behavior Across Product Categories," Marketing Science, INFORMS, vol. 17(2), pages 91-106.
    24. Jeongwen Chiang, 1995. "Competing Coupon Promotions and Category Sales," Marketing Science, INFORMS, vol. 14(1), pages 105-122.
    25. Pradeep K. Chintagunta, 2001. "Endogeneity and Heterogeneity in a Probit Demand Model: Estimation Using Aggregate Data," Marketing Science, INFORMS, vol. 20(4), pages 442-456, December.
    26. David R. Bell & James M. Lattin, 1998. "Shopping Behavior and Consumer Preference for Store Price Format: Why “Large Basket” Shoppers Prefer EDLP," Marketing Science, INFORMS, vol. 17(1), pages 66-88.
    27. Rick L. Andrews & Ajay K. Manrai, 1999. "MDS Maps for Product Attributes and Market Response: An Application to Scanner Panel Data," Marketing Science, INFORMS, vol. 18(4), pages 584-604.
    28. Kirthi Kalyanam & Daniel S. Putler, 1997. "Incorporating Demographic Variables in Brand Choice Models: An Indivisible Alternatives Framework," Marketing Science, INFORMS, vol. 16(2), pages 166-181.
    29. Wagner A. Kamakura & Byung-Do Kim & Jonathan Lee, 1996. "Modeling Preference and Structural Heterogeneity in Consumer Choice," Marketing Science, INFORMS, vol. 15(2), pages 152-172.
    30. Robert C. Blattberg & Kenneth J. Wisniewski, 1989. "Price-Induced Patterns of Competition," Marketing Science, INFORMS, vol. 8(4), pages 291-309.
    31. Pradeep K. Chintagunta, 1993. "Investigating Purchase Incidence, Brand Choice and Purchase Quantity Decisions of Households," Marketing Science, INFORMS, vol. 12(2), pages 184-208.
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