Quantity discount pricing is a common practice used by business-to-business and business-to-consumer companies. A key characteristic of quantity discount pricing is that the marginal price declines with higher purchase quantities. In this paper, we propose a choice-based conjoint model for estimating consumer-level willingness-to-pay (WTP) for varying quantities of a product and for designing optimal quantity discount pricing schemes. Our model can handle large quantity values and produces WTP estimates that are positive and increasing in quantity at a diminishing rate. In particular, we propose a tractable utility function which depends on both product attributes and product quantity and which captures diminishing marginal utility. We show how such a function embeds standard utility functions in the quantity discount literature as special cases and how to use it to estimate the WTP function and consumer value potential. We also propose an experimental design approach for implementation.
We illustrate the model using data from a conjoint study concerning online movie rental services. The empirical results show that the proposed model has good fit and predictive validity. In addition, we find that marginal WTP in this category decays rapidly with quantity. We also find that the standard choice-based conjoint model results in anomalous WTP distributions with negative WTP values and non-diminishing marginal willingness-to-pay curves. Finally, we identify four segments of consumers that differ in terms of magnitude of WTP and volume potential and derive optimal quantity discount schemes for a monopolist and a new entrant in a competitive market.
Iyengar, Raghuram, and Kamel Jedidi. "A Conjoint Model of Quantity Discounts." Marketing Science 31, no. 2 (2012): 334-350.
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