A Conjoint Model of Quantity Discounts
Posted: 24 Oct 2012
Date Written: 2012
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 WTP function that depends on both product attributes and product quantity and that captures diminishing marginal WTP. We show how such a function embeds standard WTP functions in the quantity discount literature as special cases. We also demonstrate how to use the model to estimate the consumer value potential, which is the product of the premium a consumer is willing to pay and her volume potential. Finally, we propose a parsimonious experimental design approach for implementation.
We illustrate the model using data from a conjoint study of 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 nondiminishing marginal willingness-to-pay curves. Finally, we identify four segments of consumers that differ in terms of magnitude of WTP and volume potential, and we derive optimal quantity discount schemes for a monopolist and a new entrant in a competitive market.
Keywords: quantity discounts, willingness to pay, choice models, mixed logit, conjoint analysis
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