Dynamic Pricing for New Products Using a Utility-Based Generalization of the Bass Diffusion Model

The Bass Model (BM) has an excellent track record in the realm of new product sales forecasting. However, its use for optimal dynamic pricing or advertising is relatively limited because the Generalized Bass Model (GBM), which extends the BM to handle marketing variables, uses only percentage changes in marketing variables, rather than their actual values. This restricts the GBM’s prescriptive use, for example, to derive the optimal price path for a new product, conditional on an assumed launch price, but not the launch price itself. In this paper, we employ a utility-based extension of the BM, which can yield normative prescriptions regarding both the introductory price and the price path after launch, for the new product. We offer two versions of this utility-based diffusion model, namely, the Bass-Gumbel Diffusion Model (BGDM) and the Bass-Logit Diffusion Model (BLDM), the latter of which has been previously used. We show that both the BGDM and BLDM handily outperform the GBM in forecasting new product sales using empirical data from four product categories. We discuss how to estimate the BGDM and BLDM in the absence of past sales data. We compare the optimal pricing policy of the BLDM with the GBM and derive optimal pricing policies that are implied by the BLDM under various ranges of model parameters. We illustrate a dynamic pricing approach that allows managers to derive optimal marketing policies in a computationally convenient manner and extend this approach to a competitive, multiproduct case. This paper was accepted by Gui Liberali, Management Science Special Section on Data-Driven Prescriptive Analytics.