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

Abstract:

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. This is because the Generalized Bass Model (GBM), which extends the BM to handle marketing variables, uses only percentage changes in marketing variables and not the actual values of the marketing variables. This restricts the normative use of the GBM, for example, to deriving the optimal price path for a new product, conditional on an assumed launch price, but not the launch price itself. In this paper, we propose a utility-based generalization of the BM which can yield normative prescriptions regarding both the introductory price, as well as the price path after launch, for the new product. We propose two versions of our proposed diffusion model, namely the Bass-Gumbel Diffusion Model (BGDM) and the Bass-Logit Diffusion Model (BLDM). Using empirical data from three product categories, we show that our proposed diffusion models handily outperform the GBM and BM in forecasting new product sales both in sample and out of sample, with the BLDMoutperforming the BGDM. We derive optimal pricing policies for a new product that are implied by the BLDMunder various ranges of model parameters. We explain how managers can use our proposed diffusion model to derive optimal marketing policies in a computationally convenient manner without having to explicitly solve a dynamic optimization problem.

Keywords: Dynamic Pricing, Optimal Pricing, New Products, Diffusion Model, Bass Model (BM), Generalized Bass Model (GBM), New Product Sales Forecasting