Dynamic Pricing and Product Differentiation with Cost Uncertainty and Learning

Motivated by applications in the health insurance industry, we consider a seller who designs and sells a set of vertically differentiated products to a population of quality-sensitive customers. The seller’s business environment entails an uncertainty about production costs. We characterize the seller’s optimal price-quality schedule in the cases of: (a) static cost uncertainty, and (b) dynamic learning about cost uncertainty through noisy observations on an underlying cost curve. We prove that the seller’s optimal quality allocations in (a) and (b) stand in stark contrast: While a seller facing static cost uncertainty degrades the quality in its product offering, a dynamically learning seller improves the quality of its products to accelerate information accumulation. In the case of dynamic learning, we prove that the seller exercises the most extreme experimentation on less quality-sensitive customers. We also extend our results to the cases of commonly used regulations in health insurance industry, and show how such regulations moderate the interplay between uncertainty and learning.