An Empirical Investigation of the Optimal Design of Quantity-based Subscription Plans

Abstract

We empirically investigate the effects of quantity-based subscription plans on the subscription and usage behaviors of consumers. Our goal is to help firms design an optimal menu, which involves the number of subscription plans and the size and price of each plan, that will maximize their profit. We also investigate the impact on consumer welfare under the optimal menu. Utilizing data from a fitness center that offers personal training sessions, we develop a structural model of user subscription and consumption choices under a menu of subscription plans. Our model flexibly captures rich consumer heterogeneities in exercise preferences and price sensitivities, using a Gaussian Mixture distribution specification. It also allows users to have usage uncertainties due to the time difference between subscription and consumption choices. Based on the estimation results, we run a series of counterfactuals to explore the optimal menu design. We use a two-stage neural network algorithm and show its advantages over the standard numerical search algorithm when the menu design involves a large number of decision variables under rich heterogeneities. Our research provides empirical insights and practical implications for firms who seek to capitalize on the full potential of subscription plans.