Drug Pricing for Competing Pharmaceutical Manufacturers Distributing through a Common PBM

We study the price competition among multiple branded drug manufacturers when their drugs are distributed through a common pharmacy benefit manager (PBM). The PBM develops a drug benefit plan for its clients, which includes a formulary list that specifies the copayment for each branded drug, and a list of prices to be charged to the clients for each of the branded and generic drugs. Client organizations decide whether to contract with the PBM and pay the majority of drug costs, while the plan enrollees select which drug to consume. An important feature when multiple branded drugs are distributed through a common PBM is that the PBM's market size, measured by the number of prescriptions filled, depends on the aggregate attraction of all the drugs under the PBM's plan. Therefore, the branded drug manufacturers involuntarily cooperate in affecting the PBM's market size, while competing for the market shares under the PBM's plan, which leads to an intricate co-opetition among the branded drug manufacturers. We characterize the PBM's optimal copayment and pricing decisions, and establish conditions for the equilibrium analysis of the price competition among the branded drug manufacturers. In particular, we provide a sufficient condition for the uniqueness of the equilibrium, and characterize the equilibrium in closed form. We apply our model to study the strategic implications of vertical integration between a branded drug manufacturer and the PBM. By comparing the pre- and post-integration equilibrium outcomes, we characterize the impact of vertical integration on the branded drugs' market shares and copayments, the non-integrated branded drug manufacturers' effective wholesale prices and profits, the integrated PBM's total market size and profit, the aggregate profit of all branded drug manufacturers and the PBM, consumer surplus, and social welfare. We further explore the impact of vertical integration through numerical study.