DRG prospective payment system: refine or not refine?

We present a model of contracting between a purchaser of health services and a provider (a hospital). We assume that hospitals provide two alternative treatments for a given diagnosis: a less intensive one (for example a medical treatment) and a more intensive one (surgical treatment). We assume that prices are set equal to the average cost reported by the providers, as observed in many OECD countries (yardstick competition). The purchaser has two options: 1) to set one tariff based on the diagnosis only; 2) to differentiate the tariff between the surgical and the medical treatment (i.e.to refine the tariff). We show that when tariffs are refined, the provider has always an incentive to overprovide the surgical treatment. If the tariff is not refined, the hospital underprovides the surgical treatment (and overprovides the medical treatment) if the degree of altruism is sufficiently low compared the opportunity cost of public funds. Our main result is that price refinement might not be optimal.