Patients' free choice of physicians is not always good

We present a model of learning in healthcare markets. Hospitals have junior physicians with low and senior physicians with high ability. Junior physicians turn senior if they treat enough patients. Patients face heterogeneous costs for waiting if a physician's capacity is utilized. Hospitals choose to either allocate patients to physicians randomly or let patients choose their physicians. In a monopolistic market, the hospital always chooses the welfare-maximizing allocation system. In a competitive market, inefficiencies may arise due to two externalities. If patients are free to choose their physician, the marginal patient neither internalizes her impact on other patients' waiting costs nor the learning of junior physicians.