Is waiting-time prioritisation welfare improving?

Rationing by waiting time is commonly used in health care systems with zero or low money prices. Some systems prioritise particular types of patient and offer them lower waiting times. We investigate whether prioritisation is welfare improving when the benefit from treatment is the sum of two components, one of which is not observed by providers. We show that positive prioritisation (shorter waits for patients with higher observable benefit) is welfare improving if the mean observable benefit of the patients who are indifferent about receiving the treatment is smaller than the mean observable benefit of the patients who receive the treatment. This is true (a) if the distribution of the unobservable benefit is uniform for any distribution of the observable benefit; or (b) if the distribution of the observable benefit is uniform and the distribution of the unobservable benefit is log-concave. We also show that prioritisation is never welfare increasing if and only if the distribution of unobservable benefit is negative exponential.