This paper analyzes the welfare implications of fixed-price regulation of services in a model in which consumers are heterogenous and a firm can endogenously quality discriminate. We consider two different scenarios: The first scenario is when the consumer is also the payer. The second scenario is when the payer (usually the government) is not the consumer. Our major result is that fixed-price regulation causes a distributional welfare loss. We show that it is not possible for fixed-price regulation to induce providers to supply all consumer types with the first-best quality even under perfect information, under either pricing scenario. We show that high and low demand types may receive more than their respective first-best qualities, less than their first-best qualities, or one type may receive more and the other type less depending on the level of the regulated price. It is always true that when consumers are payers, quality is higher for both types than when consumers are not the payers. In this paper, we motivate and discuss the results in terms of price regulation of hospitals where consumers are patients and patient types vary by severity of illness.