Ex Post Welfare under Alternative Health Care Systems

The implications of a societal aversion to inequality for the optimal structure of the health care system are studied. The agents are assumed to be ex ante identical, but to differ ex post in the state of their health. Inequality aversion is introduced by postulating a strictly concave ex post social welfare function. It is shown that the optimal public health care system allocates health care differently than would private health insurance; specifically, people who are relatively unhealthy with and without treatment receive more health care, and people who are relatively healthy with and without treatment receive less health care. The aggregate quantity of health care under the optimal public health care system can be either greater or smaller than under private health care insurance. If the public health care system is optimally designed, allowing agents to purchase supplementary private health care insurance cannot raise social welfare and is likely to decrease it.