Ex Post Welfare under Alternative Health Care Systems

This paper studies the implications of a societal aversion to inequality for the optimal design of a public health care system. Inequality aversion is introduced by postulating a strictly concave ex post social welfare function. Illnesses are characterized by three factors: the agent’s health with treatment, the agent’s health without treatment, and the cost of treatment. It is shown that the optimal public health care system allocates health care di¤erently than would private health insurance; speci…cally, 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 might be either greater or less 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.