If society is averse to inequality and there is some income disparity, private health care insurance is sometimes socially better and sometimes worse than public health care. However, a third system? public health care with the option to purchase supplemental health care insurance? is always socially preferred to private health care insurance. It is not always socially preferred to public health care. If a public health care system is in place, the existence of a latent demand for supplemental insurance is a sufficient but not necessary condition for the supplemental insurance system to be socially preferred to public health care.