In countries where health care is publicly provided and where equity considerations play an important role in policy decisions, it is often argued that an increase in co-payments is unacceptable as it will be particularly harmful to the less well-off in society. The present paper derives socially optimal co-payments in a simple model of health care where people differ in income and in severity of illness. The social optimum depends on the welfare weights given to persons with different levels of expected utility. Increased concern for equity may increase optimal co-payments for illnesses with homogeneous severity across the population. For illnesses where the severity varies strongly across the population, optimal copayments go down as a response to increased concern for equity, provided income differences in the society are sufficiently small.