Incentives, redistribution and social insurance

We extend the familiar income taxation model à la Mirrlees, so as to include income uncertainty, due for instance to a risk of illness. Following a line of research initiated by Blomqvist and Horn 1984] we prove that the existence of a Social Health Insurance system may be justified even when the insurance market is efficient. Moreover, if there is a negative statistical dependence between probability of illness and labor productivity, then the optimum of a Utilitarianist Social Welfare function implies that Social Insurance provides a complete coverage for every household.