We develop a simple yet realistic model of income insurance, where the individual’s ability and willingness to work is treated as a continuous variable. In this framework, income insurance not only provides income smoothing, it also relieves the individual from particularly burdensome work. As a result, the individual adjusts his labor supply in a continuous fashion to the implicit tax wedge of the insurance system. Moral hazard, in the sense that an individual receives insurance benefits without actually being fully qualified, also becomes a matter of degree. Moreover, our continuous framework makes it easy to analyze both the role of administrative rejection of claims, and the role of social norms, for the utilization of insurance.