In this paper we treat an individual’s health as a continuous variable, in contrast to the traditional literature on income insurance, where it is regularly treated as a binary variable. This is not a minor technical matter; in fact, a continuous treatment of an individual’s health sheds new light on the role and functioning of income insurance and makes it possible to capture a number of real-world phenomena that are not easily captured in binary models. In particular, moral hazard is not regarded as outright fraud, but as a gradual adjustment of the willingness to go to work when income insurance is available. Further, the model can easily encompass phenomena such as administrative rejection of claims and the role of social norms. It also gives a rich view of the desirability of insurance in the first place.