Many insurance contracts are not as complicated as the n-tuples described above-Blue Cross schedules listing maximum payments for specific illnesses and operations are an isolated example-but are instead resolvable into a fixed premium and a payment schedule that is in general a simple function of the size of the loss such as F(L) = Max [0, c(L-D)], where c X 100% is the co-insurance rate and D is the de- ductible. With such a contract when a loss occurs, determining its size is often a serious problem. In other words, finding out exactly what state of the world has occurred is not always easy. We ignore these problems. A large literature analyzes optimal insurance contracts. See, for example, Arrow (1971) and Borch (1968). 2. We assume that preferences are not state-dependent.