Suppose there are two states, 1 and 2. State 1 occurs with probability p, and wi denotes a consumer's wealth in state i.
(a) If the consumer is strictly risk-averse and w1 ? w2, show that an insurance company can provide him with insurance rendering his wealth constant across the two states so that he is better off and so that the insurance company earns positive expected profits.
(b) Suppose there are many consumers and many insurance companies and that a feasible allocation is such that each consumer's wealth is constant across states. Suppose also that in this allocation, some consumers are insuring others. Show that the same wealth levels for consumers and expected profits for insurance companies can be achieved by a feasible allocation in which no consumer insures any other.