Suppose that all individuals have the same risk of illness, but there is a fixed cost of supplying insurance. Specifically, insurers must incur a cost of F dollars per policy, regardless of the extent of coverage or whether the individual falls ill.

a)

i. Use the model of Rothschild and Stiglitz to show that when the fixed cost is sufficiently small, individuals will still prefer to purchase insurance. (Hint: You must redraw the "breakeven line," and show the optimal plan purchased by the individual.)

ii. Suppose there is no insurance moral hazard, is the optimal plan purchased by the individual (the point you found in i.) a full insurance contract (i.e., plan with zero out-of-pocket payment)?

b) Use the model of Rothschild and Stiglitz to show that when the fixed cost is sufficiently large, individuals will prefer no insurance.