A consumer has a probabilitypof becoming sick, and if he is sick, he suers a utility loss of`. With a wealth levelW, his utility isU(W)if he is healthy, and his utility isU(W)-l. if he is sick. Hence, his expected utility isU(W)-pl (Do note that illness does not cause any income loss.)

There are two treatments available. The first treatment, TreatmentA, costsC1and it eliminates a fractions1of the utility loss. In other words, if the consumer paysC1, his wealth becomesW-C1, and the loss becomes(1-s1)l. The second treatment costsC2>0and it eliminates a fractions2of the utility loss. In other words, if the consumer paysC2, his wealth becomesW-C2, and the loss becomes(1-s2)l. Assumethat0

i) For a given`, explain how the consumer decides whether to use the TreatmentA, TreatmenB, or none at all.. (6 points)

Now assume that the utility loss`is uniformly distributed on[0;1]; that is, the value of`can take any number between0and1with the density1. Assume thatC1= 0:25,s1= 0:25, andC2= 0:5ands2= 0:5. This applies to the rest of the question.

ii) Explain how you would partition the possible losses[0;1]into separate subsets of in which no treatment, TreatmentA, or TreatmentBwill be used. (6 points)

iii) Health insurance takes the form of reducing TreatmentAs costC1to1C, where0< 1<1, and of reducing TreatmentBs costC2to2C, where0< 2<1. Explain how the consumers the decision to use treatment under this health insurance may be dierent from the answer in ii). (6 points)

iv) Explain moral hazard and the production e ciency-risk spreading tradeo using the answers in ii) and iii) (7 points)