1： Suppose thatGiannina Sapienza wants to buy a used car. She knows that one-third oftheavailable used cars are good cars and two thirds are “lemons. She is willing topay $15,000 for a good car and $5,000 for a lemon. Assume that this buyercannot distinguish the good cars from the bad cars. Calculatethe equilibrium price in this used-car market. Discuss whether the describedenvironment presents adverse selection and/or moral hazard problems. [Hint:Make all the additional necessary assumptions to solve this problem.]

2： There are 10000 demanders of health insurance inCambridge, MA. They each have wealth of $10 and their utility of wealth is U(W)= W1/2. An insurance company interested in selling to them knows only that half ofCambridge’s residents are of weak constitutions and with a 60% probability willrequire $4 of medical care in the coming year, and that the other half are of strongconstitutions and will require $4 of

care with a 40% probability. The company cannot tellwhich are weak (W) and which are strong (S).

a. If the insurance company sells to all 10000 residents,what premium would allow it to break even?

b. If the insurance company charges this break-evenpremium, will all of the residents of Cambridge buy the insurance?

c. Given the set of residents of Cambridge who will buythe insurance, what profits can the company expect to earn per insuree?

3：Consider the information provided in Question 4. Given ahealth insurance premium of $1, will there be any deductible K that theinsurance company can set such that the strong residents will want to buy theinsurance and the weak residents will not?

4 It has been observed that investment bankers inToronto, ON who ride bicycles for recreation or exercise face a greater risk of havingtheir bike stolen than professional bicycle messengers. Specifically, there is an 80% chancethat a banker will lose a $1,000 bicycle during a given year but only a 20% chancethat a messenger will lose a bicycle. An equal number of bankers and messengers ownbicycles in Toronto.

a. If an insurance company cannot tell a banker from amessenger, it must therefore charge the same premium to everyone. What will theactuarially fair insurance premium be?

b. Let us say that bankers and messengers both have thelogarithmic utility functions u(C) = log C, and they both earn $10,000 a year. Will thebankers and messengers purchase bicycle insurance at a fair premium? Explain.

c. Given the answer to Part b, does the insurance companymake any profits or incurany losses? If the insurance company does not breakeven, what should the premium be for a fair policy? Would the new premium causebankers and messengers to change their decision about purchasing insurance?

d. Suppose now that the insurance company can observe the“type” of the customer. Would the answers toParts a. and b. change？