Adverse Selection and Insurance:

Problem 3. Adverse Selection and Insurance: In Clintonia, every citizen has a wealth of 16 and a utility represented by U (I) 2 VI . Clintonians occasionally get sick, and when they do, they go to the hospital and are made immediately better. A hospital visit costs 16. There are two types of Clintonians and each has a di'erent probability of getting sick (types are genetic and cannot be changed): Type Probability of Illness Vegetarian 0.25 Smoker 0.75 a. In the absence of health insurance, nd the expected utility of each type of Clintonian. b. A private health plan, Green Cross, is set up. Membership is optional, but since everyone is risk averse, the managers assume that everybody will join (for an insurance with full coverage). Green Cross sets their premiums according to the chance that an average Clintonian gets sick (Green Cross cannot distinguish between types). Assume there are equal proportions of each type in the population. What is the actuarial fair premium (i. e., the insurance policy at which the insurance company breaks even)? c. IfGreen Cross charges the actuarial fair rate, will every type of Clintonian join the plan? What is the expected utility for each type? d. After the lst year of operation, Green Cross nds they have lost money. Why? They commission a study to discover the probability that a member of Green Cross gets sick. What is the probability? They fix a new actuarial fair premium based on their study. What is the new rate? Who joins the plan in the 2nd year? e. Suppose now that Green Cross gets smart and offers two plans. The first plan is based on the plan in (d). Call it Plan I. The second plan offers a copayment system (Plan ll). For 3, Plan II pays 5 if an individual gets sick and the individual pays the rest. Who buys which plan? Why? Are these plans sustainable (i.e. the rm is not losing money)? How does this strategy solve the asymmetric information problem? h. Suppose now the government comes up with a plan that mandates health insurance. What rate will be charged (the rate will be the same for everyone and the government covers its costs)? Who gains and who loses under this plan versus the plan in (g) (i.e. who votes for the plan)? j. Suppose now that Steven Segal invents a new method to quit smoking ("boot-tothehead therapy"). This therapy is so effective that it overcomes all genetic predisposition to smoke. For a cost of only 10 you never become sick again (probability of getting sick becomes zero). If the private plan is in effect (people can choose Plan I or Plan H), will smokers undergo the Segal therapy? Suppose the government plan is in effect, will smokers undergo the therapy? Explain