Rosa has a 10% chance of getting sick in the next year. If she gets sick, her medical bills will amount to $500. She has a wealth of $1,000. Suppose she has the utility function u(x) = x0.5, where x is her net wealth at the end of the year.

(a) Calculate Rosa's risk premium.

(b) What is the most that Rosa is willing to pay for an insurance policy that fully covers against

her loss?

(c) Some insurance policies have deductibles. A deductible is an amount of a claim not covered by insurance; it's a fixed portion of the medical bills that the insured person must pay in order to make a claim to their insurer. Suppose Rosa's insurance company provides two plans. Plan A has zero deductibles but charges a high premium. Specifically, Plan A charges $55 for $500 of coverage. Plan B has a deductible of $K, where K<500, but charges a premium of just $(55 - .1K). Suppose K =b $300. Will Rosa purchase insurance and, if so, which plan? Show this mathematically.

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Yusra AneesLv10

28 Sep 2019

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harlequinrat321

Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U = ln(C), where C is the amount of consumption that people have in any period. So long as they are healthy, individuals will consume their entire income of $15,000. If they need medical attention (and have no insurance), they will have to spend $10,000 to get healthy again, leaving them with only $5,000 to consume. Smokers have a 12% chance of requiring major medical attention, while nonsmokers have a 2% chance. Insurance companies in Chimnesia can sell two types of policy. The low deductible (L) policy covers all medical costs above $3,000, while the high deductible (H) policy only covers medical costs above $8,000.

(a) What is the actuarially fair premium for each type of policy and for each group?

(b) If insurance companies can tell who is a smoker and who is a nonsmoker and charges the actuarially fair premiums for each policy and group, which policy will two groups purchase? Compute the expected utility of each group with each policy. Now suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn't.

(d) Mathematically show that it is possible for both groups to purchase insurance, with one group buying L-policies and one group buying H-policies. (show the feasibility from the perspective of smoker, nonsmoker, and insurance company, respectively)