Tennessee provides insurance coverage for up to $25,000 in annual health expenses. Of the 25,000, the most that can be spent on hospital bills is $15,000. Expenses above these thresholds are not covered by the state plan. Is Tennessee consistent with the theory of efficient insurance?

1. Medicare administrative costs are approximately $500 per year per person covered by Medicare. This is about 4.5% of the total annual health care expenses covered by Medicare. U.S. private health insurance administration costs are approximately $490 per year per person covered by private health insurance, about 8.5% of the total annual health care expenses covered by private insurers.

Consider a proposal under which everyone in the U.S. who currently has private health insurance would be offered Medicare insurance in the same way that people over age 65 receive it. What do you expect would be the effect on Medicare administration cost per person covered by Medicare? Would it rise? Fall? Stay about the same? Explain carefully what you base your prediction on. In answering, try to think what insurance administration costs are mostly related to. Are they proportional to the number of people covered? Do they also depend on the number of treatments the people receive? To answer this question, what are the most important differences between people currently covered by Medicare and other people who have private health insurance?

Q: Suppose Snake Farm Insurance provides fire insurance coverage to 10,000 homeowners in California. Based on historical data, Snake Farm

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.