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5. {ths) This question is on health insurance. There are two types of customers: low- risk and high-risk. Half the population is Mam halfthe population

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5. {ths) This question is on health insurance. There are two types of customers: low- risk and high-risk. Half the population is Mam halfthe population is low-risk. Each person has wealth 400. The low-risk people get sick with probability 0.1 and the high-risk people get sick with probability 0.5. If they get sick their medical bill is 300. S__o_ without insurance they have wealth M=100 ifthey are sick, and M=400 otherwise. Their utility from wealth M is U(M) = 1/57. People know ifthey are high- risk or low-risk. a. What is the expected value of the wealth of the low-risk and high-risk people? {2th i. Low-risk: EN]: ii. High-risk: E[U]= b. How much would fair-insurance cost for each type {iftheir type was known}? {2th i. Price of fair insurance for low-risk: M = ii. Price of fair insurance for high-risk: 39\": c. What is the expected utility of the low-risk and high-risk people without insurance? {Zpt} i. Low-Risk: E[U]= ii. High-Risk: E[U]= d. Are these people risk-averse, risk-loving, or risk-neutral? {1pt} e. Which types would be willing to buy insurance at price pL? {1pt} f. Which types would be willing to buy insurance at price pH?{1pt} 6. {Spt} Consider a market for insurance in which insurance firms are perfectly competitive {i.e. charge a price for insurance equal to its expected cost}. Insurance companies cannot tell whether people are low-risk or high-risk. They sell complete insurance {i.e. they payout 300 if someone is sick}. a. If everyone was forced to buy insurance then what price, 39, would be charged by the perfectly competitive insurance companies? {lpt} b. Suppose insurance companies offered the price 39 you calculated in (a), and people are not forced to buy insurance. Note that the expected utility of someone who has purchased insurance at price p is just (JG-00 p) {because they would be completely insured against the cost of medical bills). Use this to answer the following: i. Who would buy the insurance at price 39? Why? {lpt} ii. What would the firm's profits per contract be? {1pt} c. Continuing with the case where people are not forced to buy insurance, what is the equilibrium price of insurance and who buys it? {3pt} i. Price: ii. Low-Risk Buy: Yes I No iii. High-Risk Buy: Yes I No

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