1) Suppose Al has an income of $25,000 and faces a 20% chance of having a serious medical problem that requires $15,000 worth of medical care. Al's utility function is U(1) = 10.5 [or square root of income]. There are two possible health insurance plans available. The first has 25% coinsurance and has a premium of $2500. The second plan has a $1500 deductible then 25% coinsurance and has a premium of $2200. Which plan would Al choose, if any? What is the AFP for each plan? What is the loading factor for each plan? (loading factor is % by which premium exceeds the AFP)
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- What are some of the metrics economists use to measure health outcomes?Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utilityAn individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
- (80) purchases a whole life insurance policy of 100,000 payable at the end of the year of death. You are given: I. The policy is priced with a select period of one year. II The select mortality rate equals 80% of the mortality rate from the Standard Ultimate Life Table. III Ultimate mortality follows the Standard Ultimate Life Table. i=0.05 Calculate the actuarial present value of the death benefits for this insurance. A.58,950 B.59,050 C.59,150 D.59,250 E.59,350Tom wants to avoid any accidents on the work floor of his factory. If an accident does occur, itwould cost him $500,000 in damages. Installing safety equipment would decrease the probabilityof an accident occurring from 20% to 10%. However, the equipment costs $20,000 to install.10. What is his expected loss after installing the safety equipmenta. $20,000b. $50,000c. $100,000d. $125,000Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?