solutions_practice_module7

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Johns Hopkins University *

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Economics

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Jun 24, 2024

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Module 7 Extra Practice Problems For Questions 1 - 7, choose the best answer. 1. If Martha is willing to pay up to 350 for insurance against a loss of 7000 which will occur with a 4% probability, she is: A. risk neutral. B. risk averse. C. risk loving. D. irrational. Solution: The expected loss is 0.04( 7000), or 280. The fact that Martha is willing to pay more than her expected loss for insurance against this loss indicates that she is risk averse. 2. Which of the following are responses by insurance companies to the problem of adverse selection in the health insurance market? A. Requiring a physical examination before issuing an insurance policy. B. Offering lower prices for health insurance to members of group plans, such as all employees of a large firm, rather than simply offering lower prices to individuals. C. Including a co-pay for visits to the doctor’s office, so the policyholder has to bear some of the cost. D. Including a deductible in the insurance policy, so the policyholder has to bear the loss up to some dollar limit. E. Both (a) and (b) are true. Solution: Adverse selection arises when there is asymmetric information in the market. If there are hidden characteristics, one’s own knowledge of the state of their health, for example, then the insurance company might try to learn those characteristics, but it will be difficult to gather accurate information. If insurance companies have poor information on each individual’s level of risk, and if insurance is offered at a single price, then the worst risks are the ones most likely to buy, pushing up the price for the best risks. Insurance companies can partially solve this adverse selection problem by implementing (a) and (b) above. Note that (c) and (d) are partial solutions to the moral hazard problem.

3. Upon purchasing a new refrigerator, you are deciding whether to also purchase the two-year warranty. The consumer guides that you have read say that ten percent of new refrigerators need repairs in their second year, and the cost of repair averages 500. The rest of the refrigerators need no repair. Assume a zero discount rate. Which of the following statements is true? A. If you were risk neutral, you would definitely purchase the warranty if its price were 55. B. If you were risk neutral, you would definitely purchase the warranty if its price were 45. C. If you were risk averse, you would definitely purchase the warranty if its price were 50. D. If you were risk averse, you would definitely purchase the warranty if its price were 55. E. Both (b) and (c) are true. Solution: The expected loss, or cost of repair, is 0.10(500) = 50. If you are risk neutral, you would spend up to 50 for the warranty (if the warranty cost exactly 50 you would be indifferent between buying the warranty or not). You would not be willing to spend 55, so choice a is false. You would be willing to spend 45, so choice b is true. If you are risk averse, you would be willing to spend at least 50, so choice c is true. Choice d is false because we do know for sure that a risk-averse person will spend 55 on the warranty. We know that they are willing to spend more than 50, but we don’t know how much more. (If we observe someone paying 55 for a warranty against a loss of 50 we can infer that they must be risk averse. But knowing that they are risk averse does not give us enough information to predict exactly how much they will spend on the warranty.) Therefore, the answer is choice E (both b and c are true). 4. In the insurance market,“moral hazard” refers to the following problem: A. Insurers can’t tell high-risk customers from low-risk customers. B. High-risk customers have an incentive to give false signals to make themselves look like low-risk customers. C. Companies may unfairly lump individuals together by race, sex, age or other characteristics in an attempt to use demographic data to pinpoint high-risk populations. D. Individuals may change their behavior after the insurance is purchased, so that they behave in a more high-risk manner than before. E. Both (a) and (b) are true. Solution: This is the basic definition of the moral hazard problem. 5. Sigmund invests 25 in an investment that has a 50% chance of being worth 100 and a 50% chance of being worth 0. From this information we can infer that Sigmund is A. risk loving. B. risk neutral. C. risk averse. D. We cannot infer Sigmund’s risk preference based on the information given. Page 2

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