solutions_practice_module7

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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

Solution: Sigmund pays 25 for a gamble with an expected value of .5(100) + .5(0) = 50. A risk neutral person would be willing to pay up to 50 for this gamble. So it’s possible Sigmund is risk neutral. A risk loving person would be willing to pay something over 50 for this gamble. So it’s possible Sigmund is risk loving. A risk averse person would not be willing to pay 50 for the gamble but may be willing to pay something less. The fact that Sigmund paid 25 does not rule out that he is risk averse. Therefore, Sigmund could be any of these risk preferences. We cannot infer his risk preference based on his actions in the problem. 6. Which of the following market characteristics is most likely to lead to a single platform dominating the market? A. Weak preference for specific features B. Weak same-side network effects C. Low “multi-homing” costs D. Weak cross-side network effects Solution: A weak preference for specific features means that multiple platforms are not needed to satisfy consumer preferences. Therefore, it is less likely that additional platforms may emerge. Strong network effects and high “multi-homing” costs will also make it more likely that a single platform will dominate. 7. If an increase in the quantity purchased of a good leads to an increase in the quantity demanded of the same good then: A. a negative network externality is present. B. a positive network externality is present. C. same-side network effects exist. D. cross-side network effects exist. E. Both (B) and (C) are true. Solution: The increase in demand indicates there is a positive externality associated with the increase in quantity purchased. In addition, since there is only 1 good, the effect is the same-side of the network. Page 3

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8. A Honolulu restaurant owner must decide whether or not to expand his restaurant. He thinks that the probability is 0.6 that the expansion will prove successful and 0.4 that it will not be successful. If it is successful, he will gain 100,000. If it is not successful, he will lose 80,000. If the restaurant is not expanded, no gains or losses are expected. (a) What is the expected monetary value to the owner of expanding his restaurant? Solution: EV(change in profits if expand restaurant) = 0.6(100,000) + 0.4(-80,000) = 28,000. (Note that the EV here is the expected value of the change in current profit levels if the restaurant is expanded. We have to write the expected value this way because that is how the problem was stated, i.e., “he will gain 100,000” and “he will lose 80,000.”) (b) Would a risk-neutral owner choose to expand? A risk-averse owner? Briefly explain. State any assumptions and/or additional information you need to answer the question. Solution: The question states that if there is no restaurant expansion then there will be no gains or losses. So, EV(change in profits if don’t expand) = 0. A risk-neutral owner would maximize EV by expanding, since 28,000 ¿ 0. There is not enough information to know what a risk-averse owner would do. It depends on how risk averse the person is. The possibility of losing 80,000 may “hurt” enough so that EV = 28,000 is not sufficient to compensate them for the risk. (c) Calculate the probability of success that would make a risk-neutral restaurant owner indifferent between expanding and not expanding the restaurant. Solution: Let p = probability of expanding the restaurant. If EV(not expanding) = 0, then we need to solve for probability p in: p* 100,000 + (1-p)*(- 80,000) = 0. This gives p = 0.44. 9. Faced with a reputation for producing automobiles with poor repair records, a number of car manufac- turers have offered extensive guarantees to car purchasers (e.g., a seven year bumper-to-bumper warranty on all parts and labor associated with repairs of mechanical problems). (a) In light of your knowledge of the lemon’s problem, is this a reasonable policy? Solution: Yes, because it does two things. (1) it serves as a credible signal from car manu- facturers that they have improved the quality of their cars in recent years, thereby mitigating the adverse selection problem; (2) it provides a credible means for the car manufacturers to commit to maintaining high quality. (b) Is this policy likely to create a moral hazard problem? Explain. Solution: This policy may create a moral hazard problem among car owners who can expend less effort to care for and maintain their automobiles, knowing that the car manufacturers will have to incur some of the added expenses that arise from this neglect. Page 4

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