Exam 20: Uncertainty and Information

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  -James has a utility of wealth schedule in the above table. He is offered a job selling video games at Games Galore. James' compensation depends on how much he sells. In a poor sales period, a salesperson makes $100 per month. In a good sales period, a salesperson makes $600 per month. James is told by the manager that, in any given month, there is a 25 percent chance of a poor sales period and a 75 percent chance of a good sales period. What is James' expected utility from taking this job? -James has a utility of wealth schedule in the above table. He is offered a job selling video games at Games Galore. James' compensation depends on how much he sells. In a poor sales period, a salesperson makes $100 per month. In a good sales period, a salesperson makes $600 per month. James is told by the manager that, in any given month, there is a 25 percent chance of a poor sales period and a 75 percent chance of a good sales period. What is James' expected utility from taking this job?

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C

Expected wealth is a weighted average in which the weights are

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D

  -Roy owns a sports car worth $40,000, and that is his only wealth. Roy is a reckless driver, and there is a 30 percent chance that he will have an accident within a year. If he does have an accident, his car is worthless. Roy's utility of wealth curve is shown in the figure below. An insurance company agrees to pay a car owner like Roy the full value of his car in case of an accident if the car owner buys the company's insurance policy. The company's operating expenses are $2,000 per policy. a) What is Roy's expected wealth? b) What is Roy's expected utility? c) What is the maximum amount that Roy is willing to pay for car insurance? d) What is the minimum premium that the insurance company is willing to accept? e) Will Roy buy the insurance policy? Why or why not? -Roy owns a sports car worth $40,000, and that is his only wealth. Roy is a reckless driver, and there is a 30 percent chance that he will have an accident within a year. If he does have an accident, his car is worthless. Roy's utility of wealth curve is shown in the figure below. An insurance company agrees to pay a car owner like Roy the full value of his car in case of an accident if the car owner buys the company's insurance policy. The company's operating expenses are $2,000 per policy. a) What is Roy's expected wealth? b) What is Roy's expected utility? c) What is the maximum amount that Roy is willing to pay for car insurance? d) What is the minimum premium that the insurance company is willing to accept? e) Will Roy buy the insurance policy? Why or why not?

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a) The probability that Roy will have an accident is 0.3, and the probability that he won't have an accident is 0.7. Therefore Roy's expected wealth is $40,000 × 0.7 + $0 × 0.3 = $28,000.
b) If Roy has an accident, his utility is zero. If he does not have an accident, his utility is 100. Because the probability of an accident is 0.3, and the probability of not having an accident is 0.7, Roy's expected utility is 100 × 0.7 + 0 × 0.3 = 70. a) The probability that Roy will have an accident is 0.3, and the probability that he won't have an accident is 0.7. Therefore Roy's expected wealth is $40,000 × 0.7 + $0 × 0.3 = $28,000. b) If Roy has an accident, his utility is zero. If he does not have an accident, his utility is 100. Because the probability of an accident is 0.3, and the probability of not having an accident is 0.7, Roy's expected utility is 100 × 0.7 + 0 × 0.3 = 70.   c) With no insurance, Roy's expected utility of wealth is 70. The figure above shows that Roy gets the same utility if his wealth is $16,000 with no risk. That is, Roy's utility of a guaranteed wealth of $16,000 is the same as his utility of an expected wealth of $28,000 with the degree of risk he faces. This means that Roy is willing to pay up to $40,000 - $16,000 = $24,000 for car insurance. d) Because the probability of an accident is 0.3, the company will pay out $40,000 to 3/10 of car owners like Roy, or an average of $12,000 per person. The company covers all its costs if it offers insurance for $12,000 + $2,000 = $14,000. So $14,000 is the minimum insurance premium that the company is willing to accept. e) Roy will buy the policy because the maximum amount he is willing to pay, $24,000, is more than the minimum amount that the insurance company is willing to accept, $14,000. c) With no insurance, Roy's expected utility of wealth is 70. The figure above shows that Roy gets the same utility if his wealth is $16,000 with no risk. That is, Roy's utility of a guaranteed wealth of $16,000 is the same as his utility of an expected wealth of $28,000 with the degree of risk he faces. This means that Roy is willing to pay up to $40,000 - $16,000 = $24,000 for car insurance.
d) Because the probability of an accident is 0.3, the company will pay out $40,000 to 3/10 of car owners like Roy, or an average of $12,000 per person. The company covers all its costs if it offers insurance for $12,000 + $2,000 = $14,000. So $14,000 is the minimum insurance premium that the company is willing to accept.
e) Roy will buy the policy because the maximum amount he is willing to pay, $24,000, is more than the minimum amount that the insurance company is willing to accept, $14,000.

Joe is contemplating a job where, with probability 0.6, he will make $100,000 and with probability 0.4 he will make $30,000. What is Joe's expected income from taking the job?

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When Sardar buys insurance, on net he

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  -John's utility of wealth curve is shown in the above figure. He currently has wealth of $20,000. If there is a 10 percent chance that he could lose all his wealth, what is his expected wealth? -John's utility of wealth curve is shown in the above figure. He currently has wealth of $20,000. If there is a 10 percent chance that he could lose all his wealth, what is his expected wealth?

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In the used car market, adverse selection can be limited by

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Warranties in the used car market ________ the problem of private information thereby causing the price of good and bad used cars to ________.

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  -Beachcomber Beatrice spent her entire wealth of $100,000 to build a beach house on the Gulf of Mexico. There is a 10 percent chance that the house will be totally destroyed by a hurricane. Beatrice's utility of wealth schedule is given in the table above. What is the minimum amount that the insurance company would require Beatrice to pay for an insurance policy that pays $100,000 if her beach house is destroyed by a hurricane? (Assume the insurance company has no other costs.) -Beachcomber Beatrice spent her entire wealth of $100,000 to build a beach house on the Gulf of Mexico. There is a 10 percent chance that the house will be totally destroyed by a hurricane. Beatrice's utility of wealth schedule is given in the table above. What is the minimum amount that the insurance company would require Beatrice to pay for an insurance policy that pays $100,000 if her beach house is destroyed by a hurricane? (Assume the insurance company has no other costs.)

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A risk-averse person's marginal utility of wealth

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One way of reducing the moral hazard problem in the automobile insurance market is for drivers to

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Erika's utility with $3,000 of wealth is 6,000 and her utility with $3,001 of wealth is 6,005. Her marginal utility from gaining the additional $1 of wealth is

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Moral hazard occurs when an agreement encourages undesirable behavior.

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For a risk-averse individual, as wealth increases, total utility

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Nicole is indifferent between option A, which gives her $20,000 for sure, and option B, which gives her $10,000 with probability 0.5 or $32,000 with probability 0.5. Nicole's cost of risk for option B is

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  -Bruce Copperwood's utility of wealth curve is illustrated in the above figure. Bruce is presently employed at a salary of $100,000. There is a 10 percent probability that Bruce will be totally disabled, in which case he will have no wealth. The maximum amount that Bruce is willing to pay for a disability insurance policy that would pay him $100,000 in the case of total disability is -Bruce Copperwood's utility of wealth curve is illustrated in the above figure. Bruce is presently employed at a salary of $100,000. There is a 10 percent probability that Bruce will be totally disabled, in which case he will have no wealth. The maximum amount that Bruce is willing to pay for a disability insurance policy that would pay him $100,000 in the case of total disability is

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  -Andrew has the utility of wealth curve shown in the above figure. He owns an SUV worth $30,000 and that is his only wealth. There is a 10 percent chance that he will have an accident within a year. If he does have an accident, his SUV is worthless. Suppose all SUV owners are like Andrew. An insurance company agrees to pay each person who has an accident the full value of his/her SUV. The company's operating expenses are $1,500. What is the minimum insurance premium that the company is willing to accept? -Andrew has the utility of wealth curve shown in the above figure. He owns an SUV worth $30,000 and that is his only wealth. There is a 10 percent chance that he will have an accident within a year. If he does have an accident, his SUV is worthless. Suppose all SUV owners are like Andrew. An insurance company agrees to pay each person who has an accident the full value of his/her SUV. The company's operating expenses are $1,500. What is the minimum insurance premium that the company is willing to accept?

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Private information is a situation in which

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  -Steve owns a motorcycle valued at $5,000 and that is his only asset. There is a 5 percent chance that Steve will have an accident within a year. If he does have an accident, his motorcycle is worthless. Steve's utility of wealth curve is shown in the figure above. An insurance company agrees to pay Steve the full value of his motorcycle in case of an accident if he buys the company's insurance policy. The company's operating expenses are $500 per policy. What is the maximum insurance premium that Steve is willing to pay? -Steve owns a motorcycle valued at $5,000 and that is his only asset. There is a 5 percent chance that Steve will have an accident within a year. If he does have an accident, his motorcycle is worthless. Steve's utility of wealth curve is shown in the figure above. An insurance company agrees to pay Steve the full value of his motorcycle in case of an accident if he buys the company's insurance policy. The company's operating expenses are $500 per policy. What is the maximum insurance premium that Steve is willing to pay?

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There is a growing market for buying and selling information about the online behavior of consumers. Most people use one of only a small number of search engines (such as Google, Bing, or Yahoo!) when surfing the net. It has been hard for new search engines to gain any market share. Based only on this information, the market for search is best considered as

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