-Roy Owns a Sports Car Worth $40,000, and That Is

Question

Examlex · Accepted Answer

The Answer is 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.

-Roy Owns a Sports Car Worth $40,000, and That Is

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