Author Question: Mike has the utility of wealth curve shown in the figure above. He owns a car worth 20,000, and that ... (Read 132 times)

Themember4 · **on:** Jun 29, 2018

Mike has the utility of wealth curve shown in the figure above. He owns a car worth 20,000, and that is his only wealth. There is a 10 percent chance that Mike will have an accident within a year. If he does have an accident, his car is worthless.

a) What is Mike's expected utility? b) What is the maximum amount that Mike is willing to pay for auto insurance? c) Suppose all car owners are like Mike insofar as they have a 10 percent chance of having an accident. An insurance company agrees to pay each person who has an accident the full value of his or her car. The company's operating expenses are 1,000. What is the minimum insurance premium that the company is willing to accept? d) Will Mike buy the company's policy? Why or why not?

Question 2

Diseconomies of scale definitely means that as the firm increases its output, its

A) long-run average total cost increases.
B) long-run average total cost decreases.
C) short-run average total cost increases.
D) short-run average total cost decreases.

Natalie4ever · **Reply #1 on:** Jun 29, 2018

Answer to Question 1

a) If Mike has an accident, his utility is zero. If he does not have an accident, his utility is 100. The probability of an accident is 0.1, and the probability of not having an accident is 0.9. So Mike's expected utility is 100 0.9 + 0 0.1 = 90.

b) The probability of an accident is 0.1, and the probability of not having an accident is 0.9. So Mike's expected wealth is 20,000 0.9 + 0 0.1 = 18,000. If Mike has an accident, his utility is zero. If he does not have an accident, his utility is 100. So Mike's expected utility is 100 0.9 + 0 0.1 = 90. Given his utility of wealth curve, the figure above shows that Mike gets the same utility if his wealth is 14,000 with certainty. That is, Mike's utility of a guaranteed wealth of 14,000 is the same as his utility of an expected wealth of 18,000 with the degree of risk he faces. This result means that Mike is willing to pay up to 18,000 - 14,000 = 4,000 for auto insurance.
c) The probability of an accident is 0.1. So the company will pay out 20,000 to 1/10 of car owners, or an average of 2,000 per person. The company covers all its costs if it offers insurance for 2,000 + 1,000 = 3,000. So 3,000 is the minimum insurance premium that the company is willing to accept.
d) Mike is willing to pay up to 4,000 for auto insurance. The minimum insurance premium that the company is willing to accept is 3,000. So Mike will buy the policy because the maximum amount he is willing to pay is greater than the minimum amount that the insurance company is willing to accept.

Answer to Question 2

A