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?
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.
You might also like to view...
The real-balance effect indicates that at higher price levels
A) the real value of money holdings increase, resulting in increased saving. B) the purchasing power of money will increase. C) the real value of money holdings fall, resulting in decreased spending. D) the value of the dollar will increase.
During a recession the economy experiences
a. rising employment and income. b. rising employment and falling income. c. rising income and falling employment. d. falling employment and income.
The U.S. experience with tax cuts and tax increases since 1975 suggests that
A. tax cuts always stimulate consumption spending. B. tax changes have a stable and predictable effect on consumption spending. C. temporary tax changes are less effective than permanent changes. D. tax changes have no effect on consumption spending.
The law of comparative advantage states that
A. countries grow fastest if exports exceed imports, with payment surpluses being received in gold. B. mutually beneficial trade can always take place between two countries whose pre-trade relative opportunity costs differ. C. two countries can both gain from trade only when they have very different tastes and preferences. D. trade benefits a country only if it has comparative advantages in all goods and services.