7.3 Samantha’s utility function over this year’s net income, Y, is U(Y) = Y0.5. She owns a car for business that she will have to replace if it is stolen. If her car is not stolen her net income is $122,500. If the car is stolen her net income is reduced by the car’s replacement cost of $20,100. The probability that the car will be stolen this year is 20%.

a. Use Excel to calculate Samantha’s expected utility and to calculate the price of fair insurance that would cover the full replacement cost of the car.

b. An insurance company is considering four possible prices for full insurance for Samantha’s car: $4,020, $4,090, $4,851, and $4,164. Assume Samantha buys full insurance and use Excel to determine Samantha’s income and utility for each of these prices if the car is stolen and if it is not stolen. Then calculate Samantha’s expected income and expected utility for each of these prices. Would she buy full insurance at these prices? What is the maximum price Samantha would pay for full insurance?

c. Suppose the insurance company offers an insurance policy with a $1,000 deductible: If the car is stolen, Samantha will absorb the first

$1,000 of the loss and the company will pay the remaining $19,100. Use Excel to calculate Samantha’s expected utility if the price for this policy is $3,820. What if the price is $3,970?

Would Samantha buy the policy at either of these prices?