Question

6. You have u = x1/2 risk averse utility. Your initial wealth consists of $225 cash and a $175 Apple Pencil III. This means that your initial wealth is Xo = 225 +175 = 400. There is a n = 10% chance the pencil will die and be worth $0. Apple offers insurance. They will replace the pencil if it dies. a. What is the maximum fee F, you would pay for this insurance? b. Provide a Utility of Wealth Diagram

Answer 1

A. First we will need to calculate the expected utility without insurance.
The probability of the Apple Pencil going dead is given as 10%, so

Expected utility without insurance= .9*U(400)*+.1*U(225)
Expected utility= .9*400^.5+.1*225^.5
Expected utility= .9*20+.1*15
Expected utility=18+1.5
Expected utility=19.5.

I will be willing to pay as long as the expected utility from the insurance is at least equal to above expected utility. Lets say the insurance payment is X, so we get

(400-X)^.5=19.5
400-X=380.25
X=400-380.25
X=19.75.

Hence I will be willing to pay a maximum of 19.75USD for the insurance.

B. Since the utility function is U=x^.5, the utility diagram becomes

Utility +40 K 50 50 100 100. 150 150. 200 200. 250 250 300 300. 350 350. 400 40 Income