Question

If you have a utility function

2
U(x)=5x
2
for money when it rains and
2
U(x)=x
2
for money when there is sunshine, and the probability of rain is 0.4, you are offered an insurance contract where, for every $1 of benefit in the rain state, you pay $0.4 as a premium. When it rains, you have $100, and when there is sunshine, you have $100 without any insurance.
Should you purchase the insurance contract?
a) Yes, because it maximizes expected utility.
b) No, because it does not maximize expected utility.
c) It depends on the specific insurance terms.
d) Cannot be determined based on the information provided.
e) Both a) and c) are correct.

Answer 1

To determine whether to purchase the insurance contract, we calculate the expected utility with and without insurance. Comparing the expected utility in both states, it is more beneficial not to purchase the insurance contract.

Step-by-step explanation:

To determine whether to purchase the insurance contract, we need to compare the expected utility with and without insurance. Without insurance, the expected utility is calculated as follows:

EU(Sunshine) = 2U(100) = 2(100)^2 = 20,000

EU(Rain) = 2U(100) = 5(100)^2 = 50,000

The expected utility with insurance is calculated as follows:

EU(Sunshine) = 2U(100) - 0.4(100) + 0.4(100) = 20,000

EU(Rain) = 2U(100 - 0.4(1)) - 0.4(100) + 0.4(100) = 9,970

Since the expected utility without insurance is higher in both states (Sunshine and Rain), it is more beneficial not to purchase the insurance contract. Therefore, the answer is No, because it does not maximize expected utility.