1.

a) David owns a house which is worth $500. He also has $200 in cash (his total wealth is then $700).

The probability that his house will be destroyed in a natural disaster is 0.05.

He can buy home insurance with a sum insured of $500 (meaning that if his house is destroyed, he gets back the full value of $500 from the insurer).

Suppose that his utility function is u(w) = 10 * w 0.0025 * (w^2)

What is the maximum premium that David would pay for this insurance policy? (round your answer down to give an answer in dollars and cents).

b) Set yourself in the context of the previous part.

The price that would be paid for insurance might be different if the customer has a different level of wealth.

Suppose that Susan also owns a house worth $500, but she has $300 in cash. If she has the same utility function as David, what maximum price would she be willing to pay for insurance?

Give your answer rounded down, with two decimal places (as usual, do not include any dollar signs).

c) Now suppose that the customer from part a), David, can partially insure his house. He can buy a policy which will pay $S if his house is destroyed (where S < 500). If the premium rate is 0.06*S for a sum insured of S, what amount of insurance should David buy? (That is, what is the value of S that would maximise his expected utility?).

Round your answer to the nearest integer.