Dan Partridge is a risk averter who tries to maximize the expected value of √ c, where c is his wealth. Dan has $50,000 in safe assets and he also owns a house that is located in an area where there are lots of forest fires. If his house burns down, the remains of his house and the lot it is built on would be worth only $40,000, giving him a total wealth of $90,000. If his home doesn’t burn, it will be worth $200,000 and his total wealth will be $250,000. The probability that his home will burn down is .01.
(a) Calculate his expected utility if he doesn’t buy fire insurance.
(b) Calculate the certainty equivalent of the lottery he faces if he doesn’t buy fire insurance.
(c) Suppose that he can buy insurance at a price of $1 per $100 of insurance. For example if he buys $100,000 worth of insurance, he will pay $1,000 to the company no matter what happens, but if his house burns, he will also receive $100,000 from the company. If Dan buys $160,000 worth of insurance, he will be fully insured in the sense that no matter what happens his after-tax wealth will be _______.
(d) Therefore if he buys full insurance, the certainty equivalent of his wealth is _______, and his expected utility is _______.