1. Dan is a risk averter who tries to maximize the expected value of C1/2, 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 a lot 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, given him a total wealth of $90,000. If his home does not burn, it will be worth $200,000 and the total wealth will be $250,000.
The probability that his home will burn down is 0.01.
a. Calculate his expected utility if he does not buy fire insurance.
b. Calculate the certainty equivalent of the lottery he faces if he does not buy fire insurance.
c. Suppose that he can 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, what will be his wealth?
d. If he buy full insurance, what is his certainty equivalent of his wealth? What is his expected utility?