Question

) 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 0.01.

(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____.

Please show details thanks!!!

Answer 1

a. == 0.01 *90,000+ 0.99 *250,000= 498

b. U= c^E = (498)² = 248004

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  $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 :(2500,000 ?160,000)/10= $248,400

d.Therefore if he buys full insurance, the certainty equivalent of his wealth is $248,400 , and his expected utility is 248,400.