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.

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