Dan Partridge is a risk averter who tries to maximize his utility U = squareroot
ID: 2494994 • Letter: D
Question
Dan Partridge is a risk averter who tries to maximize his utility U = squareroot c, where c is his wealth. Dan has $50,000 in safe assets and 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 the 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 bum 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 down, he will also receive $100,000 from the insurance company. If Dan buys full insurance, what will be his expected wealth and his expected utility?Explanation / Answer
(a) if he dies not buy fire insurance
his expected utility will be :- $498
(b) certainty equivalence of the lottery if he doesn't buy fire insurance = $248,004
(.9) 2,50,000 + (.1) 90,000 = $2,48,004
(c) if dan buys full insurance then
the certainty equivalent of his wealth is $248,400 and
his expected utility is 248, 800 = 498.8.
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