Solutions to Chapter 9 Exercises
SOLVED EXERCISES
S1.
(a)
Your neighbor has a sure income of $100,000. In addition, under the insurance
contract, he will receive
x
when you have a good year and pay you $60,000 when you have a bad
year. The lowest value of
x
such that your neighbor prefers to enter the contract will be the
x
for
which his expected utility for entering the contract is equal to his utility for not entering the
contract:
0.6 * √(100,000 +
x
) + 0.4 * √40,000 = √100,000
⇒
√(100,000 +
x
) = (√100,000 – 0.4 * √40,000) / 0.6
⇒
x
= [(√100,000 – 0.4 * √40,000) / 0.6]
2
– 100,000
≈ 55,009.8818
Rounding down to $55,009.88 would make your neighbor very slightly prefer not
entering the contract, so the minimum
x
that your neighbor will agree to is $55,009.89.
(b)
Here we are looking for the level of
x
where you are indifferent between getting
insurance (where you pay
x
in a good year and receive 60,000 in a bad year) and not getting
insurance. That is, we’re looking for the
x
for which your expected utility with the insurance is
equal to your expected utility without the insurance:
0.6 * √(160,000 –
x
) + 0.4 * √100,000 = 0.6 * √160,000 + 0.4 * √40,000
⇒
0.6 * √(160,000 –
x
) + 0.4 * √100,000 = 320
⇒
√(160,000 –
x
) = (320 – 0.4 * √100,000) / 0.6
⇒
x
= 160,000 – [(320 – 0.4 * √100,000) / 0.6]
2
≈ 55,984.1891
Rounding up and paying $55,984.19 would make you very slightly prefer not having
insurance. The highest
x
you would be willing to pay in a good year and still (barely) prefer to
have insurance is $55,984.18.
Solutions to Chapter 9 Exercises
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