BRANDEIS UNIVERSITY
Department of Economics
Economics 134
Mr. Coiner
Public Sector
Spring, 2009
Answers to Problem Set 5
1.
Ch. 12, #3. a) expected income = (0.95)($50,000) + (0.05)($20,000) = $48,500
b) The fair premium is (prob. of loss)(size of the loss) = (0.05)($30,000) = $1,500
2.
Ch. 12, #12. a) The premium for Low Riders would be (0.01)($12,000) = $120.
The premium for
Speed Racers would be (0.05)($12,000) = $600.
b) i) In this case, insurance will not be offered.
Everyone will report that they are Low Riders and
qualify for the $120 premium, but the actual loss experience of the insurance company will be much
higher than $120 per person, because half of the insured will be Speed Racers.
ii) In this case, it is not certain whether insurance will be sold or not.
With no information about types,
the insurance company could attempt a pooled equilibrium where everyone was offered an “fair”
premium for the group as a whole.
This premium is (0.03)($12,000) = $360.
The Speed Racers will
definitely buy at this price, and Low Riders MAY buy, if they are sufficiently risk averse.
3.
Ch. 12, #13 modified so that utility is the square root of consumption.
a)
expected utility = (0.98)(square root of $40,000) + (0.02)(square root of $10,000) = (0.98)(200) +
(0.02)(100) = 198
b)
The fair premium is (0.02)($30,000) = $600.
If you pay the fair premium for full insurance, your
consumption is $40,000 - $600 = $39,400 for sure, and your utility is the square root of this, or
198.494.
c) The most you’d pay for full insurance is the premium that causes your utility to be 198, the same as
expected utility when you are not insured.
Let’s call this premium P.
It satisfies the equation:
(square root of $40,000 – P) = 198, or
$40,000 – P = (198)(198) = 39,204.
So P = 40,000 – 39,204 = $796.
4.