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Department of Economics
W3211
Columbia University
Fall 2011
Probl
e
m S
e
t 4
Int
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diat
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Mi
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onomi
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Prof
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S
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yhan E A rkona
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1
.
Bob's utility function is shown in the Figure below. He currently has $100 worth of property,
but there is a 50% chance that all of it will be stolen. An insurance company offers to
reimburse Bob for his loss if the money is stolen. What is the most that Bob would pay for
such a policy? Explain.
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.
An individual has an initial wealth of $35,000 and might incur a loss of $10,000 with
probability
p
.
Insurance is available that charges $
gK
to purchase $
K
of coverage.
What
value of
g
will make the insurance actuarially
f
air
?
If she is risk averse and insurance is fair,
what is the optimal amount of coverage?
3
.
Derive the ArrowPratt measure of risk aversion for the following utility functions.
Which
represents the greatest level of risk aversion according to the measure?
a
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 Fall '09
 Elmes
 Microeconomics, Utility

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