ECO 310, Fall 2007
Problem Set 8: Uncertainty
Due in class on December 17
Question 1
Satoru is an expected utility maximizer with von NeumannMorgenstern index
U
(
W
). He is ofered the Following gamble: gain $
h
with probability 1
/
2+
π
, and
lose $
h
with probability 1
/
2

π
, where
h
and
π
are small positive numbers. He
is indiferent between taking the gamble or not when his initial wealth is $
W
0
.
Give an approximation oF
π/h
in terms oF absolute risk aversion at
W
0
. (Hint:
Use the Taylor expansion to the second order.)
Question 2
You have initial wealth
W
0
dollars. With probability
π
, you will sufer a disaster
that will wipe out this wealth completely; otherwise it will stay the same. You
can insure against this loss. Denote by
p
the premium per dollar oF insurance.
This means that iF you buy
x
dollars oF insurance coverage, you have to pay
px
dollars right now, and will get
x
dollars From the insurance company iF you
sufer the disaster and nothing iF you do not.
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 Fall '08
 StephenE.Morris
 Utility, The Land, Insurance coverage, initial wealth, von NeumannMorgenstern index

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