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ECOS2001 Tutorial 12
1
ECOS 2001 Tutorial 12
1. Clarence Busen is an expected utility maximiser. His preference among
contingent commodity bundles are represented by
1/2
12 1 2
1 1
2 2
(, , , )
.
()
.
uc c
c
c
ππ
π
=+
Hjalmer has offered to bet Clarence $1000 on the outcome of the toss of a coin.
That is, if the coin comes up heads, Clarence must pay Hjalmer $1000 and if it is
tails Hjalmer must pay Clarence $1000. It is a fair coin toss (prob of each is 1/2 .)
If he doesn’t accept the bet Clarence will have $10000 with certainty. Let Event 1
be heads and let Event 2 be tails
a. If Clarence accepts the bet, then in Event 1 he will have how many dollars?
What about with Event 2?
In Event 1 gets 9000; Event 2 gets 11 000
b. If Clarence gets c1 with Event 1 and c2 with Event 2, what is the formula for
Clarence’s expected utility? What is his expected utility if he accepts the bet?
12
11
22
EU
c
c
Accepting the bet EU = 99.8746
c. If Clarence decides not to bet, what is his income under Event 1 and 2? What
his expected utility be under each Event?
EU = 100
d. Does Clarence take the bet?
No
2. The
certainty equivalent
of a lottery is the amount of money you would have to
be given with certainty to be just as welloff with that lottery. Suppose that your
expected utility function with income in the case of Event 1 and Event 2 is x and
y respectively is
(, , )
(
1
)
Uxy
x
y
−
, where
π
is the probability of event
1.
a. If
π
= 0.5, calculate the utility of a lottery that gives you $10 000 if Event 1
happens and $100 if Event 1 doesn’t happen.
55 = 0.5(100) + 0.5(10)
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2
b. If you were sure to receive $4900, what would your utility be?
U = 70
c. Given this utility function and
π
= 0.5, write a general formula for the
certainty equivalent of a lottery that gives you $x if Event 1 happens and $y if
Event 1 does not happen
1/2
21
/
2
1
/
2
2
11
22
()
EU
x
y
UCE EU
CE
EU
x
y
=+
=
==
+
Certainty equivalent CE is such that:
=
So that
/
2
1
/
2
2
CE
EU
x
y
+
d. Calculate the certainty equivalent of receiving $10 000 if Event 1 happens and
$100 if Event 1 does not happen.
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This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.
 One '09
 NONE

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