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Economics 171: Final Exam Solutions – Winter 2008
1.
(6 pts) Lottery
A
pays either $5 or $50.
Lottery
B
pays either $10 or $85.
a.
Which lottery is chosen according to the Maximax criterion?
B
is chosen because its highest payout is higher than
A
’s highest payout.
b.
Which lottery is chosen according to the Maximin criterion?
B
is chosen because its lowest payout is higher than
B
’s lowest payout.
c.
What additional information is needed to determine the expected payout of
each lottery?
The probabilities of the outcomes.
2.
(12 pts) Shelly has a choice between lottery
A
= ($10, 0.3;
$50, 0.7) and lottery
B
= ($10, 0.4;
$50, 0.4;
$70, 0.2). Assume her utility for $10 is 0 and that her
utility for $70 is 1.
Shelly is indifferent between receiving $50 with certainty and
a lottery equal to ($10, 0.1; $70, 0.9).
a.
Which lottery has a higher expected value (in terms of the dollar payout)?
E[
A
] = 0.3(10) + 0.7(50) = $38
E[
B
] = 0.4(10) + 0.4(50) + 0.2(70) = $38
The expected values are equal.
b.
Give her utility for $50.
u
($50) = EU($10, 0.1; $70, 0.9)
= 0.1
u
($10) + 0.9
u
($70)
= 0.1(0) + 0.9(1)
= 0.9
c.
Which lottery will she choose if she maximizes expected utility?
EU[
A
] = 0.3(0) + 0.7(0.9) = 0.63
EU[
B
] = 0.4(0) + 0.4(0.9) + 0.2(1) = 0.56
A
has a higher expected utility.
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(12 pts) Lottery
A
is a uniform [$4, $24] distribution.
Lottery
B
is ($4, 0.2;
$14,
0.8).
What does first order stochastic dominance say about lotteries
A
and
B
?
What does second order stochastic dominance say about lotteries
A
and
B
?
FOSD doesn’t say anything about them.
One is not always equal or below the
other.
SOSD doesn’t say anything either.
()
8
4
14
4
0
cannot SOSD
.
0
cannot SOSD
.
AB
BA
FF
d
s
B
A
d
s
A
B
−<
⇒
⇒
∫
∫
1
0.8
0.6
0.4
0.2
A
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
B
4.
(15 pts) Apu is a risk averse, von NeumannMorgenstern expected utility
maximizer.
His utility function satisfies our usual assumptions.
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This note was uploaded on 04/23/2008 for the course ECON 171 taught by Professor Newhouse during the Winter '07 term at UCSD.
 Winter '07
 Newhouse
 Economics

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