Economics 171: Final Exam Solutions – Winter 2008
1.
(6 pts) Lottery
A
pays either $25 or $50.
Lottery
B
pays either $10 or $75.
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?
A
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, 0.2;
$50, 0.8) 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, 0.2; $70, 0.8).
a.
Which lottery has a higher expected value (in terms of the dollar payout)?
E[
A
] = 0.2(10) + 0.8(50) = $42
E[
B
] = 0.4(10) + 0.4(50) + 0.2(70) = $38
A
has a higher expected value.
b.
Give her utility for $50.
u
($50) = EU($10, 0.2; $70, 0.8)
= 0.2
u
($10) + 0.8
u
($70)
= 0.2(0) + 0.8(1)
= 0.8
c.
Which lottery will she choose if she maximizes expected utility?
EU[
A
] = 0.2(0) + 0.8(0.8) = 0.64
EU[
B
] = 0.4(0) + 0.4(0.8) + 0.2(1) = 0.52
A
has a higher expected utility.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
3.
(12 pts) Lottery
A
is a uniform [$4, $24] distribution.
Lottery
B
is ($8, 0.5;
$24,
0.5).
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 .
B
A
A
B
F
F
ds
A
B
F
F
ds
B
A
−
<
⇒
−
<
⇒
∫
∫
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 Neumann-Morgenstern expected utility
maximizer.
His utility function satisfies our usual assumptions.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
This is the end of the preview.
Sign up
to
access the rest of the document.

- Winter '07
- Newhouse
- Economics, Utility,