Economics 171: Decisions Under Uncertainty
Solutions to Final Exam: Spring 2009
1.
(12 pts) Before John bicycles to school he has to decide what to wear. He can
either wear spandex or dress normally. He may or may not run into any of his
friends. If he wears spandex the trip will take 19 minutes but he will be made fun
of if he runs into any of his friends. (He won’t be made fun of if he doesn’t run
into any of his friends.) If he dresses normally the trip will take 20 minutes and he
will not be made fun of regardless of whether or not he runs into any of his
friends.
a.
What decisions are available?
{Spandex, Normal}
b.
What states of nature could occur?
{Friends, Not}
c.
What are the possible outcomes?
{19 minutes & made fun, 19 minutes & not made fun, 20 minutes}
d.
What information needs to be given to determine which action maximizes
his expected utility?
Utility of the outcomes and probability of running into his friends.
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2.
(12 pts) We use the triangle diagram to graph indifference curves for lotteries
with three possible outcomes,
x
1
<
x
2
<
x
3
. We usually graph the triangle diagram
with
p
1
, that is
p
(
x
1
), on the
x
axis and
p
3
on the
y
axis.
a.
Draw the triangle diagram with
p
1
on the
x
axis and
p
2
on the
y
axis. (This
is different from the usual way we label these axes.) Label the most
preferred lottery as point
A
.
b.
What’s the most we can say about the slope of an indifference curve? (The
correct answer might contain an upper and a lower bound or just one of
these.) Briefly explain.
First of all we know the slope must be negative. If we move directly left,
probability mass shifts from
x
1
to
x
3
which is good. Therefore to get back
on the same indifference curve we must do something bad which is a
move up. This move shifts mass from
x
3
to
x
2
.
We also know the slope of the indifference curve must be steeper than the
line connecting (
p
1
,
p
2
,
p
3
) = (0, 1, 0) and (1, 0, 0). This is because (0, 1, 0)
is preferred to (1, 0, 0).
The combination of these two things tells us the slope is less than –1.
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 Spring '09
 HERBNEWHOUSE
 Utility, good answer, actuarially fair insurance

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