Final Exam Fall 08 Suggested Answers
Q1
: 300 +
200
1
.
1
+
400
1
.
1
2
≈
812
.
3.
Q2
: Let
t
be the income allocated to asset A. Then he receives 1
.
6
t
+ 0
.
8(100

t
) =
80 + 0
.
8
t
if state 1 occurs and 0
.
7
t
+ 1
.
1(100

t
) = 110

0
.
4
t
if state 2 occurs. So
he maximizes
1
3
ln(80 + 0
.
8
t
) +
2
3
ln(110

0
.
4
t
)
The ﬁrstorder condition is
0
.
8
80 + 0
.
8
t
+ 2
·

0
.
4
110

0
.
4
t
= 0
,
which yields
t
= 25. Hence he allocates 25 to A and 75 to B.
Q3
: It gives students incentives to misreport their preferences, because if one fails
to get a seat in his best school he may have to go to a school worse that his second
best despite that he has higher priority than those who are admitted there, since
once seats in a school are ﬁlled up she cannot challenge the admitted students. This
typically causes that students pretend that their second best school is their ﬁrstbest.
Q4
: Step 1: 1
→
ω
2
, 2
→
ω
4
, 3
→
ω
6
, 4
→
ω
6
, 5
→
ω
4
, 6
→
ω
2
.
There is one cycle 2
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 Spring '10
 d
 Game Theory, common knowledge

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