Econ 145: Practice Questions I
Ichiro Obara
February 5, 2010
1. Consider a room assignment problem with 4 students and 4 rooms
{
h
1
, . . . , h
4
}
.
Room
h
i
is initially assigned to student
i.
Suppose that
the preferences of the students are as follows
h
2
Â
1
h
4
Â
1
h
1
Â
1
h
3
h
2
Â
2
h
1
Â
2
h
3
Â
2
h
4
h
1
Â
3
h
3
Â
3
h
4
Â
3
h
2
h
3
Â
4
h
4
Â
4
h
1
Â
4
h
2
where
Â
i
is student
i
’s (strict) preference over the rooms.
Answer
following questions.
(a) Is the initial allocation e
ﬃ
cient? Explain why.
(b) Find all e
ﬃ
cient allocations. Explain how you found all the e
ﬃ

cient allocations.
(c) In general, the set of e
ﬃ
cient allocations is larger than the core
allocation (given a certain initial assignment). Can you
fi
nd an
example of room assignment problem (with four students and
four rooms) such that these two sets coincide? If so,
fi
nd one. If
not, explain why.
2. Consider a room assignment problem with 3 students and 3 rooms
{
h
1
, ..., h
3
}
.
Room
h
i
is initially assigned to student
i.
Answer the
following questions.
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