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401
1
Sample questions 1
1. Let
X
=
{
a, b, c, d
}
,
B
=
±
{
a, b
}
,
{
a, c
}
,
{
a, d
}
,
{
b, c
}
,
{
b, d
}
,
{
c, d
}
,
{
d, b, c
}
,
{
a, b, d
}
,
{
a, c, d
}
²
and
(
B
, C
(
·
))
be a choice structure. Suppose
C
(
·
)
is such that
d
is the best choice whenever
d
is
available and
C
(
{
a, b
}
) =
{
a
}
, C
(
{
b, c
}
) =
{
b
}
,
and
C
(
{
c, a
}
) =
{
c
}
.
(a) Does
C
(
·
)
satisfy WARP?
(b) Is there a rational preference relation which rationalizes
C
(
·
)
on
B
?
(c) If
{
a, b, c
}
were another budget set could
C
(
·
)
satisfy WARP? Defend your
answers to (a), (b) and (c) carefully.
2. You are given the following information about a consumer’s purchases. Goods
1 and 2 are the only goods consumed.
Year 1
Year 2
Quantity
Price
Quantity
Price
Good 1
100
100
120
100
Good 2
100
100
?
80
For what values of good 2 consumed in year 2 would you conclude:
(a) that the consumer’s consumption bundle in year 1 is revealed preferred to that
in year 2?
(b) that the consumer’s consumption bundle in year 2 is revealed preferred to that
in year 1?
(c) that her/his behaviour contradicts the weak axiom?
(d) that good 1 is an inferior good
somewhere
for this consumer (assume WARP
holds)?
(e) that good 2 is an inferior good
somewhere
for this consumer (assume WARP
holds)?