2. Consider a person whose preferences are represented by the utility function,
u
(
x, y
) =
u
(
x, y
) =
x
1
/
5
y
4
/
5
.
a. For each pair of bundles
A
and
B
, indicate whether
A
(
P
)
B
,
B
(
P
)
A
or
A
(
I
)
B
.
A
B
i.
(5
,
8)
(8
,
4)
A (P) B
ii.
(3,9)
(3,7)
A (P) B
iii.
(3,6)
(3,8)
B (P) A
iv.
(5,5)
(4,5)
A (P) B
b. For the eight bundles in (a), construct a “list” starting with the most preferred bundle at
the top and ending with the least preferred at the bottom. (If two bundles are indifferent,
put them side by side on the same line in your list.)
(5, 8)
(3, 9)
(3, 8)
(3, 7)
(3, 6)
(5, 5)
(4, 5)
(8, 4)
c. Bundle
A
contains exactly 1/2 unit of
x
and a certain amount of
y
. If this consumer is
indifferent between bundle
A
and the bundle (1
,
1), how much
y
does bundle
A
contain?
Bundle
A
contains
y
*
=
4
√
2
, or
1
.
18921
units of
y
3