ANSWERS to Questions 3
‐
5/ Discussion 4
Answer to Q.3
a)
If MRS is higher than the price ratio
2
1
P
P
, then Kate will only spend her money on good 1. If
2
1
2
,
1
P
P
MRS
<
, than she spends her money only on good 2. If
2
1
P
P
MRS
=
, then any bundle on the
budget line is optimal. Kate’s MRS equals
‐
2. Hence the demand functions are:
,
2
_
,
0
2
_
],
,
0
[
2
_
,
2
1
2
1
1
2
1
1
1
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
>
=
<
=
p
p
if
p
p
if
p
m
p
p
if
p
m
x
,
2
_
,
0
2
_
],
,
0
[
2
_
,
2
1
2
1
2
2
1
2
2
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
<
=
>
=
p
p
if
p
p
if
p
m
p
p
if
p
m
x
b)
p
2
=1, m=10
At any price higher than 2 (p
1
>2), Kate only buys good 2. Hence for x
1
=0, x
2
=10. Fo p
1
=2, the budget line
has the same slope as the indifference curves, so any point on the budget line will be optimal:
(the BL, for p
1
=2). For p
1
<2, Kate only buys good 1. Hence for x
1
>5, x
2
=0. The price offer
curve is:
1
2
2
10
x
x
−
=
,
5
_
_
,
0
5
_
_
,
2
10
1
1
1
2
⎩
⎨
⎧
≥
<
−
=
x
if
x
if
x
x
To find the demand curve, we plug p
2
and m into the demand functions from part (a):

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