4.
a.
Good Y is a substitute for X, while good Z is a complement for X.
b.
X is a normal good.
c.
(
29
(
29
(
29
(
29
000
,
5
000
,
55
$
10
1
90
$
8
900
,
5
$
4
1
910
,
4
$
2
1
200
,
1
=
+

+

=
d
x
Q
d.
For the given income and prices of other goods, the demand function for good X
is
(
29
(
29
(
29
1
1
1
1,200
$5,900
8 $90
$55,000 ,
2
4
10
d
x
x
Q
P
=

+

+
which simplifies to
7,455
0.5
d
x
x
Q
P
=

. To find the inverse demand equation, solve for price to
obtain
14,910
2
.
d
x
x
P
Q
=

The demand function is graphed in Figure 22.
$0
$2,982
$5,964
$8,946
$11,928
$14,910
0
1000
2000
3000
4000
5000
6000
7000
8000
Quantity of X
Price of X
Demand
Figure 22
5.
a.
Solve the demand function for
x
P
to obtain the following inverse demand
function:
1
115
4
d
x
x
P
Q
=

.
b.
Notice that when
$35
x
P
=
,
(
29
460
4 35
320
d
x
Q
=

=
units. Also, from part a, we
know the vertical intercept of the inverse demand equation is 115. Thus,
consumer surplus is $12,800 (computed as
(
29
(
29
.5 $115 $35 320
$12,800

=
).
c.