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Chapter 2: Answers to Questions and Problems
1.
a.
Since X is a normal good, an increase in income will lead to an increase in the
demand for X (the demand curve for X will shift to the right).
b.
Since Y is an inferior good, a decrease in income will lead to an increase in the
demand for good Y (the demand curve for Y will shift to the right).
c.
Since goods X and Y are substitutes, a decrease in the price of good Y will lead to
a decrease in the demand for good X (the demand curve for X will shift to the
left).
d.
No. The term “inferior good” does not mean “inferior quality,” it simply means
that income and consumption are inversely related.
2.
a.
The supply of good X will decrease (shift to the left).
b.
The supply of good X will decrease. More specifically, the supply curve will shift
vertically up by exactly $1 at each level of output.
c.
The supply of good X will decrease. More specifically, the supply curve will
rotate counterclockwise.
d.
The supply curve for good X will increase (shift to the right).
3.
a.
(
29
(
29
50
0.5 500
5 30
50
s
x
Q
= 
+

=
units.
b.
Notice that although
(
29
(
29
50
0.5 50
5 30
175
s
x
Q
= 
+

= 
, negative output is
impossible. Thus, quantity supplied is zero.
c.
To find the supply function, insert
30
z
P
=
into the supply equation to obtain
(
29
50
0.5
5 30
200
0.5
s
x
x
x
Q
P
P
= 
+

= 
+
. Thus, the supply equation is
200
0.5
s
x
x
Q
P
= 
+
. To obtain the inverse supply equation, simply solve this
equation for
x
P
to obtain
400
2
s
x
x
P
Q
=
+
. The inverse supply function is graphed
in Figure 21.
$0.0
$200.0
$400.0
$600.0
$800.0
$1,000.0
$1,200.0
$1,400.0
$1,600.0
0
100
200
300
400
500
Quantity of X
Price of X
S
Figure 21
Managerial Economics and Business Strategy, 6e
Page 1
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View Full Document4.
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.
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 Spring '09

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