Practice Homework_ch11
Problems 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9, 11.11, 11.24, 11.25, 11.26
Answer
11.1
a)
If demand is given by
100 5
Q
P
=

, inverse demand is found by solving for
P
.
This implies inverse demand is
1
5
20
P
Q
=

.
b)
Average revenue is given by
TR
PQ
AR
P
Q
Q
=
=
=
Therefore, average revenue will be
1
5
20
P
Q
=

.
c)
For a linear demand curve
P
a bQ
=

, marginal revenue is given by
2
MR
a
bQ
=

.
In this instance demand is
1
5
20
P
Q
=

implying marginal
revenue is
2
5
20
MR
Q
=

.
11.2
a)
Since the demand curve is written in inverse form and is linear, the
MR
curve has
the same vertical intercept and twice the slop as the demand curve. Thus,
MR =
40 – 4
Q.
b)
Total revenue will be maximized when
MR =
0, or when
Q
= 10.
At that
quantity, the price will be
P =
40 – 2
Q =
20.
Total revenue is
PQ =
20(10) =
200.
11.3
+
=
∆
∆
+
=
∆
∆
+
=
P
Q
P
Q
P
P
Q
P
Q
P
Q
P
MR
,
1
1
1
ε
.
Since
P >
0,
MR =
0 if and only if 1 +
(
29
P
Q
,
/
1
= 0, which is equivalent to
1
/
1
,

=
P
Q
or
1
,

=
P
Q
.
11.4
If demand is
9
P
Q
= 
, then
9 2
MR
Q
= 
.
If the firm sets
7
Q
=
, then
5
MR
= 
.
At
this point, if the firm lowered its output it would increase total revenue, and with the
lower level of output total cost would fall.
Thus, decreasing output would increase profit.
Therefore, a profitmaximizing monopolist facing this demand curve would never choose
7
Q
=
.