Answer to Practice Homework9
12.3
a)
With demand
20
P
Q
=

,
20
2
MR
Q
=

.
A profitmaximizing firm charging a
uniform price will set
MR
MC
=
.
20
2
2
5
Q
Q
Q

=
=
At this quantity, price will be
15
P
=
.
At this price and quantity profit will be
2
15(5)
(
5 )
50
F
F
π
π
=

+
=

Therefore, the firm will earn positive profit as long as
50
F
<
.
b)
A firm engaging in firstdegree price discrimination with this demand will
produce where demand intersects marginal cost: 20 –
Q =
2
Q
or
Q =
6.67 units.
Its total revenue will be the area underneath the demand curve out to
Q =
6.67
units;
.5(20
13.33)(6.67)
13.33(6.67)
111.16
TR
=

+
=
.
Profit will be
2
111.16
(
6.67 )
66.67
F
F
π
π
=

+
=

Therefore, profit will be positive as long as
66.67
F
<
.
Comparing the solution
to parts (a) and (b), for values of
F
between 50 and 66.67 the firm would be
unwilling to operate unless it is able to practice firstdegree price discrimination.
12.4
a)
The firm would maximize profit by producing until
MR = MC
, or 40 – 6
Q =
2
Q
.
Thus
Q =
5 and the profitmaximizing price is
P =
25.
With
MC =
2
Q
and no
fixed costs, its total costs are
C = Q
2
, so
π
=
25(5) – 5
2
= 100.
b)
With perfect first degree price discrimination, the firm will charge a price on the
demand curve for all units up to the quantity at which the demand curve intersects
the marginal cost curve. The demand curve intersects the marginal cost curve
when 40 – 3
Q
= 2
Q
, or when
Q
= 8. Total revenue will be the area under the
demand curve, or 0.5(40 – 16)8 + 16(8) = 224. Total variable cost is the area of
the triangle under its marginal cost curve up to the quantity produced, that is,
0.5(16)(8) = 64. Economic profit will be 224 – 64 = 160. So by price
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 Spring '08
 Bryant
 Firm

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