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Chptr 6 Homework Answers
P6.3
Revenue vs. Profit Maximization.
The Best Buy Company, Inc., is a leading
specialty retailer of consumer electronics, personal computers, entertainment
software and appliances.
The Company operates retail stores and commercial Web
sites, the best known of which is bestbuy.com.
Recently, this site offered a Sony 600-
Watt Home Theater with combination 600-total-watt surround sound receiver, 5-disc
DVD player with DVD, CD, CD-R/RW and MP3 playback and digital AM/FM tuner
plus matching 6-speaker set including subwoofer.
At a price of $1,100, weekly sales
totaled 2,500 units.
After a $100 online rebate was offered, weekly sales jumped to
5,000 units.
Using these two price-output combinations, the relevant linear demand and
marginal revenue curves can be estimated as:
P = $1,200 - $0.04Q and MR = $1,200 - $0.08Q
A.
Calculate the revenue-maximizing price-output combination and revenue level.
If Best Buy
=
s marginal cost per unit is $800, calculate profits at this activity
level assuming TC = MC
Η
Q.
B.
Calculate the profit-maximizing price-output combination.
Also calculate
revenues and profits at the profit-maximizing activity level.
P6.3
SOLUTION
A.
To find the revenue-maximizing price-output rental rate, set MR = 0, and solve for Q.
Because
TR
= P
Η
Q
= ($1,200 - $0.04Q)Q
= $1,200Q - $0.04Q
2
MR
=
Μ
TR/
Μ
Q
MR
= $1,200 - $0.08Q = 0
0.08Q
= 1,200
Q
= 15,000

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2
At Q = 15,000,
P =
$1,200 - $0.04(15,000)
=
$600
Total revenue at a price of $600 is:
TR = P
Η
Q
= $600
Η
15,000
=
$9 million per week
π
= TR - TC
=
$1,200Q - $0.04Q
2
- $800Q
=
$1,200(15,000) - $0.04(15,000
2
) - $800(15,000)
=
-$3 million per week (loss)
(
Note:
Μ
2
TR/
Μ
Q
2
< 0.
This is a revenue-maximizing output level because total
revenue is decreasing for output beyond Q > 15,000 units.)
B.
To find the profit-maximizing output level analytically, set MR = MC, or set M
π
= 0,
and solve for Q.
Because
MR = MC
$1,200 - $0.08Q = $800
0.08Q = 400
Q = 5,000
At Q = 5,000,
P = $1,200 - $0.04(5,000)
= $1,000