# Suppose there are two firms with one demand function.

November 24, 2016

1. Suppose there are two firms with one demand function. This same (common) demand
function is:
Q = 1,000 – 40P

with MR = 25 – 0.05Q

However, each firm has its own cost function which is different. These two different cost
functions are shown below respectively:
Firm 1: 4,000 + 5Q
Firm 2: 3,000 + 7Q
a. What price should each firm charge if it wants to maximize its profit (or minimize its
loss)?
FIRM 1
FIRM 2
4000 + 5Q
3000 + 7Q
MC = 5
MC = 7
MR = MC
MR = MC
25 – 0.05Q = 5
25 – 0.05Q = 7
20 = 0.05Q
18 = 0.05Q
400 = Q
360 = Q
P = 25 – .025Q
P = 25 – .025Q
P = 25 – .025(400)
P = 25 – .025(360)
P = \$15
P = \$16
TO MAXIMIZE ITS PROFIT FIRM 1 SHOULD CHARGE \$15 AND FIRM 2
SHOULD CHARGE \$16
b. If price war breaks out, most likely price will fall. Two most likely prices in that event are
\$13 and \$12. Which company, firm 1 and firm 2, is more vulnerable to price war when P
= \$13 and why?
Q = 1,000 – 40(13); Q = 480
TR = \$13 x 480 = \$6,240
FIRM 1
TC = 4000+5(480) = 6,400; 6,240 – 6,400 = LOSS OF \$160
FIRM 2
TC = 3000+7(480) = 6,360; 6,240 – 6,360 = LOSS OF \$120
THUS FIRM 1 IS MORE VULNERABLE TO A PRICE WAR WHEN P=\$13 BECAUSE
THEY HAVE MORE OVERHEAD COMPARED TO FIRM 2.

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