What price should each firm charge if it wants to maximize its profit

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Suppose there are two firms with one demand function.

Suppose there are two firms with one demand function.

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

Suppose there are two firms with one demand function.

 
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