Hi, I'm having trouble with this question:
Two firms face a market demand curve of p=5-q1-q2. Suppose firm 1 is considering improving production. The initial cost will be $2.00. Once this investment is made the marginal cost will be $1.00. Firm 2 marginal cost is $4.
i) what will be the output of each firm, when firm one implements the technology.
rev=pq
=(5-q1-q2)(q1)
=5q1-q1^2-q1q2
MR= 5-2q1-q2
MC=1
MR=MC
5-2q1-q2=1
(4-q2)/2=q1
2-0.5q2=q1
firm 2
rev=pq
=(5-q1-q2)(q2)
=5q2-q1q2-q2^2
MR= 5-q1-2q2
MC=4
5-q1-2q2=4
(1-q1)/2=q2
0.5-0.5q1=q2
2-0.5(0.5-0.5q1)=q1
2-0.25+0.25q1=q1
1.75=0.75q1
2.33=q1
0.5-0.5(2.33)=q2
-0.665=q2
so firm 2 will just choose not to produce?
Thank you!
Two firms face a market demand curve of p=5-q1-q2. Suppose firm 1 is considering improving production. The initial cost will be $2.00. Once this investment is made the marginal cost will be $1.00. Firm 2 marginal cost is $4.
i) what will be the output of each firm, when firm one implements the technology.
rev=pq
=(5-q1-q2)(q1)
=5q1-q1^2-q1q2
MR= 5-2q1-q2
MC=1
MR=MC
5-2q1-q2=1
(4-q2)/2=q1
2-0.5q2=q1
firm 2
rev=pq
=(5-q1-q2)(q2)
=5q2-q1q2-q2^2
MR= 5-q1-2q2
MC=4
5-q1-2q2=4
(1-q1)/2=q2
0.5-0.5q1=q2
2-0.5(0.5-0.5q1)=q1
2-0.25+0.25q1=q1
1.75=0.75q1
2.33=q1
0.5-0.5(2.33)=q2
-0.665=q2
so firm 2 will just choose not to produce?
Thank you!
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