A project with an initial investment of $438,500 will generate equal annual cash flows over its 9-year life. The project has a r
1 answer:
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Answer:
option (2) q1 = 16; q2 = 12
Explanation:
Given:
P = 100 - 2(q1 + q2)
here,
q1 is the output of Firm 1 and q2 is the output of Firm 2
Firm 1's marginal cost = $12
Firm 2's marginal cost = $20
Now,
Profit maximising level of output is attained where the marginal revenue equals the marginal cost
Thus,
for firm 1,
Total revenue, TR = P×Q
TR = (100 - 2q1 - 2q2) × q1
or
TR = 100q1 - 2(q1)² - 2(q1)(q2)
also,
MR =
thus,
MR = 100 - 4q1 - 2q2
MC = $12
now
MR = MC
or
100 - 4q1 - 2q2 = 12
or
88 = 4q1 + 2q2
or
q2 = 44 - 2q1 ............... (1)
also,
for firm 2, we have
TR = (100 - 2q1 - 2q2) × q2
or
TR = 100q2 - 2(q1)(q2) - 2(q2)²
and,
or
MR = 100 - 2q1 - 4q2
and
MC = $20
Now,
MR = MC
or
100 - 2q1 - 4q2 = 20
or
80 - 4q2 = 2q1
or
40 - 2q2 = q1 .....................(2)
Now,
substituting the value of q2 from (1), we get
q1 = 40 - 2(44 - 2q1)
or
q1 = 40 - 88 + 4q1
or
3q1 = 48
or
q1 = 16 units
substituting the value of q1 in equation (1) , we get
q2 = 44 - 2 × 16
or
q2 = 12 units
Therefore,
The correct answer is option (2) q1 = 16; q2 = 12