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In a given market the inverse demand function is P = 170 - Q per year
In a given market the inverse demand function is P = 170 - Q per year. The interest rate is r = 0.05 and the cost structure of a firm is given by C(q) = 80 q.
Assume the market is monopolized and answer the following:
A research institute develops a new technology that reduces marginal cost to 50 and upon entering the market it competes on quantity with the incumbent (who cannot access the new technology). As a result, per year profits for the firms are:
Group of answer choices
800 for the incumbent and 1200 for the entrant.
400 for the incumbent and 2500 for the entrant.
600 for the incumbent and 3000 for the entrant.
200 for the incumbent and 3000 for the entrant.
Expert Solution
Computation of Per Year Profits for the Firm:
Given,
Firm 1= Incumbent
Firm 2= Entrant
MR1=170-2q1-q2
MC1=80
170-2q1-q2=80
170-80 = 2q1+q2
90 = 2q1+q2
Q1 = (90-q2)/2
Q1=45-0.5q2
MR2=170-2q2-q1
MC1=50
170-2q2-q1=50
170 - 50 = 2q2-q1
120 = 2q2-q1
Q2 = (120-q1)/2
Q2=60-0.5q1
Putting Q2 into q1,
Q1=45-0.5(60-0.5q1)
Q1=45-30+0.25q1
Q1=15/0.75=20
Q2=60-0.5*20=50
P=170-20-50=100
Profit 1=(100-80)*20=400
Profit 2=(100-50)*50=2500
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