Duopoly, quantity-setting firms face the market demand p = 270 - Q. Each firm has a...

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Duopoly, quantity-setting firms face the market demand p = 270 - Q. Each firm has a marginal cost of $30 per unit. What is th

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Answer 1

Answer #1

ANS: q1= 80

q2= 80

Working notes:

p=270-q

p=270-(q1-q2)

p=270-q1-q2

Calculation of quantity for firm 1 (q1)

TR=pxq1

=(270-q1-q2)q1

TR=270q1-q12-q1q2

MR= change inTR/change in q

MR=270-2q1-q2

TC=30q

MC=30

MR=MC

270-2q1-q2=30

q1=120-0.5q2------->equation 1

Calculation of quantity for firm 2 (q2)

TR=pxq2

=(270-q1-q2)q2

TR=270q2-q22-q1q2

MR= change inTR/change in q

MR=270-2q2-q1

TC=30q

MC=30

MR=MC

270-2q2-q1=30

q2=120-0.5q1----->equation 2

Now lets substitute equation 2 with equation 1

q1=120-0.5q2

=120-0.5(120-0.5q1)

q1= 80

Now lets substitute the value of q1 in equation 2

q2=120-0.5q1

q2=80

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