Two Cournot duopolists produce in a market with demand P = 100 Q. The marginal c

Question

Two Cournot duopolists produce in a market with demand P = 100 Q. The marginal cost for
firm 1 is constant and equals 10. The marginal cost for firm 2 is also constant and it equals 25.
The two firms want to merge. They argue for the merger on the grounds that marginal production
costs would fall to 10 for all units of output after the merger since all production would be at
the low marginal cost. Given this information, would you recommend the merger? Explain by
calculating the benefits and costs from the merger.

Explanation / Answer

Before merger he wo duopolist would be producing the following :

Market demand : P = 100-Q

where Q = Q1+Q2

Firm 1: TR1 = P*Q1= 100Q1-Q12 - Q1Q2

MR = dTR1/dQ1 = 100 - 2Q1 - Q2

MC = 10

Equating MR and MC

100-2Q1 - Q2 = 10

2Q1 + Q2 = 90 units or Q2 = 2Q1-90 ..... eq i

and P = 100- (Q1 + 2Q1 - 90) = $190 - 3Q1

Profit = P*Q - Q*MC = 190Q1 - 3Q12 - 10Q1

And Firm 2:

MR = d (100Q2 - Q22 -Q1Q2)/dQ2 = 100 - 2Q2 - Q1

MC = 25

Equaing MR and MC

100-2Q2 - Q1 = 25

2Q2 + Q1 = 75 or Q2 = (75-Q1)/2 eq ii

From eq i and ii

4Q1 - 180 = 75 - Q1

Q1 = 51

and Q2 = 2(51) - 90 = 12

and Q = 12+ 51 = 63

and P = 100-63 = $37

Profi of firm 1 = P*Q - MC*Q = 37*51 - 10*51 = $1377

Profi of firm 2 = 37*12 - 25*12 = $144

Afer merger:

MR = 100 - 2Q

MC = 10

Equaing MR and MC

100-2Q = 10

Q = 45

and P = 100-45 = 55

Profi = 55*45 - 10*45 = $2025.

firms should merge as profi has increased.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.