Question

Please show all your work.

Your firm has total costs equal to 40Q₁. The demand you face is P=4000-5Q.

The second firm now has bad management, increasing its costs to 50Q₂. You are still playing Cournot. What is your output and

profits?

Answer 1

Q1 = output of firm 1 and Q2 = output of firm 2

Q = Q1 + Q2

Firm 1:

MR1 = d(PQ1) / dQ1 = 4000 - 10Q1 - 5Q2

MC1 = dC1/dQ1 = 40

Profit is maximized where MR = MC:

10Q1 + 5Q2 = 3960

Firm 2:

MR2 = d(PQ2) / dQ2 = 4000 - 10Q2 - 5Q1

MC2 = dC2/dQ2 = 50

Profit is maximized where MR = MC:

10Q2 + 5Q1 = 3950

Q1 = 264.47

Q2 = 262.67

P = 1363.33

Profit (firm 1) = PQ1 - C1 = 1363.33 x 264.67 - 40 x 264.67 = 350242.2