Question

Consider a Cournot duopoly, the firms face an (inverse) demand function: Pb = 41500 - 98 Qb. The marginal cost for firm 1 is given by mc1 = 1137 Q. The marginal cost for firm 2 is given by mc2 = 813 Q. What quantity will of output will the duopoly produce ? (Assume firm 1 has a fixed cost of $ 9150 and firm 2 has a fixed cost of $ 400 .) Ans. 66.69

Answer 1

Each firm uses MR = MC so we have

41500 – 196Q1 – 98Q2 = 1137Q1 and 41500 – 196Q2 – 98Q1 = 813Q2

41500 – 1333Q1 – 98Q2 = 0 and 41500 – 1009Q2 – 98Q1 = 0

Q1 = 41500/1333 – 98Q2/1333

Use this expression in the second equation

41500 – 1009Q2 – 98*(41500/1333 – 98Q2/1333) = 0

38449 – 1001.8Q2 = 0

Q2 = 38.38

Q1 = 28.31

Total quantity = 38.38 + 28.31 = 66.69 units