Question

Assume that you observe two firms operating in a Bertrand oligopoly. The inverse demand function for the market is P = 200 – 2Q and each firm has the same cost function of C(Q) = 20Q. What is the level of production for each firm, market price, and profit of each firm? What would happen if both firms merge to form a single monopoly with a cost function of C(Q) = 20Q?

Answer 1

Bertrand duopolist compete for prices so that when goods sold are identical, they end up charging a price P = MC. Here MC is 20. Hence Price is 20. Now total quantity is (200 - 20)/2 = 90 units and each of the two firms would be producing 45 units. There is no profit because MC = AC = P = 20.

Under a monopoly, they face MR = MC where MR = 200 - 4Q. This gives Q = (200 - 20)/4 = 45 units for both, a market price of P = 200 - 2*45 = $110 and a combined profit of (110*45 - 20*45) =  4050 for both of these firms.