Consider two identical firms (A and B) that face the following linear market demand curve and marginal cost:

P = 1200 - Q, where Q = Q1 + Q2 and MC = 0.

a) Derive firms A and B output-reaction curves.

b) Calculate the Cournot equilibrium quantity per firm and price in this market.

Each firm will choose output to maximize profit. To do so, each firm produces until the marginal revenue is equal to marginal cost.

• For firm 1, the marginal revenue curve is Q1(1200 - Q) = Q1(1200 - Q1 - Q2). Marginal revenue is 1200 - 2Q1 - Q2. Marginal cost is zero. So to maximize profit, the optimal quantity is given by 1200 - 2Q1 - Q2 = 0.
• For firm 2, the marginal revenue curve is Q2(1200 - Q) = Q2(1200 - Q1 - Q2). Marginal revenue is 1200 - Q1 - 2Q2. Marginal cost is zero. So to maximize profit, the optimal quantity is given by 1200 - Q1 - 2Q2 = 0.

b. In the Cournot equilibrium, both firms simultaneously choose the optimal quantity, given choice of the other firm, i.e., we need to solve the following two equations simultaneously:

• 1200 - 2Q1 - Q2 = 0,
• 1200 - Q1 - 2Q2 = 0.

And the solution is Q1 = Q2 = 400. The price each firm sets = 1200 - (400 + 400) = $400.