Suppose the demand for pizza in a small isolated town is p = 10 - Q. There are only two firms, A and B, and each has a cost function TC = 2 + Q

Question

Compare the firms' profits if they behave as Cournot duopolists with their profits if they form a cartel and share the market.

Answer 1

First, the Cournot equilibrium. Firm A's profit is ? = [10 - (qA + qB)]qA - 2 - qA. Maximizing with respect to its own output yields qA = 4.5 - qB/2. Similarly, firm B's best response is qB = 4.5 - qA/2. The equilibrium occurs when both firms produce 3 units. Price is
10 - 3 - 3 = 4. Total revenue is 12 and total cost is 5. Profit is 7 for each firm. As a cartel, maximize joint profit by setting marginal revenue equal to their joint marginal cost, or
10 - 2Q = 1. Q = 4.5, so each firm produces 2.25 units. Price is 5.5. Total revenue is 12.375;
total cost is 4.25. Each firm earns a profit of 8.125.