Duopolists A and B face the following demand curves: Q_A = 100 - 2P_A + 2P_B and Q_B = 100 - 2P_B + 2P_A.If both firms have zero marginal cost,what are the profit-maximizing prices and quantities? A) P_A = 100, Q_A = 60, P_B = 80, Q_B = 140. B) P_A = 25, Q_A = 100, P_B = 25, Q_B = 100. C) P_A = 50, Q_A = 80, P_B = 40, Q_B = 120. D) P_A = 50, Q_A = 100, P_B = 50, Q_B = 100. E) P_A = 60, Q_A = 60, P_B = 40, Q_B = 140.

Question

Quizplus · Accepted Answer

To find the profit-maximizing prices and quantities, we need to find the point where the firms’ profit is maximized. We know that both firms have zero marginal cost, so their profit equals total revenue. We can solve for the equilibrium prices and quantities using the following steps: 1. Set Q_A equal to Q_B and solve for P_A: 100 - 2P_A + 2P_B = 100 - 2P_B + 2P_A 4P_A = 4P_B P_A = P_B 2. Substitute P_A = P_B into either demand equation and solve for Q_A: Q_A = Q_B = 100 - 2P_A + 2P_B Q_A = Q_B = 100 - 4P_A 3. Substitute the equilibrium prices into either demand equation or supply equation to solve for the equilibrium quantities: Q_A = 100 - 2P_A + 2P_B Q_A = 100 - 2P_B + 2P_A Q_A + Q_B = 200 - 2P_A - 2P_B Q_A + Q_B = 200 - 4P_A Q_A = Q_B = 100 - 2P_A + 2P_B = 50 Therefore, the profit-maximizing prices and quantities are: P_A = P_B = 50 Q_A = Q_B = 100 Therefore, the answer is D, P_A = 50, Q_A = 100, P_B = 50, Q_B = 100.

Duopolists a and B Face the Following Demand Curves: QA

Duopolists a and B Face the Following Demand Curves: Q_A