Kate and Alice are small-town ready-mix concrete duopolists.The market demand function is Q^d = 20,000 - 200P,where P is the price of a cubic yard of concrete and Q^d is the number of cubic yards demanded per year.Marginal cost is $80 per cubic yard.The Cournot model describes the competition in this market.What is Alice's marginal revenue function?

Question

Quizplus · Accepted Answer

Alice's marginal revenue function is MR = 100 - 0.005Q_A - 0.01Q_K. This is because the market demand function is Q^d = 20,000 - 200P, and Alice's output is Q_A. The total output in the market is Q = Q_A + Q_K, where Q_K is Kate's output. Therefore, the inverse demand function is P = 100 - 0.005Q. Alice's marginal revenue function is then MR = d(P*Q_A)/dQ_A = P + Q_A*dP/dQ_A = 100 - 0.005Q_A - 0.01Q_K.

Kate and Alice Are Small-Town Ready-Mix Concrete Duopolists