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.Which of the following best represents Alice's inverse residual demand function?

Question

Quizplus · Accepted Answer

In the Cournot model, each firm assumes that the output of their competitor is fixed. Therefore, Alice's inverse residual demand function can be derived by subtracting Kate's output from the total market demand and solving for P. Total market demand = Q^d = 20,000 - 200P Assuming Kate produces Q_K cubic yards, Alice's inverse residual demand function becomes: P(Q_A) = (20,000 - 200(Q_A + Q_K)) / Q_A P(Q_A) = (200 - 0.005Q_A) - 0.005Q_K Therefore, the correct choice is B.

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