Kate and Alice are small-town ready-mix concrete duopolists.The market demand function is 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 total output in the Nash equilibrium?

Question

Quizplus · Accepted Answer

In the Cournot model, each firm chooses its quantity of output given the quantity produced by its competitor. The profit-maximizing output for each firm is where marginal revenue equals marginal cost.

The inverse demand function can be rewritten as P = 11 - 0.2Q, where Q is total output in the market. The total revenue for each firm can be calculated as TR = P*Q = (11 - 0.2Q)Q = 11Q - 0.2Q^2.

Taking the derivative of total revenue with respect to quantity gives MR = 11 - 0.4Q. Setting MR equal to marginal cost of $80 gives 11 - 0.4Q = 80, or Q = 258.33 for each firm.

Thus, total output in the market is 2*258.33 = 516.66 cubic yards per year. Rounded to the nearest integer, the answer is 2,667 cubic yards per year.

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