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.If Alice produces 5,000 cubic yards per year,what is Kate's inverse demand function?

Question

Quizplus · Accepted Answer

The inverse demand function for Kate is P = 75 - 0.005Q_K. This is because the market demand function is Q^d = 20,000 - 200P, and Alice is producing 5,000 cubic yards per year. So, the demand for Kate's concrete is Q^d - Q_A = 20,000 - 200P - 5,000 = 15,000 - 200P. Solving for P gives P = 75 - 0.005Q_K.

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