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 the difference in the deadweight loss compared to a monopoly in this market?

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Quizplus · Accepted Answer

In Cournot competition, each firm assumes that its competitor's output remains constant and decides its own output level accordingly. In this case, let's assume that Kate produces QK cubic yards and Alice produces QA cubic yards. Then, the market supply function is given by Q = QK + QA, where Q = Q^d. From the demand function, we know that P = (20,000/Q) - 100. To find the Cournot equilibrium, each firm maximizes its profit given the assumed output of its competitor. This leads to the following reaction functions: QK = (6,250 - QA)/4 QA = (6,250 - QK)/4 Substituting these into the market supply function, we get: Q = (12,500 - Q)/4 Solving for Q, we get Q = 5,000 cubic yards. Thus, each firm produces 2,500 cubic yards at a price of $75 per cubic yard. The total surplus in the market is the area between the demand curve and the supply curve. In a monopoly, the monopolist would produce where marginal revenue equals marginal cost, which in this case is at an output of 9,375 cubic yards and a price of $56.25 per cubic yard. The deadweight loss compared to perfect competition is the triangle between the monopoly output level, the Cournot output level, and the demand curve. Using the formula for the area of a triangle, the deadweight loss under monopoly is: DWL = (1/2) x (9,375-5,000) x (100-56.25) = $5,555.56 Hence, the answer is option C, which says that a monopoly would create $5,555.56 more deadweight loss than in the Cournot equilibrium.

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