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 the amount of the deadweight loss?

Question

Quizplus · Accepted Answer

The market demand function is: P = 240 - 0.05Q^d The inverse demand function is: Q^d = 4800 - 20P Given that Kate and Alice are duopolists, each firm's production will have an impact on the market price. The market quantity demanded at a price of $80 per cubic yard is: Q^d = 4800 - 20P Q^d = 4800 - 20(80) Q^d = 3200 Kate and Alice will split the market evenly, so each firm will produce half of the total market quantity: q1 = q2 = Q^d/2 = 1600 cubic yards Each firm's total revenue will be: TR1 = P(q1) = 80(1600) = $128,000 TR2 = P(q2) = 80(1600) = $128,000 Each firm's total cost will be: TC1 = MC(q1) = $80(1600) = $128,000 TC2 = MC(q2) = $80(1600) = $128,000 Each firm's profit will be: π1 = TR1 - TC1 = $0 π2 = TR2 - TC2 = $0 The total surplus in the market is: CS = 0.5(P - MC)q CS = 0.5(80 - 80)1600 = $0 Consumer surplus is zero because buyers are willing to pay up to $240 for a cubic yard of concrete but the market price is only $80. The deadweight loss is the loss of surplus that occurs when output is not at the socially optimal level. In this case, output is not socially optimal because it is zero. Therefore, the deadweight loss is: DWL = CS - PS DWL = $0 - $0 = $0 There is no deadweight loss in this case because output is zero.

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