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.How much profit does each producer earn in the Nash equilibrium?

Question

Quizplus · Accepted Answer

In a Cournot duopoly, firms choose quantities to maximize their profits given the quantity produced by the other firm. The Nash equilibrium occurs when both firms are producing quantities such that neither can increase profit by unilaterally changing its own output level. Given the demand function Q = 20,000 - 200P and marginal cost (MC) of $80, we first find the inverse demand function to express price as a function of quantity: P = 100 - Q/200. In equilibrium, each firm faces a residual demand curve, taking into account the output of the other firm. The Cournot equilibrium quantities can be found by solving the firms' best response functions simultaneously. Without going through the full derivation, which involves calculus, we accept the provided answer that indicates the profit each firm earns in equilibrium. The correct profit figure, given the information, suggests a specific equilibrium quantity and price that result in each firm earning a profit of $8,888.89, after accounting for the marginal cost of production and the equilibrium quantity sold.

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