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.How much does Kate produce in the Nash equilibrium?

Question

Quizplus · Accepted Answer

In the Cournot model, each duopolist chooses its own quantity to produce, taking the competitor's quantity as given. The profit function of each firm is: π = (P - 80)Q1(Q2^d) Setting the first-order condition (FOC) of the profit function of each firm to zero, we have: dπ/dQ1 = P - 160Q1 - 80Q2 = 0 dπ/dQ2 = P - 80Q1 - 160Q2 = 0 Substituting P = 11ea8a01_e3c3_5141_8b44_5362fabb49d5_TB1639_11/2 - (Q1 + Q2) gives: -80Q1 + 40Q2 = - 5ea02a11_2f34_59d3_b67a_d921f72dd262_TB1639_11 40Q1 - 80Q2 = - 5ea02a11_2f34_59d3_b67a_d921f72dd262_TB1639_11 Solving for Q1 and Q2, we get: Q1 = 1/2(7000-125(11ea8a01_e3c3_5141_8b44_5362fabb49d5_TB1639_11)) Q2 = 1/2(7000-125(11ea8a01_e3c3_5141_8b44_5362fabb49d5_TB1639_11)) Q1 = 1333.33 and Q2 = 1333.33 Therefore, Kate produces 1,333.33 cubic yards in the Nash equilibrium.

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