In a Cournot market with two firms, the inverse market demand curve is P = 50 - 2Q, where Q = q₁ + q₂ (Firm 1's output = q₁; Firm 2's output = q₂). If Firm 2 produces 10 units of output, what is Firm 1's residual demand curve?

Question

Quizplus · Accepted Answer

The residual demand curve for Firm 1 is found by substituting Firm 2's output into the total market demand equation and solving for P in terms of q₁. Given Firm 2's output is 10 units, Q = q₁ + 10. Substituting into the inverse demand function P = 50 - 2Q gives P = 50 - 2(q₁ + 10) = 50 - 2q₁ - 20 = 30 - 2q₁, which matches choice A.

In a Cournot Market with Two Firms, the Inverse Market