The market inverse demand curve is P = 90 - Q, where Q is the total market output consisting of Firm 1's output, q₁, and Firm 2's output, q₂. Both firms have a constant marginal cost of $10. If Firm 1 selects its output level first, how much output does each firm produce?

Question

Quizplus · Accepted Answer

Firm 1 maximizes its profit by setting MR = MC. The MR curve is the derivative of the total revenue curve, which is TR = P * Q = (90 - Q) * Q = 90Q - Q^2. So, MR = dTR/dQ = 90 - 2Q. Setting MR = MC = 10, we get 90 - 2Q = 10, which implies Q = 40. Since Firm 1 produces half of the total market output, q₁ = 40/2 = 20. Therefore, q₂ = Q - q₁ = 40 - 20 = 20.

The Market Inverse Demand Curve Is P = 90 -