A monopolist faces an inverse demand curve $P = 300 - 6 Q$ and has a constant marginal cost of 20. The monopolist's profit-maximizing output is

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, set marginal revenue (MR) equal to marginal cost (MC). The demand curve is $P = 300 - 6Q$, so total revenue (TR) is $TR = P \times Q = (300 - 6Q)Q$. The marginal revenue is the derivative of TR: $MR = 300 - 12Q$. Set $MR = MC$: $300 - 12Q = 20$. Solving for $Q$ gives $Q = 23.33$.

A Monopolist Faces an Inverse Demand Curve P=300−6QP = 300 - 6 QP=300−6Q

A Monopolist Faces an Inverse Demand Curve $P = 300 - 6 Q$