Inverse demand for a monopolist's product is given by $P = 300 - 6 Q$ while the monopolist's marginal cost is given by $M C = 3 Q$ . The profit-maximizing price for this monopolist is

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To find the profit-maximizing price, set marginal revenue (MR) equal to marginal cost (MC). The inverse demand is $P = 300 - 6Q$, so total revenue $TR = P \times Q = 300Q - 6Q^2$. The marginal revenue is $MR = \frac{d(TR)}{dQ} = 300 - 12Q$. Set $MR = MC$: $300 - 12Q = 3Q$. Solving gives $Q = 20$. Substitute $Q = 20$ into the demand equation to find the price: $P = 300 - 6(20) = 180$.

Inverse Demand for a Monopolist's Product Is Given By P=300−6QP = 300 - 6 QP=300−6Q

Inverse Demand for a Monopolist's Product Is Given By $P = 300 - 6 Q$