To maximize profits, a firm produces where its marginal revenue equals its marginal cost, regardless of market structure (perfect competition, monopoly, oligopoly, etc.).
What makes the monopoly case different from perfect competition is that the monopolist knows its quantity choice will affect the market price, while firms in perfect competition are price-takers.
In particular, under monopoly, the marginal revenue is not constant and equal to the market price.
Numerical Example: A monopolist sells \(Q = 8\) units at \(P = 30\), but to sell \(Q = 9\), the monopolist must charge \(P = 29.50\).
\[ MR = TR(9) - TR(8) = 29.50 \times 9 - 30 \times 8 = \underbrace{29.50}_{P} + \underbrace{(29.50 - 30)}_{\Delta P} \times \underbrace{8}_{Q} \]
In general:
\[ \boxed{MR = \dfrac{\Delta TR}{\Delta Q} = P + \dfrac{\Delta P}{\Delta Q} \times Q} \]
Notice: \(\Delta P < 0\) which implies that \(MR < P\): the marginal revenue curve lies below the demand curve.
TODO
TODO
TODO