Why a Monopolist's MR Lies Below Demand

A monopolist faces the whole market demand curve, so it only sells more by lowering price for everybody. Selling one more unit brings in the new unit's price, but it also costs the firm revenue on every unit it was already selling, because those units now go for less too. Marginal revenue is the net of those two effects: the gain from the extra unit minus the loss from the price cut spread across all earlier units.

This is why marginal revenue sits below demand everywhere except the very first unit. Economists call the loss from cutting price on existing units the price effect, and it grows as output grows, since more units are getting the lower price. On a straight-line demand curve P = a - bQ, this works out exactly: marginal revenue is MR = a - 2bQ, falling twice as steeply as demand. Both lines start at the same price-intercept, but MR hits zero at half the quantity where demand hits zero.

This gap between price and marginal revenue is what drives the monopolist's output choice next: it sets MR equal to marginal cost, then charges the higher price demand allows at that quantity, leaving output below the competitive level and creating deadweight loss. A perfectly competitive firm has no such gap, since it can sell more without affecting price, so MR equals price for it, which is why monopoly outcomes diverge from competitive ones.