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A monopolist is the sole seller in a market, facing a downward-sloping demand curve, and is therefore a price-maker. Marginal revenue is less than price (MR < P) because selling an additional unit requires lowering price on all units. The monopolist maximizes profit at MR = MC and then reads the price off the demand curve, producing less and charging more than the competitive equilibrium. This results in deadweight loss (foregone surplus from trades that would have been mutually beneficial). The Lerner Index (P − MC) / P measures the degree of monopoly power and equals 1/|PED|.
Derive MR algebraically from a linear demand curve, then solve the monopoly optimum both graphically and numerically. Compare the monopoly solution to the competitive one to quantify deadweight loss.
You know that a competitive firm is a price taker: it sells as much as it wants at the market price, and its marginal revenue equals that price. A monopolist breaks this assumption entirely. As the sole seller, it faces the entire downward-sloping market demand curve — if it wants to sell more, it must lower its price. This single difference transforms everything about how profit maximization works.
The key insight is why MR < P for a monopolist. Suppose the current price is $60 and you sell 40 units. To sell a 41st unit, you must drop the price to, say, $59 — but that new price applies to all 41 units, not just the last one. You gain $59 from the new sale but lose $1 on each of the 40 existing sales. MR = $59 − $40 = $19, far below the $59 price. More generally, for a linear demand curve P = a − bQ, the marginal revenue is MR = a − 2bQ — same intercept, twice the slope downward. The monopolist's MR curve lies below the demand curve everywhere (except the first unit).
Given this, profit maximization still follows the MR = MC rule — produce until the revenue gained from the last unit equals its cost. But because MR < P, the monopolist stops at a lower quantity than the competitive outcome (where P = MC). Having found the profit-maximizing quantity, the monopolist reads the price off the demand curve (not off MR). This is the two-step monopoly solution: (1) find Q where MR = MC, (2) find P from the demand curve at that Q. The gap between price and marginal cost is where monopoly profit comes from — and where social harm originates.
That social harm takes the form of deadweight loss: transactions that would have been mutually beneficial (for consumers willing to pay above MC but below the monopoly price) never occur. Resources that could have been used productively are not. The Lerner Index (P − MC) / P = 1 / |PED| quantifies the markup as a fraction of price and connects it to demand elasticity — a monopolist with inelastic demand can charge a large markup; one facing elastic demand cannot. This explains why pharmaceutical companies (with patented drugs that have few substitutes) earn larger margins than, say, gasoline retailers.
A common misconception is that the monopolist charges "the highest possible price." In fact, raising price beyond the optimum reduces quantity so much that total profit falls — the lost sales more than offset the higher margin per unit. The monopolist is constrained by demand, not unconstrained. It is a price-maker, not a price-ignorer. Understanding this distinction prepares you for studying price discrimination, where a monopolist extracts more surplus by charging different prices to different buyers — and potentially eliminates deadweight loss in the extreme case of perfect price discrimination.