Lecture 11 · Week 13 · Besanko & Braeutigam ch. 11 · about 50 min

Monopoly Markets

The opposite extreme from perfect competition: a single seller facing the whole market demand curve, why marginal revenue lies below price, the MR = MC output rule, and the deadweight loss monopoly creates relative to competition.

By the end you can

Explain why a monopolist's marginal revenue curve lies below its demand curve
Apply the MR = MC rule to find a monopolist's profit-maximising price and quantity
Compute monopoly profit and compare it with the competitive outcome
Compute the deadweight loss created by monopoly pricing

The monopolist faces the whole market demand curve

Unlike a competitive firm, a monopolist — the sole seller of a good with no close substitutes — is not a price taker. To sell more, it must lower price on every unit sold, not just the marginal one, which is what makes its marginal revenue different from price.

Monopoly marginal revenue (linear demand)Key formulaFormula sheet →

P = a - bQ \quad\Longrightarrow\quad MR = a - 2bQ

$a$: the demand curve's price intercept
$b$: the demand curve's slope magnitude

Use it when demand is linear and you need marginal revenue directly, without differentiating total revenue from scratch each time.

Profit maximisation: MR = MC

Monopoly profit-maximising ruleKey ruleFormula sheet →

\text{Choose } Q^* \text{ where } MR(Q^*) = MC(Q^*); \text{ then find } P^* = P(Q^*) \text{ from the demand curve}

Use it when you need a monopolist's profit-maximising price and quantity. Note the two-step process: MR = MC pins down quantity, and price is then read off the DEMAND curve, not the MR curve, at that quantity.

Try it: monopoly pricing and deadweight loss

Monopoly profit

Monopoly versus perfect competition: deadweight loss

If this same market were perfectly competitive with the same constant $MC=20$ , the competitive rule $P=MC$ would apply instead: $100-Q=20 \Rightarrow Q_c = 80$ , at price $P_c=20$ — a much larger quantity at a much lower price than the monopoly outcome ( $Q^*=40$ , $P^*=60$ ).

Monopoly deadweight lossKey formulaFormula sheet →

DWL = \tfrac{1}{2}\big(Q_c - Q^*\big)\big(P^* - MC\big)

$Q_c$: the competitive (efficient) quantity
$Q^*$: the monopoly quantity
$P^*$: the monopoly price

Use it when you need the efficiency cost of monopoly relative to the competitive benchmark, using the standard deadweight-loss triangle.

Exam practice

Summary and review

For linear demand $P=a-bQ$ : $MR = a-2bQ$ — same intercept, twice the slope.
MR lies below demand because selling one more unit requires cutting price on all units, not just the marginal one.
Profit-maximising rule: find $Q^*$ where $MR=MC$ , then find $P^*$ from the demand curve at $Q^*$ (never from MR).
Monopoly profit $= P^*Q^* - TC(Q^*)$ .
Monopoly produces less and charges more than the competitive benchmark, creating deadweight loss $= \tfrac12(Q_c-Q^*)(P^*-MC)$ .