Source: Sample Midterm 1, Q1
Difficulty: Intermediate | Prerequisites: Basic understanding of supply and demand, cost curves, revenue concepts.
Monopoly is one of the core market structures in introductory microeconomics, and the profit-maximisation problem for a monopolist is a staple exam topic. This material builds on the general idea that firms choose output to maximise profit, but adds a twist: because a monopolist faces the entire market demand curve, its marginal revenue behaves differently from a competitive firm's. You should already be comfortable with marginal cost, marginal revenue, and the basic mechanics of how a firm decides how much to produce.
A monopolist maximises profit by producing where marginal revenue equals marginal cost (MR = MC), not where price equals marginal cost (P = MC). Because the monopolist must lower its price to sell additional units, MR is always less than P, so the profit-maximising quantity is lower than the quantity a competitive firm would choose.
Marginal revenue (MR)
The addition to total revenue from selling one more unit. For a monopolist, MR is less than price because selling an extra unit requires lowering the price on all units. In simple terms, each additional sale brings in less new revenue than the sticker price suggests.
Marginal cost (MC)
The addition to total cost from producing one more unit. Think of it as the cost of "one more" at the margin.
Profit-maximisation condition (MR = MC)
The rule that a firm produces up to the point where the revenue gained from the last unit exactly equals the cost of producing it. Every unit before that point adds to profit; every unit after it subtracts.
Monopolist
A single seller in a market facing the entire downward-sloping market demand curve. Because there are no close competitors, the monopolist has pricing power but must still lower its price to sell more.
Deadweight loss (in the monopoly context)
The reduction in total surplus that arises because the monopolist produces less than the socially efficient quantity. In simple terms, some trades that would benefit both buyer and seller never happen.
A monopolist faces a downward-sloping demand curve. To sell one more unit, it must reduce the price on all units, not just the marginal one.
The revenue gained from the extra unit (price received) is partly offset by the revenue lost on all the units that were previously sold at the higher price.
Therefore, marginal revenue is always below the demand curve (below price) for a monopolist.
A firm maximises profit by producing at the quantity where MR = MC.
For every unit where MR > MC, producing that unit adds to profit. For every unit where MR < MC, producing that unit subtracts from profit.
The optimal quantity (Q₁ on the standard diagram) is where MR crosses MC.
Producing at the quantity where P = MC (labelled Q_C on the diagram) would mean the firm keeps producing units past the point where MR = MC.
Between Q₁ and Q_C, marginal cost exceeds marginal revenue on every additional unit. Each of those units loses money.
The total profit lost by producing at Q_C instead of Q₁ is shown by the triangle between the MC and MR curves from Q₁ to Q_C.
The demand curve (D) slopes downward. The MR curve lies below D and is steeper.
MC slopes upward. The profit-maximising output is at the intersection of MR and MC.
The monopolist then charges the price consumers are willing to pay for that quantity, read off the demand curve above Q₁.
Profit-maximisation condition:
MR = MCMarginal revenue for a linear demand curve P = a - bQ:
MR = a - 2bQNote that MR has the same intercept as the demand curve but twice the slope. This is a handy exam shortcut for linear demand.
Diagram: The standard monopoly diagram has P on the vertical axis and Q on the horizontal. D slopes down, MR lies below D (same intercept, steeper), MC slopes up. The profit-maximising quantity Q₁ is at the MR-MC intersection. The price charged is read off D at Q₁. The "loss triangle" between MC and MR from Q₁ to Q_C shows the profit forfeited by overproducing to the P = MC point.
Pharmaceutical companies with patent protection operate as monopolists for their drugs. They set prices well above marginal cost precisely because MR < P, and they restrict quantity to maximise profit. This is also why a single airline on a regional route charges higher fares and offers fewer seats than you would see in a competitive market.
Students often think a monopolist should produce where P = MC, because that is the rule for competitive firms. It is not. The competitive firm's MR happens to equal P (because it is a price taker). A monopolist's MR is below P, so the two rules diverge.
Some students believe a monopolist "picks" any price it wants. The monopolist is still constrained by the demand curve: it chooses a quantity, and the demand curve determines the price consumers will pay.
Confusing the direction of the loss: the profit penalty from producing at P = MC rather than MR = MC comes from overproducing (units where MR < MC), not from underproducing.
Forgetting to draw MR below D in the diagram. MR always lies below the demand curve for a monopolist; placing them on top of each other will cost marks.
⚠️ The diagram and a clear explanation of why MR < P are worth the bulk of the marks. Get those right and you are most of the way there.
⚠️ You need to explain why producing at MR = MC maximises profit (units before add to profit, units after subtract). A diagram alone without this reasoning will not earn full credit.
⚠️ Showing the shaded triangle of lost profit between Q₁ and Q_C is a nice extra but is not required for full marks.
True or false: A monopolist maximises profit where P = MC. (False, it is where MR = MC.)
Fill in the blank: For a monopolist, marginal revenue is always ______ than price. (less)
True or false: A monopolist can charge any price it wants regardless of demand. (False, the demand curve constrains it.)
Fill in the blank: The profit lost by producing at Q_C instead of Q₁ is shown by the ______ between MC and MR. (triangle / area)
True or false: MR lies above the demand curve for a monopolist. (False, MR lies below D.)
Q: Using a diagram, explain why a monopolist does not maximise profit by producing where price equals marginal cost.
A: Draw a standard monopoly diagram with D, MR (below D), and MC. The profit-maximising quantity is Q₁ where MR = MC. At the quantity Q_C where P = MC, the firm has produced additional units for which MR < MC, meaning each of those units costs more to produce than it adds to revenue. The result is lower total profit. The lost profit is represented by the triangle between MC and MR from Q₁ to Q_C.
Q: Why is marginal revenue less than price for a monopolist?
A: A monopolist faces the entire market demand curve, which slopes downward. To sell one more unit, it must lower the price not just on that unit but on all previously sold units. The revenue gained from the additional unit (the price it sells for) is partially offset by the revenue lost from the price cut on existing units. So MR < P.
Q: A monopolist is currently producing where MR > MC. Should it increase or decrease output to raise profits? Explain.
A: Increase output. If MR > MC, the next unit adds more to revenue than it adds to cost, so producing it raises profit. The firm should keep expanding until MR = MC.
This connects directly to welfare analysis and deadweight loss: the monopolist's restriction of output below the competitive level creates a deadweight loss triangle, which you will revisit when studying market efficiency and government intervention. It also links to price discrimination, where a monopolist tries to capture more of the consumer surplus by charging different prices to different buyers.
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