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CFA Level I Exam · The Firm and Market Structures

Monopoly and Pricing Strategies: Profit Maximization and Regulation

Updated 7 October 2026 · Fact-checked

A monopoly is a market with one seller, no close substitutes and high barriers to entry. Because it must cut price to sell more units, marginal revenue falls below price. To solve questions, set marginal revenue equal to marginal cost, read the price from the demand curve, then compare with average cost and regulation outcomes.

Understand Monopoly and Pricing Strategies

A monopoly has a single seller of a product with no close substitutes. Barriers to entry keep rivals out. These can be legal (patents, licences), control of a key resource, or economies of scale. The monopolist is a price maker: it chooses price or quantity, but not both. Demand fixes the link between them.

The firm faces the whole market demand curve, which slopes down. A single-price monopolist must cut the price on all units to sell one more. So the extra revenue from one more unit (marginal revenue, MR) is less than the price. You gain the new price on the extra unit, but you lose revenue on every unit you could have sold at the old, higher price. With a straight-line demand curve, the MR curve starts at the same intercept and has twice the slope.

Profit is maximized where MR = MC. This is the same rule as in every market structure. What differs is that price is above MR. So you find the quantity from MR = MC, then go up to the demand curve to read the price. The price is above marginal cost, output is lower than under perfect competition, and a deadweight loss appears. Economic profit is not guaranteed. If price is below average total cost at the best output, the monopolist makes a loss. A monopolist also has no supply curve, because its output depends on demand and MR, not on price alone. It operates only where demand is elastic, because MR must be positive to equal MC.

Price discrimination means charging different prices for the same product when cost differences do not explain the gap. It needs market power, the ability to separate buyers, and no resale between them. First-degree (perfect) discrimination charges each buyer their maximum willingness to pay. Output reaches the efficient level, consumer surplus goes to zero and the monopolist takes all the surplus. Second-degree discrimination varies price by quantity or product version, such as volume discounts. Third-degree discrimination splits buyers into groups with different demand elasticity, such as student and adult tickets, and charges the group with less elastic demand more.

A natural monopoly arises when long-run average cost keeps falling over the range of market demand, so one firm can serve the market at lower cost than two. Regulators have two main price rules. Marginal cost pricing sets P = MC. It is efficient, but because MC is below average cost the firm makes a loss and needs a subsidy or a two-part tariff. Average cost pricing sets P = average total cost. The firm earns a normal profit, with output lower than the efficient level, so some deadweight loss remains. Regulators can also use cost-of-service (rate of return) regulation, price caps, or output regulation.

Key formulas to remember

Total and marginal revenue
TR = P × Q; MR = ΔTR ÷ ΔQ
For a single-price monopolist, MR < P at every positive output.
Linear demand and MR
P = a − bQ → MR = a − 2bQ
MR has the same intercept as demand and twice the slope.
Profit-maximizing rule
MR = MC; then price from demand at that Q
Read price from the demand curve, not from the MR curve.
MR and elasticity
MR = P × (1 − 1 ÷ |E|)
MR > 0 only when |E| > 1. A monopolist does not produce where demand is inelastic.
Economic profit
Profit = (P − ATC) × Q
Positive, zero or negative depending on price versus average total cost.
Regulated natural monopoly pricing
Average cost pricing: P = ATC. Marginal cost pricing: P = MC
Average cost pricing gives normal profit with some deadweight loss. Marginal cost pricing is efficient but causes a loss for the firm.

How to solve Monopoly and Pricing Strategies questions

Use this order for any monopoly question, numerical or conceptual.

  1. 1Identify the market: one seller, no close substitutes, high barriers. Check whether the question allows one price or price discrimination.
  2. 2If given a demand equation P = a − bQ, write MR = a − 2bQ. If given a table, compute MR as the change in total revenue per extra unit.
  3. 3Set MR = MC and solve for Q. If MC is not given, use the information on cost to find it.
  4. 4Substitute Q into the demand equation to get the price. Never substitute into the MR equation.
  5. 5Compute profit as (P − ATC) × Q. Compare P with ATC to decide on profit, normal profit or loss.
  6. 6For efficiency questions, find the competitive output where P = MC. The deadweight loss is the triangle between demand and MC from the monopoly Q to the competitive Q.
  7. 7For discrimination questions, name the type: individual maximum price (first), quantity or version (second), customer group (third). Recall that perfect discrimination removes the deadweight loss.
  8. 8For regulation questions, apply P = ATC or P = MC and state the consequence: normal profit with some deadweight loss, or efficient output with a loss for the firm.

Quickest way: Double the slope, then plug back into demand

When to use it: Use when demand is linear and you need price, quantity or profit fast.

  1. Write MR with the same intercept and double the slope of demand.
  2. Solve MR = MC for Q in one line.
  3. Put Q back into demand to get P. Check that P is greater than MC.
  4. For the deadweight loss, find the competitive Q from demand = MC. The loss is half × (P − MC) × (competitive Q − monopoly Q).
  5. Eliminate options quickly: any answer with price equal to MR or price at or below MC is wrong for a single-price monopolist.

Common mistakes in Monopoly and Pricing Strategies

  • Reading the price off the MR curve at the MR = MC output.

    The MR = MC step produces a quantity, and students stop at the number they just found.

    Fix: After finding Q, always go up to the demand curve for the price. MR is only used to pick the quantity.

  • Treating MR as equal to price, as in perfect competition.

    Students carry over the perfect competition rule P = MR.

    Fix: For a single-price monopolist, MR is below price at every positive output. Only perfect price discrimination makes MR equal to demand.

  • Assuming a monopolist always earns an economic profit.

    Market power sounds like guaranteed profit.

    Fix: Compare price with average total cost at the chosen output. If P < ATC, the firm makes a loss.

  • Saying a monopolist operates on the inelastic part of demand.

    Students link high prices with inelastic demand.

    Fix: MR is negative when demand is inelastic, and MC is positive. So MR = MC can only occur where demand is elastic.

  • Mixing up average cost pricing and marginal cost pricing for a natural monopoly.

    Both are regulatory pricing rules and the names look alike.

    Fix: P = MC is efficient but gives a loss because MC is below ATC. P = ATC gives normal profit but output is below the efficient level.

  • Saying perfect price discrimination creates the largest deadweight loss.

    It sounds like the most extreme form of market power.

    Fix: It produces the efficient output, so there is no deadweight loss. The monopolist captures all consumer surplus instead.

Worked examples

Example 1

A single-price monopolist faces the demand curve P = 100 − 2Q, with constant marginal cost of $20 and no fixed costs. What price will it charge? A) $40 B) $60 C) $80

Show the solution
  1. Demand is P = 100 − 2Q, so MR = 100 − 4Q.
  2. Set MR = MC: 100 − 4Q = 20, so 4Q = 80 and Q = 20.
  3. Price comes from demand: P = 100 − 2(20) = 100 − 40 = $60.
  4. Check: P of $60 is above MC of $20, as expected. MR at Q = 20 is 100 − 80 = $20, which matches MC.
  5. Profit = (60 − 20) × 20 = $800 (average cost equals MC here because there are no fixed costs). The competitive output is where 100 − 2Q = 20, which is Q = 40, so the deadweight loss is 0.5 × 40 × 20 = $400.

Answer: B) $60. Quantity is 20 units, profit is $800 and the deadweight loss is $400.

Example 2

A monopolist has marginal cost of €12. At its profit-maximizing output, the absolute price elasticity of demand is 4. What price does it charge? A) €12 B) €16 C) €20

Show the solution
  1. Use MR = P × (1 − 1 ÷ |E|).
  2. With |E| = 4: MR = P × (1 − 0.25) = 0.75P.
  3. Profit maximization requires MR = MC: 0.75P = 12.
  4. P = 12 ÷ 0.75 = €16.
  5. Check: MR = 0.75 × 16 = €12, which equals MC. Price is above MC, as it must be for a monopolist.

Answer: B) €16. Price is €16, a markup of one-third over marginal cost.

Exam tips

  • Expect three-option questions that test one idea: MR below price, MR = MC, or price from demand. Eliminate options where price equals MC for a single-price monopolist.
  • If the question gives a linear demand equation, doubling the slope for MR is the fastest route. Only the TI BA II Plus or HP 12C is permitted in the exam, and this method needs only simple arithmetic on either.
  • Learn the three discrimination types by what they depend on: buyer (first), quantity or version (second), group (third). Questions often describe an example and ask you to name the type.
  • For natural monopoly regulation, memorize the trade-off in one line: MC pricing is efficient but loses money, ATC pricing breaks even with some deadweight loss.
  • Read the wording for conditions: single-price versus discriminating monopolist, and whether fixed costs exist. These change the answer for profit and deadweight loss.

Practice questions from The Firm and Market Structures

Monopoly and Pricing Strategies in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Monopoly and Pricing Strategies: frequently asked questions

Why is marginal revenue less than price for a monopolist?

To sell one more unit, a single-price monopolist must lower the price on all units. It gains the new price on the extra unit but loses revenue on the units it could have sold at the higher price. So marginal revenue is below price.

How do you find the monopolist's price from MR = MC?

Solve MR = MC for the quantity. Then substitute that quantity into the demand curve to read the price. The price is not found on the MR curve.

What are the three types of price discrimination?

First-degree charges each buyer their maximum willingness to pay. Second-degree varies price by quantity or product version. Third-degree charges different groups different prices based on how sensitive each group is to price.

What is the difference between average cost pricing and marginal cost pricing for a natural monopoly?

Average cost pricing sets price equal to average total cost, so the firm earns a normal profit, but some deadweight loss remains. Marginal cost pricing sets price equal to marginal cost, which is efficient, but the firm makes a loss because marginal cost is below average cost. It then needs a subsidy or a different pricing scheme.