Business Economics · Profit maximisation under perfect competition and monopoly

Monopoly: Pricing and Output Decisions Using MR = MC

Updated 11 October 2026 · Fact-checked

A monopolist is the only seller, so it faces the whole downward-sloping market demand curve. It maximises profit by producing where MR = MC, with MC cutting MR from below. It then reads the price off the demand curve at that output. Price ends up above MC, and supernormal profit is possible.

Understand Monopoly: Pricing and Output Decisions

A monopoly has one seller and barriers to entry. Because the firm is the whole market, its demand curve is the market demand curve. It slopes downward. To sell more, the monopolist must cut the price.

This is why marginal revenue (MR) is below average revenue (AR). AR is the price. When the firm cuts the price to sell one more unit, it gains the price on that extra unit. But it also loses revenue on all the units it could have sold at the higher price. So MR = price minus that loss, which is less than price. For a straight-line demand curve, the MR curve starts at the same point on the price axis and falls twice as steeply.

The profit-maximising rule is the same as for any firm: produce where MR = MC. If MR > MC, one more unit adds more to revenue than to cost, so expand. If MR < MC, cut output. The second-order condition is that MC cuts MR from below at that output.

The monopolist does not read the price off the MR curve. It goes up from the MR = MC output to the demand (AR) curve and charges that price. So price > MC. This gap is the source of the welfare loss compared with perfect competition, where price = MC.

Profit = (P − AC) × Q. If price is above average cost at the chosen output, the monopolist earns supernormal profit. Entry barriers let this continue in the long run. A monopolist is not guaranteed a profit, though. If AC is above demand at every output, it makes a loss. A monopolist also never chooses to operate on the inelastic part of demand, because MR is negative there.

Key rules to remember

Total revenue: TR = P × Q; For a monopolist, P depends on Q through the demand curve.
Marginal revenue: MR = d(TR)/dQ; Always below price for a downward-sloping demand curve.
MR for linear demand: If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ; MR has the same intercept as demand and twice the slope.
Profit-maximising condition: MR = MC, with MC cutting MR from below; Use the second condition to reject any other crossing point.
MR and elasticity: MR = P × (1 − 1/|e|), where e is price elasticity of demand; MR > 0 only if |e| > 1. So a monopolist operates where demand is elastic.
Mark-up rule: (P − MC) ÷ P = 1 ÷ |e|; Follows from MR = MC. Lower elasticity means a bigger mark-up.
Profit: Profit = TR − TC = (P − AC) × Q; Supernormal if P > AC at the chosen output.

How to solve Monopoly: Pricing and Output Decisions questions

Use this method for any numerical or diagram question on monopoly equilibrium.

1Write down the demand curve (AR) as P in terms of Q. If given Q in terms of P, invert it first.
2Find TR = P × Q and differentiate to get MR. For linear demand, double the slope.
3Write down MC. If you are given TC, differentiate it. If MC is constant, use that value.
4Set MR = MC and solve for Q. Check that MC cuts MR from below, for example that MC has a slope greater than MR's slope.
5Substitute Q into the demand curve to get the price. Never substitute into MR or MC.
6Find AC at that Q (TC ÷ Q). Compute profit = (P − AC) × Q, or TR − TC.
7State the conclusion: P > MC, and whether profit is supernormal. Where asked, compare with the competitive outcome (P = MC).

Quickest way: Linear demand shortcut

When to use it: Use when demand is a straight line P = a − bQ and you are asked for output, price or profit under time pressure.

Write MR = a − 2bQ straight away.
Set a − 2bQ = MC and solve: Q = (a − MC) ÷ 2b when MC is constant.
Price = a − bQ. With constant MC, this equals (a + MC) ÷ 2.
Profit = (P − AC) × Q. Check that P is above AC.
Sense check: Q must be positive, P above MC, and MR positive at that Q.

Common mistakes in Monopoly: Pricing and Output Decisions

Reading the price off the MR curve at MR = MC.
Students stop once they have found the intersection and treat its height as the price.
Fix: The MR = MC point only gives output. Go vertically up to the demand curve for the price.
Using MR = P, as in perfect competition.
The rule MR = MC is the same for all firms, so students carry over the competitive MR.
Fix: For a monopolist, MR is below AR. Differentiate TR = P × Q with P depending on Q.
Doubling the intercept instead of the slope when finding MR from linear demand.
Memory of 'twice as steep' gets muddled.
Fix: MR has the same intercept a and slope 2b. Check by differentiating aQ − bQ².
Assuming a monopolist always earns supernormal profit.
The textbook diagram always shows a profit rectangle.
Fix: Compare price with AC at the chosen output. If AC is above price, it is a loss.
Choosing an output where MR = MC but MC cuts MR from above.
Students stop at the first solution of a non-linear equation.
Fix: Check the second-order condition. Profit is maximised only where MC cuts MR from below.
Saying the monopolist can set both price and quantity freely.
Monopoly power is confused with unlimited power.
Fix: It chooses one point on the demand curve. Choosing the price fixes the quantity, and vice versa.

Worked examples

Example 1

A monopolist faces demand P = 100 − 2Q and has constant marginal cost MC = 20 with no fixed costs, so AC = 20. Find the profit-maximising output, price and profit, and compare price with MC.

Show the solution

TR = P × Q = 100Q − 2Q².
MR = d(TR)/dQ = 100 − 4Q.
Set MR = MC: 100 − 4Q = 20, so 4Q = 80 and Q = 20.
Check the second-order condition: MC has slope 0 and MR has slope −4, so MC cuts MR from below.
Price from demand: P = 100 − 2(20) = 60.
Profit = (P − AC) × Q = (60 − 20) × 20 = 800.
Price (60) is well above MC (20).

Answer: Q = 20, P = 60, profit = 800 (supernormal). Price exceeds MC by 40.

Example 2

A monopolist faces demand Q = 50 − 0.5P, so P = 100 − 2Q. Total cost is TC = 200 + 10Q + Q². Find the equilibrium output, price and profit. Also find the price elasticity of demand at the equilibrium and check the mark-up rule.

Show the solution

Demand: P = 100 − 2Q, so TR = 100Q − 2Q² and MR = 100 − 4Q.
MC = d(TC)/dQ = 10 + 2Q.
Set MR = MC: 100 − 4Q = 10 + 2Q, so 90 = 6Q and Q = 15.
Second-order check: MC slope is 2, MR slope is −4, so MC cuts MR from below.
Price: P = 100 − 2(15) = 70.
TR = 70 × 15 = 1,050. TC = 200 + 150 + 225 = 575. Profit = 1,050 − 575 = 475.
Elasticity: from Q = 50 − 0.5P, dQ/dP = −0.5. So |e| = 0.5 × P ÷ Q = 0.5 × 70 ÷ 15 = 35 ÷ 15 = 7/3 ≈ 2.33, which is above 1.
MC at Q = 15 is 10 + 30 = 40. Mark-up: (P − MC) ÷ P = (70 − 40) ÷ 70 = 3/7. And 1 ÷ |e| = 3/7. The rule holds.

Answer: Q = 15, P = 70, profit = 475. |e| = 7/3, which is above 1, and (P − MC) ÷ P = 1 ÷ |e| = 3/7.

Exam tips

In MCQs, first check whether the question wants output, price or profit. Many wrong options are the MR value or MC value at the optimum.
In written answers, state the formula MR = MC and the second-order condition before calculating. This earns method marks.
If a diagram is asked for, draw demand, MR (steeper, same intercept), MC and AC. Mark Q at MR = MC, P on the demand curve, and shade the profit rectangle.
Link the result to elasticity: a monopolist never settles where demand is inelastic, because MR would be negative.
When comparing with perfect competition, say clearly that a monopoly typically produces less and charges more, with price above MC.

Practice questions from Profit maximisation under perfect competition and monopoly

Monopoly: Pricing and Output Decisions in other exams

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

Monopoly: Pricing and Output Decisions: frequently asked questions

Why is MR below AR for a monopolist?

AR is the price, and the monopolist must lower the price to sell more. The lower price applies to every unit sold, not just the extra one. The revenue lost on earlier units makes MR smaller than price.

How do I find the monopoly price after finding output?

Put the output from MR = MC into the demand (AR) curve. Do not put it into the MR or MC equation. That gives the price consumers will pay for that quantity.

Does a monopolist always make supernormal profit?

No. It earns supernormal profit only if price is above average cost at the chosen output. If AC is higher than the demand price at every output, it makes a loss. Entry barriers just let any supernormal profit last.

How is price elasticity linked to monopoly pricing?

MR = P(1 − 1/|e|), so MR is positive only where demand is elastic. A monopolist therefore prices where |e| > 1. The lower the elasticity, the larger the mark-up over MC.