Business Economics · Profit maximisation under imperfect competition

Profit Maximisation of a Monopoly: MR = MC, Price and Output

Updated 11 October 2026 · Fact-checked

A monopoly maximises profit by producing the output where marginal revenue equals marginal cost, with MC cutting MR from below. It then reads the price from the demand curve at that output. Price is above MC, so the firm can earn supernormal profit and output is lower than under perfect competition, causing a deadweight loss.

Understand Profit Maximisation of a Monopoly

A monopoly is the only seller in a market. Because it is the whole market, it faces the downward-sloping market demand curve. To sell more, it must cut the price. This is why a monopolist is a price maker, not a price taker.

The price cut applies to all units sold, not just the extra one. So the extra revenue from one more unit, marginal revenue (MR), is less than the price. This means the MR curve lies below the demand (AR) curve. For a straight-line demand curve, MR has the same intercept on the price axis and twice the slope.

The firm adds output as long as the extra revenue exceeds the extra cost. It stops where MR = MC. Beyond that point each extra unit adds more to cost than to revenue. The second-order condition is that MC cuts MR from below at that output. Once you have the output, you go up to the demand curve to find the price the market will pay for it. Do not read the price off the MR curve.

Profit is (P − AC) × Q. If price is above average cost at the chosen output, the monopolist earns supernormal profit. Barriers to entry stop new firms competing it away, so it can last in the long run. A monopolist is not guaranteed a profit, though. If demand lies below AC everywhere, it makes a loss.

Compared with perfect competition, where P = MC, the monopolist charges a higher price and produces less. At the monopoly output, the value consumers place on the last unit (the price) exceeds its cost (MC). Trades that would benefit both sides do not happen. The lost surplus is the deadweight loss, the triangle between demand and MC from the monopoly output up to the competitive output.

Key rules to remember

Profit-maximising rule: MR = MC, with MC cutting MR from below; Gives the output. Then find the price from the demand curve.
Total and marginal revenue: TR = P × Q; MR = dTR ÷ dQ; For discrete changes, MR = change in TR ÷ change in Q.
Linear demand and MR: If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ; MR has the same intercept as demand and twice the slope.
Supernormal profit: Profit = (P − AC) × Q = TR − TC; AC is read at the profit-maximising output, not at the price.
Deadweight loss (linear curves): DWL = ½ × (Qc − Qm) × (Pm − MCm); Qc is the competitive output where P = MC. Qm and Pm are monopoly output and price. This formula applies when MC is constant or linear and the triangle is a true triangle.
Lerner index (MR = MC link): (P − MC) ÷ P = 1 ÷ |PED|; Follows from MR = P(1 − 1/|PED|). Shows a monopolist operates where demand is elastic.

How to solve Profit Maximisation of a Monopoly questions

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

1Write down the demand function (price in terms of Q) and the cost function.
2Derive TR = P × Q, then differentiate to get MR. For P = a − bQ, MR = a − 2bQ.
3Derive MC from the cost function. For TC = F + cQ + dQ², MC = c + 2dQ.
4Set MR = MC and solve for Q. Check that MC cuts MR from below, so the second-order condition holds.
5Substitute Q into the demand function to get the price. Never put Q into MR for the price.
6Compute profit = TR − TC, or (P − AC) × Q. State whether it is supernormal profit, normal profit or a loss.
7For welfare, find the competitive output where P = MC, then calculate the deadweight loss triangle. On a diagram, label MR, MC, AR, AC, Qm, Pm and shade the areas.

Quickest way: Equate, then go up to demand

When to use it: Use for MCQs and short numerical questions with linear demand and linear or constant cost.

For P = a − bQ, write MR = a − 2bQ immediately.
Set it equal to MC and solve for Q.
Put Q into the demand curve for P.
Profit = (P − AC) × Q. Use AC at that Q.
For DWL with constant MC, find Qc from a − bQ = MC. Then DWL = ½ × (Qc − Qm) × (Pm − MC).

Common mistakes in Profit Maximisation of a Monopoly

Reading the price from the MR curve at the MR = MC point.
Students stop once MR = MC is found and forget the firm sells along the demand curve.
Fix: After finding Q, always go vertically up to the demand (AR) curve and read the price there.
Using MR = P for a monopolist.
This is the perfect competition rule, which gets carried over.
Fix: For a monopolist, P > MR because the price cut applies to all units. Derive MR from TR.
Calculating profit as (P − MC) × Q.
MC is at hand from the MR = MC step, so it is used by habit.
Fix: Profit uses average cost: (P − AC) × Q. Read AC at the profit-maximising output.
Assuming a monopolist always earns supernormal profit.
Textbook diagrams usually show a profit.
Fix: Compare P with AC at Qm. If AC is above price, there is a loss. The firm may still produce in the short run if P covers average variable cost.
Drawing the deadweight loss triangle with the wrong corners.
Students shade the profit rectangle or the whole lost surplus.
Fix: The triangle lies between demand and MC, from Qm to Qc. Its top corner is at the monopoly price and output on the demand curve.
Doubling the demand slope wrongly, giving MR = a − bQ or MR = 2a − 2bQ.
Rushed algebra.
Fix: Derive TR = aQ − bQ² and differentiate. MR = a − 2bQ, so the intercept stays the same.

Worked examples

Example 1

A monopolist faces demand P = 100 − 2Q and has total cost TC = 200 + 20Q. Find the profit-maximising output, price and profit. Compare with the competitive output and find the deadweight loss.

Show the solution

TR = PQ = 100Q − 2Q². So MR = 100 − 4Q.
MC = 20 (constant).
Set MR = MC: 100 − 4Q = 20, so 4Q = 80 and Q = 20.
Price from demand: P = 100 − 2(20) = 60.
TR = 60 × 20 = 1,200. TC = 200 + 20 × 20 = 600. Profit = 1,200 − 600 = 600.
Competitive output: P = MC gives 100 − 2Q = 20, so Q = 40.
DWL = ½ × (40 − 20) × (60 − 20) = ½ × 20 × 40 = 400.

Answer: Q = 20, P = 60, supernormal profit = 600. Competitive output is 40 and the deadweight loss is 400.

Example 2

A monopoly has demand P = 50 − Q and total cost TC = 100 + 5Q + 0.5Q² (money in ₹ thousand). Find the profit-maximising output, price and profit, and state whether the profit is supernormal.

Show the solution

TR = 50Q − Q². So MR = 50 − 2Q.
MC = 5 + Q.
Set MR = MC: 50 − 2Q = 5 + Q, so 3Q = 45 and Q = 15.
Second-order check: MC slopes up (slope 1) and MR slopes down (slope −2), so MC cuts MR from below.
Price: P = 50 − 15 = 35.
TR = 35 × 15 = 525.
TC = 100 + 5 × 15 + 0.5 × 225 = 100 + 75 + 112.5 = 287.5.
Profit = 525 − 287.5 = 237.5. AC = 287.5 ÷ 15 = 19.17, which is below P = 35, so profit is supernormal.

Answer: Q = 15, P = ₹35 thousand per unit, profit = ₹237.5 thousand. This is supernormal profit because P exceeds AC.

Exam tips

In diagram questions, draw demand, MR, MC and AC. Mark Qm at MR = MC, go up to demand for Pm, and go down to AC to show the profit rectangle.
Write MR = MC and the second-order condition in words. Examiners award marks for stating the rule, not only the numbers.
For welfare questions, compare monopoly with perfect competition on price, output, consumer surplus and efficiency. Name allocative inefficiency, since P > MC.
Check units. If Q is in thousands or money in ₹ lakh, carry that through to the profit.
In MCQs, test each option quickly: price must lie on demand, and profit must use AC.

Practice questions from Profit maximisation under imperfect competition

Profit Maximisation of a Monopoly in other exams

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

Profit Maximisation of a Monopoly: frequently asked questions

Why is MR below price for a monopolist?

To sell one more unit the monopolist must lower the price on every unit, not just the extra one. The revenue gained from the new unit is partly offset by the revenue lost on earlier units. So MR is less than price.

How do I find the monopoly price after finding output?

Substitute the output from MR = MC into the demand equation. On a diagram, go vertically up from Qm to the demand curve. That height is the price.

What is deadweight loss in a monopoly?

It is the surplus lost because the monopolist produces less than the competitive output. Between Qm and Qc, consumers value units above their cost, but those units are not made. The loss is the triangle between demand and MC over that range.

Does a monopolist always make supernormal profit?

No. It earns supernormal profit only if price exceeds average cost at the chosen output. If demand is weak or costs are high, it can make normal profit or a loss.