Business Economics · Production, costs, revenue and profit in price and output decisions

Profit Maximisation and Price-Output Decisions Explained

Q: Why does profit maximise where MR = MC?

If MR exceeds MC, producing one more unit adds more revenue than cost, so profit rises. If MC exceeds MR, the last unit reduces profit. Profit stops rising exactly where the two are equal, provided MC is rising.

Q: What is the difference between normal profit and supernormal profit?

Normal profit is the minimum return that keeps the owner in the business and is counted as a cost, so economic profit is zero when AR = AC. Supernormal profit is any profit above that level, earned when AR > AC.

Updated 11 October 2026 · Fact-checked

A firm maximises profit by producing the output where marginal revenue equals marginal cost (MR = MC), with MC cutting MR from below. Then read the price from the demand (AR) curve at that output. Compare price with average cost to find supernormal profit, normal profit or loss, and check the shutdown rule.

Understand Profit Maximisation and Price-Output Decisions

A firm earns profit as total revenue minus total cost. Economists count opportunity cost as a cost. This includes the return the owner could earn elsewhere on their own capital and effort. So the cost used in this topic already contains a fair return to the owner.

That gives two ideas. Normal profit is the minimum return needed to keep the owner in the business. It is earned when total revenue equals total cost, that is, when AR = AC. Supernormal profit (also called abnormal or economic profit) is any profit above normal profit. It is earned when AR > AC.

Now the rule. Marginal revenue (MR) is the extra revenue from selling one more unit. Marginal cost (MC) is the extra cost of making it. If MR > MC, one more unit adds more to revenue than to cost, so profit rises. If MR < MC, the last unit lost money, so cut output. Profit is highest where MR = MC. The second condition is that MC must be rising through MR, so that MC is above MR for higher output. Otherwise you may have found a profit minimum.

The rule gives output only. To find the price, go up from that output to the demand curve (AR). In perfect competition the firm is a price taker, so P = AR = MR and the rule becomes P = MC. For a firm with market power, the demand curve slopes down and MR lies below it, so the price is above MC.

Loss-making firms face two decisions. In the short run, a firm should keep producing if price covers average variable cost (P ≥ AVC), because it then recovers some fixed cost. If P < AVC it should shut down. In the long run, a firm must cover all costs (P ≥ AC), otherwise it exits. The break-even point is where AR = AC, which gives normal profit.

Key rules to remember

Profit: π = TR − TC = (AR − AC) × Q; With AR = price. Positive means supernormal profit.
Profit-maximising rule: MR = MC, with MC cutting MR from below; Second condition: slope of MC is greater than slope of MR at that output.
Marginal revenue and cost: MR = ΔTR ÷ ΔQ; MC = ΔTC ÷ ΔQ; With calculus: MR = dTR/dQ, MC = dTC/dQ.
Perfect competition: P = AR = MR, so profit maximum at P = MC; Firm is a price taker, with a horizontal demand curve.
Normal profit (break-even): AR = AC, so TR = TC; Economic profit is zero. Owner earns exactly the opportunity cost.
Supernormal profit and loss: AR > AC: supernormal profit; AR < AC: loss; Total profit is the gap (AR − AC) multiplied by Q.
Short-run shutdown rule: Shut down if P < AVC; Continue if AVC ≤ P < AC, because the loss is smaller than fixed cost.
Second-order condition (calculus): d²π/dQ² < 0; Equivalent to MC rising faster than MR at the optimum.

How to solve Profit Maximisation and Price-Output Decisions questions

Use this method for any question on profit-maximising output, price and profit.

1Identify the market structure. If the price is given and fixed, use MR = P. If a demand equation or schedule is given, find TR and then MR.
2Write the revenue function. From a demand equation P = a − bQ, TR = PQ = aQ − bQ², so MR = a − 2bQ.
3Write the cost function and derive MC. For TC = F + cQ + dQ², MC = c + 2dQ.
4Set MR = MC and solve for Q. Check the second-order condition: MC must be rising faster than MR, or d²π/dQ² < 0.
5Find the price from the demand (AR) curve at that Q, not from the MR or MC curve.
6Compute profit as (P − AC) × Q, or TR − TC. State whether it is supernormal profit, normal profit or loss.
7If profit is negative, test shutdown. Compare P with AVC in the short run and with AC in the long run. State your decision with the reason.
8State the answer with units, and sketch the diagram if the question asks for one.

Quickest way: Table method for schedule questions and the calculus shortcut

When to use it: Use it when you get a table of output, TR and TC, or a linear demand with a quadratic or linear cost.

For a table, calculate MR and MC from the changes in TR and TC for each extra unit.
Pick the highest output at which MR ≥ MC. Stop when MR first falls below MC.
Read the price as TR ÷ Q at that output and compute profit as TR − TC.
For linear demand P = a − bQ, remember MR = a − 2bQ. It has the same intercept and twice the slope.
Substitute Q into the demand equation for price, then into AC for cost per unit. Profit = (P − AC) × Q.
For shutdown, compare P with AVC (drop fixed cost from TC before dividing by Q).

Common mistakes in Profit Maximisation and Price-Output Decisions

Reading the price off the MC or MR curve at the optimum output.
The rule is MR = MC, so students stop at the point where the curves meet.
Fix: After finding Q, go up to the demand (AR) curve. That height is the price. Then compare it with AC at the same Q.
Using MR = P for a firm with a downward-sloping demand curve.
Students memorise P = MR from perfect competition.
Fix: P = MR only for a price taker. For P = a − bQ, MR = a − 2bQ. Check the market structure first.
Thinking a firm earning normal profit is making zero return.
The word 'normal' sounds like nothing, and accounting profit is confused with economic profit.
Fix: Normal profit is a cost of staying in business. It means economic profit is zero, so TR = TC where TC includes the owner's opportunity cost.
Shutting down whenever the firm makes a loss.
Students compare price with average total cost in the short run.
Fix: In the short run, compare P with AVC. If P ≥ AVC, the firm covers variable cost and part of fixed cost, so it should keep producing.
Ignoring the second condition and picking a point where MC cuts MR from above.
Curves can cross more than once and students take the first crossing.
Fix: Choose the crossing where MC is rising and cuts MR from below. At the other crossing, extra output would raise profit.
Including fixed cost in AVC or in MC.
Students divide total cost by Q without removing fixed cost.
Fix: MC comes only from variable cost, since fixed cost does not change with output. AVC = (TC − fixed cost) ÷ Q.

Worked examples

Example 1

A monopolist faces demand P = 100 − 2Q (P in ₹, Q in units) and total cost TC = 200 + 20Q + Q². Find the profit-maximising output, price and profit, and state whether the firm earns supernormal profit.

Show the solution

TR = PQ = 100Q − 2Q². So MR = 100 − 4Q.
TC = 200 + 20Q + Q². So MC = 20 + 2Q.
Set MR = MC: 100 − 4Q = 20 + 2Q, so 80 = 6Q and Q = 13.33 (to 2 decimal places, 40/3).
Second-order check: d²π/dQ² = −4 − 2 = −6 < 0, so this is a maximum.
Price from demand: P = 100 − 2 × (40/3) = 100 − 26.67 = ₹73.33.
TR = 73.33 × 13.33 = ₹977.78 (exact: (220/3) × (40/3) = 8800/9).
TC = 200 + 20 × 13.33 + 13.33² = 200 + 266.67 + 177.78 = ₹644.44 (exact: 5800/9).
Profit = 977.78 − 644.44 = ₹333.33 (exact: 3000/9).

Answer: Output = 13.33 units (40/3), price = ₹73.33, profit = ₹333.33. Profit is positive, so the firm earns supernormal profit.

Example 2

A perfectly competitive firm sells at a market price of ₹30 per unit. Its total cost is TC = 400 + 10Q + Q². (a) Find the profit-maximising output and profit. (b) If price falls to ₹8, should the firm produce in the short run?

Show the solution

(a) Perfect competition: MR = P = 30. MC = 10 + 2Q.
Set MR = MC: 30 = 10 + 2Q, so Q = 10.
TR = 30 × 10 = ₹300. TC = 400 + 100 + 100 = ₹600.
Profit = 300 − 600 = −₹300. The firm makes a loss at its best output.
Check shutdown at P = ₹30: fixed cost is ₹400 and variable cost is 10Q + Q² = ₹200. TR of ₹300 exceeds variable cost of ₹200 by ₹100, so loss (₹300) is less than fixed cost (₹400). Keep producing.
(b) AVC = (10Q + Q²) ÷ Q = 10 + Q. The minimum AVC is at Q = 0, where AVC = ₹10.
At P = ₹8, MC = P gives 8 = 10 + 2Q, so Q = −1, which is impossible. Price is below the lowest AVC of ₹10, so every unit sold loses money on variable cost.
Shutting down gives a loss equal to fixed cost, ₹400. Producing would give a larger loss.

Answer: (a) Q = 10 units, profit = −₹300. This is a loss, but the firm should still produce because price covers AVC (loss ₹300 is less than fixed cost ₹400). (b) At ₹8 price is below minimum AVC (₹10), so the firm should shut down in the short run.

Exam tips

Draw the diagram first in written answers: MC, AC, MR and AR, with Q found at MR = MC. Shade the profit rectangle between P and AC.
In calculation questions, show MR, MC, the equation MR = MC and the second-order check. Examiners award marks for the method as well as the answer.
Write the market structure at the start. It tells you whether MR = P or MR lies below AR.
For MCQs, test the options quickly: if price is below AVC the answer is shutdown, and if AR = AC the answer is normal profit.
Always state the profit type in words (supernormal, normal or loss) and the decision (produce, shut down, exit). Do not leave a number alone.

Practice questions from Production, costs, revenue and profit in price and output decisions

Profit Maximisation and Price-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.

Profit Maximisation and Price-Output Decisions: frequently asked questions

Why does profit maximise where MR = MC?

If MR exceeds MC, producing one more unit adds more revenue than cost, so profit rises. If MC exceeds MR, the last unit reduces profit. Profit stops rising exactly where the two are equal, provided MC is rising.

What is the difference between normal profit and supernormal profit?

Normal profit is the minimum return that keeps the owner in the business and is counted as a cost, so economic profit is zero when AR = AC. Supernormal profit is any profit above that level, earned when AR > AC.

What is the shutdown point in perfect competition?

It is the price equal to the minimum of average variable cost. Below it, the firm cannot cover variable cost and should stop producing in the short run. Above it, the firm should keep producing even if it makes a loss.

How do I find the profit-maximising price?

First find output where MR = MC. Then substitute that output into the demand (AR) equation or read it from the demand curve. Do not use the MC value as the price unless the firm is a price taker.