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Profit maximisation at MC = MR

Normal profit, abnormal profit and losses on one diagram.

Games Workshop turned £660 million of sales into £276 million of profit.

Games Workshop, based in Nottingham, makes Warhammer miniatures and games. In the year to 31 May 2026 its revenue was £659.7 million and its profit before tax £275.7 million: about 42p of profit for every pound of sales. Its copyright and trade marks mean no other firm can sell official Warhammer models.

How does a firm decide how much to make and what to charge, and how do you show a profit like that on a diagram?

Source: Games Workshop Group results for the 52 weeks to 31 May 2026.

Think first

At a firm’s current output, the last unit it sold added £8 to its revenue and £5 to its costs.

If it wants to make as much profit as possible, what should it do?

Each extra unit adds £3 more to revenue than to cost, so making it raises profit. The firm should keep going until the next unit adds the same to revenue as to cost: MC = MR.

Step by step

  1. Start with the assumptions. The firm aims to make as much profit as possible, and it has some market power, so it faces downward-sloping demand: AR, with MR twice as steep below it. Profit is total revenue minus total cost. An accountant counts only the costs the firm pays out. An economist also counts the opportunity cost of the owners’ time and money: normal profit, the least they need to keep their resources in this use. So normal profit is already inside ATC. Profit above it is abnormal (also called supernormal) profit; less than it is a loss, or subnormal profit.

    Check: A café owner’s accounts show a profit of £30,000 a year. She could earn £35,000 as a manager elsewhere. In economic terms, she is making:

    Her opportunity cost is the £35,000 she gives up. Take that off the £30,000 accounting profit and she is £5,000 short of normal profit: a subnormal profit, or loss.

  2. Then the costs, in exam order: MC first as the tick, then ATC through MC’s lowest point.

  3. Find where MC = MR. Why there? Up to this output, the next unit adds more to revenue than to cost, so making it raises profit. Beyond it, the next unit adds more to cost than to revenue, so profit would fall. Profit is highest where the two are equal.

    Check: At its current output a firm’s MR is £8 and its MC is £5. To raise profit it should:

    While MR is above MC, each extra unit adds to profit. The firm should expand until MC = MR.

  4. Go straight up from MC = MR to the demand curve for the price, Pm: the most buyers will pay for that output. Down to the axis for the output, Qm. Up to demand, not across from MC = MR.

  5. This is the step most students get wrong. Read average cost at Qm, the output the firm actually makes: go up from Qm to ATC. Not the lowest point of ATC. The firm is not producing there.

    Check: Where do you read the firm’s average cost from?

    Average cost depends on how much the firm makes. It makes Qm, so its cost per unit is ATC at Qm.

  6. At Qm, AR is above ATC. Profit per unit is AR − ATC, so abnormal profit is (AR − ATC) × Qm: the shaded box. This is Games Workshop’s position: its copyright stops rivals selling official Warhammer models, so its profit is not competed away.

    Teacher tip: Mark both readings on the price axis: Pm from AR and ATC at Qm. The box runs between those two lines and stops at Qm. An unlabelled box can lose marks even if its shape is right.

    Check: At Qm a firm sells 200 units at a price of £15. Its ATC at Qm is £11. What is its abnormal profit?

    Profit per unit is AR − ATC = £15 − £11 = £4. Multiply by the 200 units sold: £800.

  7. Now suppose a fixed cost, such as rent, rises. ATC shifts up, but MC does not move, so Qm and Pm stay the same. If ATC rises until it just touches AR at Qm, then AR = ATC: normal profit. The firm covers all its costs, including the return its owners need, and no more.

  8. If fixed costs rise further, ATC3 sits above AR at Qm: the firm makes a loss, the shaded box from ATC3 down to the price. Producing at MC = MR still gives the smallest loss. Whether it should keep going at all is the next lesson: shutdown points.

    Check: Suppose wages rise instead of rent. What happens to the profit-maximising output?

    Wages are a variable cost, so each extra unit costs more to make. MC shifts up and cuts MR at a lower output.

  9. A rise in a variable cost, such as wages, is different. MC shifts up to MC2, so MC2 = MR at a lower output, Q2, and the price rises to P2. A fixed cost change does not move MC, so it does not change the profit-maximising price or output.

    Check: A profit-maximising firm’s business rates rise. In the short run, its price:

    Business rates are a fixed cost. They raise ATC but not MC, so MC = MR at the same output and the price on demand is unchanged. Only profit falls.

What your diagram must show

  • AR and MR from the same point, MR twice as steep
  • MC cutting ATC at its lowest point
  • Output Qm where MC = MR
  • Price Pm read up from Qm to AR
  • Average cost read at Qm, not at the lowest point of ATC
  • Abnormal profit box between Pm and ATC at Qm, shaded and labelled

A common mistake

They read average cost at the lowest point of ATC. The firm produces Qm, so its cost per unit is ATC at Qm, which is higher. Their box overstates the profit.

Exam question

Explain why a firm maximises profit where MC = MR, and how its profit is shown on a diagram.

Model answer

A firm maximises profit where marginal cost equals marginal revenue.

If, at a given output, MR is greater than MC, the next unit adds more to revenue than it adds to cost, so producing it raises profit. The firm should expand. If MC is greater than MR, the next unit adds more to cost than to revenue, so producing it reduces profit, and the firm should cut output. Profit is therefore at its highest where MC = MR, at output Qm.

[Diagram: AR and MR, MC cutting ATC at its lowest point. Qm where MC = MR, Pm read up to AR, ATC read at Qm, abnormal profit box between Pm and ATC.]

The firm charges the highest price buyers will pay for Qm, read from the demand curve: Pm. Its average cost is ATC at Qm. If AR is above ATC, it makes abnormal profit equal to (AR − ATC) × Qm. If AR equals ATC it makes normal profit, and if AR is below ATC it makes a loss.

However, this assumes the firm knows its MC and MR and aims only for profit. In practice many firms set prices with rules of thumb such as cost-plus pricing, and a firm run by managers may pursue sales or revenue instead, so whether it produces at MC = MR depends on who controls it and how much it knows about its demand.

Source: Games Workshop Group annual results (July 2026). Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.