Why MR falls twice as fast as AR, and why TR peaks where MR is zero.
On 7 April 2026 the price of a first class stamp rose from £1.70 to £1.80, and a second class stamp from 87p to 91p. Royal Mail blamed the rising cost of delivery. It also says 70% fewer letters are sent than 20 years ago, while the number of addresses it delivers to has grown by four million to 32 million.
When a firm raises its price and sells fewer units, does its revenue rise or fall?
Source: MoneySavingExpert (March 2026), reporting Royal Mail’s announcement.
A firm cuts its price and sells more units.
What happens to its total revenue?
If demand is price elastic, quantity rises by proportionately more than the price falls, so revenue rises. If demand is inelastic, it falls. On a straight-line demand curve, both happen: elastic at the top, inelastic at the bottom.
Start with the definitions. Total revenue is price × quantity. Average revenue is TR ÷ Q, which is just the price. Marginal revenue is the change in TR from selling one more unit. A price taker in perfect competition sells every unit at the same price, so its AR = MR, a horizontal line. This lesson is about a firm with some market power: it faces a downward-sloping demand curve, so to sell more it must cut its price. Its demand curve is its AR curve.
Check: A price-taking firm sells every unit at £5, however many it sells. What is its marginal revenue?
Each extra unit sells for £5 and no other unit’s price falls, so each one adds exactly £5 to TR. For a price taker AR = MR.
MR starts at the same point as AR and falls twice as steeply. Put numbers on it. At £9 the firm sells 2 units: TR £18. At £8.50 it sells 3: TR £25.50. The third unit brings in £8.50, but the first two now sell for 50p less each, so MR is only £7.50.
Teacher tip: Draw MR from exactly the point where AR meets the price axis, and make it cut the output axis halfway to where AR does. A parallel MR, or one that starts lower, gives the wrong output on every diagram that follows.
Check: Why does a firm’s MR curve lie below its AR curve?
The price cut needed to sell the extra unit also applies to all the units it was already selling, so the extra revenue is less than the new price.
Now TR, beside it, on the same output scale. Each extra unit adds its MR to total revenue. While MR is positive, TR rises, but by less and less as MR falls.
MR reaches zero halfway along AR, at Q1. That is exactly where TR is highest: the next unit adds nothing. Beyond Q1, MR is negative and TR falls. Revenue maximisation means producing where MR = 0. Costs play no part in it.
Check: Which condition gives the revenue-maximising output?
TR rises while MR is positive and falls once MR is negative, so it peaks where MR = 0. MC = MR is profit maximisation; AR = ATC is sales maximisation.
This is PED again. Above the midpoint of AR, demand is price elastic: a price cut raises TR, so MR is positive. Below the midpoint, demand is price inelastic: a price cut lowers TR, so MR is negative. At the midpoint PED is −1 and TR is at its peak.
Check: A firm’s MR is negative at its current output. A price rise would:
Negative MR means the firm is on the inelastic part of demand. A higher price cuts quantity by proportionately less, so revenue rises.
Back to Royal Mail. While demand for letters is price inelastic, each stamp price rise brings in more revenue even though fewer letters are sent. But each rise moves it up the demand curve, towards the elastic section, where the next rise would cut revenue. Meanwhile email keeps shifting demand for letters to the left.
Check: Email shifts demand for letters to the left. What happens to Royal Mail’s MR curve?
MR is drawn from AR, so when demand shifts left MR shifts left with it, starting where the new AR meets the price axis and falling twice as steeply.
If demand rises, AR shifts right to AR2, and MR shifts with it to MR2. MR always starts where AR meets the price axis and falls twice as steeply, so never shift one without the other. Draw AR2 first, then MR2.
Their MR is parallel to AR and starts below it. MR must start at the same point as AR on the price axis and fall twice as steeply, reaching zero halfway along.
Explain why a firm’s marginal revenue is below its average revenue, and why its total revenue is highest where MR = 0.
A firm facing a downward-sloping demand curve can only sell more by lowering its price. Its average revenue is the price, so the demand curve is the AR curve.
When it cuts the price to sell one more unit, the lower price applies to every unit it sells, not just the extra one. The extra revenue from that unit, its marginal revenue, is therefore less than its price. So MR lies below AR, and for a straight-line demand curve it starts at the same point and falls twice as steeply.
Total revenue rises as long as MR is positive, because each extra unit adds something to it. Once MR becomes negative, each extra unit reduces total revenue. So TR is at its highest where MR = 0, halfway along the demand curve. Above that point demand is price elastic; below it, demand is price inelastic.
However, the revenue-maximising output is not the profit-maximising one. As long as MC is positive, MR = 0 lies beyond the output where MC = MR, so a firm only produces there if it cares more about sales than profit, which depends on its objectives and on who controls it.
Source: MoneySavingExpert (March 2026). Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.