Total and marginal utility, the law of diminishing marginal utility, buying up to MU = P, why that makes the demand curve slope down, the paradox of value, the equi-marginal principle, and the income and substitution effects of a price change.
The average household in England and Wales pays £639 a year for water and sewerage in 2026/27, about £1.75 a day for everything: drinking, cooking, washing, flushing. On South East Water’s meter the water itself costs £3.01 a cubic metre, which is 0.3p a litre. A 500ml bottle of the same stuff from a kiosk on a hot platform costs more than £1, several hundred times the price per litre, and people queue for it.
In 1776 Adam Smith called this the paradox of value: water is essential and cheap, diamonds are useless and dear. He could not explain it. The answer came in the 1870s and is the subject of this lesson.
What decides how much something is worth to you, and why does that fall the more of it you have?
Source: Water UK, average household bills 2026/27 (published 29 January 2026); South East Water, metered charges 2026/27.
Utility is the satisfaction or benefit a consumer gets from consuming a good. Economists measure it in utils or, more usefully, in money: the most you would pay for the unit.
Total utility is the satisfaction from all the units consumed. Marginal utility is the extra satisfaction from one more unit: MU = change in TU ÷ change in quantity.
The law of diminishing marginal utility: as you consume more of a good in a given period, the extra satisfaction from each additional unit falls. The first slice of pizza is wonderful; the sixth is a chore. Total utility still rises while MU is positive, peaks when MU is zero, and falls if you carry on.
A rational consumer buys a unit when its marginal utility is at least its price, so buys up to the point where MU = P, and spreads spending so that the last pound on each good gives the same satisfaction: the equi-marginal principle, MUA/PA = MUB/PB.
When a price falls, the consumer buys more for two reasons: the substitution effect (it is now cheaper relative to other goods) and the income effect (the same money goes further).
Metered tap water in Kent costs £3.01 a cubic metre in 2026/27: about 0.3p a litre. A 500ml bottle from a station kiosk costs more than £1.
Nothing is more useful than water. You can live without diamonds, bottled or otherwise.
Why is the price of something so essential so close to zero?
Adam Smith’s paradox of value, solved a century later: we do not pay for the usefulness of water as a whole but for one more litre at the margin. When you already have 349 litres a day, the next one is worth a fraction of a penny. The one bottle on a hot platform is worth £1.50 because it is the first, not the four-hundredth.
Friday night, a pizza, and a hungry eater. Measure utility in pounds: the most each slice is worth to them. The first slice is worth £5. After two slices total utility is £9; after three, £12; four, £14; five, £15. The sixth adds nothing. **Total utility** rises, but by less each time, and then stops.
Check: Total utility rises from £12 after three slices to £14 after four. The marginal utility of the fourth slice is:
MU is the change in total utility: 14 − 12 = £2.
Now **marginal utility**: what each slice adds. £5, £4, £3, £2, £1, then £0. The curve falls: diminishing marginal utility. Where MU reaches zero, total utility is at its peak: the eater is satiated. A seventh slice would have negative MU and total utility would fall. Nobody rational eats it, even free.
Teacher tip: MU is the slope of the TU curve. Students confuse “TU is rising” with “MU is rising”. TU rises as long as MU is positive, even while MU is falling.
Check: Which statement describes the marginal utility curve correctly?
Each slice adds less than the one before: £5, £4, £3, £2, £1, £0. The MU curve slopes down.
Put a price on it: £2 a slice. The rational rule: buy a slice if it is worth at least what it costs, MU ≥ P. Slices one to four are worth £5, £4, £3, £2: buy them. The fifth is worth £1 and costs £2: stop. So at a price of £2 the eater buys **four**. The consumer surplus on the first three is £3 + £2 + £1 = £6.
Check: Slices cost £2 each. A rational consumer buys:
Buy while MU ≥ P. The fourth slice is worth exactly £2; the fifth is worth £1 but costs £2, so it is not worth buying.
Cut the price to £1 and the fifth slice becomes worth buying: the eater takes **five**. At every price the rule MU = P picks the quantity, so the marginal utility curve is the consumer’s demand curve. Demand slopes down because marginal utility diminishes. Add up everyone’s MU curves and you have the market demand curve.
Check: The price falls to £1. The consumer now buys 5 slices. What does this show?
At each price the consumer buys up to the slice whose MU equals that price, so the MU curve maps prices to quantities: it is the individual’s demand curve.
Most people buy more than one thing. The rule becomes the equi-marginal principle: spend so that the last pound on each good gives the same marginal utility, **MU<sub>A</sub>/P<sub>A</sub> = MU<sub>B</sub>/P<sub>B</sub>**. If a pound on cola gives more than a pound on pizza, switch towards cola; its MU falls as you buy more and pizza’s rises as you buy less, until they balance.
Check: Pizza is £2 a slice with MU £4 (2 utils per £). Cola is £1 a can with MU £3 (3 per £). To raise total utility the consumer should:
The last pound on cola gives more satisfaction than the last pound on pizza, so moving a pound from pizza to cola raises total utility, until MU/P is the same for both.
Why does the price cut from £2 to £1 raise the quantity? Two effects. The substitution effect: pizza is now cheaper relative to everything else, so the consumer switches towards it. The income effect: £8 that bought four slices now buys eight, so the consumer is better off and spends part of the gain on more pizza. For a normal good both push the same way.
Check: The price of pizza falls. The substitution effect is:
The substitution effect is the pure relative-price effect. The income effect is the second part: the same money now buys more in total.
Back to the paradox of value. Price reflects marginal utility, not total. The total utility of water is enormous, but with 349 litres a day flowing through the house the marginal litre is worth a fraction of a penny. Diamonds have low total utility, but the marginal diamond, when you have none, is worth a great deal. Smith measured the wrong thing; Jevons, Menger and Walras measured the margin.
Check: Which best explains why water is cheap and diamonds are dear?
Total utility from water is enormous, but we pay at the margin. Abundance pushes the marginal unit far down the MU curve.
Marginal utility is drawn rising. With TU rising more slowly each slice, MU must be falling: each slice adds less than the one before. A rising MU would mean the sixth slice was the best of the night.
Explain how the law of diminishing marginal utility helps to explain why the demand curve for a good slopes downwards, and assess the usefulness of utility theory in explaining consumer behaviour.
Marginal utility is the extra satisfaction a consumer gets from one more unit of a good, measured in utils or in the money they would pay for it. The law of diminishing marginal utility states that as more of a good is consumed in a period, the extra satisfaction from each additional unit falls: the first slice of pizza may be worth £5 to a hungry eater, the second £4, the fifth only £1.
A rational consumer buys a unit when it is worth at least its price, and so consumes up to the point where marginal utility equals price. At £2 a slice the eater buys four, because the fourth is worth £2 and the fifth only £1. If the price falls to £1, the fifth slice becomes worth buying and quantity demanded rises to five. Because each extra unit is worth less, only a lower price persuades the consumer to take it: the marginal utility curve is the individual’s demand curve, and it slopes down because marginal utility diminishes. Market demand is the sum of these curves. The same idea resolves the paradox of value: water is cheap because the marginal litre, when we have hundreds a day, is worth almost nothing, however great its total utility.
The theory also explains consumer surplus, the gap between MU and price on all but the last unit, and the equi-marginal principle, that spending is allocated so the last pound on each good yields equal utility. A price fall raises quantity through a substitution effect, as the good becomes relatively cheaper, and an income effect, as real income rises.
**However,** utility cannot be observed, measured or compared between people, which is why economists moved to revealed preference. The theory assumes a rational, fully informed consumer, and behavioural economics shows habits, anchoring, loss aversion and social pressure driving choices that no MU calculation would predict. For inferior goods the income effect pulls against the substitution effect, and for a Giffen good it can reverse the slope. Utility theory is best seen as a benchmark: it explains the general shape of demand and gives a clear standard against which real behaviour, and its departures, can be understood.
Water charges: South East Water metered volumetric charge for 2026/27 (£3.01 per cubic metre); Water UK average household bill for 2026/27 (£639). The utility figures on the diagram are invented, chosen so the arithmetic is clear. Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed.