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7.1 Utility

Syllabus
9708–2026–2027
Topic
7.1
Level
A2

Calculate marginal utility from changes in total utility

Total utility (TU) is the total satisfaction from consuming a stated quantity. Marginal utility (MU) is the extra satisfaction from a change in consumption: MU = ΔTU / ΔQ. Utility is expressed in analytical units called utils.

Quantity TU MU of the added unit
2 40 —
3 52 (52 − 40)/(3 − 2) = 12
4 58 (58 − 52)/(4 − 3) = 6
MU What happens to TU
Positive TU rises
Zero TU is stationary/maximised locally
Negative TU falls

MU is the difference between neighbouring TU values, not TU divided by quantity. Diminishing MU is the next objective; do not infer it merely because MU is below TU.

Diminishing marginal utility makes total utility rise more slowly

The law of diminishing marginal utility states that, as a person consumes successive units of a good in a given period, the extra utility from each additional unit tends to fall, other things such as tastes and unit quality unchanged.

MU pattern TU pattern
Positive and diminishing TU rises at a decreasing rate
MU = 0 TU reaches a maximum
MU < 0 TU falls

For a thirsty person, successive cups might add 20, 12, 5, 0 and −3 utils. TU still rises through the third cup, peaks at the fourth, and falls only after the fifth.

Because later units usually give less MU, a consumer is willing to pay less for additional units. This supports the downward-sloping individual demand curve that is derived formally in 7.1.4.

The law is conditional, not universal. Complementary units, learning, addiction or completing a collection can make a later unit unusually valuable; these are limitations rather than evidence that TU and MU are identical.

Maximise utility by ranking the next unit's MU per price

For an interior optimum, a rational consumer allocates a given budget so the utility from the last money unit is equal across goods: MUx/Px = MUy/Py (= marginal utility of money), with the budget spent.

For a discrete table: (1) calculate MU/P for every successive unit; (2) rank available units from highest MU/P; (3) buy the highest affordable next unit, respecting that earlier units of a good come first; (4) continue until the budget is exhausted; (5) check that no affordable reallocation raises total utility.

Next unit MU Price MU/P Decision
Tea 18 $3 6 Buy before fruit
Fruit 8 $2 4 Buy after higher-ratio units

If MUx/Px is greater than MUy/Py, shift spending toward X. Diminishing MUx and reduced consumption of Y move the ratios toward equality. A rise in X's price lowers MUx/Px; a rise in the utility attached to Y raises MUy/Py, so the chosen bundle changes.

Do not equalise MU, TU, quantities or expenditure. Equal MU is optimal only when prices are equal; discrete goods can leave unequal final ratios when no further affordable swap improves utility.

Own-price changes generate an individual's demand curve

Derive an individual demand curve by changing only the good's own price while holding money income, tastes, other goods' prices and the marginal utility of money constant. Record the utility-maximising quantity at each price.

At the initial choice, MUx/Px equals the marginal utility of the last money unit elsewhere. If Px falls, MUx/Px becomes too high at the old quantity. The consumer buys more X; diminishing MUx lowers the ratio until equilibrium is restored. A price rise reverses the chain.

Price of X Re-optimised quantity of X Demand point
6∣2∣(6 | 2 | (6, 2)
4∣3∣(4 | 3 | (4, 3)
2∣5∣(2 | 5 | (2, 5)

Plot price vertically and quantity horizontally, then join the points. The usual downward slope follows from diminishing MU: additional units are chosen only at a lower price. An own-price change is a movement along this curve.

Income, tastes or another price changing would create a new demand schedule rather than derive a movement along the existing curve. This marginal-utility derivation does not require indifference curves or budget lines from 7.2.

Marginal-utility predictions depend on restrictive assumptions

Marginal-utility theory is a simplified model of consumer choice. It can explain ordinary downward demand under its assumptions, but utility is not directly observable and real consumers need not perform its calculation.

Assumption Why it limits the model
Utility is cardinal, measurable and comparable across a person's choices Utils cannot be observed objectively; ordinal ranking may be more defensible
Rational, consistent consumer with perfect information Bounded rationality, habits, advertising, uncertainty and behavioural biases alter choices
Stable tastes; other prices and income unchanged Real changes require a new demand schedule and weaken ceteris-paribus prediction
Constant marginal utility of money An extra dollar need not have equal value at different incomes or spending levels
Divisible, substitutable goods with independent utility Houses, sets, complements and one-off purchases do not fit smooth MU schedules
Diminishing MU and a simple two-good allocation Consumers choose among many goods; addiction or collection effects may violate the pattern

The theory does not separate income and substitution effects, so it cannot adequately explain upward-sloping Giffen demand. It derives individual demand; a market curve also requires horizontal addition of many heterogeneous consumers' quantities.

Use the model as a conditional benchmark: it clearly links diminishing MU, price and ordinary quantity demanded, especially for repeated divisible purchases. Its adequacy is weaker for expensive infrequent goods, interdependent choices, imperfect information and systematically non-rational behaviour.

A violated assumption does not make the model useless; it narrows where its prediction is reliable. Evaluation should identify the assumption, explain the resulting prediction problem and reach a context-based judgement.