Economics · Lesson 6

Utility, consumer equilibrium & consumer surplus

JAMBWAECNECO

What the syllabus asks

JAMB: Theory of consumer behaviour: cardinal and ordinal utility; total and marginal utility; diminishing marginal utility; consumer equilibrium; indifference curve and budget line; consumer surplus; paradox of value

WAEC: Theory of consumer behaviour: utility (total, average and marginal); law of diminishing marginal utility; consumer equilibrium (equi-marginal principle); derivation of the demand curve; consumer surplus; budget line and indifference curve (basic treatment)

NECO: Theory of consumer behaviour: utility (total, average and marginal); law of diminishing marginal utility; consumer equilibrium (equi-marginal principle); derivation of the demand curve; consumer surplus; budget line and indifference curve (basic treatment)

What you will learn

Define utility and calculate total, average and marginal utility.
State and explain the law of diminishing marginal utility and its exceptions.
Determine consumer equilibrium using the equi-marginal principle.
Derive the downward-sloping demand curve from marginal utility.
Calculate and explain consumer surplus and the paradox of value.
Draw and interpret budget lines and indifference curves and find the consumer’s equilibrium.

Key points

Utility is subjective satisfaction; MU = ΔTU; AU = TU ÷ Q.
Law of diminishing MU: extra satisfaction from successive units falls, other things equal.
TU is maximum where MU = 0; falls when MU is negative.
Equilibrium (cardinal): MUx ÷ Px = MUy ÷ Py with income spent.
Diminishing MU explains the downward-sloping demand curve.
Consumer surplus = willingness to pay − amount paid; area above price below demand.
Paradox of value: price reflects marginal, not total, utility.
Budget line: intercepts M ÷ Px and M ÷ Py; slope −Px ÷ Py; income shifts it, one price pivots it.
ICs slope down, are convex, never cross; higher ICs are preferred.
Ordinal equilibrium: budget line tangent to highest IC (MRS = Px ÷ Py).

Start here: Meaning of utility; total and marginal utility

Aisha is very thirsty after a football match in Kaduna. The first sachet of cold water is wonderful, the second is good, the third is just fine, and by the sixth she does not want any more. Economists call the satisfaction she gets utility.

Utility is the satisfaction or benefit a consumer derives from consuming a good or service. It is subjective: the same good gives different utility to different people at different times.
Total utility (TU): total satisfaction from all units consumed.
Marginal utility (MU): the addition to TU from consuming one more unit: MUₙ = TUₙ − TUₙ₋₁.
Average utility (AU) = TU ÷ Q.

Note that "utility" is not the same as "usefulness": a harmful good (cigarettes) can still give utility to the person who wants it.

Sachets (Q)	TU (utils)	MU
0	0	–
1	10	10
2	18	8
3	24	6
4	28	4
5	30	2
6	30	0
7	28	−2

Worked example 6.1

From the table (illustrative utils), find MU of the 4th sachet and AU at 4 sachets.

MU₄ = TU₄ − TU₃ = 28 − 24 = 4.
AU = 28 ÷ 4 = 7.

MU = 4; AU = 7

Worked example 6.2

MU of the first three plates of rice are 15, 11 and 6. Find TU of three plates.

TU = sum of MUs = 15 + 11 + 6 = 32.

32 utils

⚠️ Common mistake: thinking TU falls as soon as MU falls. TU keeps rising as long as MU is positive; it only falls when MU is negative.

Try it yourself. At what quantity is TU maximum in the table, and what is MU there?

Show solution

At 6 sachets (TU = 30, the 6th unit adds nothing): MU = 0.

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Practice questions

1. Utility means the

satisfaction derived from consuming a good
usefulness of a good to society
price of a good
cost of production

Show answer

A: satisfaction derived from consuming a good
Utility is subjective satisfaction.

2. Total utility is at its maximum when marginal utility is

maximum
negative
equal to price
zero

Show answer

D: zero
TU stops rising once MU reaches zero.

3. TU from 1, 2 and 3 oranges is 10, 18 and 24. The marginal utility of the third orange is

Show answer

C: 6
24 − 18 = 6.

4. The law of diminishing marginal utility states that as more units are consumed,

satisfaction is constant
the extra satisfaction from each additional unit falls
total utility always falls
price must rise

Show answer

B: the extra satisfaction from each additional unit falls
Other things being equal, MU declines.

5. A consumer buying two goods is in equilibrium when

MUx ÷ Px = MUy ÷ Py
MUx = MUy
Px = Py
TUx = TUy

Show answer

A: MUx ÷ Px = MUy ÷ Py
Equi-marginal principle with income spent.

Key words

Utility: The satisfaction a consumer gets from consuming a good or service.
Total utility (TU): Total satisfaction from consuming a given quantity of a good.
Marginal utility (MU): Change in total utility from consuming one more unit.
Average utility: Total utility divided by quantity consumed.
Law of diminishing marginal utility: As more units of a good are consumed, the extra satisfaction from each additional unit eventually falls.
Cardinal utility: Approach assuming utility can be measured in numbers (utils).
Ordinal utility: Approach assuming consumers can only rank combinations, not measure satisfaction.
Util: Imaginary unit of satisfaction.
Consumer equilibrium: The position where a consumer, given income and prices, gets maximum satisfaction.
Equi-marginal principle: Utility is maximised when the MU per naira is equal for all goods.
Consumer surplus: Difference between what a consumer is willing to pay and what is actually paid.
Paradox of value: Water is essential but cheap; diamonds are inessential but dear (explained by marginal utility).

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