Cambridge A Level Economics: Utility, indifference curves and budget lines (9708) – Revision Notes

These notes condense sections 7.1 (Utility) and 7.2 (Indifference curves and budget lines), outcomes 7.1.1 to 7.2.4, of the Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028. Topics 1 to 6 are AS Level content and topics 7 to 11 are A Level content, so this unit is A Level only. For full explanations, read the study guide. Then test yourself with the practice questions. All figures are invented, and money is in currency units (cu).

Use the course hub and the printable checklist to see what is left, and take a free 10-minute diagnostic to find weak spots. The price system revision notes cover the supply and demand background.

Definitions

Term	Meaning
Utility	Satisfaction from consuming a good
Total utility (TU)	Satisfaction from all units consumed in a period
Marginal utility (MU)	Extra satisfaction from one more unit: change in TU ÷ change in quantity
Diminishing marginal utility	MU falls as more units are consumed in a given time
Indifference curve	All combinations of two goods giving equal satisfaction
Budget line	All combinations affordable at given income and prices
Marginal rate of substitution (MRS)	Amount of one good given up for one more unit of the other, keeping satisfaction constant
Substitution effect	Change in quantity from the change in relative price, with real income held constant
Income effect	Change in quantity from the change in real income caused by the price change
Price effect	Substitution effect plus income effect
Giffen good	A good whose quantity demanded rises when its price rises, because a negative income effect outweighs the substitution effect

Formulae and results

Item	Result
Marginal utility	MU = change in TU ÷ change in quantity
TU and MU	TU rises while MU is positive, peaks when MU = 0, falls when MU is negative
Equi-marginal principle	MU of A ÷ price of A = MU of B ÷ price of B
Budget line intercepts	Income ÷ price of X, and income ÷ price of Y
Budget line slope	Price of X ÷ price of Y (absolute value)
Consumer’s optimum	MRS = price of X ÷ price of Y, at the highest affordable curve
Price effect	Price effect = substitution effect + income effect

Method: maximising utility with the equi-marginal principle

1. Work out MU per cu for each unit of each good: MU ÷ price.
2. Buy units in order of highest MU per cu.
3. Stop when the budget is spent.
4. Check that the last unit of each good has about the same MU per cu, and that total spending equals income.
5. If the ratios differ, spend less on the good with the lower ratio.

Quick reminder. TU after each unit: 10, 18, 24, 28, 30, 30. MU = 10, 8, 6, 4, 2, 0. For the third unit, MU = 24 − 18 = 6. MU is falling while TU is still rising.

Quick reminder. MU of A = 18 and price of A = 3 gives 6. MU of B = 20 and price of B = 5 gives 4. The ratio is higher for A, so the consumer should buy more A and less B until the ratios are equal.

Method: deriving an individual demand curve

1. State the assumption that each cu has a constant marginal utility, for example 4 utils.
2. For each price, buy a unit while MU is at least 4 × price.
3. Plot price against quantity.

Quick reminder. MU of successive units: 20, 16, 12, 8, 4. At a price of 2.50 cu, units with MU of at least 10 are bought: 20, 16 and 12. That gives 3 units. At 1.50 cu, MU must be at least 6, so 4 units. The curve slopes down.

Method: budget lines

1. Maximum X = income ÷ price of X. Maximum Y = income ÷ price of Y. Join the intercepts.
2. Income change: parallel shift.
3. One price change: pivot on the intercept of the good whose price did not change.
4. Both prices change in the same proportion: parallel shift, equal to a change in income.

Quick reminder. Income 200 cu, X at 10 cu, Y at 25 cu. Intercepts: 20 X and 8 Y. Slope = 10 ÷ 25 = 0.4. Income rises to 250 cu: 25 X and 10 Y. Price of Y falls to 20 cu: the Y intercept becomes 10 and the X intercept stays at 20.

Method: splitting a price effect

1. Find the original optimum and the new optimum.
2. Work out the income that would be needed to buy the original bundle at the new prices.
3. Find the compensated point, where a line at the new price ratio touches the original curve. Its income is slightly below the figure in step 2.
4. Substitution effect: original to compensated. Income effect: compensated to new.

Quick reminder. Income 90 cu, price of X falls from 3 to 2 cu, Y at 6 cu. Original bundle: 18 X and 6 Y (54 + 36 = 90). Buying the original bundle at the new price would cost 2 × 18 + 36 = 72 cu. The compensated bundle is 24 X and 3.6 Y (48 + 21.6 = 69.6 cu, slightly below 72). The new bundle is 27 X and 6 Y (54 + 36 = 90). Substitution effect = 24 − 18 = +6. Income effect = 27 − 24 = +3. Price effect = +9. X is a normal good.

Must-know distinctions

Good	Substitution effect of a price fall	Income effect of a price fall	Demand curve
Normal	Raises quantity	Raises quantity	Slopes down
Inferior	Raises quantity	Lowers quantity, smaller	Slopes down
Giffen	Raises quantity	Lowers quantity, larger	Slopes up

• Substitution effects always work in the opposite direction from the price change.
• Every Giffen good is inferior, but most inferior goods are not Giffen.
• Total utility and marginal utility are different: TU can be rising while MU is falling.
• A pivot is a change in one price; a parallel shift is a change in income or in both prices together.
• Marginal utility theory measures utility in numbers. Indifference curve analysis needs only a ranking of bundles.

Evaluation chains

• Marginal utility theory: assumes measurable utils and a constant MU of money, so the numbers are unreliable. But it explains why demand curves slope down, so it is a sensible starting point.
• Rationality: habit, advertising and limited information mean real consumers may not equalise MU per cu. The theory is a benchmark for behaviour rather than a description of it.
• Indifference curves: only two goods, no observable curves, fixed tastes and prices. But the method separates income and substitution effects clearly, which the MU approach cannot.
• Giffen goods: theoretically sound, but hard to find in practice, because few goods are both inferior and a large share of spending.

Quick self-test

1. Define marginal utility.
2. TU is 10, 18, 24, 28 for four units. What is the marginal utility of the fourth?
3. MU of A = 18, price of A = 3. MU of B = 20, price of B = 5. What should the consumer do?
4. Income 200 cu, X at 10 cu, Y at 25 cu. State the intercepts and slope of the budget line.
5. Income rises to 250 cu. What are the new intercepts?
6. The price of Y falls to 20 cu. What happens to the budget line?
7. A consumer moves from 4 X and 20 Y to 5 X and 14 Y on the same indifference curve. Calculate the MRS.
8. At the consumer’s optimum, what does the MRS equal if X is 10 cu and Y is 25 cu?
9. A price fall gives a substitution effect of +5 and an income effect of −2. Classify the good and state the price effect.
10. A price rise gives a substitution effect of −3 and an income effect of +5. Classify the good.
11. Give two limitations of indifference curve analysis.

Answers

1. The extra satisfaction from consuming one more unit.
2. 28 − 24 = 4 utils.
3. A: 18 ÷ 3 = 6. B: 20 ÷ 5 = 4. Buy more A and less B.
4. 200 ÷ 10 = 20 X, 200 ÷ 25 = 8 Y. Slope = 10 ÷ 25 = 0.4.
5. 250 ÷ 10 = 25 X and 250 ÷ 25 = 10 Y.
6. 200 ÷ 20 = 10 Y. It pivots outward on the X intercept (20), with the Y intercept rising from 8 to 10.
7. 6 Y given up for 1 X: MRS = 6.
8. 10 ÷ 25 = 0.4, the price ratio.
9. The income effect opposes the substitution effect but is smaller: inferior good, not Giffen. Price effect = 5 − 2 = +3.
10. Price effect = −3 + 5 = +2. Quantity rises when price rises: Giffen good.
11. Any two: only two goods, curves cannot be observed, stable tastes assumed, rational consumer assumed, fixed prices and no saving or borrowing.

Where marks are usually lost

• Writing the budget line slope as price of Y ÷ price of X.
• Dividing change in TU by the wrong quantity change, or using TU where MU is asked for.
• Choosing a bundle with the highest MU rather than the highest MU per cu.
• Pivoting a budget line on the wrong intercept after one price changes.
• Not holding real income constant when finding the substitution effect.
• Calling every inferior good a Giffen good.
• Listing limitations with no judgement on how serious each is.
• Saying a consumer is “indifferent” between points on different curves.

Official syllabus

Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028, sections 7.1 and 7.2 (Cambridge University Press & Assessment).