Cambridge International AS and A Level Economics: Utility, indifference curves and budget lines (9708)

This guide covers sections 7.1 (Utility) and 7.2 (Indifference curves and budget lines), outcomes 7.1.1 to 7.1.5 and 7.2.1 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 and is not examined at AS. Every consumer, good and figure below is invented, and money is in currency units (cu).

Use the Cambridge A Level Economics hub and printable checklist to track the course. After this guide, use the revision notes and the practice questions. For background, see the price system study guide. To find weak spots first, take a free 10-minute diagnostic.

What this guide covers

Outcome	What you must be able to do
7.1.1	Define and calculate total utility (TU) and marginal utility (MU)
7.1.2	Explain diminishing marginal utility
7.1.3	Apply the equi-marginal principle
7.1.4	Derive an individual demand curve
7.1.5	Assess the limitations of marginal utility theory and rational behaviour
7.2.1	Explain an indifference curve and a budget line
7.2.2	Explain causes of a shift in the budget line
7.2.3	Show income, substitution and price effects for normal, inferior and Giffen goods
7.2.4	Assess the limitations of indifference curve analysis

7.1.1 and 7.1.2: total and marginal utility

Utility is the satisfaction from consuming a good. Total utility is the satisfaction from all units consumed. Marginal utility is the extra satisfaction from one more unit.

MU = change in TU ÷ change in quantity

Diminishing marginal utility means that, as a consumer takes more units in a given time, the extra satisfaction from each extra unit falls.

Worked example. An invented consumer eats bowls of soup at lunch. Utility is measured in utils, an invented unit.

Bowls	1	2	3	4	5	6	7
TU	20	36	48	56	60	60	56
MU	20	16	12	8	4	0	−4

For the third bowl, MU = 48 − 36 = 12 utils. MU falls with every bowl, which is diminishing marginal utility. TU rises while MU is positive, reaches its maximum of 60 when MU is zero (at five or six bowls) and falls when MU is negative. A rational consumer facing a zero price would stop at the sixth bowl, where MU = 0.

7.1.3: the equi-marginal principle

A consumer with a limited income maximises total utility by spending so that the marginal utility per cu is equal across all goods:

MU of A ÷ price of A = MU of B ÷ price of B

Worked example. A consumer has 20 cu to spend on snack bars (2 cu each) and smoothies (4 cu each).

Unit	1	2	3	4	5	6
MU of snack bars	24	20	16	12	8	4
MU per cu, snack bars	12	10	8	6	4	2
MU of smoothies	40	32	24	16	8	4
MU per cu, smoothies	10	8	6	4	2	1

Buy the units with the highest MU per cu first, until the budget runs out. All units worth 6 or more per cu are: snack bars 1 to 4 and smoothies 1 to 3. Cost = 4 × 2 + 3 × 4 = 20 cu, so the budget is exactly spent. At this bundle, 12 ÷ 2 = 6 and 24 ÷ 4 = 6, so the ratios are equal.

TU = (24 + 20 + 16 + 12) + (40 + 32 + 24) = 72 + 96 = 168 utils.

Two other bundles costing 20 cu give less: two snack bars and four smoothies give 44 + 112 = 156 utils, and six snack bars and two smoothies give 84 + 72 = 156 utils.

If the ratios differ, move spending from the good with the lower ratio to the higher. At two snack bars and four smoothies, the ratios are 10 (second bar) and 4 (fourth smoothie), so buy fewer smoothies. Each switch lowers the ratio of the good bought more and raises it for the other, until they meet.

7.1.4: deriving an individual demand curve

A consumer buys a unit if its marginal utility is worth at least its price. To turn utils into cu, assume the marginal utility of money is constant. Suppose each cu given up costs 2 utils.

Worked example. MU of bottles of juice: 48, 40, 32, 24, 16, 8. The consumer buys a unit while MU ÷ price is at least 2.

Price (cu)	22	18	14	10	6
Units bought	1	2	3	4	5

At 14 cu: 32 ÷ 14 = 2.29, which is at least 2, so the third unit is bought. 24 ÷ 14 = 1.71, which is below 2, so the fourth is not. Plot price against quantity. The curve slopes down because marginal utility diminishes: a lower price makes a lower-value unit worth buying. A change in income or tastes shifts the curve. A market demand curve sums individual curves horizontally.

7.1.5: limitations of marginal utility theory

• Utils cannot be measured. The theory assumes you can say the third bowl gives exactly 12 utils.
• The marginal utility of money is unlikely to stay constant when a price change is large.
• Consumers may not be rational. Habit, advertising, limited information and addiction can break the rules, and for some goods MU may rise at first.
• Goods are treated as independent, though complements and substitutes affect each other’s MU.

Evaluate by asking how much damage each limit does. The theory still explains why demand curves usually slope down, but its numbers cannot be tested.

7.2.1: indifference curves and budget lines

An indifference curve shows all combinations of two goods that give the consumer the same satisfaction. A higher curve means higher satisfaction. Curves slope down, are convex to the origin and do not cross. Along a curve, the marginal rate of substitution (MRS) is the amount of one good the consumer will give up for one more unit of the other.

Worked example. One indifference curve, IC1, holds all combinations of X and Y with X × Y = 150 (an invented curve):

Combination	(5, 30)	(6, 25)	(10, 15)	(15, 10)	(25, 6)	(30, 5)
MRS of the move to the next point	5	2.5	1	0.4	0.2

From (5, 30) to (6, 25), the consumer gives up 5 Y for 1 X: MRS = 5. From (15, 10) to (25, 6), 4 Y buys 10 X: MRS = 0.4. The MRS diminishes, which gives the convex shape.

A budget line shows all combinations the consumer can afford at given income and prices. With income 120 cu, X at 6 cu and Y at 4 cu:

• Maximum X = 120 ÷ 6 = 20. Maximum Y = 120 ÷ 4 = 30.
• Slope = price of X ÷ price of Y = 1.5 (in absolute value). One X costs 1.5 Y.

The consumer maximises utility where the budget line just touches the highest affordable indifference curve: MRS = price of X ÷ price of Y. Here this is (10, 15), which costs 60 + 60 = 120 cu. Other points on IC1 cost more than 120 cu: (6, 25) costs 136 and (15, 10) costs 130. Tangency matches the equi-marginal principle, because MRS = MU of X ÷ MU of Y.

7.2.2: shifts of the budget line

Cause	Effect (income 120, X at 6 cu, Y at 4 cu)
Rise in income to 150 cu (a fall shifts it inward)	Parallel outward shift: intercepts become 25 X and 37.5 Y
Fall in price of X to 4 cu (a rise pivots it inward)	Pivots outward on the Y intercept: 30 X, still 30 Y, and the slope falls to 1
Both prices up 25 per cent (7.5 cu and 5 cu)	Parallel inward shift: intercepts 16 X and 24 Y

The last row matches an income of 96 cu at the old prices, since 96 ÷ 6 = 16 and 96 ÷ 4 = 24.

7.2.3: income, substitution and price effects

The price effect is the total change in quantity demanded after a price change. It splits into two parts.

• The substitution effect is the change in quantity because the good is now relatively cheaper or dearer, holding real income (the same indifference curve) constant. It always works against the price change: a fall in price raises quantity.
• The income effect is the change in quantity because the price change alters real income. For a normal good, a fall in price raises real income and raises demand. For an inferior good, it lowers demand.

To split the effects, draw an imaginary budget line parallel to the new one and tangent to the original indifference curve. The move to that point is the substitution effect. The move from there to the actual new optimum is the income effect.

Normal good. Take IC1 again. Income stays at 120 cu, Y at 4 cu, and the price of X falls from 6 to 4 cu.

Step	X	Y
Original optimum (budget 6X + 4Y = 120)	10	15
Compensated point (new prices, tangent to IC1)	12.25	12.25
New optimum (budget 4X + 4Y = 120)	15	15

Substitution effect on X = 12.25 − 10 = +2.25. Income effect = 15 − 12.25 = +2.75. Price effect = +5. Both effects work in the same direction, so X is a normal good. Reading off price and quantity gives the demand curve: 6 cu for 10 units, 4 cu for 15, 3 cu for 20 and 2 cu for 30.

Inferior good. Income 120 cu, Y at 6 cu, and the price of X falls from 4 to 3 cu. The consumer starts at 15 X and 10 Y. Buying that bundle at the new price would cost 15 × 3 + 60 = 105 cu. The compensated budget line must touch the original indifference curve, so it needs slightly less than that: 102 cu. At 102 cu the consumer buys 22 X and 6 Y (66 + 36 = 102). This is a substitution effect of +7. With the full 120 cu, the consumer buys 21 X. The income effect is 21 − 22 = −1. The price effect is +6. The income effect opposes the substitution effect but is smaller, so the demand curve still slopes down.

Giffen good. Income 100 cu, Y at 5 cu, and the price of X rises from 2 to 2.50 cu. The consumer starts at 30 X and 8 Y. At the new price, the original bundle would cost 30 × 2.5 + 40 = 115 cu. The compensated budget line needs slightly less: 114 cu. At 114 cu the consumer buys 26 X and 9.8 Y (65 + 49 = 114): a substitution effect of −4. At the real income of 100 cu, the consumer buys 32 X: an income effect of +6. The price effect is +2. The income effect outweighs the substitution effect, so a price rise raises quantity demanded. A Giffen good must be inferior, takes a large share of the budget and has few cheaper substitutes.

Good	Substitution effect	Income effect	Result of a price fall
Normal	Raises quantity	Raises quantity	Quantity rises
Inferior	Raises quantity	Lowers quantity, smaller	Quantity rises
Giffen	Raises quantity	Lowers quantity, larger	Quantity falls

7.2.4: limitations of indifference curve analysis

• Only two goods are drawn, unlike a real basket of goods.
• Indifference curves cannot be observed directly, and tastes must be stable and consistent.
• The consumer is assumed rational, well informed and able to compare every bundle.
• The budget line assumes fixed prices, no bulk discounts and no saving or borrowing. Goods are assumed perfectly divisible.
• Giffen goods are theoretically possible, but clear evidence is hard to find.

Common errors

• Saying utility falls when only MU falls. TU still rises while MU is positive.
• Writing the budget line slope as price of Y ÷ price of X.
• Treating all inferior goods as Giffen goods. Giffen goods are a special case.
• Not holding real income constant in the substitution effect.

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).