Analyse utility
Distinguish total and marginal utility and apply the law of diminishing marginal utility.
Marginal Utility and Consumer Choice
Why does a consumer usually buy less of a good when its price rises? This chapter develops the theory of demand through utility, then uses budget lines and indifference curves to show how a rational consumer chooses between goods and responds to changes in income and prices.
Marginal utilityDiminishing MUEqui-marginal principleBudget lineIndifference curvesIncome & substitution effects
What this chapter prepares you to do
Explain demand
Show how marginal utility can help explain a downward-sloping individual demand curve and utility-maximising consumption.
Model consumer choice
Interpret budget lines, indifference curves, marginal rate of substitution and consumer equilibrium.
Separate price effects
Break a price change into substitution and income effects for normal, inferior and Giffen goods.
High-grade habit: do not merely state that a curve shifts. Explain why: an income change shifts the entire budget line parallel, while a change in the price of one good rotates the line because the relative price has changed.
Chapter sections
14.1
Utility
Utility is the satisfaction a consumer receives from consuming a good or service. The theory does not require utility to be physically observable; it is a way of representing the consumer's preferences and choices.
Total utility (TU)
The total satisfaction obtained from all units of a good consumed.
Marginal utility (MU)
The additional satisfaction obtained from consuming one more unit.
Marginal utility formulaMU = change in total utility ÷ change in quantity consumed. When quantity rises one unit at a time, MU is simply the change in total utility between successive quantities.
The law of diminishing marginal utility
As a consumer consumes more units of the same good within a period, the additional satisfaction from each extra unit tends to fall. This is the law of diminishing marginal utility. The consumer may still gain total satisfaction from more units, but the extra gain becomes smaller.
A marginal utility curve
As Majida consumes more chocolate bars, the marginal utility gained from each additional bar falls. The first bar gives 30 utils, the second 26, then 21, 15 and 8; by the sixth bar marginal utility has fallen to zero. This illustrates the law of diminishing marginal utility.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Total utility and marginal utility
- If MU is positive, TU rises.
- If MU is falling but positive, TU rises at a decreasing rate.
- If MU = 0, TU is at its maximum.
- If MU became negative, extra consumption would reduce TU.
Worked example: if total utility rises from 56 utils after two units to 77 utils after three units, the marginal utility of the third unit is 21 utils.
Book example — Majida and chocolate: Majida’s marginal utility from successive chocolate bars is 30, 26, 21, 15, 8 and 0 utils. Total utility therefore keeps rising while marginal utility is positive, but by progressively smaller amounts. When marginal utility reaches zero on the sixth bar, total utility is at its maximum.
Marginal utility and the demand curve
If utility is expressed in money terms, the consumer will buy units up to the point where the marginal utility of the final unit equals its price. If price is above the consumer's marginal valuation, the unit is not worth buying; if price is below marginal valuation, buying another unit increases satisfaction.
An individual’s demand curve
If marginal utility is measured in money terms, the consumer purchases up to the point where the price equals the marginal utility of the last unit. At Q*, marginal utility is MU*. A higher price would reduce the quantity purchased, helping explain why an individual demand curve slopes downward.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Ceteris paribus: changes in income, preferences or the prices of other goods shift the demand/MU curve. A change in the good's own price causes movement along it.
This approach helps explain why individual demand is normally downward sloping: because marginal utility falls as more units are consumed, a lower price is needed to make additional units worthwhile.
The equi-marginal principle
Consumers usually divide a limited budget across several goods. To maximise total utility, spending should be allocated so that the marginal utility per unit of currency is equal across the goods purchased.
Equi-marginal conditionMUX / PX = MUY / PY. If the ratios are unequal, the consumer can increase total utility by transferring spending toward the good with the higher MU per unit of currency.
Example: if the next unit of X gives 24 utils and costs $4, MU/P = 6. If the next unit of Y gives 15 utils and costs $5, MU/P = 3. The consumer can increase total utility by shifting some spending from Y toward X until the ratios are equalised, subject to the budget.
Book example — apples and cola: Abdul faces apples at 20 cents each and cola at 40 cents. He compares MU/P, not marginal utility alone. At two apples and two colas, MU/P is 7 for each good, so reallocating one dollar of spending between the two goods cannot raise his total utility. This is the equi-marginal condition.
Limitations of marginal utility theory
Utility cannot be objectively measured
There is no observable unit that allows economists to measure or compare the satisfaction received by different consumers.
Many-goods decisions are complex
Real consumers choose among many goods whose demands are interdependent, making simple MU calculations difficult to apply directly.
Rationality is not guaranteed
The model assumes consumers deliberately maximise utility, yet actual decisions may be influenced by impulse, emotion, advertising and other psychological factors.
Behavioural economics and rational choice
Behavioural economics studies how psychology influences economic decision-making. It challenges the assumption that consumers always make carefully calculated utility-maximising choices. This does not make utility theory useless, but it is an important limitation when applying the model to real behaviour.
14.2
Indifference curves and budget lines
The indifference-curve model analyses how a consumer chooses between two goods when income and prices constrain what can be afforded.
The budget line
A budget line shows the combinations of two goods that can be purchased when the consumer spends the available budget, given the prices of the two goods. Points beyond the line are unaffordable; points inside it are affordable but do not use the whole budget.
Budget line intercepts and slopeIf income is I, price of X is PX and price of Y is PY, the maximum X is I/PX, the maximum Y is I/PY, and the slope reflects the relative price PX/PY.
Abdul’s budget line
With $1.20 to spend, apples at $0.20 each and cola at $0.40 per bottle, Abdul can buy at most six apples or three bottles of cola. The budget line joins all affordable combinations that use the whole budget, and its slope reflects the relative prices of the two goods.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
What changes the line?
- Higher income: parallel outward shift if both prices are unchanged.
- Lower income: parallel inward shift.
- Price of X falls: X-intercept moves outward; the line pivots.
- Price of Y rises: Y-intercept moves inward; the line pivots.
Exam warning: an income change does not change the relative prices, so the slope stays the same. A change in the price of one good changes relative prices, so the slope changes.
Budget-line logic: an increase in income, with prices unchanged, shifts the line outward in parallel. A change in the price of one good rotates the line around the intercept of the good whose price has not changed. This distinction is essential when analysing income and substitution effects.
Indifference curves
An indifference curve shows combinations of two goods that give the consumer the same total utility. The consumer is indifferent between points on the same curve. Higher curves represent higher utility when more of both goods is preferred to less.
Abdul’s indifference curves
Each indifference curve shows combinations of apples and cola that give Abdul the same total utility. Curves farther from the origin represent higher utility because more is preferred to less. The slope of an indifference curve is the marginal rate of substitution.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Marginal rate of substitution
The marginal rate of substitution (MRS) is the amount of one good the consumer is willing to give up to obtain more of the other while maintaining the same utility.
It is represented by the slope of the indifference curve and is linked to the ratio of marginal utilities.
Interpretation: as a consumer has more X and less Y, they normally become less willing to give up Y for another unit of X. This gives the standard bowed shape.
Consumer equilibrium
The consumer maximises utility at the highest attainable indifference curve. With a smooth interior solution, this occurs where the budget line is tangent to an indifference curve.
Abdul’s choice
Abdul maximises utility at point A, where the budget line is tangent to the highest indifference curve he can afford. At this point the slope of the indifference curve equals the slope of the budget line, linking the marginal rate of substitution to relative prices.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Consumer equilibriumThe point where the highest attainable indifference curve touches the budget line. At that point the consumer cannot reallocate the budget to reach a higher level of utility.
A point on a lower curve wastes an opportunity to gain more utility. A point on a higher but unattainable curve is beyond the consumer's budget.
An increase in income
If income rises while both prices remain unchanged, the budget line shifts outward in parallel. The new tangency may show increased consumption of both goods if both are normal. If consumption of one good falls as income rises, that good is inferior.
A change in Abdul’s budget
When Abdul’s spending budget rises from $1.20 to $2.00 while prices remain unchanged, the budget line shifts outward in parallel from BL₀ to BL₁. He moves from A to B and consumes more of both goods, showing that in this example both apples and cola are normal goods.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
A change in Abdul’s budget when cola is an inferior good
A rise in income shifts the budget line outward, but a consumer does not have to buy more of every good. Here Abdul moves from A to B, consuming more apples but less cola. Cola is therefore an inferior good over this income range.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Normal versus inferior response
| When income rises | Consumption response |
|---|---|
| Normal good | Quantity consumed rises. |
| Inferior good | Quantity consumed falls. |
The shape of preferences determines whether the chosen amount of a particular good rises or falls after the budget line shifts.
A change in the price of one good
If the price of X falls while income and the price of Y remain unchanged, the maximum affordable quantity of X rises. The budget line therefore rotates outward from the Y-intercept. A price rise rotates it inward.
A fall in the price of apples
When the price of apples falls, the apple intercept of the budget line moves outward while the cola intercept is unchanged. Abdul can afford more apples and reaches a higher indifference curve. The total response to the price change contains both a substitution effect and an income effect.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Two effects occur together
- Substitution effect: the good whose relative price falls becomes cheaper compared with the other good, encouraging substitution toward it.
- Income effect: the price fall increases real purchasing power because the same money income can buy more.
Income and substitution effects
How to separate the price effect: Start at the original equilibrium A. Draw a compensated budget line with the new slope but tangent to the original indifference curve. The move from A to the compensated point is the substitution effect; the remaining move to the final equilibrium is the income effect.
| Type of good | Price of X rises | Relationship of the two effects |
|---|---|---|
| Normal good | Substitution effect reduces X; lower real income also reduces X. | Both effects reinforce each other. |
| Inferior good | Substitution effect reduces X, but lower real income increases demand for X. | The effects work in opposite directions; normally substitution dominates. |
| Giffen good | The negative real-income effect on purchasing power causes such a large increase in demand for the inferior good that it more than offsets substitution away from it. | Income effect dominates, producing an upward-sloping demand relationship. |
Income and substitution effects of a price change
After the price of apples changes, the move from A to C isolates the substitution effect using the compensated budget line BL*, while the move from C to B shows the income effect. For a normal good the two effects reinforce one another.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Income and substitution effects of a price change when apples are an inferior good
When apples are an inferior good, the substitution effect and income effect work in opposite directions. The substitution effect still moves consumption away from the relatively more expensive good, while the income effect partly offsets that change. Only if the income effect became stronger than the substitution effect would the good behave as a Giffen good.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
Price changesRelative price and real purchasing power change
→Substitution effectConsumer moves toward the relatively cheaper good
→Income effectReal income changes, affecting normal or inferior demand
→Total price effectThe two effects combine to determine the final quantity
Exam warning: for an inferior good, do not say that the demand curve must slope upward. Usually the substitution effect is stronger than the opposing income effect, so demand still slopes downward. A Giffen good is the exceptional case in which the income effect is strong enough to dominate; it is mainly a theoretical possibility and is rarely identified in practice.
Giffen-good exception: for an inferior good, the income effect works against the substitution effect. Normally the substitution effect is larger, so demand still slopes downward. A Giffen good is the exceptional theoretical case in which the income effect is so strong that it more than offsets the substitution effect, producing an upward-sloping demand response.
Limitations of the indifference-curve model
Indifference curves are not observable
The consumer's actual budget can be identified, but the map of equal-utility curves cannot be directly observed.
Expected utility may differ from experienced utility
Advertising, recommendations or uncertainty can mean the satisfaction actually obtained differs from what the consumer expected.
Consumers may not behave rationally
If choices are influenced by impulses or psychological biases, a model built on utility maximisation will not explain every decision.
Chapter 14 revision checklist
Define utility, total utility and marginal utility.
Calculate marginal utility from changes in total utility.
Explain the law of diminishing marginal utility.
Explain the relationship between MU and TU.
Use marginal utility to explain a downward-sloping demand curve.
State and apply the equi-marginal principle.
Calculate marginal utility per unit of currency.
Explain limitations of marginal utility theory.
Explain why rational consumer behaviour is an assumption.
Describe the role of behavioural economics.
Define and draw a budget line.
Explain how income changes shift a budget line.
Explain how a price change rotates a budget line.
Define an indifference curve.
Explain the marginal rate of substitution.
Identify consumer equilibrium at tangency.
Explain the effect of higher income for normal and inferior goods.
Distinguish the substitution effect from the income effect.
Explain price changes for normal, inferior and Giffen goods.
Evaluate the limitations of the indifference-curve model.
20 questions. Each answer is marked immediately with a short explanation of why it is correct or incorrect.