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How does demand respond to changes in income and to the prices of other goods?

Define and calculate income and cross elasticity of demand, and use their signs to classify goods

A focused answer to the H2 Economics learning outcome on income and cross elasticity. The formulae and calculations for YED and XED, and how their signs distinguish normal, inferior, substitute and complement goods.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to define and calculate the income elasticity of demand (YED) and the cross elasticity of demand (XED), and to use the sign and magnitude of each to classify goods (normal versus inferior, substitute versus complement). The central insight is that while PED is about a good's own price, these two elasticities capture how demand responds to income and to the prices of other goods, which is what firms and governments use to forecast demand.

The answer

Income elasticity of demand (YED)

YED measures how responsive demand is to a change in consumer income. Its sign classifies the good and its size measures the strength of response:

Positive YED: a normal good (demand rises as income rises).
- $0 < YED < 1$ : income inelastic, a necessity (demand rises less than proportionately).
- $YED > 1$ : income elastic, a luxury or superior good (demand rises more than proportionately).
Negative YED: an inferior good (demand falls as income rises, because consumers switch to superior alternatives).

Cross elasticity of demand (XED)

XED measures how responsive demand for one good is to a change in the price of another. Its sign reveals the relationship:

Positive XED: the goods are substitutes (a rise in B's price raises demand for A as consumers switch). Tea and coffee.
Negative XED: the goods are complements (a rise in B's price lowers demand for A as they are consumed together). Cars and petrol.
XED near zero: the goods are unrelated.

The magnitude measures how strong the relationship is: a large positive XED means close substitutes; a large negative XED means strong complements.

Worked example

A supermarket finds that when the price of branded coffee rises by $20\%$ , sales of its own-label coffee rise by $30\%$ , and when average incomes rise by $4\%$ , sales of its premium ready-meals rise by $8\%$ . Classify the relationships.

Step 1: Compute XED for the two coffees

$XED = \dfrac{+30\%}{+20\%} = +1.5$ . The sign is positive, so own-label and branded coffee are substitutes.

Step 2: Interpret the XED magnitude

The value $1.5$ is well above zero, indicating fairly close substitutes: a rise in the branded price drives a more than proportionate switch to own-label. The supermarket can expect own-label sales to gain whenever branded prices rise.

Step 3: Compute YED for the ready-meals

$YED = \dfrac{+8\%}{+4\%} = +2$ . The sign is positive, so premium ready-meals are a normal good.

Step 4: Interpret the YED magnitude

The value $2 > 1$ means the meals are income elastic, a luxury: demand rises more than proportionately with income. The supermarket should expect strong growth in premium-meal sales as incomes rise, and a sharper fall if incomes drop.

Examples in context

Example 1. Forecasting demand as Singapore grows. As incomes rise, demand for income-elastic luxuries such as overseas travel, dining out and premium goods grows faster than income, while demand for inferior goods (some basic staples or budget substitutes) falls. Firms use YED to forecast which product lines will expand with rising prosperity, and governments use it to anticipate shifts in consumption patterns.

Example 2. Pricing related products. A firm selling printers and ink uses XED: printers and ink are complements (negative XED), so a low printer price boosts ink demand. A firm facing close substitutes (a high positive XED with a rival) knows it has little pricing power, because a price rise sends customers to the competitor.

Try this

Q1. Income rises 10 percent and demand for a good falls 5 percent. Calculate YED and classify the good. [2 marks]

Cue. $YED = \dfrac{-5\%}{+10\%} = -0.5$ ; the negative sign means it is an inferior good.

Q2. Explain why two goods with a strongly negative XED are complements. [2 marks]

Cue. A negative XED means a rise in one good's price reduces demand for the other; this happens when goods are used together, so they are complements, and a large magnitude means a strong link.

Q3. Distinguish a necessity from a luxury using YED. [3 marks]

Cue. Both have positive YED (normal goods), but a necessity is income inelastic ( $0 < YED < 1$ , demand rises less than proportionately), while a luxury is income elastic ( $YED > 1$ , demand rises more than proportionately).

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original6 marksWhen incomes rise by

5\%

, demand for a good rises by

15\%

. Calculate the income elasticity of demand and classify the good.

Show worked answer →

A 6 mark calculation rewards the formula, the value, and the classification.

Formula: $YED = \dfrac{\%\,\Delta\,\text{quantity demanded}}{\%\,\Delta\,\text{income}}$ .
Value: $YED = \dfrac{+15\%}{+5\%} = +3$ .
Classification: $YED$ is positive, so the good is normal; because it exceeds $1$ , demand is income elastic, which means it is a luxury (superior) good: demand rises more than proportionately with income.

Markers reward the correct formula, the value $+3$ , and the classification as a normal, income-elastic luxury good.

Original8 marksExplain, with examples, how cross elasticity of demand distinguishes substitutes from complements, and why its magnitude matters.