What is income elasticity of demand?

$YED = \%\ change in quantity demanded\%\ change in income$

What is cross elasticity of demand?

$XED = \%\ change in quantity demanded of good A\%\ change in price of good B$

SingaporeEconomicsSyllabus dot point

How does demand respond to a change in income, or to a change in the price of another good?

Define income elasticity and cross elasticity of demand, calculate them, and interpret their signs

A clear O-Level answer on income and cross elasticity of demand. The two formulas, how the sign of YED shows a normal or inferior good, and how the sign of XED shows substitutes or complements.

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

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

Have a quick question? Jump to the Q&A page

Jump to a section

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

What this dot point is asking

The syllabus wants you to define income elasticity of demand and cross elasticity of demand, calculate each, and interpret their signs. The big idea is that demand responds not only to a good's own price (covered by PED) but also to changes in income and to changes in the prices of other goods, and the sign of these elasticities tells us what kind of good we are dealing with.

The answer

Income elasticity of demand

\text{YED} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}}

The sign of YED tells us the type of good:

Positive YED: the good is a normal good (demand rises as income rises). If YED is greater than $1$ , it is a luxury (income elastic); if between $0$ and $1$ , it is a necessity (income inelastic).
Negative YED: the good is an inferior good (demand falls as income rises), such as instant noodles.

Cross elasticity of demand

\text{XED} = \frac{\%\ \text{change in quantity demanded of good A}}{\%\ \text{change in price of good B}}

The sign of XED tells us the relationship between the two goods:

Positive XED: the goods are substitutes (a rise in the price of B raises demand for A, as buyers switch to A). Example: tea and coffee.
Negative XED: the goods are complements (a rise in the price of B lowers demand for A, because they are used together). Example: cars and petrol.
XED near zero: the goods are unrelated.

Why the sign matters most

For PED we mainly cared about the size. For YED and XED, the sign is the key piece of information, because it classifies the good (normal or inferior) or the relationship (substitutes or complements). The size then tells us how strong the effect is.

Worked example

A supermarket finds that when incomes rose by $10\%$ , demand for its budget own-brand rice fell by $4\%$ , while demand for premium rice rose by $15\%$ . Show how to classify each good using income elasticity.

Step 1: Calculate YED for the budget rice

$\text{YED} = \dfrac{-4\%}{+10\%} = -0.4$ . The sign is negative.

Step 2: Classify the budget rice

A negative YED means an inferior good: as incomes rose, consumers bought less budget rice and switched to better alternatives. This is typical of a basic, low-cost version of a product.

Step 3: Calculate YED for the premium rice

$\text{YED} = \dfrac{+15\%}{+10\%} = +1.5$ . The sign is positive and the value is above $1$ .

Step 4: Classify the premium rice

A positive YED means a normal good, and a value above $1$ means it is income elastic, behaving like a luxury: demand rose by a larger percentage than income. The supermarket would expect premium rice sales to grow fastest as incomes rise.

Examples in context

Example 1. Rising incomes in Singapore. As average incomes in Singapore have risen, demand for income-elastic goods such as overseas holidays and dining out has grown quickly (high positive YED), while demand for some inferior goods has fallen. Firms use YED to predict which products will grow as the economy gets richer.

Example 2. Substitutes in transport. Ride-hailing services and taxis are substitutes, so they have a positive XED: if taxi fares rise, demand for ride-hailing rises as commuters switch. A transport firm watching a rival's price change uses XED to predict the effect on its own demand.

Try this

Cue. State what a negative income elasticity of demand tells you about a good. It is an inferior good: demand falls as income rises, because consumers switch to preferred alternatives.
Cue. Two goods have a cross elasticity of demand of $-0.8$ . State the relationship and give an example. The negative sign means they are complements (used together), such as cars and petrol.
Cue. Explain why the sign of YED matters more than its size at O-Level. The sign classifies the good as normal (positive) or inferior (negative), which is the key information; the size only adds how strongly demand responds.

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.

Original4 marksConsumer incomes rise by

20\%

and the quantity of restaurant meals demanded rises by

30\%

. Calculate the income elasticity of demand and state what type of good restaurant meals are.

Show worked answer →

A 4 mark calculation rewards the formula, the value, and the correct classification.

Income elasticity of demand (YED): $\dfrac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}} = \dfrac{+30\%}{+20\%} = +1.5$ .

The value is positive, so restaurant meals are a normal good (demand rises with income). Because the value is greater than $1$ , they are also income elastic, which is typical of a luxury: demand rises by a larger percentage than income.

Markers reward the correct formula and value, the positive sign meaning a normal good, and the recognition that a value above $1$ indicates a luxury.

Original4 marksThe price of tea rises by

10\%

and the quantity of coffee demanded rises by

5\%

. Calculate the cross elasticity of demand and explain what it shows about the relationship between tea and coffee.

Show worked answer →

A 4 mark calculation rewards the formula, the value, and the correct interpretation of the sign.

Cross elasticity of demand (XED): $\dfrac{\%\ \text{change in quantity demanded of coffee}}{\%\ \text{change in price of tea}} = \dfrac{+5\%}{+10\%} = +0.5$ .

The value is positive, which shows that tea and coffee are substitutes: when tea becomes dearer, consumers switch to coffee, so the quantity of coffee demanded rises. A positive XED always indicates substitutes.

Markers reward the correct formula and value, and the explanation that a positive XED means the two goods are substitutes.