Price, income and cross elasticities of demand

CIE A-Level Economics· 35 min read

1. Price Elasticity of Demand (PED)★★☆☆☆⏱ 15 min

📘 Definition

Price Elasticity of Demand

$P E D = \frac{%Δ Q _{d}}{%Δ P}$

Measures the responsiveness of quantity demanded of a good to a change in its own price, holding all other factors constant (ceteris paribus). The negative sign reflects the inverse relationship between price and quantity demanded per the law of demand.

Example:

A 10% fall in price leading to a 20% rise in quantity demanded gives $P E D = - 2$ .

📐 Worked Example

The price of bread rises from $2.00 per loaf to $2.30 per loaf. Weekly quantity demanded falls from 500 loaves to 425 loaves. Calculate PED using the simple percentage method.

1
1. Calculate percentage change in price:
2
$%\Delta P = \frac{(2.30 - 2.00)}{2.00} \times 100 = +15\%$
3
1. Calculate percentage change in quantity demanded:
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$%\Delta Q_d = \frac{(425 - 500)}{500} \times 100 = -15\%$
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1. Apply the PED formula:
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$PED = \frac{-15\%}{+15\%} = -1$
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The value of PED = -1, so demand is unit elastic.

2. Income Elasticity of Demand (YED)★★★☆☆⏱ 20 min

📘 Definition

Income Elasticity of Demand

$Y E D = \frac{%Δ Q _{d}}{%Δ Y}$ , where $Y$ = consumer income

Measures the responsiveness of quantity demanded of a good to a change in consumer income, ceteris paribus. The sign tells us if the good is normal or inferior.

Example:

A 5% rise in income leading to a 10% rise in quantity demanded of restaurant meals gives $Y E D = + 2$ .

📐 Worked Example

Average consumer incomes rise by 10% in a year. Quantity demanded for public transport falls by 3%. Calculate YED and classify the good.

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1. Identify the given values: ,
2
1. Apply the YED formula:
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$YED = \frac{-3\%}{+10\%} = -0.3$
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1. Classify the good:
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Negative YED means public transport is an inferior good. The absolute value of $0.3 < 1$ , so demand is income inelastic.

$Y E D > 0$ : Normal good (Qd rises as income rises)
$Y E D > 1$ : Normal good, income elastic (luxury good)
$0 < Y E D < 1$ : Normal good, income inelastic (necessity)
$Y E D < 0$ : Inferior good (Qd falls as income rises)

3. Cross Elasticity of Demand (XED) and Applications★★★☆☆⏱ 20 min

📘 Definition

Cross Elasticity of Demand

$X E D = \frac{%Δ Q _{d, X}}{%Δ P _{Y}}$ , for goods $X$ and $Y$

Measures the responsiveness of quantity demanded of good X to a change in the price of good Y, ceteris paribus. The sign tells us if the goods are substitutes or complements.

Example:

A 10% rise in the price of tea leading to a 5% rise in quantity demanded of coffee gives $X E D = + 0.5$ .

📐 Worked Example

When the price of printers falls by 20%, quantity demanded for ink cartridges rises by 30%. Calculate XED and state the relationship between the two goods.

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1. Identify values: (ink cartridges = X), (printers = Y)
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1. Apply the XED formula:
3
$XED = \frac{+30\%}{-20\%} = -1.5$
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1. Interpret the result:
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Negative XED means printers and ink cartridges are complements. The absolute value of $1.5 > 1$ means they are strong complements.

Elasticity values are used widely in business and policy: firms use PED to predict how price changes affect total revenue, use XED to predict the impact of competitor price changes, and governments use YED to plan infrastructure and tax policy. This topic makes up a core part of almost all microeconomics questions in CIE A-Level Economics.

4. Common Pitfalls

Wrong move:

Forgetting to include or use the sign of YED/XED when classifying goods/relationships

Why:

CIE mark schemes award specific marks for correct classification, which depends entirely on the sign of the elasticity

Correct move:

Always retain the sign through calculation and explicitly use it to classify the good or relationship

Wrong move:

Swapping the numerator and denominator in elasticity formulas

Why:

All demand elasticities measure responsiveness of quantity demanded to a change in another variable, so % change in quantity must always be the numerator

Correct move:

Memorise: %ΔQd is always on top for all demand elasticities

Wrong move:

Classifying a positive YED between 0 and 1 as a luxury good

Why:

Luxury goods are defined as income elastic, which requires YED greater than 1

Correct move:

Positive YED between 0 and 1 is a necessity (normal good), YED > 1 is a luxury good

Wrong move:

Claiming negative PED means demand is inelastic

Why:

The negative sign for PED only reflects the inverse relationship between price and quantity, it does not indicate elasticity

Correct move:

Judge PED elasticity by the absolute value: |PED| > 1 = elastic, |PED| < 1 = inelastic

5. Quick Reference Cheatsheet

Elasticity Type	Formula	Sign Meaning	Value Interpretation
PED	$\frac{%\Delta Q_d}{%\Delta P}$	Negative (law of demand)	\|PED\|>1 = elastic; \|PED\|<1 = inelastic
YED	$\frac{%\Delta Q_d}{%\Delta Y}$	Positive = normal; Negative = inferior	YED>1 = luxury; 0<YED<1 = necessity; YED<0 = inferior
XED	$\frac{%\Delta Q_X}{%\Delta P_Y}$	Positive = substitutes; Negative = complements	Larger absolute value = stronger relationship

6. Frequently Asked

Do I need to include the negative sign for PED?

Most CIE mark schemes accept both, but you should always include the sign unless the question explicitly asks for the absolute value. Examiners award marks for correct application of the formula, so retaining the sign shows you understand the inverse relationship between price and quantity.

What is the difference between a necessity and a luxury good in terms of YED?

Both are normal goods (positive YED). Necessities have income inelastic demand: $0 < Y E D < 1$ , meaning quantity demanded rises slower than income. Luxuries have income elastic demand: $Y E D > 1$ , meaning quantity demanded rises faster than income.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
Calculate YED and classify the good
2023 · 2
Compare XED for substitutes/complements
2021 · 3
Interpret three elasticity values in context

Going deeper

syllabusCIE 9708 Official SyllabusCheck section 2 for full topic requirements

What's Next

Elasticities of demand form the foundation of almost all applied microeconomic analysis in CIE A-Level Economics. The concepts you have mastered here will be used to analyse the impact of government policies like indirect taxes, subsidies, and price controls, as well as to evaluate firm pricing and output strategies. Next, you will explore the determinants of price elasticity of demand, which explains why PED varies between different goods, before moving on to study elasticity of supply. Mastery of calculations and interpretation here is essential for earning high marks in both multiple choice and longer answer questions, so practice with a range of values before moving forward.