Calculate
Use percentage changes correctly to calculate PED, YED, XED and PES.
Elasticity
Elasticity measures how strongly demand or supply responds when an economic influence changes. This chapter develops four measures — PED, YED, XED and PES — and shows how firms and governments can use them in decision making.
Book-aligned notesClear worked examplesExplained figuresPESCalculations + interpretation
What this chapter prepares you to do
Classify
Distinguish elastic, inelastic, unitary, perfectly elastic and perfectly inelastic responses.
Interpret
Explain what the sign and size of an elasticity coefficient mean in context.
Apply
Use elasticity to analyse pricing, revenue, changing incomes, related goods and supply responsiveness.
Core exam skill: do not stop after calculating an elasticity. State what the value means for the good, market, firm or policy being discussed.
Chapter sections
3.1
Price elasticity of demand (PED)
Price elasticity of demandA measure of how sensitive quantity demanded is to a change in the price of a good or service.
PED =% change in quantity demanded÷% change in price
A normal demand curve slopes downwards, so price and quantity demanded move in opposite directions. PED is therefore normally negative. In many discussions economists focus on the absolute size of PED, but in calculations you should keep the negative sign unless instructed otherwise.
| PED value | Classification | Meaning |
|---|---|---|
| 0 | Perfectly inelastic | Quantity demanded does not respond to price. |
| Between 0 and −1 | Inelastic | Quantity demanded changes proportionately less than price. |
| −1 | Unitary elastic | Quantity demanded changes by the same percentage as price. |
| Less than −1 | Elastic | Quantity demanded changes proportionately more than price. |
| Approaches −∞ | Perfectly elastic | A tiny price rise would reduce quantity demanded to zero at the market price shown. |
Worked PED calculation
Example: price rises by 8% and quantity demanded falls by 20%.
PED = −20% ÷ 8% = −2.5.
Demand is price elastic because the absolute value is greater than 1: buyers respond proportionately more than the price change.
PED = −20% ÷ 8% = −2.5.
Demand is price elastic because the absolute value is greater than 1: buyers respond proportionately more than the price change.
Book calculation with pencils: When price falls from 40c to 35c, quantity demanded rises from 20 to 30. Quantity rises by 50% while price falls by 12.5%, so PED = 50 ÷ −12.5 = −4 (elastic). At a much lower price, a fall from 10c to 9c raises quantity from 80 to 82: PED = 2.5 ÷ −10 = −0.25 (inelastic). This shows why PED changes along a straight-line demand curve.
Exam warning: elasticity is a percentage concept. Do not divide the absolute change in quantity by the absolute change in price unless the question has first converted both to percentages.
PED varies along a straight-line demand curve
For a straight downward-sloping demand curve, demand is relatively elastic near the upper part, unit elastic at the midpoint and relatively inelastic near the lower part. This happens because elasticity depends on percentage changes, not simply on the slope of the line.
The price elasticity of demand varies along a straight line
Along a straight-line demand curve, demand is price elastic at the upper part of the curve, unit elastic at the midpoint and price inelastic at the lower part. This happens because elasticity is based on percentage changes, not simply on the slope of the line.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
PED and total revenue
Total revenue (TR) is price × quantity sold. Because the response of quantity demanded differs according to PED, the effect of a price change on revenue also differs.
| PED | If price rises | If price falls | Reason |
|---|---|---|---|
| Elastic | TR falls | TR rises | Quantity changes by a larger percentage than price. |
| Unit elastic | TR unchanged | TR unchanged | The percentage effects offset each other. |
| Inelastic | TR rises | TR falls | Quantity changes by a smaller percentage than price. |
Fast memory rule: with elastic demand, price and total revenue move in opposite directions. With inelastic demand, they move in the same direction.
Same pencil example, now for total revenue: At 40c and 20 pencils, total revenue is 800 cents. At 35c and 30 pencils, it rises to 1,050 cents because demand is elastic. At the lower-price end, revenue falls from 800 cents (10 × 80) to 738 cents (9 × 82) because demand is inelastic. This makes the PED–revenue relationship much easier to see.
Interpreting a real estimate used in the book: A study in Pakistan estimated the PED for household electricity at −0.63. This is inelastic. A 10% increase in electricity price would therefore be associated with an estimated 6.3% fall in quantity demanded, other things equal.
Factors affecting PED
Close substitutes
More and closer substitutes make switching easier, so demand tends to be more elastic.
Necessity or luxury
Necessities tend to be more inelastic; luxuries tend to be more elastic.
Share of expenditure
Goods taking a large share of income tend to attract a stronger response to price changes.
Time
Demand often becomes more elastic in the long run because consumers have more time to adjust.
Extreme cases
Perfectly elastic and inelastic demand
A vertical demand curve is perfectly inelastic: quantity demanded does not change when price changes, so PED is zero. A horizontal demand curve is perfectly elastic: at the stated price buyers will purchase the available quantity, but a price rise above that level causes demand to fall to zero.
Adapted from Cambridge International AS & A Level Economics, Second Edition, by Peter Smith (with Adam Wilby and Mila Zasheva).
3.2
Income elasticity of demand (YED)
Income elasticity of demandA measure of how sensitive quantity demanded is to a change in consumer income.
YED =% change in quantity demanded÷% change in consumer income
Unlike PED, YED can be positive or negative. The sign tells you whether a good is normal or inferior, while the size tells you how strongly demand responds to income.
| YED value | Classification | Interpretation |
|---|---|---|
| Below −1 | Elastic inferior good | Demand falls proportionately more than income rises. |
| Between −1 and 0 | Inelastic inferior good | Demand falls, but proportionately less than income rises. |
| 0 | No income relationship | Demand does not respond to income. |
| Between 0 and 1 | Inelastic normal good | Demand rises by a smaller percentage than income; often associated with necessities. |
| Above 1 | Elastic normal good | Demand rises proportionately more than income; often associated with luxury-type purchases. |
Book example 1: if incomes rise by 10% and demand for an economics magazine rises by 7%, YED = 7 ÷ 10 = +0.7. The magazine is a normal good and demand is income inelastic.
Book example 2: if the YED for coach travel is −0.3, a 10% rise in income would be associated with a 3% fall in demand. Coach travel is therefore an inferior good in this example.
Necessity goodA good for which demand changes relatively little as income changes. In the book, essentials such as food, water or essential medicines are used to illustrate goods that are likely to be income inelastic.
Interpret both parts: a YED of +1.4 does not merely mean “elastic”. It means demand is income elastic and the good is normal.
3.3
Cross elasticity of demand (XED)
Cross elasticity of demandA measure of how sensitive demand for one good is to a change in the price of another good.
XED =% change in quantity demanded of Good X÷% change in price of Good Y
XED is especially useful for identifying relationships between products. The sign indicates the type of relationship and the magnitude indicates its strength.
| XED | Relationship | What it means |
|---|---|---|
| Positive | Substitutes | A rise in the price of Y raises demand for X. A larger positive value suggests closer substitutes. |
| Negative | Complements | A rise in the price of Y reduces demand for X. A larger absolute negative value suggests a stronger complementary relationship. |
| Zero | Unrelated goods | A change in the price of Y has no measured effect on demand for X. |
Substitutes: if the price of Good Y rises by 10% and demand for Good X rises by 6%, XED = +0.6. The goods are substitutes.
Complements: if the price of Good Y rises by 20% and demand for Good X falls by 4%, XED = −0.2. The goods are complements.
Book examples: an XED of −0.087 for sugar with respect to the price of coffee indicates that coffee and sugar are weak complements: a 10% rise in coffee’s price would be associated with about a 0.87% fall in sugar demand. An XED of +0.532 between mangoes and pineapples indicates substitutes: a 10% change in the relevant other price would be associated with a 5.32% change in demand in the same direction.
Keep the goods straight: the numerator is the percentage change in quantity demanded of X; the denominator is the percentage change in the price of Y.
3.4
Price elasticity of supply (PES)
Price elasticity of supplyA measure of how sensitive quantity supplied is to a change in the price of the good or service.
PES =% change in quantity supplied÷% change in price
Because the basic supply curve slopes upwards, price and quantity supplied normally move in the same direction. PES is therefore normally positive.
| PES value | Classification | Meaning |
|---|---|---|
| 0 | Perfectly inelastic supply | The quantity available is fixed. |
| Between 0 and 1 | Inelastic supply | Quantity supplied changes proportionately less than price. |
| 1 | Unitary elastic supply | Quantity supplied changes by the same percentage as price. |
| Above 1 | Elastic supply | Quantity supplied changes proportionately more than price. |
| ∞ | Perfectly elastic supply | Firms are willing to supply any amount at the going price. |
Example: price rises by 20% and quantity supplied rises by 8%. PES = 8 ÷ 20 = 0.4. Supply is price inelastic.
Extreme PES example from the book: Imagine that only a fixed amount of fish is available in a market today and no more can be obtained, whatever the price. Supply is perfectly inelastic and the supply curve is vertical. If the fish cannot be stored, sellers may also be willing to sell the available amount even at a very low price because unsold fish may have little value tomorrow.
What determines PES?
Time period
Supply is usually more elastic in the long run because firms have more time to adjust plant, machinery and production plans.
Spare capacity
A firm near full capacity may find it difficult to raise output quickly, making short-run supply less elastic.
Access to inputs
Availability of labour, machinery and raw materials affects how easily production can expand.
Storage also matters in some markets. If a product is highly perishable, firms may have little ability to hold it back or increase available supply immediately, making short-run supply less responsive.
Key distinction: a flatter or steeper curve may help visualise responsiveness, but elasticity is defined by percentage changes. Always support diagram language with the elasticity concept.
3.5
Usefulness and significance of elasticities
Elasticity measures help economic decision-makers estimate how buyers and sellers may react when market conditions change. Their value lies in turning a qualitative idea — “demand may change” — into a measure of expected responsiveness.
| Measure | Useful to firms | Useful to government / policy |
|---|---|---|
| PED | Helps assess how a price change may affect sales and total revenue. | Helps estimate how demand and possible tax revenue may respond to indirect taxes or price-changing policies. |
| YED | Helps forecast demand during economic growth or recession and identify whether a product is normal or inferior. | Can help anticipate how changing household incomes may alter spending patterns. |
| XED | Helps identify close competitors, substitutes and complementary products when setting strategy. | Can help assess wider effects when policy changes the price of one product that is linked to others. |
| PES | Shows how easily output can be expanded when market prices rise. | Helps judge whether producers can respond quickly to incentives intended to increase supply. |
Integrated decision example: The book asks you to think like a bus company facing a recession while rail fares are rising. The information given is PED −1.58, YED −2.43, XED with rail fares +2.21 and PES +1.15. A strong answer does not treat the numbers separately: recession can raise demand for an inferior service, higher rail fares can also raise bus demand because the modes are substitutes, and elastic PED means any price change has an important effect on revenue. The exercise is designed to show why several elasticity measures may matter at the same time.
Limits of elasticity estimates
- Reliable numerical estimates may be difficult and costly to obtain.
- Elasticity can change over time as preferences, technology, competitors and incomes change.
- PED may vary along a demand curve, so one estimate should not automatically be applied to every possible price change.
- Elasticity is most useful when interpreted with the specific market circumstances rather than used as an isolated number.
1. CalculateFind the elasticity using percentage changes.
→2. ClassifyUse the sign and magnitude correctly.
→3. ApplyExplain the effect on revenue, demand, competition, policy or supply.
High-mark habit: after giving the coefficient, write one contextual interpretation. Example: “YED = −1.3, so the product is an income-elastic inferior good; if real incomes rise, demand is expected to fall proportionately more than the income increase.”
Chapter 3 revision checklist
Define elasticity as responsiveness or sensitivity.
State and use the PED formula.
Explain why PED is normally negative.
Classify elastic, inelastic and unitary PED.
Recognise perfectly elastic and perfectly inelastic demand.
Explain why PED varies along a straight-line demand curve.
Calculate and interpret PED values.
Explain the relationship between PED and total revenue.
Explain the four main factors affecting PED.
State and use the YED formula.
Use YED to distinguish normal and inferior goods.
Distinguish income-elastic and income-inelastic goods.
State and use the XED formula.
Use XED to identify substitutes, complements and unrelated goods.
Interpret the magnitude of XED.
State and use the PES formula.
Classify elastic, inelastic, unitary and extreme PES values.
Explain why PES is normally positive.
Explain why supply tends to be more elastic in the long run.
Evaluate how firms and governments can use elasticity estimates.
20 questions. Each answer is marked immediately with a short explanation of why it is correct or incorrect.