Elasticities

PED, YED & XED — formulae, calculations, interpretation and real-world applications

SPEC 1.3 • PRICE, INCOME & CROSS ELASTICITIES

What is Elasticity?

Elasticity is the core quantitative tool in Theme 1. It measures how responsive one variable is to a change in another. Every elasticity follows the same structure:

Core Concept

Elasticity = % change in dependent variable ÷ % change in independent variable

Three elasticities are tested heavily across Papers 1 and 3:

PED

Price Elasticity of Demand — how Qd responds to a change in the good's own price.

YED

Income Elasticity of Demand — how Qd responds to a change in consumer income.

XED

Cross Elasticity of Demand — how Qd of Good A responds to a change in the price of Good B.

PED — Formula & Definition

Exam Definition

Price elasticity of demand is the responsiveness of quantity demanded to a change in the price of that good.PED = % change in Quantity Demanded ÷ % change in Price

PED is always negative for normal goods — price and quantity demanded move in opposite directions (the Law of Demand). The exam uses the absolute value |PED| to classify elasticity.

ValueClassificationWhat it means

|PED| > 1Elastic demand% change in Qd > % change in P — consumers are sensitive to price

|PED| < 1Inelastic demand% change in Qd < % change in P — consumers are less sensitive

|PED| = 1Unit elastic% change in Qd = % change in P — proportional response

|PED| = 0Perfectly inelasticNo change in Qd — vertical demand curve

|PED| = ∞Perfectly elasticAny price rise → Qd falls to zero — horizontal curve

PED — Determinants (SPLAT)

Use the mnemonic SPLAT to remember what determines PED. These are AO3 analysis points in essays.

FactorMore Elastic When…More Inelastic When…

S ubstitutesMany close substitutes exist (e.g. Pepsi/Coke)Few substitutes (e.g. insulin)

P roportion of incomeHigh % of income spent (e.g. house)Small % of income (e.g. salt)

L uxury vs necessityLuxury good (e.g. foreign holiday)Necessity (e.g. petrol for commuters)

A ddiction / habitNo habit or dependencyAddictive goods (e.g. cigarettes)

T imeLong run — consumers find alternativesShort run — limited adjustment time

Exam Tip

Always link a determinant to a consequence: "Because petrol has few substitutes, PED is inelastic, so a price rise leads to a smaller than proportionate fall in Qd — meaning most of a tax can be passed on to consumers."

PED — Elastic vs Inelastic Diagrams

Diagram required for top marks in essay questions. The shape of the demand curve shows PED visually.

Examiner Alert

Never say "the demand curve is perfectly vertical/horizontal" without stating what that means. Always label axes (Price on Y, Quantity on X). Examiners deduct marks for unlabelled diagrams.

PED & Total Revenue — Key Application

The relationship between PED and Total Revenue (TR = P × Q) is one of the most frequently tested applications in the course.

PEDPrice RisePrice CutWhy?

Elastic (|PED| > 1)TR falls ↓TR rises ↑% fall in Q > % rise in P

Inelastic (|PED| < 1)TR rises ↑TR falls ↓% fall in Q < % rise in P

Unit elastic (|PED| = 1)TR unchangedTR unchanged% change in Q = % change in P

Real-World Chain

Petrol price rises→PED inelastic (few substitutes)→Qd falls less than proportionately→TR rises for producer→Government tax revenue rises

AO4 Evaluation

Apply PED to tax policy: "The government taxes petrol and tobacco specifically because they are PED inelastic — meaning tax revenue is maximised and demand is not substantially reduced." AO4: counter that if PED rises over time as alternatives emerge, tax revenue may fall in the long run.

PED — Worked Calculation

Always show all working — method marks are available even if the final answer is wrong.

Example

Price of a train ticket rises from £20 to £25. Quantity demanded falls from 5,000 to 4,000 journeys per week. Calculate PED.

Step-by-Step Solution

Step 1: % change in Price = (25 − 20) / 20 × 100 = +25%

Step 2: % change in Qd = (4000 − 5000) / 5000 × 100 = −20%

Step 3: PED = −20 ÷ +25 = −0.8

Step 4 — Interpret: |PED| = 0.8 < 1, so demand is inelastic. A 25% price rise leads to only a 20% fall in quantity demanded. Total revenue rises for the train operator.

Common Error

Students divide by the new price instead of the original. Always use the original value as the denominator when calculating % change.

YED — Income Elasticity of Demand

Exam Definition

Income elasticity of demand is the responsiveness of quantity demanded to a change in consumer income.YED = % change in Quantity Demanded ÷ % change in Income

Unlike PED, the sign of YED tells you what type of good it is:

YED ValueGood TypeExampleImplication

YED > 1Luxury goodSports cars, foreign holidaysDemand rises more than proportionately as income rises

0 < YED < 1Normal necessityBread, bus travelDemand rises as income rises, but less than proportionately

YED < 0Inferior goodValue-brand food, bus passesDemand falls as income rises — consumers switch to better alternatives

Exam Tip — Business Strategy

YED matters for business strategy: luxury goods (YED > 1) are more vulnerable during recessions. A firm should diversify its product range to include some YED < 1 necessities to stabilise revenue across the economic cycle.

YED — Worked Calculation

Example A — Normal Luxury

Average income rises by 10%. Demand for foreign holidays increases by 25%. Calculate and interpret YED.

Solution

YED = +25% ÷ +10% = +2.5

YED = +2.5 > 1 → Luxury good. Demand rises more than proportionately with income. This good is income-elastic.

Example B — Inferior Good

Average income rises by 8%. Demand for economy ready meals falls by 4%. Calculate and interpret YED.

Solution

YED = −4% ÷ +8% = −0.5

YED = −0.5 < 0 → Inferior good. As incomes rise, consumers switch away from economy brands to premium products. Demand falls as incomes rise.

XED — Cross Elasticity of Demand

Exam Definition

Cross elasticity of demand is the responsiveness of quantity demanded of Good A to a change in the price of Good B.XED = % change in Qd of Good A ÷ % change in Price of Good B

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

XED ValueRelationshipExampleWhy?

XED > 0SubstitutesPepsi & Coca-Cola; butter & margarineIf Price of B rises, consumers switch to A → Qd of A rises

XED < 0ComplementsCars & petrol; printers & ink cartridgesIf Price of B rises, Qd of B falls → Qd of A also falls

XED = 0Unrelated goodsBananas & trainersNo relationship in demand

Key Insight — Market Power

A higher positive XED means goods are closer substitutes — the firm has less pricing power. A very negative XED means the goods are strong complements — producers benefit from pricing one good cheaply (e.g. Gillette razors) to boost sales of the complementary good (razor blades).

XED — Worked Calculation

Example

Costa Coffee raises the price of a latte by 15%. Demand for Starbucks lattes rises by 9%. Calculate and interpret XED.

Solution

Step 1: XED (Starbucks w.r.t. Costa) = +9% ÷ +15% = +0.6

Step 2 — Interpret: XED = +0.6 > 0 → the goods are substitutes. A 15% rise in Costa's price leads to a 9% rise in demand for Starbucks. The relatively low value suggests the goods are imperfect substitutes — consumers don't fully switch, possibly due to brand loyalty or location differences.

AO4 Evaluation: The magnitude of XED matters. XED close to zero even between apparent substitutes suggests strong brand loyalty — meaning Costa has some pricing power despite competition.

Common Error

Students sometimes confuse which good goes in the numerator (the good whose demand we're measuring) vs the denominator (the good whose price changed). Qd of A ÷ Price of B — always write it out clearly.

Formula Card — All Three Elasticities

ElasticityFormulaSign RuleBusiness Use

PED%ΔQd ÷ %ΔPAlways negative (normal goods). |PED|>1 elastic, <1 inelasticPricing strategy, tax incidence, total revenue

YED%ΔQd ÷ %ΔIncome+>1: luxury; 0 to +1: necessity; negative: inferiorProduct positioning, recession planning

XED%ΔQd(A) ÷ %ΔP(B)Positive: substitutes; Negative: complements; Zero: unrelatedMarket definition, competitive strategy

Method Mark Reminder

In any 4-mark calculate question: (1) state the formula, (2) substitute values with working shown, (3) calculate the answer, (4) state the interpretation with the correct term. All four steps earn marks independently.

Good Classification Grid

Use this grid to classify goods and choose the correct elasticity interpretation instantly.

Good TypeYEDPED (typical)XED (w/ substitute)Examples

Normal Necessity0 to +1Inelastic (|PED| < 1)Low positiveBread, electricity, basic clothing

Normal Luxury> +1Elastic (|PED| > 1)VariesSports cars, foreign holidays, designer goods

Inferior GoodNegativeVariesHigh positive vs. superior substituteValue supermarket brands, bus passes, instant noodles

Substitute goodsDepends on typeDependsPositive XEDPepsi/Coke; butter/margarine; Aldi/Lidl

Complement goodsDepends on typeDependsNegative XEDCars/petrol; smartphones/data plans; coffee/milk

Examiner Alert

A common error: students assume luxury goods are always PED elastic and necessities always inelastic. This is usually true but not always — examiners reward nuance. Always justify your classification with a named determinant (e.g. "few substitutes", "high proportion of income").

Application: Tax Incidence & Elasticity

One of the most important applications of PED and PES (covered in Lesson 1.04) is tax incidence — who actually pays an indirect tax.

Government imposes tax

Supply shifts left

Price rises by less than full tax

Incidence split between consumer & producer

PED Rule for Tax Incidence

More inelastic demand → greater consumer burden. If |PED| is low (e.g. petrol, cigarettes), consumers bear most of the tax — the price they pay rises nearly by the full tax amount. If |PED| is high, producers absorb more of the tax to maintain sales volume.

AO4 Evaluation Toolkit

PED changes over time — inelastic in short run may become elastic in long run as substitutes emerge

Regressive impact: if inelastic goods are consumed by lower-income groups, taxes create inequality

Behavioural factors: PED may underestimate response if nudges or information campaigns change behaviour

Practice Question — 4 Marks

Data: When the price of avocados falls from £1.20 to £1.00, quantity demanded rises from 4,000 to 5,200 per week.

(a) Calculate the PED for avocados. Show all working. [2 marks]

(b) Using your answer, explain whether a supermarket should cut avocado prices to increase total revenue. [2 marks]

1

% change in Qd = (5200 − 4000) / 4000 × 100 = +30%

2

% change in P = (1.00 − 1.20) / 1.20 × 100 = −16.7%

3

PED = +30 ÷ −16.7 = −1.8 → |PED| = 1.8 > 1 → Elastic demand

4

Since demand is price elastic, a price cut increases total revenue — the % rise in Qd (30%) is larger than the % fall in price (16.7%), so TR = P × Q rises. Yes, the supermarket should cut prices.

Practice Question — 4 Marks

Data: When average household income rises by 5%, demand for organic food rises by 9%, while demand for value-brand pasta falls by 2%.

(a) Calculate and interpret the YED for organic food. [2 marks]

(b) Calculate and interpret the YED for value-brand pasta. [2 marks]

1

YED (organic food) = +9% ÷ +5% = +1.8 → YED > 1 → Luxury / income-elastic normal good. Demand rises more than proportionately with income.

2

YED (value pasta) = −2% ÷ +5% = −0.4 → YED < 0 → Inferior good. As incomes rise, consumers switch away from value brands to premium alternatives; demand falls.

AO4 Evaluation Toolkit — Elasticities

Use these points to push your essay answers into Level 3/4. Always tie evaluation back to the specific context given in the question.

1. Elasticity Changes Over Time

PED is usually more inelastic in the short run and more elastic in the long run, as consumers find alternatives. A policy or price change may have limited demand response immediately but larger effects later — long-run elasticity should inform government policy design.

2. Classification Depends on Consumer Group

The same good may be a luxury for low-income consumers (high YED) but a necessity for high-income consumers (low YED). Average elasticity figures can mask distributional effects — AO4 opportunity to discuss equity.

3. XED and Market Definition

Competition authorities use XED to define markets. A high positive XED between two products suggests they are in the same market — relevant to merger decisions. This directly links elasticity to competition policy.

4. Firms Can Shift PED

Through branding, advertising, and creating switching costs, firms can reduce PED (make demand more inelastic) — giving them greater pricing power. Apple is a textbook example: high brand loyalty → low PED → ability to charge premium prices.

Summary — Elasticities

Formula Quick Reference

ElasticityFormulaSign Means

PED%ΔQd ÷ %ΔPAlways −ve; |>1| elastic, |<1| inelastic

YED%ΔQd ÷ %ΔIncome+>1 luxury; 0–1 necessity; −ve inferior

XED%ΔQd(A) ÷ %ΔP(B)+ substitutes; − complements; 0 unrelated

PED — Total Revenue Rule

Elastic → price cut raises TR. Inelastic → price rise raises TR. Use for pricing strategy and tax incidence.

YED — Good Classification

+ve normal good. −ve inferior. >1 luxury. Matters for recession resilience and business positioning.

Exam Tip

In any calculation question: state formula → substitute with working → calculate → interpret with correct terminology. Each step earns marks independently. Never skip the interpretation step.