Quantitative Skills Masterclass
MODULE 0 • EXAM FOUNDATIONS
Every required calculation — formulae, method, worked examples & interpretation rules. 20% of all exam marks are quantitative.
Why Quantitative Skills Win Marks
At least 20% of all marks on Edexcel 9EC0 require mathematical or quantitative skills. These appear in every paper — and they are among the most reliable marks available if you learn the method.
The Golden Rule
Always: (1) State the formula, (2) Substitute values, (3) Calculate, (4) Interpret the result. Method marks are available at every stage — you can still score 3/4 with an arithmetic error if your method is clear.
Calculations Required
% change
PED, YED, XED
PES
Total Revenue
Multiplier
Real values / index numbers
Terms of Trade
GDP per capita
Where They Appear
Paper 1 Section A (MCQ data)
Paper 2 Section A (MCQ data)
Short-answer (c) parts — 2–4 marks
Essay KAA application — 2–3 marks
Data Response context questions
Exam Tip
A 2-mark calculation question requires: formula + correct answer. A 4-mark question requires: formula + substitution + calculation + interpretation. Never skip steps.
% Change — The Foundation Skill
Every elasticity calculation depends on percentage changes. Get this right first.
Formula
% Change = ((New Value − Old Value) ÷ Old Value) × 100
Examiner Alert — #1 Error
Students divide by the new value instead of the old value. Always use the original/base value as the denominator. If price rises from £10 to £12, the denominator is £10, not £12.
Worked Example
1Price rises from £40 to £50. Calculate the % change in price.2% change = (50 − 40) ÷ 40 × 100 = +25%3Quantity demanded falls from 200 to 160. % change = (160 − 200) ÷ 200 × 100 = −20%
Exam Tip
Always state the sign (+ or −). A fall in Qd is negative. A rise in Qd is positive. This matters for interpreting elasticity signs correctly.
Price Elasticity of Demand (PED)
Definition & Formula
The responsiveness of quantity demanded to a change in price.PED = % change in Quantity Demanded ÷ % change in Price
Interpretation rules — always state these after calculating:
PED < −1
Elastic — a 1% rise in price causes >1% fall in Qd. TR falls if P rises.
−1 < PED < 0
Inelastic — a 1% rise in price causes <1% fall in Qd. TR rises if P rises.
PED = −1
Unit elastic — % change in Qd exactly equals % change in P. TR unchanged.
Examiner Alert
PED is always negative for a normal good (inverse P/Qd relationship). Do not write PED = +1.5. Examiners report that students omit the negative sign regularly — this costs a mark on interpretation.
Total Revenue Rule
TR = P × Q. If elastic: ↑P → ↓TR. If inelastic: ↑P → ↑TR. This is the most-tested PED application in essays.
PED — Worked Calculation
Question: The price of a train ticket rises from £20 to £25. As a result, daily passenger numbers fall from 4,000 to 3,200. Calculate PED and interpret the result.
1
State the formula: PED = % change in Qd ÷ % change in P
2
Calculate % change in Qd: (3,200 − 4,000) ÷ 4,000 × 100 = −800 ÷ 4,000 × 100 = −20%
3
Calculate % change in P: (25 − 20) ÷ 20 × 100 = 5 ÷ 20 × 100 = +25%
4
Calculate PED: −20 ÷ 25 = PED = −0.8
5
Interpret: PED = −0.8, so demand is price inelastic. A 1% rise in price causes only a 0.8% fall in Qd. Train operators' total revenue will increase when they raise fares.
Method Marks Available
Even if you miscompute the final figure, you earn marks for correctly stating the formula and showing correct % change calculations.
Income Elasticity of Demand (YED)
Definition & Formula
The responsiveness of quantity demanded to a change in consumer income.YED = % change in Quantity Demanded ÷ % change in Income
Interpretation — sign AND magnitude both matter:
YED > 1
Luxury good — demand rises proportionally more than income (e.g. foreign holidays, sports cars)
0 < YED < 1
Normal necessity — demand rises, but less than proportionally (e.g. food, clothing)
YED < 0
Inferior good — demand falls as income rises (e.g. value brands, bus travel)
Worked Example
Income rises by 10%. Demand for restaurant meals rises from 500 to 560 per week.
% change in Qd = (560 − 500) ÷ 500 × 100 = +12%
YED = +12 ÷ +10 = +1.2 → Luxury good
Examiner Alert
Students confuse YED = negative with PED = negative. PED is always negative (normal goods). YED can be positive or negative — the sign tells you normal vs inferior. The examiner specifically rewards correct identification of good type.
Cross Elasticity of Demand (XED)
Definition & Formula
The responsiveness of the 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
XED > 0 → Substitutes
When P(B) rises, consumers switch to A — Qd(A) rises. E.g. Coca-Cola and Pepsi. Higher XED = closer substitutes = more competitive market.
XED < 0 → Complements
When P(B) rises, demand for A falls too — goods used together. E.g. petrol and cars. Negative XED = complementary relationship.
Worked Example
Price of Uber rises by 15%. Demand for black taxis rises from 800 to 920 rides/day.
% change in Qd(taxis) = (920 − 800) ÷ 800 × 100 = +15%
XED = +15 ÷ +15 = +1.0 → Close substitutes
Exam Application
XED is tested in business strategy (pricing power, market definition) and in competition policy (defining the relevant market). Examiners reward linking XED magnitude to the degree of competition.
Price Elasticity of Supply (PES)
Definition & Formula
The responsiveness of quantity supplied to a change in price.PES = % change in Quantity Supplied ÷ % change in Price
PES is always positive (positive relationship between P and Qs).
PES > 1
Elastic supply — firms can respond quickly to price changes. Time, spare capacity, stock available.
0 < PES < 1
Inelastic supply — limited ability to increase output. E.g. agricultural goods, skilled labour.
PES = 0
Perfectly inelastic — vertical supply curve. Fixed supply regardless of price (e.g. land, Picasso paintings).
Tax Incidence Application
If PES is elastic and PED is inelastic → more tax falls on consumer. If PES is inelastic and PED is elastic → more tax falls on producer. Chain: relative elasticities → tax burden distribution.
Examiner Alert
Students state PES is negative. It is always positive. Confusing PES sign with PED sign is one of the most common errors in elasticity questions.
The Keynesian Multiplier
Definition & Formulae
The ratio of the final change in national income to the initial injection into the circular flow.Multiplier = 1 ÷ (1 − MPC) or Multiplier = 1 ÷ MPWwhere MPW = MPS + MPT + MPM | MPC + MPW = 1ΔY = Multiplier × Initial Injection
Variables
MPC — marginal propensity to consume
MPS — marginal propensity to save
MPT — marginal propensity to tax
MPM — marginal propensity to import
Key Relationships
Higher MPC → larger multiplier
Higher MPM (open economy) → smaller multiplier
MPC + MPS + MPT + MPM = 1
Worked Example
MPC = 0.8. The government increases spending by £5bn. Calculate the multiplier and ΔY.
Multiplier = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5
ΔY = 5 × £5bn = £25bn
Multiplier — Leakages Method
Exam questions often give you MPS, MPT, MPM rather than MPC. Use the leakages formula:
Leakages Formula
Multiplier = 1 ÷ (MPS + MPT + MPM)
Worked Example — Leakages
1Given: MPS = 0.1, MPT = 0.2, MPM = 0.152MPW = 0.1 + 0.2 + 0.15 = 0.453Multiplier = 1 ÷ 0.45 = ≈ 2.224If initial injection = £10bn: ΔY = 2.22 × £10bn = £22.2bn
Examiner Alert
Students forget MPM when calculating MPW. In an open economy, imports are a major leakage. The UK has a high MPM — this is why the UK multiplier is relatively small. Always include all three leakages (MPS + MPT + MPM).
Real Values & Index Numbers
Nominal values are distorted by inflation. Real values allow meaningful comparison over time.
Formulae
Real Value = (Nominal Value ÷ Price Index) × 100Index Number = (Value in current year ÷ Value in base year) × 100
Real Value — Example
Nominal GDP = £2,400bn. Price index = 120.
Real GDP = (2,400 ÷ 120) × 100 = £2,000bn
Index Number — Example
Wages in 2020 = £500/week. Wages in 2024 = £575/week. Base year = 2020.
Index = (575 ÷ 500) × 100 = 115
Wages are 15% higher in real index terms.
Examiner Alert
When comparing wages or GDP across years, you must deflate by the price index to get real values. Stating that "incomes rose from £30,000 to £33,000" does not mean real incomes rose — inflation may have eroded purchasing power. Examiners reward this caveat.
Terms of Trade (ToT)
Definition & Formula
The ratio of a country's export prices to its import prices, expressed as an index.ToT = (Export Price Index ÷ Import Price Index) × 100
ToT > 100
Favourable — each unit of exports buys more than one unit of imports. Standard of living tends to improve (more imports per unit exported).
ToT < 100
Unfavourable — exports worth less relative to imports. A country must export more to afford the same quantity of imports.
Worked Example
Export price index = 115. Import price index = 110.
ToT = (115 ÷ 110) × 100 = 104.5
Interpretation: Terms of trade are favourable (above 100) — each unit of exports buys more imports than in the base year. This suggests an improvement in the country's trading position.
Exam Application
ToT is tested in Theme 4 (Global Economy). A currency appreciation typically improves ToT (exports become more expensive → higher export prices) but may harm export competitiveness. This is a classic evaluation trade-off.
GDP Per Capita & Other Index Calculations
GDP Per Capita Formula
GDP per capita = GDP ÷ Population
Worked Example
Country A: GDP = £2.4 trillion. Population = 60 million.
GDP per capita = £2,400,000m ÷ 60,000,000 = £40,000 per person
Examiner Alert — Limitations
GDP per capita does not capture: (1) distribution of income — Gini coefficient is needed, (2) non-market activity, (3) negative externalities, (4) quality of life. Always evaluate GDP per capita as a measure of living standards by referencing at least one limitation.
Concentration Ratio
Sum of market shares of the n largest firms. 5-firm CR > 80% = highly concentrated oligopoly.
Gini Coefficient
Area between Lorenz curve and equality line ÷ total area. 0 = perfect equality. 1 = perfect inequality. UK ≈ 0.35.
Complete Formula Reference Card
CalculationFormulaKey Interpretation
% Change((New−Old)÷Old)×100Always use original value as denominator
PED%ΔQd ÷ %ΔPAlways negative; |PED|>1 elastic; TR inverse of P if elastic
YED%ΔQd ÷ %ΔIncome+ve = normal; >1 = luxury; −ve = inferior
XED%ΔQd(A) ÷ %ΔP(B)+ve = substitutes; −ve = complements
PES%ΔQs ÷ %ΔPAlways positive; >1 elastic; 0 = perfectly inelastic
Multiplier1÷(1−MPC) or 1÷MPWΔY = Multiplier × Injection
Real Value(Nominal ÷ Price Index)×100Removes effect of inflation
Terms of Trade(XPI ÷ MPI)×100>100 = favourable; improving = each export buys more imports
GDP per capitaGDP ÷ PopulationAverage standard of living; ignores distribution
Total RevenueTR = P × QUse with PED to assess impact of price change
Practice Question 1 — PED & Revenue
A cinema currently charges £10 per ticket and sells 2,000 tickets per week. It raises the price to £12, and weekly ticket sales fall to 1,700.
(a) Calculate the price elasticity of demand. Show all working. [3 marks]
(b) Calculate the change in total revenue resulting from the price increase. [2 marks]
(c) Using your PED result, explain whether your TR calculation is consistent with elasticity theory. [2 marks]
(a)
% change in Qd: (1,700 − 2,000) ÷ 2,000 × 100 = −300 ÷ 2,000 × 100 = −15%
•
% change in P: (12 − 10) ÷ 10 × 100 = +20%
•
PED = −15 ÷ 20 = −0.75 (price inelastic)
(b)
TR before: £10 × 2,000 = £20,000. TR after: £12 × 1,700 = £20,400. Change in TR = +£400
(c)
Consistent — PED = −0.75, which is inelastic (|PED| < 1). When demand is price inelastic, a price rise increases total revenue, because the percentage fall in Qd is smaller than the percentage rise in price. This is confirmed: TR rose from £20,000 to £20,400.
Practice Question 2 — Multiplier
In Country X: MPS = 0.05, MPT = 0.25, MPM = 0.20. The government announces a fiscal stimulus of £8bn in infrastructure spending.
(a) Calculate the value of the multiplier. [2 marks]
(b) Calculate the predicted change in national income. [1 mark]
(c) Explain one reason why the actual change in national income may be lower than predicted. [2 marks]
(a)
MPW = MPS + MPT + MPM = 0.05 + 0.25 + 0.20 = 0.50
•
Multiplier = 1 ÷ 0.50 = 2
(b)
ΔY = 2 × £8bn = £16bn
(c)
The multiplier assumes constant leakages, but if households save a higher proportion of their additional income (↑MPS), or if more of the extra income is spent on imports (↑MPM), the actual increase in national income will be smaller than the model predicts. Time lags also mean the full multiplier effect may not be realised within the policy period.
Practice Question 3 — Real Values & ToT
Country Y's nominal GDP rose from £1,600bn in 2020 to £1,920bn in 2024. The GDP deflator was 100 in 2020 and 128 in 2024.
(a) Calculate real GDP in 2020 and 2024. [2 marks]
(b) Has real GDP actually increased? By how much? [2 marks]
Country Y's export price index is 110 and import price index is 115.
(c) Calculate the Terms of Trade and state whether they are favourable or unfavourable. [2 marks]
(a)
Real GDP 2020 = (1,600 ÷ 100) × 100 = £1,600bn (base year, same as nominal)
•
Real GDP 2024 = (1,920 ÷ 128) × 100 = £1,500bn
(b)
Real GDP has actually decreased from £1,600bn to £1,500bn — a fall of £100bn. Although nominal GDP rose by £320bn, this was entirely due to inflation (price level rose by 28%). Real output fell.
(c)
ToT = (110 ÷ 115) × 100 = 95.7. This is below 100, so the Terms of Trade are unfavourable — Country Y must export more than one unit to afford one unit of imports.
Top Examiner Errors — Quantitative Questions
CalculationCommon Student ErrorCorrect Approach
% ChangeDividing by new valueAlways divide by original/base value
PEDGiving positive value (e.g. PED = +0.8)PED is always negative for normal goods
PESGiving negative valuePES is always positive
YEDNot stating whether good is normal/inferior/luxuryAlways interpret the sign AND magnitude
MultiplierForgetting MPM in MPW calculationMPW = MPS + MPT + MPM
Real valuesStating nominal increase = real increaseDeflate by price index: (Nominal ÷ PI) × 100
Terms of TradeNot stating whether favourable/unfavourable>100 = favourable; always interpret relative to 100
All calculationsNo formula stated, jumping to answerState formula → substitute → calculate → interpret
Summary — Quantitative Skills Masterclass
Key Formulae (Memorise Word-for-Word)
FormulaOne-line Rule
PED = %ΔQd ÷ %ΔPAlways negative; elastic if |PED|>1 → TR falls when P rises
YED = %ΔQd ÷ %ΔY+ve = normal; >1 = luxury; −ve = inferior
XED = %ΔQd(A) ÷ %ΔP(B)+ve = substitutes; −ve = complements
PES = %ΔQs ÷ %ΔPAlways positive; >1 elastic
Multiplier = 1÷(1−MPC)Higher MPC / lower MPW → larger multiplier
Real value = (Nominal ÷ PI)×100Remove inflation to compare across time
ToT = (XPI÷MPI)×100>100 = favourable
4-Step Method
1. State formula → 2. Substitute values → 3. Calculate → 4. Interpret result. Never skip step 4 — interpretation earns the final mark.
20% of All Marks
Quantitative skills are the most reliably learnable marks on the paper. Master the method and you guarantee marks even if you make a small arithmetic error.
Final Exam Tip
In essays: use calculations to support KAA. Quote PED values when analysing tax incidence. Quote multiplier values when assessing fiscal policy effectiveness. A calculation embedded in analysis scores AO2 + AO3 simultaneously.
Next: Why Quantitative Skills Win Marks