1.2.3 Price, Income & Cross Elasticities of Demand
Edexcel A-Level Economics (9EC0) | Theme 1.2.3
Specification Coverage: This topic requires
students to understand, calculate, and interpret PED, YED, and XED
values. Students should be able to analyse how these elasticities
influence firm revenue and government policy decisions, using
real-world examples.
Price Elasticity of Demand (PED)
Definition: Measures the responsiveness of quantity demanded (\(Q_D\)) to a change in price (\(P\)), calculated as:
\[ \text{PED} = \frac{\%\Delta Q_D}{\%\Delta P} \]
Calculation Protocol: Always use the
midpoint method for accuracy: \[ \%\Delta =
\frac{\text{New} - \text{Old}}{(\text{New} + \text{Old})/2}
\times 100 \]
Worked Example
| Scenario: | Price \(\uparrow\) £10 → £15 | \(Q_D\) \(\downarrow\) 100 → 40 units |
| Step 1: \(\%\Delta Q_D\) | \(\frac{40-100}{(40+100)/2} \times 100 = \mathbf{-85.7\%}\) |
| Step 2: \(\%\Delta P\) | \(\frac{15-10}{(15+10)/2} \times 100 = \mathbf{+40\%}\) |
| Step 3: PED | \(\frac{-85.7}{40} = \mathbf{-2.14}\) (Elastic) |
Real-World Application: Netflix's 2022 price
hike resulted in only 3% subscriber loss (\(\text{PED} =
-0.27\)).
PED Classification Spectrum
| Value Range | Elasticity Type | Characteristics | Examples |
|---|---|---|---|
| \(\text{PED} = 0\) | Perfectly Inelastic | \(Q_D\) unchanged by price | Insulin |
| \(0 < |\text{PED}| < 1\) | Relatively Inelastic | \(\%\Delta Q_D < \%\Delta P\) | Petrol (0.4) |
| \(|\text{PED}| = 1\) | Unitary Elastic | \(\%\Delta Q_D = \%\Delta P\) | Theoretical benchmark |
| \(1 < |\text{PED}| < \infty\) | Relatively Elastic | \(\%\Delta Q_D > \%\Delta P\) | Restaurant meals (2.3), Foreign holidays (3.8) |
| \(\text{PED} = \infty\) | Perfectly Elastic | Infinite \(Q_D\) response | Agricultural commodities at fixed prices |
Critical Determinants of PED
- Substitutability: More substitutes → Higher \(|\text{PED}|\) (e.g., Coca-Cola vs generic cola)
- Necessity vs Luxury: Essentials tend to be inelastic (bread: 0.2) vs luxuries elastic (designer handbags: 4.1)
- Time Lag: Short-run PED for petrol: 0.2 | Long-run: 0.7 (find alternatives)
- Proportion of Income: Big-ticket items (cars: 1.2) vs small purchases (salt: 0.1)
Income Elasticity of Demand (YED)
Definition: Measures how \(Q_D\) responds to changes in consumer income (\(Y\)):
\[ \text{YED} = \frac{\%\Delta Q_D}{\%\Delta Y} \]
YED Typology
| YED Range | Good Classification | Economic Implications |
|---|---|---|
| \(\text{YED} < 0\) | Inferior Goods | Demand \(\downarrow\) as income \(\uparrow\) (Bus travel: -0.4) |
| \(0 < \text{YED} < 1\) | Normal Necessities | Demand \(\uparrow\) proportionally less than income \(\uparrow\) (Food: 0.3) |
| \(\text{YED} > 1\) | Normal Luxuries | Demand \(\uparrow\) proportionally more than income \(\uparrow\) (Sports cars: 2.5) |
Business Strategy Insight: During the 2020
pandemic, Lidl reported 12% sales growth as YED data showed
consumers switching from Waitrose (\(\text{YED}: 1.2\)) to
discounters (\(\text{YED}: -0.3\)) during income shocks.
Cross Elasticity of Demand (XED)
Definition: Measures responsiveness of \(Q_D\) for Good A to price changes in Good B:
\[ \text{XED} = \frac{\%\Delta Q_{D_A}}{\%\Delta P_B} \]
XED Interpretation Guide
| XED Value | Relationship | Real-World Example |
|---|---|---|
| \(\text{XED} < 0\) | Complements | PlayStation consoles (-1.8) & games |
| \(\text{XED} = 0\) | Unrelated | Butter (0.02) & mobile phones |
| \(\text{XED} > 0\) | Substitutes | Coca-Cola (+0.8) & Pepsi |
Evaluation Tip: The
magnitude matters as much as the sign. XED of
-0.2 suggests weak complements, while -2.5 indicates strong
complements. Always contextualize the value.
Strategic Applications
Firm-Level Decisions
Pricing Strategy
- Inelastic goods: Price \(\uparrow\) → Revenue \(\uparrow\) (Pharmaceuticals)
- Elastic goods: Price \(\downarrow\) → Revenue \(\uparrow\) (Airline seats)
Product Portfolio
- Balance inferior (\(\text{YED} < 0\)) & normal goods (\(\text{YED} > 0\)) for economic cycles
- Bundle strong complements (\(\text{XED} < -1\)) to increase sales
Government Policy
| Objective | Tool | Elasticity Consideration |
|---|---|---|
| Reduce smoking | Excise tax | \(\text{PED} = -0.4\) → 10% price \(\uparrow\) → 4% \(Q_D\) \(\downarrow\) |
| Encourage renewables | Subsidies | Solar panels: \(\text{PED} = -1.8\) → 10% price \(\downarrow\) → 18% \(Q_D\) \(\uparrow\) |
Exam Preparation Toolkit
Recent Exam Questions:
- "Evaluate the view that knowledge of price elasticity of demand is more important to a firm than income elasticity of demand" (Edexcel 2023, 25 marks)
- "Using cross elasticity of demand, analyse how an increase in the price of electric vehicles might affect the market for charging stations" (Edexcel 2022, 15 marks)
- "Discuss the significance of elasticity coefficients for government tax revenue" (Edexcel 2021, 20 marks)
Advanced Analysis Structure
| Evaluation Angle | PED | YED | XED |
|---|---|---|---|
| Time Horizon | SR vs LR elasticity differences | Cyclical demand patterns | Changing substitution possibilities |
| Market Structure | Monopoly vs competitive markets | Luxury brand positioning | Complementary goods ecosystems |
Examiner's Report Insight: In 2023, 68% of
students could calculate elasticities correctly, but only 32%
effectively applied them to business scenarios. Top scripts
referenced Tesla's price cuts (\(\text{PED} = -1.9\)) and the
Netflix/Disney+ substitution effect (\(\text{XED} = +0.6\)).