Price Elasticity of Demand (PED)
1. Definition (Cambridge wording)
Price elasticity of demand measures how the quantity demanded of a good responds to a change in its price. In the IGCSE syllabus the formula is written as
\[
\text{PED}= \left|\frac{\%\Delta Q_d}{\%\Delta P}\right|
\]
where the absolute value is taken so that the classification (elastic, inelastic, etc.) uses a positive number.
2. Mid‑point (arc) formula – the recommended method for exam calculations
\[
\text{PED}= \frac{\displaystyle\frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}}{\displaystyle\frac{P_2-P_1}{\frac{P_1+P_2}{2}}}
\]
- \(P_1,\;Q_1\) = initial price and quantity demanded
- \(P_2,\;Q_2\) = new price and quantity demanded
This method eliminates the problem of direction‑dependence (i.e. whether the price is increasing or decreasing).
3. Step‑by‑step calculation (AO2 command words)
- Record the initial values \(P_1\) and \(Q_1\).
- Record the new values \(P_2\) and \(Q_2\).
- Calculate the percentage change in quantity demanded:
\[
\%\Delta Q = \frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}\times 100\%
\]
- Calculate the percentage change in price:
\[
\%\Delta P = \frac{P_2-P_1}{\frac{P_1+P_2}{2}}\times 100\%
\]
- Divide the two percentages and take the absolute value:
\[
\text{PED}= \Bigl|\frac{\%\Delta Q}{\%\Delta P}\Bigr|
\]
4. Worked examples
Example 1 – Inelastic demand (price rise)
Price of a cup of tea rises from £1.00 to £1.20 and quantity demanded falls from 1 000 to 850 cups.
| Variable | Initial | New |
|---|
| Price (£) | 1.00 | 1.20 |
| Quantity demanded | 1 000 | 850 |
- Mid‑point price = \((1.00+1.20)/2 = 1.10\)
- Mid‑point quantity = \((1 000+850)/2 = 925\)
- \(\%\Delta Q = \dfrac{850-1 000}{925}\times100 = -16.22\%\)
- \(\%\Delta P = \dfrac{1.20-1.00}{1.10}\times100 = 18.18\%\)
- \(\displaystyle \text{PED}= \Bigl|\frac{-16.22}{18.18}\Bigr| = 0.89\)
Interpretation: \(|\text{PED}| = 0.89 < 1\) → demand is **inelastic**. The percentage fall in quantity is smaller than the percentage rise in price.
Example 2 – Elastic demand (price fall)
Price of a cinema ticket falls from £8.00 to £6.00 and quantity demanded rises from 1 200 to 1 800 tickets per week.
| Variable | Initial | New |
|---|
| Price (£) | 8.00 | 6.00 |
| Quantity demanded | 1 200 | 1 800 |
- Mid‑point price = \((8.00+6.00)/2 = 7.00\)
- Mid‑point quantity = \((1 200+1 800)/2 = 1 500\)
- \(\%\Delta Q = \dfrac{1 800-1 200}{1 500}\times100 = 40.0\%\)
- \(\%\Delta P = \dfrac{6.00-8.00}{7.00}\times100 = -28.57\%\)
- \(\displaystyle \text{PED}= \Bigl|\frac{40.0}{-28.57}\Bigr| = 1.40\)
Interpretation: \(|\text{PED}| = 1.40 > 1\) → demand is **elastic**. The percentage increase in quantity is larger than the percentage fall in price.
5. Classification of PED (exact syllabus wording)
| Range of \(|\text{PED}|\) | Elasticity description | Typical example |
|---|
| 0 | Perfectly inelastic | Life‑saving drug with no substitutes |
| 0 < |\text{PED}| < 1 | Inelastic | Petrol in the short‑run |
| 1 | Unitary elastic | Some luxury goods where total revenue is unchanged |
| 1 < |\text{PED}| < ∞ | Elastic | Restaurant meals, fashion clothing |
| ∞ | Perfectly elastic | Perfect substitutes in a perfectly competitive market |
6. Determinants of PED (syllabus emphasis)
- Availability of close substitutes – the most important determinant; more close substitutes → higher elasticity.
- Proportion of income spent on the good – a larger share of the consumer’s budget makes demand more elastic.
- Nature of the good – luxuries are more elastic than necessities.
- Time horizon – demand becomes more elastic in the long run as consumers can adjust habits and find alternatives.
7. Total‑revenue test (AO3 evaluation link)
Because total revenue (TR) = Price × Quantity, the sign of PED tells us how TR will move when price changes.
- If \(|\text{PED}| > 1\) (elastic) → a **price decrease** raises TR, a **price increase** reduces TR.
- If \(|\text{PED}| < 1\) (inelastic) → a **price increase** raises TR, a **price decrease** reduces TR.
- If \(|\text{PED}| = 1\) (unitary) → TR is unchanged by a price change.
Numerical illustration (Example 1 – inelastic)
- Initial TR = £1.00 × 1 000 = £1 000
- New TR = £1.20 × 850 = £1 020
- Because demand is inelastic, the price rise leads to a higher total revenue.
Numerical illustration (Example 2 – elastic)
- Initial TR = £8.00 × 1 200 = £9 600
- New TR = £6.00 × 1 800 = £10 800
- Because demand is elastic, the price fall raises total revenue.
Evaluation prompt (AO3)
Discuss how a government could use a tax on a good with inelastic demand (e.g., tobacco). In your answer consider:
- Likely impact on total revenue for the government.
- Effect on consumer welfare (consumer surplus) and producer surplus.
- Potential for a “dead‑weight loss” and why it might be relatively small for inelastic goods.
8. Relevance for decision‑makers
- Consumers – understand how a price change will affect the amount they can afford and whether they might switch to alternatives.
- Firms – choose pricing strategies, forecast revenue, and decide whether to invest in product differentiation (which can reduce elasticity).
- Government – design taxes, subsidies, or price controls; assess tax incidence and welfare effects, especially for goods with very inelastic or very elastic demand.
- Workers – in industries where the product has elastic demand, changes in labour costs may quickly affect employment and wages.
9. Diagrammatic illustration
Below is a simple sketch showing the two points used in the mid‑point calculation and the five characteristic demand‑curve shapes.
Price
|
P2 * | * = (P2 , Q2)
| /
P1 * | /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| /
| * (P1 , Q1)
+------------------- Quantity
Q1 Q2
Five elasticity‑type demand curves (draw separately):
- Perfectly inelastic – vertical line.
- Inelastic – steep downward slope.
- Unitary elastic – rectangular hyperbola (constant % change).
- Elastic – shallow downward slope.
- Perfectly elastic – horizontal line.
10. Quick revision checklist
- Know the exact formula and that the absolute value is taken.
- Memorise the mid‑point (arc) method – it is the only method awarded marks in the exam.
- Be able to classify PED using the five ranges.
- Recall the four main determinants, especially “availability of close substitutes”.
- Apply the total‑revenue test and be ready to evaluate government policies.
- Practice drawing the demand‑curve sketch with two points and the five elasticity shapes.