Price Elasticity of Demand (PED)
Definition (2.6.1) – PED measures how responsive the quantity demanded of a good or service is to a change in its price. In the Cambridge IGCSE the magnitude is expressed as an absolute value, |PED|, so that the sign (negative because of the law of demand) is ignored.
1. Formula and sign convention (2.6.2)
\[
\text{PED}= \frac{\%\Delta Q_{d}}{\%\Delta P}
\]
- Qd = quantity demanded
- P = price
- Because the demand curve slopes downwards, a rise in price gives a negative percentage change in quantity. The syllabus requires us to use the absolute value: ignore the negative sign and work with |PED|. This lets us focus purely on the size of the response.
2. Determinants of PED (2.6.4)
| Determinant | Why it matters |
|---|
| Availability of close substitutes | More substitutes give consumers an easy alternative, so a price rise leads them to switch – demand becomes more elastic. |
| Proportion of income spent on the good | If a good takes up a large share of the budget, a price change noticeably affects the consumer’s spending power, making demand more elastic. |
| Nature of the good (luxury vs. necessity) | Luxuries are not essential; consumers can cut back when price rises → higher elasticity. Necessities are bought even if price rises → lower elasticity. |
| Time‑frame | In the long run consumers can find substitutes, change habits or adjust income, so demand is usually more elastic than in the short run. |
3. Interpreting the PED value (2.6.3)
| |PED| range | Elasticity type | Interpretation |
|---|
| 0 | Perfectly inelastic | Quantity demanded does not change at all when price changes; consumers are completely unresponsive. |
| 0 < |PED| < 1 | Inelastic | Quantity changes proportionally less than price. Total‑revenue moves in the same direction as price. |
| 1 | Unitary elastic | Percentage change in quantity equals the percentage change in price. Total‑revenue is unchanged. |
| 1 < |PED| < ∞ | Elastic | Quantity changes proportionally more than price. Total‑revenue moves opposite to price. |
| → ∞ | Perfectly elastic | Any price increase drives quantity demanded to zero; any price decrease would generate an infinitely large quantity demanded. |
4. PED, consumer expenditure and firms’ revenue (2.6.5)
- Consumer expenditure (P × Q) follows the same pattern as a firm’s total‑revenue because it is the same product of price and quantity.
- When demand is elastic, a price rise reduces both total‑revenue and the amount consumers spend; a price fall raises both.
- When demand is inelastic, a price rise increases total‑revenue and consumer spending, while a price fall reduces both.
- At unitary elasticity total‑revenue and consumer expenditure remain unchanged after a price change.
5. PED and total‑revenue relationship (summary)
- Inelastic (|PED| < 1): price ↑ → TR ↑ price ↓ → TR ↓
- Unitary (|PED| = 1): price ↑ or ↓ → TR unchanged
- Elastic (|PED| > 1): price ↑ → TR ↓ price ↓ → TR ↑
Suggested diagram: three demand curves (elastic, unitary, inelastic) on the same graph. Show a small price rise and the resulting movement along each curve, then illustrate the corresponding total‑revenue curves to highlight the direction of change.
6. Worked example (including total‑revenue impact)
Price of a product rises from \$10 to \$12 and quantity demanded falls from 500 units to 400 units.
- Percentage change in price
\[
\%\Delta P = \frac{12-10}{10}\times100 = 20\%
\]
- Percentage change in quantity demanded
\[
\%\Delta Q_{d} = \frac{400-500}{500}\times100 = -20\%
\]
- Calculate |PED| (ignore the sign)
\[
|{\text{PED}}| = \frac{| -20\% |}{20\%}=1
\]
- Interpretation
- |PED| = 1 → demand is unitary elastic.
- Total‑revenue before the change: \(10 \times 500 = \$5{,}000\).
- Total‑revenue after the change: \(12 \times 400 = \$5{,}000\).
- Because demand is unitary elastic, total‑revenue (and consumer expenditure) is unchanged.
7. Practical implications
- Pricing decisions – Firms with elastic demand must be cautious about raising prices, as revenue will fall.
- Tax policy – A tax on an inelastic good (e.g., tobacco, petrol) raises government revenue with only a small fall in quantity; the tax burden falls largely on consumers.
- Subsidies – Subsidising a good with elastic demand can markedly increase the quantity purchased.
- Link to supply – The same concepts apply to price elasticity of supply (PES). See syllabus section 2.7 for definition and determinants.
8. Suggested diagrams for the lesson
- Four separate demand curves illustrating perfectly inelastic, inelastic, elastic and perfectly elastic demand. Show a small price increase on each and the resulting quantity change.
- Total‑revenue curves for the three elasticity cases (elastic, unitary, inelastic) with a price‑change arrow to demonstrate the direction of TR movement.
Key points to remember
- |PED| = 0 → Perfectly inelastic – no change in quantity.
- 0 < |PED| < 1 → Inelastic – quantity changes less than price; TR moves with price.
- |PED| = 1 → Unitary elastic – proportional change; TR unchanged.
- |PED| > 1 → Elastic – quantity changes more than price; TR moves opposite to price.
- |PED| → ∞ → Perfectly elastic – any price rise eliminates demand.
- Determinants: substitutes, income share, necessity vs. luxury, time‑frame (each explained above).
- Tax incidence: the more inelastic the demand, the larger the consumer’s share of a tax burden.
- Same elasticity ideas apply to supply (PES).