Definition of PED
The Allocation of Resources – Price Elasticity of Demand (PED)
Learning Objective
By the end of this lesson students will be able to:
- Define price elasticity of demand (PED) and write the correct formula(s).
- Calculate PED using the mid‑point (arc) method for both price rises and price falls.
- Interpret the size of a PED value (elastic, unit‑elastic, inelastic, perfectly elastic, perfectly inelastic) and recall the numeric thresholds.
- Identify the main determinants of PED.
- Explain how PED affects total revenue, consumer expenditure and the decisions of households, firms, workers and government.
- Read and label a demand‑curve diagram that shows the three elasticity zones.
1. Definition and Formulae
Price Elasticity of Demand (PED) measures the responsiveness of the quantity demanded of a good or service to a change in its price.
Two formulae are used in the Cambridge IGCSE/ A‑Level exams:
- Standard (percentage‑change) formula
\[
\text{PED}= \frac{\%\Delta Q_d}{\%\Delta P}
\]
where \(\%\Delta Q_d\) is the percentage change in quantity demanded and \(\%\Delta P\) is the percentage change in price.
- Mid‑point (arc) formula – the method recommended for exam calculations because it gives the same result whether price rises or falls.
\[
\text{PED}= \frac{\displaystyle\frac{Q2-Q1}{\frac{Q1+Q2}{2}}}{\displaystyle\frac{P2-P1}{\frac{P1+P2}{2}}}
\]
\(P1,Q1\) are the initial price and quantity; \(P2,Q2\) are the new price and quantity.
Since the law of demand implies a negative relationship, the sign is usually omitted and the absolute value \(|\text{PED}|\) is reported.
2. Worked Examples
Example 1 – Price Rise
Price rises from £10 to £11 (a 10 % increase). Quantity demanded falls from 200 to 160 units (a 20 % decrease).
- Calculate the percentage changes using the mid‑point formula:
\[
\%\Delta P = \frac{11-10}{\frac{10+11}{2}}\times100 = \frac{1}{10.5}\times100 \approx 9.52\%
\]
\[
\%\Delta Q_d = \frac{160-200}{\frac{200+160}{2}}\times100 = \frac{-40}{180}\times100 \approx -22.22\%
\]
- Apply the PED formula:
\[
\text{PED}= \frac{-22.22\%}{9.52\%}= -2.33
\]
- Take the absolute value (exam convention):
\[
|\text{PED}| = 2.33 \; (>1)
\]
Hence demand is elastic.
Example 2 – Price Fall
Price falls from £8 to £6 (a 25 % decrease). Quantity demanded rises from 120 to 150 units (a 25 % increase).
- Mid‑point percentage changes:
\[
\%\Delta P = \frac{6-8}{\frac{8+6}{2}}\times100 = \frac{-2}{7}\times100 \approx -28.57\%
\]
\[
\%\Delta Q_d = \frac{150-120}{\frac{120+150}{2}}\times100 = \frac{30}{135}\times100 \approx 22.22\%
\]
- Apply the PED formula:
\[
\text{PED}= \frac{22.22\%}{-28.57\%}= -0.78
\]
- Absolute value:
\[
|\text{PED}| = 0.78 \; (<1)
\]
Hence demand is inelastic.
3. Interpreting PED Values
| \(|\text{PED}|\) (absolute value) | Elasticity Type | Interpretation |
|---|---|---|
| 0 < |\text{PED}| < 1 | Inelastic | Quantity demanded changes less than proportionally to price. |
| |\text{PED}| = 1 | Unit‑elastic | Quantity demanded changes exactly proportionally to price. |
| |\text{PED}| > 1 | Elastic | Quantity demanded changes more than proportionally to price. |
| |\text{PED}| = 0 | Perfectly inelastic | Quantity demanded does not respond to price changes (vertical demand curve). |
| |\text{PED}| = ∞ | Perfectly elastic | Any price increase drives quantity demanded to zero (horizontal demand curve). |
Remember the numeric rule: elastic if > 1, unit‑elastic if = 1, inelastic if < 1.
4. Determinants of PED
Four (sometimes five) key factors explain why some goods have a higher or lower PED:
- Availability of close substitutes – the more substitutes, the higher the PED.
- Proportion of income spent on the good – goods that take up a large share of a consumer’s budget tend to have a higher PED.
- Nature of the good – luxuries have a higher PED than necessities.
- Time horizon – demand is usually more elastic in the long run because consumers have more time to adjust.
- Brand loyalty / habit formation (optional for A‑Level) – strong loyalty reduces PED.
5. PED and Total Revenue (TR)
Total revenue is calculated as TR = P × Q. The relationship between PED and the direction of TR when price changes is shown below:
| PED Category | Effect of a Price Rise | Effect of a Price Fall |
|---|---|---|
| Elastic (|\text{PED}| > 1) | TR falls (quantity falls proportionally more than price rises) | TR rises |
| Unit‑elastic (|\text{PED}| = 1) | TR unchanged | TR unchanged |
| Inelastic (0 < |\text{PED}| < 1) | TR rises (quantity falls proportionally less than price rises) | TR falls |
| Perfectly inelastic (|\text{PED}| = 0) | TR rises (price rises, quantity unchanged) | TR falls |
| Perfectly elastic (|\text{PED}| = ∞) | TR falls to zero (any price rise eliminates sales) | TR falls to zero (any price fall eliminates sales) |
6. Using PED in Decision‑Making
- Households – decide how much of a good to buy when its price changes; a high PED means they will switch to alternatives.
- Firms
- Pricing strategy – raise price only if demand is inelastic; cut price to boost revenue if demand is elastic.
- Tax incidence – with inelastic demand, most of a tax burden falls on consumers.
- Product positioning – develop brand loyalty or differentiate to make demand more inelastic.
- Workers – the concept mirrors the elasticity of labour supply; a high PED for a good may affect the demand for labour in its production.
- Government
- Indirect taxes – choose goods with inelastic demand to raise revenue with minimal reduction in quantity sold.
- Subsidies – subsidies on goods with elastic demand can significantly increase consumption.
7. Diagrammatic Illustration
8. Summary Checklist
- Definition: PED = %ΔQd / %ΔP (use the mid‑point formula in exams).
- Report the absolute value: |\text{PED}|.
- Elasticity thresholds – > 1 (elastic), = 1 (unit‑elastic), < 1 (inelastic).
- Determinants – substitutes, income share, nature of the good, time, (optional) brand loyalty.
- Elastic demand → price rise → TR falls; Inelastic demand → price rise → TR rises.
- Apply PED to pricing, tax, subsidy and production decisions for households, firms, workers and government.