Main influences on whether demand is elastic or inelastic
Price Elasticity of Demand (PED) – Cambridge IGCSE/A‑Level (2.6)
2.6.1 Definition
Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good or service to a change in its price.
2.6.2 Calculating PED
The formula (Cambridge 2.6.2) is
\$\text{PED}=\frac{\%\Delta Q_{d}}{\%\Delta P}\$
Step‑by‑step method
- Calculate the percentage change in quantity demanded:
\$\%\Delta Q{d}= \frac{Q{2}-Q{1}}{Q{1}}\times 100\$
- Calculate the percentage change in price:
\$\%\Delta P= \frac{P{2}-P{1}}{P_{1}}\times 100\$
- Divide the two percentages. Use the absolute values to discuss the magnitude, but retain the sign to show the direction of the relationship.
Worked example – elastic demand (|PED| > 1)
| Step | Values / Calculation |
|---|---|
| Initial price and quantity | P₁ = £20, Q₁ = 500 units |
| New price and quantity | P₂ = £22 (↑10 %), Q₂ = 400 units (↓20 %) |
| ΔP (%) | \(\frac{22-20}{20}\times100 = 10\%\) |
| ΔQ (%) | \(\frac{400-500}{500}\times100 = -20\%\) |
| PED | \(\frac{-20\%}{10\%}= -2\) |
Interpretation: PED = ‑2. The negative sign reflects the law of demand; the absolute value |PED| = 2 > 1 shows that demand is elastic – a 1 % price rise causes a more than 1 % fall in quantity demanded.
Worked example – inelastic demand (0 < |PED| < 1)
| Step | Values / Calculation |
|---|---|
| Initial price and quantity | P₁ = £5, Q₁ = 1 000 litres |
| New price and quantity | P₂ = £5.50 (↑10 %), Q₂ = 950 litres (↓5 %) |
| ΔP (%) | \(\frac{5.5-5}{5}\times100 = 10\%\) |
| ΔQ (%) | \(\frac{950-1000}{1000}\times100 = -5\%\) |
| PED | \(\frac{-5\%}{10\%}= -0.5\) |
Interpretation: PED = ‑0.5. |PED| = 0.5 < 1 → demand is inelastic; quantity reacts less than proportionally to the price change.
Worked example – unitary elasticity (|PED| = 1)
| Step | Values / Calculation |
|---|---|
| Initial price and quantity | P₁ = £8, Q₁ = 200 units |
| New price and quantity | P₂ = £9 (↑12.5 %), Q₂ = 180 units (↓10 %) |
| ΔP (%) | \(\frac{9-8}{8}\times100 = 12.5\%\) |
| ΔQ (%) | \(\frac{180-200}{200}\times100 = -10\%\) |
| PED | \(\frac{-10\%}{12.5\%}= -0.80\) (≈ ‑1 when rounded to one decimal place) |
Interpretation: |PED| ≈ 1 → demand is unitary elastic; the percentage change in quantity is almost exactly the same as the percentage change in price.
2.6.3 Interpreting PED values
- Perfectly inelastic (PED = 0) – Quantity demanded does not change when price changes.
Example: life‑saving medication with no substitute.
- Inelastic (0 < |PED| < 1) – Quantity changes proportionally less than price.
Example: petrol in the short run.
- Unitary elastic (|PED| = 1) – Quantity changes by exactly the same proportion as price.
- Elastic (|PED| > 1) – Quantity changes proportionally more than price.
Example: luxury handbags.
- Perfectly elastic (PED = ∞) – Any increase in price drives quantity demanded to zero.
Example: a perfectly competitive commodity where identical substitutes are available at the market price.
2.6.4 Determinants of PED (Cambridge wording)
| Determinant | Effect on elasticity | Reason |
|---|---|---|
| Availability of close substitutes | More elastic | Consumers can switch easily, so a price rise causes a large fall in quantity demanded. |
| Proportion of income spent on the good | More elastic when the share is large | Goods that take up a big part of the budget (e.g., cars) provoke a stronger response to price changes. |
| Definition of the market (broad vs. narrow) | Broad markets → more inelastic; narrow markets → more elastic | A broad category like “food” has few close substitutes, whereas “brand X cereal” is narrowly defined. |
| Time horizon (short‑run vs. long‑run) | More elastic in the long run | Consumers need time to adjust habits, find alternatives or change production methods. |
| Nature of the good (necessity vs. luxury) | Necessities → inelastic; luxuries → elastic | Essential items are bought even if price rises; non‑essential items can be postponed or forgone. |
| Brand loyalty / habit formation | More inelastic | Strong preferences reduce sensitivity to price changes. |
| Durability and storage possibilities | Non‑durable goods → more elastic; durable goods → more inelastic | Perishable items cannot be stored, so consumers react quickly to price changes. |
2.6.4 – PED, consumer expenditure & firms’ revenue
- Total Revenue (TR) = Price × Quantity.
- If demand is elastic (|PED| > 1), a price rise reduces TR because the fall in quantity outweighs the higher price.
- If demand is inelastic (0 < |PED| < 1), a price rise increases TR because the loss in quantity is proportionally smaller than the price gain.
- Tax revenue: Governments consider PED when levying excise taxes.
- For a good with inelastic demand, a tax raises revenue with only a small reduction in quantity (e.g., tobacco taxes).
- For a good with elastic demand, a tax may cause a large fall in consumption, reducing the expected revenue.
- Consumer expenditure: When price falls for an elastic good, total expenditure (P × Q) rises, indicating a strong substitution effect; for an inelastic good, expenditure falls.
2.6.5 Significance of PED (Why it matters)
PED is a key tool for:
- Firms – to set optimal prices, forecast the impact of price changes on revenue, and decide on production levels.
- Governments – to design taxes, subsidies, and price‑control policies that achieve desired revenue or social outcomes.
- Resource allocation – understanding how price signals affect the quantity of a good that consumers are willing to buy, which in turn guides how resources are distributed across the economy.
Diagram – elastic vs. inelastic demand and total revenue
Connection to market failure and government intervention (Unit 2.9‑2.10)
Goods with highly inelastic demand that generate negative externalities (e.g., cigarettes, alcohol) are prone to market failure because consumers continue to purchase them despite high social costs. Governments therefore intervene – often by imposing a specific tax or setting a price ceiling – relying on PED to estimate how much consumption will fall and how much revenue will be raised.
Key points to remember for the exam
- PED is a ratio of percentage changes; it is unit‑free.
- Always write the sign (negative for the law of demand) first, then discuss the absolute value.
- Elasticity varies with the determinants listed above and with the time horizon.
- Long‑run elasticities are generally larger than short‑run elasticities.
- When answering questions, link PED to total revenue, tax revenue, and the broader implications for resource allocation and government policy.