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

1. Calculate the percentage change in quantity demanded: $$\%\Delta Q_{d}= \frac{Q_{2}-Q_{1}}{Q_{1}}\times 100$$
2. Calculate the percentage change in price: $$\%\Delta P= \frac{P_{2}-P_{1}}{P_{1}}\times 100$$
3. 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)

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)

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)

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)

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.