IGCSE Economics 0455 – Price Elasticity of DemandAllocation of Resources – Price Elasticity of Demand (PED)
Learning Objective
Understand how the price elasticity of demand influences the amount consumers spend and the total revenue earned by firms.
Key Concepts
- Price Elasticity of Demand (PED): measures the responsiveness of quantity demanded to a change in price.
- Formula: \$PED = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}\$
- Interpretation of the coefficient:
- |PED| > 1 – Elastic demand
- |PED| = 1 – Unit‑elastic demand
- |PED| < 1 – Inelastic demand
Relationship Between PED and Consumer Expenditure
Consumer expenditure on a good is \$E = P \times Q\$, where \$P\$ is price and \$Q\$ is quantity demanded.
- If demand is elastic (|PED| > 1):
- A price decrease leads to a proportionally larger increase in quantity demanded.
- Result: \$E\$ rises because the increase in \$Q\$ outweighs the lower \$P\$.
- If demand is inelastic (|PED| < 1):
- A price decrease causes a smaller proportional increase in quantity demanded.
- Result: \$E\$ falls because the reduction in \$P\$ is not fully compensated by the rise in \$Q\$.
- If demand is unit‑elastic (|PED| = 1):
- The percentage change in \$Q\$ exactly matches the percentage change in \$P\$.
- Result: \$E\$ remains unchanged.
Relationship Between PED and Firm Revenue
For a firm, total revenue (TR) is also \$TR = P \times Q\$.
| PED Category | Effect of a Price Increase | Effect on Total Revenue | Effect of a Price Decrease | Effect on Total Revenue |
|---|
| Elastic (|PED| > 1) | Quantity demanded falls proportionally more | TR falls | Quantity demanded rises proportionally more | TR rises |
| Unit‑elastic (|PED| = 1) | Quantity falls proportionally the same | TR unchanged | Quantity rises proportionally the same | TR unchanged |
| Inelastic (|PED| < 1) | Quantity falls proportionally less | TR rises | Quantity rises proportionally less | TR falls |
Graphical Illustration
Suggested diagram: Two demand curves (elastic and inelastic) showing the impact of a price change on total revenue.
Worked Example
Suppose the price of a product falls from \$10 to \$8 and the quantity demanded rises from 100 units to 150 units.
\$\$
\%\Delta P = \frac{8-10}{10}\times100 = -20\%
\$\$
\$\$
\%\Delta Q = \frac{150-100}{100}\times100 = 50\%
\$\$
\$\$
PED = \frac{50\%}{-20\%} = -2.5\;(\text{elastic})
\$\$
Because demand is elastic, total revenue increases:
\$\$
TR_{\text{initial}} = 10 \times 100 = \$1{,}000
\$\$
\$\$
TR_{\text{new}} = 8 \times 150 = \$1{,}200
\$\$
Revenue rises by $200, confirming the rule for elastic demand.
Key Take‑aways
- When demand is elastic, a price cut increases both consumer expenditure and firm revenue.
- When demand is inelastic, a price cut decreases consumer expenditure and firm revenue.
- Understanding PED helps firms set prices to maximise revenue and informs policymakers about the likely impact of taxes or subsidies.