Relationship between PED and the amount spent by consumers and revenue raised by firms

Published by Patrick Mutisya · 14 days ago

IGCSE Economics 0455 – Price Elasticity of Demand

Allocation 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.

  1. 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\$.

  2. 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\$.

  3. 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 CategoryEffect of a Price IncreaseEffect on Total RevenueEffect of a Price DecreaseEffect on Total Revenue
Elastic (|PED| > 1)Quantity demanded falls proportionally moreTR fallsQuantity demanded rises proportionally moreTR rises
Unit‑elastic (|PED| = 1)Quantity falls proportionally the sameTR unchangedQuantity rises proportionally the sameTR unchanged
Inelastic (|PED| < 1)Quantity falls proportionally lessTR risesQuantity rises proportionally lessTR 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.