Effect of price changes on the amount spent by consumers and revenue raised by firms, shown both in a diagram and as a calculation

📈 The Allocation of Resources – Price Elasticity of Demand (PED)

What is Price Elasticity of Demand?

PED measures how much the quantity demanded of a good changes when its price changes. It tells us whether consumers are elastic (sensitive to price) or inelastic (not very sensitive).

Formula (inline): \$Ed = \frac{\% \Delta Qd}{\% \Delta P}\$

Or in block form:

\$Ed = \frac{\Delta Qd / Q_d}{\Delta P / P}\$

Why Do We Care?

  • Helps firms decide price changes to maximise revenue.

  • Shows how consumer spending shifts with price.

  • Key concept in the allocation of resources in economics.

A Simple Example – Pizza 🍕

Suppose a pizza shop raises the price of a pizza from \$5 to \$6. The quantity sold falls from 100 pizzas to 90 pizzas.

  1. Calculate the percentage change in price: \$\% \Delta P = \frac{6-5}{5} \times 100 = 20\%\$

  2. Calculate the percentage change in quantity demanded: \$\% \Delta Q_d = \frac{90-100}{100} \times 100 = -10\%\$

  3. Compute PED: \$E_d = \frac{-10\%}{20\%} = -0.5\$

Because |PED| < 1, demand is inelastic. A price rise will increase total revenue.

Effect on Total Revenue

Total revenue (TR) is calculated as: \$TR = P \times Q\$

Using the pizza example:

Price ($)Quantity (pizzas)Total Revenue ($)
5100500
690540

The revenue rises from \$500 to \$540 because demand was inelastic.

Diagram – Demand Curve & Revenue

Price
|
|      D
|     /  
|    /    
|   /      
|  /       
| /        
|/ Quantity
90  100

The shaded area between the two price points shows the increase in revenue.

Exam Tip Box

Tip: When answering questions on PED, always:

  1. State the formula clearly.

  2. Show each step of the calculation.

  3. Interpret the sign and magnitude of PED.

  4. Explain the effect on total revenue.

Use the pizza example as a quick illustration if you need to.

Key Take‑aways

  • Elasticity > 1: Demand is elastic; price rise decreases revenue.

  • Elasticity < 1: Demand is inelastic; price rise increases revenue.

  • Elasticity = 1: Demand is unit‑elastic; revenue stays the same.

  • Use the PED formula to decide whether a price change is likely to help or hurt a firm.

Quick Practice Question

A brand‑name cereal costs £2.50 per box. After a 10% price increase, sales drop by 15%. Calculate PED and state whether the cereal is elastic or inelastic. What happens to revenue?

(Try it yourself before checking the answer in the next lesson.)