2.7 Price Elasticity of Demand (PED)

---

1. What is Price Elasticity of Demand (PED)?

Price Elasticity of Demand (PED) measures how responsive (sensitive) the quantity demanded of a product is to a change in its price.

In other words: if a shop raises its price, by how much will sales fall? PED gives us a number that answers this question.

We already know from the law of demand that when price goes up, quantity demanded goes down — and when price goes down, quantity demanded goes up. PED tells us how much quantity demanded changes.

---

2. The PED Formula

$$\text{PED} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$$

Or written out step by step:

$$\text{PED} = \frac{\dfrac{Qd_2 - Qd_1}{Qd_1} \times 100}{\dfrac{P_2 - P_1}{P_1} \times 100}$$

Where:

• Qd₁ = original (old) quantity demanded
• Qd₂ = new quantity demanded
• P₁ = original (old) price
• P₂ = new price

---

Step-by-Step Worked Example

A firm raises the price of a product from £10 to £12. Sales fall from 1,000 to 500 units.

Step 1: Calculate % change in quantity demanded

$\frac{500 - 1000}{1000} \times 100 = \frac{-500}{1000} \times 100 = -50\%$

Step 2: Calculate % change in price

$\frac{12 - 10}{10} \times 100 = \frac{2}{10} \times 100 = +20\%$

Step 3: Divide

$$\text{PED} = \frac{-50\%}{+20\%} = -2.5$$

Interpretation: The PED value is –2.5. The negative sign simply shows that price and quantity move in opposite directions (price up → quantity down). Economists often ignore the minus sign and just use the number 2.5.

This means: a 1% change in price causes a 2.5% change in quantity demanded.