The definition and formula for price elasticity of demand (PED)

Price elasticity of demand (PED) shows how much the quantity demanded of a good or service changes in response to a shift in its price.

PED is calculated using this formula:

$\text{PED}=\frac{\%\mathrm{\Delta }{\text{Q}}_{\text{d}}}{\%\mathrm{\Delta }\text{P}}=\frac{\frac{{\text{Q}}_2-{\text{Q}}_1}{{\text{Q}}_1}}{\frac{{\text{P}}_2-{\text{P}}_1}{{\text{P}}_1}}=\frac{{\text{Q}}_2-{\text{Q}}_1}{{\text{P}}_2-{\text{P}}_1}\times \frac{{\text{P}}_1}{{\text{Q}}_1}$

Where:

• %∆Q_d = Percentage change in quantity demanded
• %∆P = Percentage change in price
• Q₁ = Original quantity demanded
• Q₂ = New quantity demanded
• P₁ = Original price
• P₂ = New price

Price and quantity demanded usually move in opposite directions, following the law of demand. This makes PED a negative value, but it is often expressed as a positive number for simplicity by ignoring the minus sign. However, keep the sign during calculations to ensure accuracy.

The degrees of price elasticity of demand

The value of PED indicates how responsive demand is to price changes.

Price elastic demand (PED > 1)

When PED is greater than 1, the percentage change in quantity demanded exceeds the percentage change in price. Demand is relatively responsive, so a price rise leads to a larger drop in quantity demanded. On a demand curve, this appears as a relatively flat, downward-sloping line.

Price inelastic demand (0 < PED < 1)

When PED is between 0 and 1, the percentage change in quantity demanded is smaller than the percentage change in price. Demand is relatively unresponsive, meaning consumers continue buying even if prices increase. On a demand curve, this shows as a steep, downward-sloping line.

Unit elastic demand (PED = 1)

When PED equals 1, the percentage change in quantity demanded matches the percentage change in price exactly. This is represented by a curved demand line (rectangular hyperbola) that does not touch the axes.

Perfectly elastic demand (PED → ∞)

When PED approaches infinity, even a tiny price change causes an enormous shift in quantity demanded. This is shown as a horizontal line on a demand curve.

Perfectly inelastic demand (PED = 0)

When PED is 0, quantity demanded stays the same regardless of price changes. It appears as a vertical line on a demand curve.

Note that along a straight-line demand curve, PED varies continuously. The special cases (unit, perfectly elastic, perfectly inelastic) maintain constant PED throughout.

How to calculate PED and interpret the results

Calculating PED involves using the formula to find the elasticity value. Remember to include signs in calculations but interpret the absolute value for the degree of elasticity.

Worked example - Calculating PED from percentage changes

Assume that a price decrease of 10% results in a 14% rise in quantity demanded. Calculate the PED and determine the degree of elasticity.

Step 1: Identify the values

• %∆Q_d = +14%
• %∆P = -10%

Step 2: Apply the PED formula

$\text{PED}=\frac{+14\%}{-10\%}=-1.4$

Step 3: Interpret the result

The absolute value is 1.4, so PED > 1, meaning demand is price elastic.

Worked example - Calculating PED from price and quantity data

Assume the price of a product rises from £10 to £12, causing quantity demanded to drop from 20,000 units to 18,000 units. Calculate the PED and determine the degree of elasticity.

Step 1: Identify the values

• Q₁ = 20,000 units
• Q₂ = 18,000 units
• P₁ = £10
• P₂ = £12

Step 2: Apply the PED formula

$\text{PED}=\frac{\mathrm{18,000}-\mathrm{20,000}}{12-10}\times \frac{10}{\mathrm{20,000}}=\frac{-\mathrm{2,000}}{2}\times \frac{10}{\mathrm{20,000}}=-\mathrm{1,000}\times \frac{1}{\mathrm{2,000}}=-0.5$

Step 3: Interpret the result

The absolute value is 0.5, so 0 < PED < 1, meaning demand is price inelastic.

Worked example - Calculating percentage change in quantity from PED

Assume PED is -0.65 and price rises by 8%. Calculate the percentage change in quantity demanded.

Step 1: Identify the values

• PED = -0.65
• %∆P = +8%

Step 2: Rearrange and apply the PED formula

$\text{PED}=\frac{\%\mathrm{\Delta }{\text{Q}}_{\text{d}}}{\%\mathrm{\Delta }\text{P}}$

$-0.65=\frac{\%\mathrm{\Delta }{\text{Q}}_{\text{d}}}{+8\%}$

$\%\mathrm{\Delta }{\text{Q}}_{\text{d}}=-0.65\times 8\%=-5.2\%$

Step 3: Interpret the result

Quantity demanded decreases by 5.2%, moving in the opposite direction to the price increase, as expected from the law of demand.