2.10 - Price Elasticity of Demand (PED)

Definition and formula for 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 drawn well away from the origin. In the diagram below, a rise in the price per unit (P) from P1 to P2 along the demand curve D pulls the quantity per period (Q) down from Q1 to Q2, and that fall in quantity is proportionately larger than the rise in price.

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, again drawn away from the origin. In the diagram below, the same rise in the price per unit (P) from P1 to P2 along the demand curve D moves the quantity per period (Q) only from Q1 to Q2, a proportionately smaller fall than the rise in price.

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. In the diagram below, the demand curve D bends away from both axes without ever reaching them, so a rise in the price per unit (P) from P1 to P2 is matched by an equally proportionate fall in the quantity per period (Q) from Q1 to Q2, and the same holds at every point along the curve.

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. In the diagram below the demand curve D is flat at the price per unit P, so buyers will take any quantity per period (Q) offered at that price but nothing at all once the price rises above it.

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. In the diagram below the demand curve D is vertical, so the quantity per period (Q) that buyers take at the higher price per unit P2 is exactly the quantity they take at P1.

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 - 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 - PED from price and quantity

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 - Quantity change 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.