How to Calculate Price and Income Elasticity of Demand
Learn how to calculate price and income elasticity of demand using percentage changes, worked examples and clear guidance on interpreting PED and YED results.
To calculate price elasticity of demand (PED), divide the percentage change in quantity demanded by the percentage change in price. To calculate income elasticity of demand (YED), divide the percentage change in quantity demanded by the percentage change in consumer income.
PED=% change in quantity demanded% change in priceYED=% change in quantity demanded% change in income\text{PED}=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}} \qquad \text{YED}=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in income}}PED=% change in price% change in quantity demandedYED=% change in income% change in quantity demandedElasticity measures how strongly demand responds to a change. For either calculation, find each percentage change using the original value:
% change=new value−original valueoriginal value×100\%\text{ change}=\frac{\text{new value}-\text{original value}}{\text{original value}}\times 100% change=original valuenew value−original value×100For PED, compare a change in price with the resulting change in quantity demanded. For YED, compare a change in income with the resulting change in quantity demanded. The answer has no units because you divide one percentage by another. If the percentage change in price or income is zero, the relevant calculation is undefined: you cannot divide by zero.
Worked Examples
Suppose a business raises its price from £10\pounds 10£10 to £12\pounds 12£12, and quantity demanded falls from 100100100 to 808080 units. Price changes by 20%20\%20%, while quantity demanded changes by −20%-20\%−20%. Therefore, PED=−20%÷20%=−1\text{PED}=-20\%\div20\%=-1PED=−20%÷20%=−1. The negative sign shows that demand fell when price rose. Its magnitude is 111, so demand is unit elastic: the percentage changes are equal in size. A PED magnitude above 111 means elastic demand; below 111 means inelastic demand. This helps a business assess how sensitive customers are to price changes.
Now suppose consumer income rises from £2,000\pounds 2{,}000£2,000 to £2,200\pounds 2{,}200£2,200, and demand for a product rises from 100100100 to 110110110 units. Income changes by 10%10\%10% and demand changes by 10%10\%10%, so YED=10%÷10%=1\text{YED}=10\%\div10\%=1YED=10%÷10%=1. A positive YED indicates a normal good: demand rises as income rises. A negative YED indicates an inferior good: demand falls as income rises.
Exam Check
Use the original figure as the denominator when calculating each percentage change. Do not divide the change in units directly by the change in pounds: elasticity compares percentage changes, not absolute changes. Keep the sign of PED in your calculation, even when discussing how elastic demand is using its magnitude.
