How Do You Calculate Price Elasticity of Demand?
Learn how to calculate price elasticity of demand using percentage changes, follow a worked example, and interpret the sign and size of your PED answer.
Calculate price elasticity of demand (PED) by dividing the percentage change in quantity demanded by the percentage change in price:
PED=% change in quantity demanded% change in price\text{PED}=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}PED=% change in price% change in quantity demandedThis is part of AS Level Economics, under Price elasticity, income elasticity and cross elasticity of demand (syllabus point 2.2.2).
How to work it out
Find each percentage change using the original value as the starting point:
% 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×100Then divide the percentage change in quantity demanded by the percentage change in price. PED measures how responsive buyers are to a price change: a larger absolute value means quantity demanded responds more strongly.
Use the values before the price change as your starting point for both calculations. A price rise gives a positive percentage change in price; a fall in quantity demanded gives a negative percentage change in quantity. The percentage units cancel when you divide, so PED has no units.
Worked example
Suppose a product’s price rises from $10{\char36}10$10 to $12{\char36}12$12, while quantity demanded falls from 100100100 to 808080 units.
% change in price=12−1010×100=20%\%\text{ change in price}=\frac{12-10}{10}\times 100=20\%% change in price=1012−10×100=20% % change in quantity demanded=80−100100×100=−20%\%\text{ change in quantity demanded}=\frac{80-100}{100}\times 100=-20\%% change in quantity demanded=10080−100×100=−20%So:
PED=−20%20%=−1\text{PED}=\frac{-20\%}{20\%}=-1PED=20%−20%=−1The negative sign shows that price and quantity demanded moved in opposite directions. The absolute value means the number without its sign. Here it is 111, so demand is unitary elastic: the percentage changes are equal in size. An absolute value greater than 111 indicates elastic demand; one between 000 and 111 indicates inelastic demand.
Check the order of your division: quantity demanded goes on top and price goes underneath. Reversing them gives a different answer. In this example, each change is one fifth of its original value, which is why the two percentage changes have the same size. The quantity change is negative because fewer units are bought after the price rise.
Common mistake: dividing the change in units by the change in price. PED compares percentage changes, not raw changes. Use the original price and original quantity as the denominators in both percentage calculations.
