Price elasticity of demand
Knowing that demand falls when price rises is useful. Knowing by how much is far more useful. Elasticity measures responsiveness.
What elasticity measures
Price elasticity of demand measures how strongly quantity demanded responds to a price change: \(E_d = \frac{\%\Delta Q_d}{\%\Delta P}\). It is usually reported as a positive number (ignoring the negative sign). If a 10% price rise cuts quantity by 20%, elasticity is 2.
Elastic and inelastic
If elasticity is greater than 1, demand is elastic: quantity responds more than proportionally. If it is less than 1, demand is inelastic. If it equals 1, it is unit elastic. Perfectly inelastic demand (0) means quantity does not change at all; perfectly elastic demand means any price rise loses all buyers.
The midpoint method
Percentage changes depend on the starting point, so economists often use the midpoint formula: \(\%\Delta Q = \frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}\), and similarly for price. This gives the same answer whether price rises or falls between two points.
Determinants of elasticity
Demand is more elastic when close substitutes exist (one brand of cereal), when the good is a luxury rather than a necessity, when it takes a large share of the budget, when the market is narrowly defined, and over longer time periods as people adjust. Insulin, petrol in the short run, and salt are inelastic; particular restaurant meals are elastic.
Elasticity and total revenue
Total revenue is price times quantity. If demand is elastic, raising price lowers total revenue, because quantity falls by a larger percentage. If demand is inelastic, raising price raises total revenue. If unit elastic, revenue stays the same. This is the total revenue test.
Elasticity along a straight-line demand curve
Even a straight-line demand curve has different elasticities at different points. At high prices and low quantities, demand is elastic; at low prices and high quantities, it is inelastic. Revenue is maximised at the midpoint, where elasticity is exactly 1.
Applications
Firms use elasticity to set prices: airlines charge business travellers (inelastic) more than tourists (elastic). Governments tax goods with inelastic demand, like cigarettes and petrol, to raise revenue reliably. Drug policy debates turn on elasticities: cutting supply of addictive drugs with inelastic demand raises prices and dealers' revenue.
Worked example
A cinema raises tickets from 10 to 12 dollars, and weekly sales fall from 1,000 to 900. Using midpoints: quantity change is -100/950, about -10.5%; price change is 2/11, about 18.2%. Elasticity is about 0.58, inelastic. Revenue rises from 10,000 to 10,800 dollars, as the total revenue test predicts.
Key takeaways
Price elasticity of demand is the percentage change in quantity divided by the percentage change in price. Above 1 is elastic, below 1 inelastic. Substitutes, luxury status, budget share, narrow definitions, and time make demand more elastic. Raising price increases revenue only when demand is inelastic. Elasticity changes along a straight-line demand curve.
Flashcard
%change in Qd / %change in P
Check your understanding
A bakery raises the price of bread and its total revenue falls. Demand for its bread must be: