The PED formula, percentage changes from the old value, what a figure such as −0.4 means, and using PED to predict sales and spending.
That is the World Bank’s estimate for richer countries: a price elasticity of demand for cigarettes of about −0.4. It is why governments tax tobacco so heavily. People keep buying, so the tax raises a lot of money, but they do buy a little less.
What does −0.4 actually measure, and how do you work it out?
Source: World Bank, Curbing the Epidemic: Governments and the Economics of Tobacco Control (1999).
Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in the good’s own price.
PED = % change in quantity demanded ÷ % change in price
Each percentage change is (new − old) ÷ old × 100. Always divide by the old value.
Two assumptions: only the price changes (ceteris paribus), and demand slopes down, so price and quantity move in opposite directions. That makes PED negative. You classify it by its size, ignoring the sign, but keep the sign in your answer.
A café cuts the price of a coffee by 10%.
It sells 5% more coffees.
Is demand for its coffee price elastic or price inelastic?
Compare the size of the two percentage changes. Quantity rose by 5%, less than the 10% change in price, so demand is price inelastic. "Elastic" means quantity responds by more than price, not just that it responds.
A shop sells 20 a week at £10. That is the starting point, so every percentage change is worked out from these numbers.
It cuts the price to £8 and sales rise to 26 a week. Work out the two percentage changes from the old values.
Check: The shop cuts its price from £10 to £8. What is the percentage change in price?
(8 − 10) ÷ 10 × 100 = −20%. Divide by the old price, £10. Dividing by £8 gives −25%, the common mistake.
Quantity: (26 − 20) ÷ 20 × 100 = +30%. Price: (8 − 10) ÷ 10 × 100 = −20%. PED = +30 ÷ −20 = −1.5.
Interpret it in words, which is what "outline what a PED of −1.5 means" asks for: a 1% change in price causes a 1.5% change in quantity demanded, in the opposite direction. Quantity responds more than proportionately, so demand is price elastic.
Check: What does a PED of −1.5 mean?
PED is the % change in quantity for each 1% change in price. The minus sign tells you they move in opposite directions.
A different good, starting at the same point. The price rises from £10 to £12, which is +20%. Sales fall from 20 to 18, which is −10%. PED = −10 ÷ 20 = −0.5. Quantity responds less than proportionately: price inelastic.
So, ignoring the sign: bigger than 1 is elastic; between 0 and 1 is inelastic; exactly 1 is unitary elastic. Two extremes: 0 is perfectly inelastic, where quantity does not change at all, and infinity is perfectly elastic, where any price rise loses every sale.
Check: PED for a good is −1. A 6% rise in price will cause quantity demanded to:
Unitary elasticity: quantity changes by the same percentage as price, in the opposite direction.
Rearrange the formula to predict: % change in quantity = PED × % change in price. Cigarettes, with PED −0.4: a 10% price rise gives −0.4 × 10 = a 4% fall in smoking.
They divided the % change in price by the % change in quantity: 20 ÷ −10 = −2. PED puts quantity on top: −10 ÷ 20 = −0.5, which is inelastic, not elastic.
The PED for cigarettes is estimated at −0.4. Outline what this means.
Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its own price. It is the percentage change in quantity demanded divided by the percentage change in price.
A PED of −0.4 means that a 1% rise in the price of cigarettes causes a 0.4% fall in the quantity demanded, so a 10% price rise would cut the quantity smoked by about 4%. The minus sign shows that price and quantity demanded move in opposite directions, as the law of demand predicts.
Because 0.4 is less than 1, ignoring the sign, demand for cigarettes is price inelastic: quantity demanded changes proportionately less than price. This is likely because cigarettes are addictive and have few close substitutes.
However, −0.4 is an estimate based on past data and assumes other things stay the same. Demand is likely to become more elastic in the long run, as smokers have time to quit or switch to vapes, and it may be more elastic for young smokers, for whom cigarettes take a bigger share of income.
Cigarette elasticity: World Bank, Curbing the Epidemic (1999). Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.