The law of demand tells you that a price rise makes people buy less. Useful, but not enough. If you run a business or a treasury, the question you actually need answered is how much less. That single question is what price elasticity of demand measures, and it is one of the highest-value calculations in the whole course.
📚 What you need to know
PED measures how responsive quantity demanded is to a change in price.
PED = percentage change in quantity demanded ÷ percentage change in price.
The answer is always negative because price and quantity move in opposite directions. Economists then drop the sign when describing the size.
PED bigger than 1 means elastic (responsive). Between 0 and 1 means inelastic (unresponsive). Exactly 1 is unit elastic.
Never write the answer as a percentage. PED has no units.
Five things determine PED: substitutes, share of income, necessity or luxury, habit, and time.
PED changes as you move along a straight-line demand curve, even though the slope stays the same.
The formula, and how to use it properly
Price elasticity of demand
PED = % change in quantity demanded ÷ % change in price
And to get each percentage change
% change = (new value − old value) ÷ old value × 100
Two habits will save you marks every single time. First, always work out the two percentage changes separately and write them down before you divide. Second, keep the minus signs while you calculate and only drop them at the end when you describe the result.
Think of PED as a ratio of stretchiness. A PED of 3 says quantity moves three times as hard as price. A PED of 0.2 says quantity barely budges. Once you see it as “how many times”, the numbers stop feeling abstract.
Elastic and inelastic demand on a diagram
A shallow demand curve means a small price change produces a large change in quantity. A steep one means even a big price change barely moves quantity. Compare the two side by side and the difference is obvious.
Same axes, same scale — only the steepness differs. That is what makes the two situations comparable at a glance.
The five values of PED
PED runs from 0 to infinity. Two of the five cases are theoretical extremes you will almost never meet in real life, but you still need to recognise their diagrams.
Steeper always means less elastic. The vertical line is quantity that cannot move at all; the horizontal line is quantity that collapses the moment price rises.
Case
What it means
Closest real example
Perfectly inelastic (0)
Quantity does not change at all when price changes
A patient who needs life-saving insulin buys it whatever it costs
Relatively inelastic (0 to 1)
Quantity changes by proportionally less than price
Petrol, bread, cigarettes
Unit elastic (1)
Quantity changes by exactly the same proportion as price
A 5% price rise on a mobile plan causing a 5% drop in subscribers
Relatively elastic (above 1)
Quantity changes by proportionally more than price
A particular brand of trainers, budget airline seats
Perfectly elastic (infinite)
Any price rise wipes out demand completely
A single seller of an identical commodity in a market with hundreds of sellers
What makes demand elastic or inelastic
Five factors decide it. Rather than memorising a list, turn each one into a question you ask about the good in front of you.
Factor
Ask yourself
Effect on PED
Substitutes
Can I easily switch to something else?
Many close substitutes makes demand more elastic
Share of income
Does this take a big slice of my budget?
Cheap items barely noticed are more inelastic
Necessity or luxury
Do I have to have it?
Necessities are inelastic; luxuries are elastic
Habit or addiction
Would I struggle to stop?
Addictive goods behave like necessities, so inelastic
Time
How long have I had to react?
Demand is more elastic in the long run, as people find alternatives
Substitutes is the big one. Almost every other factor works through it. A necessity is inelastic because there is nothing to swap to; demand gets more elastic over time because people eventually find something to swap to. If you only have space for one factor in an answer, use this one.
Always ask how the good is defined. Demand for “petrol” is inelastic because you need to drive. Demand for “petrol from the Shell station on the corner” is very elastic, because the BP down the road is a perfect substitute. Narrow definition, elastic demand.
PED changes along a straight-line demand curve
This trips people up every year, so slow down here. A straight demand curve has one slope all the way down. But PED is not the slope. PED compares percentage changes, and percentages depend on where you started.
Near the top of the curve, price is high and quantity is low. A one-unit change in quantity is a big percentage of a small number, so PED is large. Near the bottom the reverse is true. Same line, different elasticity.
Worked from the demand equation P = 10 − 0.1Q. At Q = 20 elasticity is 4, at Q = 50 it is exactly 1, and at Q = 80 it has fallen to 0.25.
Worked examples
WORKED EXAMPLE 1
A cafe raises the price of a sandwich from $10 to $12. Weekly sales fall from 500 to 400. Calculate the PED and state what it means. [4]
Step 1: percentage change in quantity demanded(400 − 500) ÷ 500 × 100 = −20%Step 2: percentage change in price(12 − 10) ÷ 10 × 100 = +20%Step 3: dividePED = −20 ÷ 20 = −1PED = 1 (unit elastic)Quantity changed by exactly the same proportion as price, so total revenue is unchanged.
WORKED EXAMPLE 2
The PED for a bus route is 0.4. Fares rise by 15%. Current passenger numbers are 2,000 per day. Calculate the new number of passengers. [3]
Step 1: rearrange the formula
% change in QD = PED × % change in P
Step 2: substitute (remember QD falls)−0.4 × 15 = −6%Step 3: apply to the current number2,000 × 0.06 = 120 passengers lost2,000 − 120 = 1,8801,880 passengers per dayFares rose 15% but passengers fell only 6% — that is what inelastic demand looks like in practice.
WORKED EXAMPLE 3
A firm knows PED for its product is 2.5. It wants quantity demanded to rise by 20%. By what percentage should it cut the price? [2]
Step 1: write the formula with X for the unknown2.5 = 20 ÷ XStep 2: solve for XX = 20 ÷ 2.5 = 8A price cut of 8%This “substitute X and solve” style appears often in Paper 2. Practise it in both directions.
💡 Exam tip
Show both percentage changes before dividing. If you slip up on the final step you still pick up a working mark.
Never write a % sign on the PED answer. It is a plain number and adding units loses a mark.
State the answer and interpret it. “PED = 0.3, so demand is price inelastic” is worth more than the number alone.
Use old value as the denominator. Dividing by the new value is the most common arithmetic error here.
When asked to explain why a good has that PED, name a determinant and apply it to the good in the question.
If a question gives PED and one percentage change, just substitute and solve for X.
⚠️ Common mix-up
Confusing slope with elasticity. A straight line has one slope but many elasticities.
Forgetting the negative sign exists. The value is negative; economists just report the size. Say so if the question asks about the sign.
Mixing up elastic and inelastic. Elastic stretches easily, so quantity moves a lot. Steep line = inelastic.
Treating “inelastic” as “no change”. That is perfectly inelastic. Relatively inelastic still means some change.
Using PED language for supply questions. PED is about consumers only.
Answering “why” questions with the formula. The formula tells you the value, not the reason. The reason is a determinant.
Up next: Why PED Matters for Revenue and Policy — now that you can calculate it, we look at what firms and governments actually do with the number. This is where the marks get easier and the analysis gets deeper.
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