You already know demand falls when price rises. The useful question is by how much. Put the price of petrol up 10% and people barely change their driving. Put one brand of crisps up 10% and half the shelf stays full. Price elasticity of demand is the number that captures that difference.
📘 What you need to know
PED measures how responsive quantity demanded is to a change in price.
PED = % change in quantity demanded ÷ % change in price.
The answer is almost always negative, because price and quantity move in opposite directions. Say so, then use the size of the number to describe it.
Two theoretical extremes: perfectly elastic (PED = infinity, a horizontal curve) and perfectly inelastic (PED = 0, a vertical curve).
What decides PED: SPLAT — Substitutes, Proportion of income, Luxury or necessity, Addictiveness, Time.
PED is not the slope. On one straight-line demand curve, PED changes from high at the top to low at the bottom.
Calculating PED
There is one formula, and it only ever needs two percentage changes. Work them out first, then divide.
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
Keep the minus sign until the very end. Write “PED = −0.8, so demand is price inelastic”. That one sentence shows the examiner you know the sign is negative and that you read the size correctly.
WORKED EXAMPLE
A bakery raises the price of a loaf from $8 to $10. Weekly sales fall from 500 loaves to 400. Calculate the PED and comment on it. [3]
Step 1: % change in quantity demanded(400 − 500) ÷ 500 × 100 = −20%Step 2: % change in price(10 − 8) ÷ 8 × 100 = +25%Step 3: dividePED = −20 ÷ 25 = −0.8PED = −0.8, so demand is price inelastic0.8 is less than 1, so quantity changed proportionally less than price.
WORKED EXAMPLE
A cinema knows its PED is −1.6. It cuts ticket prices by 10%. Sales were 250 tickets a night. Estimate the new sales figure. [2]
Step 1: rearrange the formula% change in QD = PED × % change in PStep 2: substitute−1.6 × −10 = +16%Step 3: apply the percentage to the old quantity250 × 1.16 = 290Sales rise to about 290 tickets a nightTwo negatives multiply to a positive — a price cut raises quantity, as it should.
Reading the number
Once you have a value, describe it. The size tells you how strongly buyers reacted, and the shape of the curve on a diagram shows the same thing: a shallow curve is elastic, a steep curve is inelastic.
Both diagrams show the same idea from opposite directions. What matters is the size of the quantity change compared with the size of the price change.
The two extremes and the middle case
Three more values come up in the syllabus. Two of them barely exist in real life, but examiners like them because they show you understand what the number means.
A useful mental picture: the flatter the curve, the more easily buyers walk away.
What makes demand elastic or inelastic: SPLAT
Five things decide how much buyers react. The acronym SPLAT is the quickest way to remember them, and naming the relevant one is usually where the marks are.
In an exam, pick the one or two letters that actually matter for the good in the question and explain them properly. Listing all five earns less than explaining two.
Going through the letters
S — Substitutes. The more close alternatives there are, the more elastic demand is. One brand of fizzy drink is elastic; fizzy drinks as a whole are not.
P — Proportion of income. A 20% rise in the price of a box of matches is not worth noticing. A 20% rise in the price of a car very much is. Cheap items tend to be inelastic.
L — Luxury or necessity. You can skip a holiday. You cannot skip bread, medicine or the bus to school. Necessities are inelastic.
A — Addictiveness. Habit turns a want into a need. Cigarettes and caffeine have low PED for exactly this reason.
T — Time. Given time, people find substitutes and change their habits. Demand for heating oil is inelastic this winter and much more elastic over five years, once households can switch systems.
Definition matters. Elasticity depends on how narrowly you define the good. “Bananas” has substitutes and is fairly elastic; “fruit” has fewer substitutes and is more inelastic. Say which you mean.
PED changes along a straight demand curve
This is the point students most often get wrong. The slope of a straight demand curve never changes, but the elasticity does. High up the curve the price is high and the quantity small, so a small price change is a small percentage while the quantity change is a big percentage — demand is elastic. Low down the curve it is the other way round.
The midpoint of a straight demand curve is always unit elastic. Above it demand is elastic, below it inelastic.
WORKED EXAMPLE
On the demand curve above, calculate PED for a price fall from $8 to $6, then for a price fall from $4 to $2. Comment on your answers. [4]
Step 1: read the quantities off the diagram$8 → 20 units, $6 → 40 units, $4 → 60 units, $2 → 80 unitsStep 2: top of the curve, $8 to $6%QD = +100%, %P = −25%, PED = −4Step 3: bottom of the curve, $4 to $2%QD = +33.3%, %P = −50%, PED = −0.67Elastic (−4) at the top, inelastic (−0.67) at the bottomSame line, same slope, completely different elasticity. That is the whole point.
🧩 A safe order for any PED question
% change in quantity demanded first, using the old value on the bottom.
% change in price next, again over the old value.
Divide quantity by price — never the other way round.
Keep the minus sign and state it.
Describe the size: above 1 elastic, below 1 inelastic, exactly 1 unit elastic.
Explain it with SPLAT if the question asks why.
💡 Exam tip
Show every line of working. Most PED questions give a mark for method even if the final number is wrong.
Quantity on top, price on the bottom. Flipping the formula is the most common way to lose both marks.
Round sensibly and keep two decimal places unless told otherwise.
If a question gives you PED and one percentage change, rearrange rather than guessing: %QD = PED × %P.
When asked why a good has a certain PED, name the SPLAT factor and explain it in a sentence. Do not just list the acronym.
Never call a steep curve inelastic without checking where on it you are — on one straight line, elasticity changes.
⚠ Common mix-up
Putting price on top. PED is quantity over price, always.
Dividing by the new value when finding a percentage change. It is always the old value.
Ignoring the negative sign completely. Mention it, then work with the size.
Confusing elastic with “big demand”. Elasticity is about responsiveness, not about how much is bought.
Treating slope as elasticity. A straight line has one slope but many PED values.
Saying a good is inelastic “because people need it” without naming the determinant. Use the word necessity and explain.
Forgetting that time changes the answer. Almost everything is more elastic in the long run.
Up next: PED, Total Revenue and Decision Making — where this number stops being maths and starts telling firms and governments what to actually do.
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