📈 Why it is negative
Price and quantity demanded normally move in opposite directions. One percentage is positive and the other is negative, so dividing them gives a negative answer.
Elasticity » Price Elasticity of Demand: Calculating PED
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.1.4 (a)-(c) and (e)
- What price elasticity of demand (PED) means
- How to work out percentage changes and calculate PED
- How to read a PED value: inelastic, unitary or elastic
- Why PED has a minus sign
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Unlock This CourseHow much do buyers react to a price change?
When petrol prices rise, drivers still need fuel, so quantity demanded barely falls: price inelastic
This topic is examined on Paper 1 (Microeconomics and Business Economics). In the lessons on demand you saw that when the price goes up, the quantity demanded usually goes down. But how far does it go down? If a shop raises its price a little, do customers walk away in crowds, or hardly notice? Economists measure the answer with a number.
Key terms:
- Price elasticity of demand (PED): a measure of how much the quantity demanded of a good changes when its price changes.
- Percentage change: how big a change is compared with the starting value, written as a percentage.
- Price elastic demand: quantity demanded changes by a bigger percentage than the price.
- Price inelastic demand: quantity demanded changes by a smaller percentage than the price.
The PED formula
Formula
PED = percentage change in quantity demanded ÷ percentage change in price
The formula needs two percentages. Sometimes the question gives them to you. Sometimes it gives old and new numbers, and you must work out the percentages first.
Worked example: percentages given
A shop raises the price of its trainers by 10%. The quantity demanded falls by 20%.
PED = −20 ÷ 10 = −2.
Working out a percentage change
Formula
Percentage change = (change ÷ original value) × 100
The change is the new value minus the original value. Always divide by the original value, the one you started with. A rise gives a positive answer. A fall gives a negative answer.
Worked example: finding the percentages first
The price of a box of pens rises from £5 to £6. The quantity demanded falls from 200 to 190 boxes a week.
1. Change in price = 6 − 5 = £1. Percentage change in price = (1 ÷ 5) × 100 = +20%.
2. Change in quantity = 190 − 200 = −10. Percentage change in quantity = (−10 ÷ 200) × 100 = −5%.
3. PED = −5 ÷ 20 = −0.25.
Worked example: a price fall
A concert ticket falls in price from £50 to £40. Sales rise from 400 to 500 tickets.
1. Percentage change in price = (−10 ÷ 50) × 100 = −20%.
2. Percentage change in quantity = (100 ÷ 400) × 100 = +25%.
3. PED = +25 ÷ −20 = −1.25.
The minus sign
✍️ What to write
Keep the minus sign in your answer, for example −2. When you decide how elastic demand is, look at how big the number is, ignoring the sign.
Reading the number
Fresh fruit stalls have lots of rivals, so a small price rise sends buyers next door: price elastic
The size of the PED tells you how strongly buyers react to the price change.
| PED value | Name | What it means |
|---|---|---|
| 0 | Perfectly price inelastic | Quantity demanded does not change at all when the price changes. |
| Between 0 and −1 | Price inelastic | Quantity demanded changes by a smaller percentage than price. |
| −1 | Unitary price elasticity | Quantity demanded changes by exactly the same percentage as price. |
| Beyond −1 (for example −2) | Price elastic | Quantity demanded changes by a bigger percentage than price. |
| Infinity | Perfectly price elastic | Buyers will buy any amount at one price, but quantity demanded falls to zero if the price rises even slightly. |
Look back at the worked examples. The pens had a PED of −0.25, between 0 and −1, so demand is price inelastic. The concert tickets had a PED of −1.25, beyond −1, so demand is price elastic.
Worked example: unitary
A café raises the price of a sandwich from £4.00 to £4.40. The quantity demanded falls from 300 to 270 a day.
Percentage change in price = (0.40 ÷ 4.00) × 100 = +10%.
Percentage change in quantity = (−30 ÷ 300) × 100 = −10%.
PED = −10 ÷ 10 = −1. Demand has unitary price elasticity.
Two special cases are mostly used in theory. A perfectly price inelastic good would have a PED of 0, because buyers take exactly the same quantity at any price. A perfectly price elastic good would have a PED of infinity. You will see how these look on diagrams in the next lesson, PED Diagrams and What Affects PED.
Common mistakes
- Dividing by the new value instead of the original value when finding a percentage change.
- Turning the formula upside down. The quantity change goes on top and the price change goes underneath.
- Leaving out the minus sign, or thinking −2 is "smaller" than −1. Ignoring the sign, 2 is bigger than 1, so demand is elastic.
- Giving the answer without saying what it means. Many questions ask you to interpret the value, so say inelastic, unitary or elastic.
Exam-style question
A ferry company raises the price of a day return ticket from £20 to £25. The number of passengers per week falls from 800 to 600.
(a) Define price elasticity of demand. [2 marks]
(b) Calculate the price elasticity of demand. You must show your working. [4 marks]
(c) State what your answer to (b) shows about demand for the ferry. [2 marks]
(d) A good has a PED of −0.4. Which one of the following describes demand for this good? [1 mark]
A Perfectly price inelastic B Price inelastic C Unitary price elasticity D Price elastic
Model answer
(a) PED measures how much the quantity demanded changes (1) when the price changes (1).
(b) Percentage change in price = (5 ÷ 20) × 100 = +25% (1). Percentage change in quantity = (−200 ÷ 800) × 100 = −25% (1). PED = percentage change in quantity demanded ÷ percentage change in price (1) = −25 ÷ 25 = −1 (1).
(c) The PED is −1, so demand has unitary price elasticity (1). The quantity demanded changes by exactly the same percentage as the price (1).
(d) B (1).
Exam tip
In a calculation, write out each percentage change on its own line, then the formula, then the answer with its minus sign. Even if you slip on the last step, you can still collect the working marks.