🧮 Step 1: price
Work out the percentage change in price: (new price − old price) ÷ old price × 100.
Price Elasticity of Demand » Price Elasticity of Demand: Definition and Calculation
What you'll learn this session
Study time: 30 minutes
Cambridge spec: 2.6.1, 2.6.2
- What price elasticity of demand (PED) means
- How to calculate percentage changes and PED using the formula
- What the PED value tells you: perfectly inelastic, inelastic, unitary, elastic and perfectly elastic
- Why the minus sign is ignored when you interpret the answer
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Unlock This CourseHow much do buyers respond to a price change?
Bread is bought whatever the price - its demand is inelastic, so a price rise barely changes how much people buy
When the price of a good rises, the quantity demanded falls. You already know that. But by how much? If the price of bread goes up, most people still buy bread. If the price of a holiday goes up, many people stay at home instead. Economists need a way to measure this difference.
Key terms:
- Price elasticity of demand (PED): a measure of how responsive the quantity demanded of a good is to a change in its price.
- Percentage change: the size of a change compared with the starting (original) amount, written as a percentage.
The word "responsive" is the key idea. If a small price change causes a big change in quantity demanded, demand is very responsive. If a big price change causes only a small change in quantity demanded, demand is not very responsive.
The PED formula
PED is worked out by comparing two percentage changes.
Formula
PED = percentage change in quantity demanded ÷ percentage change in price
To find a percentage change, use this:
Percentage change
Percentage change = (change ÷ original value) × 100
Always divide by the original value, not the new one. A rise gives a positive change. A fall gives a negative change.
📦 Step 2: quantity
Work out the percentage change in quantity demanded in the same way, using the old and new quantities.
➖ Step 3: divide
Divide the percentage change in quantity demanded by the percentage change in price. Then say what the answer means.
Worked example 1: bread
Worked example
In the town of Tavira, the price of a loaf of bread rises from $2.00 to $2.20. The quantity demanded falls from 500 loaves a day to 490 loaves a day. Calculate PED.
Price: change = $0.20. 0.20 ÷ 2.00 × 100 = +10%.
Quantity: change = −10. −10 ÷ 500 × 100 = −2%.
PED: −2 ÷ 10 = −0.2.
Price went up 10%, but quantity demanded fell by only 2%. Buyers hardly responded.
What does the value tell you?
The size of the PED number tells you how responsive demand is. There are five named cases.
| PED value (ignoring the minus sign) | Name | What it means |
|---|---|---|
| 0 | Perfectly inelastic | Quantity demanded does not change at all when price changes. |
| Between 0 and 1 | Inelastic | Quantity demanded changes by a smaller percentage than price. |
| 1 | Unitary | Quantity demanded changes by exactly the same percentage as price. |
| Greater than 1 | Elastic | Quantity demanded changes by a larger percentage than price. |
| Infinity | Perfectly elastic | Any rise in price, however small, causes quantity demanded to fall to zero. |
Key terms:
- Elastic demand: PED is greater than 1. Buyers are very responsive to price.
- Inelastic demand: PED is between 0 and 1. Buyers are not very responsive to price.
- Unitary demand: PED is exactly 1.
- Perfectly inelastic demand: PED is 0.
- Perfectly elastic demand: PED is infinity.
Why we ignore the minus sign
Because price and quantity demanded move in opposite directions, a PED answer is almost always negative. The minus sign only tells you that. What matters is the size of the number. So when you say whether demand is elastic or inelastic, ignore the minus sign. A PED of −0.2 is treated as 0.2, which is inelastic. A PED of −1.6 is treated as 1.6, which is elastic.
Worked example 2: a rise in price, elastic demand
Raise the gym fee and lots of members quit - when quantity changes by a bigger % than price, demand is elastic
Worked example
A gym in Corvane charges $40 a month. It raises the price to $50. The number of members falls from 400 to 240. Calculate PED and say what it shows.
Price: change = $10. 10 ÷ 40 × 100 = +25%.
Quantity: change = −160. −160 ÷ 400 × 100 = −40%.
PED: −40 ÷ 25 = −1.6.
Ignoring the minus sign, 1.6 is greater than 1, so demand is elastic. Members were very responsive to the price rise.
Worked example 3: a fall in price
Worked example
A shop in Zandor cuts the price of a game from $10 to $8. The quantity demanded rises from 1,000 to 1,500 a week. Calculate PED.
Price: change = −$2. −2 ÷ 10 × 100 = −20%.
Quantity: change = +500. 500 ÷ 1,000 × 100 = +50%.
PED: 50 ÷ −20 = −2.5. Demand is elastic.
Notice that the answer is still negative. A price fall leads to a rise in quantity, so the two percentage changes still have opposite signs.
Common mistakes
Common mistakes
- Dividing by the new value. Percentage change always uses the original value.
- Turning the formula upside down. Quantity goes on top, price goes underneath.
- Using the raw change. A $10 rise is not 10%. Convert to a percentage first.
- Saying a PED of −3 is inelastic because it is negative. Ignore the minus sign. 3 is greater than 1, so it is elastic.
- Mixing up the words. Elastic means a big response. Inelastic means a small response.
Exam-style question
The island of Peldor has one company that runs ferries to the mainland. The company raised the price of a ticket from $20 to $25. The number of tickets sold each week fell from 800 to 640.
(a) Define price elasticity of demand. [2 marks]
(b) Calculate the price elasticity of demand for ferry tickets. Show your working. [3 marks]
(c) State whether demand is elastic or inelastic and give a reason for your answer. [2 marks]
Model answer
(a) Price elasticity of demand is a measure of the responsiveness (1) of quantity demanded to a change in price (1).
(b) Percentage change in price = 5 ÷ 20 × 100 = 25% (1). Percentage change in quantity demanded = −160 ÷ 800 × 100 = −20% (1). PED = −20 ÷ 25 = −0.8 (1).
(c) Demand is inelastic (1) because the PED, ignoring the minus sign, is 0.8, which is between 0 and 1 (1).
Exam tip
In a "calculate" question, write each percentage change on its own line. Even if you slip at the end, you can still earn marks for correct working.