What this lesson teaches
I can use price, income and cross elasticities to judge how large those changes will be.
Syllabus 9570, 2.1.2(g). Demand and Supply Analysis and its Applications: These outcomes can be affected by price elasticities of demand and supply, income and cross elasticities of demand
Make a guess
A hawker raises the price of chicken rice by 10% and sells 5% fewer plates. Is demand for her chicken rice elastic or inelastic?
- Elastic. Sales fell, so buyers responded to the price.
- Inelastic. Quantity changed by a smaller percentage than price.
- Elastic. The PED is negative, which means a strong response.
Show the answer
Inelastic. Quantity changed by a smaller percentage than price.
PED = -5 / 10 = -0.5. Ignore the sign: 0.5 is below 1, so demand is price inelastic.
PED = % change in quantity demanded / % change in price. Above 1 is elastic; below 1 is inelastic.
Price elasticity of demand (PED) measures how much quantity demanded responds to a change in the good's own price, ceteris paribus.
PED = percentage change in quantity demanded / percentage change in price. Work out each percentage change as (new - old) / old x 100.
PED is negative, because price and quantity demanded move in opposite directions. To classify it, ignore the minus sign.
If the value is more than 1, demand is price elastic: quantity changes by a bigger percentage than price. If it is less than 1, demand is price inelastic. Exactly 1 is unit elastic.
- PED
- % change in Qd / % change in P.
- Elastic
- |PED| > 1.
- Inelastic
- |PED| < 1.
| Value | Name | Meaning |
|---|---|---|
| 0 | Perfectly inelastic | Quantity does not change |
| 0 to 1 | Inelastic | Quantity changes less than price |
| 1 | Unit elastic | Same percentage change |
| More than 1 | Elastic | Quantity changes more than price |
Worked example: Cinema tickets
A cinema raises its ticket price from $10 to $12. Weekly tickets sold fall from 1,000 to 700.
- % change in price = (12 - 10) / 10 x 100 = +20%.
- % change in quantity demanded = (700 - 1,000) / 1,000 x 100 = -30%.
- PED = -30 / 20 = -1.5.
- Ignoring the sign, 1.5 is more than 1, so demand is price elastic: quantity responds more than proportionally to the price change.
Try it step by step
Problem 1
A bubble tea shop raises its price from $4.00 to $5.00. Weekly cups sold fall from 1,200 to 900.
Show the working
- Percentage change in price: (5 - 4) / 4 x 100 = +25%
- Percentage change in quantity demanded: (900 - 1,200) / 1,200 x 100 = -25%
- PED: PED = -25 / 25 = -1
- Elastic or inelastic?: Ignoring the sign, the value is exactly 1, so demand is unit elastic.
Problem 2
A bookshop cuts the price of a novel from $20 to $16. Monthly sales rise from 500 to 650.
Show the working
- Percentage change in price: (16 - 20) / 20 x 100 = -20%
- Percentage change in quantity demanded: (650 - 500) / 500 x 100 = +30%
- PED: PED = 30 / -20 = -1.5
- Elastic or inelastic?: Ignoring the sign, 1.5 is more than 1, so demand is price elastic.
Problem 3
A gym raises its monthly fee from $80 to $100. Members fall from 2,000 to 1,900.
Show the working
- Percentage change in price: (100 - 80) / 80 x 100 = +25%
- Percentage change in quantity demanded: (1,900 - 2,000) / 2,000 x 100 = -5%
- PED: PED = -5 / 25 = -0.2
- Elastic or inelastic?: Ignoring the sign, 0.2 is well below 1, so demand is price inelastic.
Watch out for this
A PED of -2 means demand is inelastic because the number is negative.
The minus sign only shows that price and quantity move in opposite directions. Classify by the size: 2 is more than 1, so demand is elastic.
Check your understanding
A price rises by 8% and quantity demanded falls by 4%. What is the PED?
- +0.5, which means it is a normal good.
- -0.5, inelastic.
- -2, elastic.
Show the answer
-0.5, inelastic.
Right. -4 / 8 = -0.5, and 0.5 is less than 1.