📉 Elastic: opposite
Price and total revenue move in opposite directions. A price cut helps revenue.
Elasticity » PED and Total Revenue
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.1.4 (g)
- How to work out total revenue (price x quantity)
- Why a price change moves total revenue in opposite directions when demand is elastic
- Why a price change moves total revenue in the same direction when demand is inelastic
- How to use a change in total revenue to decide if demand is elastic or inelastic
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Unlock This CourseTotal revenue: the money coming in
Total revenue is price times quantity: every ticket sold at the gate adds to it
This topic is examined on Paper 1 (Microeconomics and Business Economics). So far you have judged elasticity by working out a PED number. There is a second way. You can look at what happens to the money a firm takes in when it changes its price.
Key terms:
- Total revenue: the total money a firm receives from selling its output. Total revenue = price x quantity sold.
Total revenue only counts the money coming in. It does not take away any costs.
When a firm changes its price, two things happen at once. The price per item changes. The number of items sold changes too, because of the law of demand. Total revenue depends on which of the two changes wins. The answer is decided by elasticity.
Elastic demand: price and revenue move in opposite directions
If demand is price elastic, buyers react a lot. The percentage change in quantity demanded is bigger than the percentage change in price.
Worked example 1: elastic demand
A shop sells yoga mats for 20 pounds. It sells 100 a week.
Total revenue = 20 x 100 = 2,000 pounds.
The shop cuts the price to 16 pounds. Sales rise to 150 a week.
New total revenue = 16 x 150 = 2,400 pounds.
The price fell and total revenue rose. They moved in opposite directions, so demand is price elastic.
Check with PED: % change in quantity = 50 / 100 x 100 = +50%. % change in price = -4 / 20 x 100 = -20%. PED = +50 / -20 = -2.5. The number ignoring the minus sign is above 1, so demand is elastic.
Why does this happen? The price cut loses a little on each item, but it brings in many more buyers. The extra sales are worth more than the money lost. If this shop raised its price, it would lose so many buyers that total revenue would fall.
Inelastic demand: price and revenue move in the same direction
Raise the price of a train ticket people need for work and revenue goes up: demand is price inelastic
If demand is price inelastic, buyers react only a little. The percentage change in quantity demanded is smaller than the percentage change in price.
Worked example 2: inelastic demand
A local newspaper costs 2.00 pounds. It sells 500 copies a week.
Total revenue = 2.00 x 500 = 1,000 pounds.
The paper raises its price to 2.50 pounds. Sales fall to 450 copies.
New total revenue = 2.50 x 450 = 1,125 pounds.
The price rose and total revenue rose. They moved in the same direction, so demand is price inelastic.
Check with PED: % change in quantity = -50 / 500 x 100 = -10%. % change in price = 0.50 / 2.00 x 100 = +25%. PED = -10 / +25 = -0.4. The number ignoring the minus sign is below 1, so demand is inelastic.
Here the price rise adds more on every copy than is lost from the few buyers who leave. If the paper cut its price, it would gain very few new buyers, so total revenue would fall.
The rule in one table
| Type of demand | Price rises | Price falls |
|---|---|---|
| Price elastic (PED above 1, ignoring the sign) | Total revenue falls | Total revenue rises |
| Price inelastic (PED below 1, ignoring the sign) | Total revenue rises | Total revenue falls |
📈 Inelastic: same
Price and total revenue move in the same direction. A price rise helps revenue.
With unitary price elasticity (PED of 1, ignoring the sign), the percentage change in quantity matches the percentage change in price, so total revenue stays the same.
Using revenue to decide: the three-step method
Worked example 3: deciding from the figures
A bike repair shop charges 8 pounds for a puncture repair and does 200 a month. It raises the price to 10 pounds and does 140.
Step 1. Work out total revenue before: 8 x 200 = 1,600 pounds.
Step 2. Work out total revenue after: 10 x 140 = 1,400 pounds.
Step 3. Compare the directions. Price rose, total revenue fell. They moved in opposite directions, so demand is price elastic.
Always say what happened to the price and what happened to total revenue. The conclusion needs both.
Common mistakes
- Saying total revenue always rises when price rises. It only rises when demand is inelastic.
- Adding price and quantity instead of multiplying them.
- Saying "revenue fell, so demand is elastic" without checking which way the price moved. A fall in revenue after a price cut means demand is inelastic.
- Mixing up revenue and profit. Revenue is money coming in. Profit also takes away costs.
Exam-style question
A cinema charges 10 pounds a ticket and sells 400 tickets on a Tuesday night. It cuts the price to 8 pounds and sells 450 tickets.
(a) Calculate total revenue before and after the price cut. [2 marks]
(b) Explain whether demand for the tickets is price elastic or price inelastic, using your answers to part (a). [2 marks]
(c) Calculate the PED. Show your working. [2 marks]
(d) The owner now wants to raise total revenue. Explain whether raising the price above 8 pounds is likely to help. [2 marks]
Model answer
(a) Before: 10 x 400 = 4,000 pounds (1). After: 8 x 450 = 3,600 pounds (1).
(b) The price fell and total revenue fell (1), so they moved in the same direction and demand is price inelastic (1).
(c) % change in quantity = 50 / 400 x 100 = +12.5% (1). % change in price = -2 / 10 x 100 = -20%. PED = 12.5 / -20 = -0.625 (1).
(d) Demand is inelastic, so the percentage fall in quantity demanded would be smaller than the percentage rise in price (1). Total revenue is therefore likely to rise (1).
Exam tip
For part (b) write two short facts: what the price did and what total revenue did. Then link them to elastic or inelastic. Marks are awarded for the link.