📏 Draw the axes and curve
Put Price on the vertical axis and Quantity on the horizontal axis. Draw a downward-sloping demand curve and label it D.
Price Elasticity of Demand » PED, Consumer Spending and Firms' Revenue
What you'll learn this session
Study time: 30 minutes
Cambridge spec: 2.6.4
- How to work out consumer spending and a firm's revenue from price and quantity
- How to show spending and revenue as a rectangle on a demand diagram
- What happens to spending and revenue when price rises or falls, for inelastic, elastic and unitary demand
- How to use PED to predict the change in revenue, with calculations
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Unlock This CourseSpending and revenue are the same money
Every coin this customer spends is revenue for the shop - price x quantity gives both
When you buy a bar of chocolate, the money you spend is the money the shop receives. So the amount spent by consumers and the revenue raised by the firm are the same number, seen from two sides. Both are worked out in the same way.
The formula
Consumer spending = firm's revenue = price × quantity sold
Key terms:
- Consumer expenditure: the total amount of money consumers spend on a good.
- Revenue: the money a firm receives from selling its goods, found by price multiplied by quantity sold.
Remember that PED measures how much quantity demanded responds to a price change. This lesson uses PED to predict what happens to the money.
Showing revenue on a diagram
Revenue is an area on a demand diagram, because area = length × width. Draw it like this:
📈 Draw the rectangle
Pick a price, P1. Draw a horizontal line from P1 across to the curve, then a vertical line down to the quantity axis at Q1. The rectangle from the origin to this point is the revenue (P1 × Q1).
Now raise the price to P2. Move up the curve and draw a second rectangle with price P2 and quantity Q2. The new rectangle is taller but narrower. Two areas matter:
- The strip you gain: the extra price on the units still sold.
- The strip you lose: the units no longer sold, at the old price.
If the gained strip is bigger, revenue rises. If the lost strip is bigger, revenue falls. How big each strip is depends on how steep the curve is, which is PED.
Inelastic demand: a price rise increases revenue
With inelastic demand (PED less than 1), buyers hardly change what they buy. The curve is steep, so the quantity lost is small and the gained strip is bigger.
Worked example 1: petrol
A made-up petrol station in Norrin raises its price from $1.00 to $1.20 per litre. Daily sales fall from 1,000 litres to 950 litres.
Percentage change in price = 0.20 ÷ 1.00 × 100 = 20%. Percentage change in quantity = 50 ÷ 1,000 × 100 = 5%. PED = 5 ÷ 20 = 0.25, so demand is inelastic.
Revenue before = $1.00 × 1,000 = $1,000. Revenue after = $1.20 × 950 = $1,140. Revenue rises by $140.
The price rise of 20% beat the fall in sales of 5%. Consumers spend more in total, and the firm earns more.
Elastic demand: a price rise reduces revenue
Empty seats mean lost money: cinema demand is elastic, so raising ticket prices can cut total revenue
With elastic demand (PED greater than 1), buyers react strongly. The curve is shallow, so the lost strip is bigger than the gained strip.
Worked example 2: cinema tickets
A made-up cinema in Pelmar raises its ticket price from $10 to $12. Weekly tickets sold fall from 500 to 350.
Percentage change in price = 2 ÷ 10 × 100 = 20%. Percentage change in quantity = 150 ÷ 500 × 100 = 30%. PED = 30 ÷ 20 = 1.5, so demand is elastic.
Revenue before = $10 × 500 = $5,000. Revenue after = $12 × 350 = $4,200. Revenue falls by $800.
A price fall does the opposite. If the cinema cuts the price from $10 to $8 (a 20% fall) and sales rise from 500 to 700 (a 40% rise), PED is 2. Revenue goes from $5,000 to $8 × 700 = $5,600. For elastic demand, a price cut increases revenue.
Unitary demand: no change in revenue
With unitary demand (PED = 1), the percentage change in quantity equals the percentage change in price. The gained strip and lost strip are equal, so revenue stays the same.
| Price ($) | Quantity | Revenue ($) |
|---|---|---|
| 12 | 50 | 600 |
| 10 | 60 | 600 |
| 8 | 75 | 600 |
This is a made-up schedule for a unitary demand curve. Whatever the price, price × quantity is always $600.
Putting it together
| Type of demand | Price rises | Price falls |
|---|---|---|
| Inelastic (PED < 1) | Revenue rises | Revenue falls |
| Unitary (PED = 1) | No change | No change |
| Elastic (PED > 1) | Revenue falls | Revenue rises |
A quick way to remember: price and revenue move in the same direction when demand is inelastic, and in opposite directions when demand is elastic.
Common mistakes
- Saying a price rise always raises revenue. It only does if demand is inelastic.
- Using the new price with the old quantity. Always use the new price × the new quantity.
- Mixing up revenue and profit. Revenue is only price × quantity sold. Costs are not taken off.
- Answering with a number and no explanation. Always say whether demand is elastic or inelastic and why revenue changed.
Exam-style question
The Ardel Theatre in the made-up country of Calvoria raises its ticket price from $20 to $25. The number of tickets sold each week falls from 400 to 360.
(a) Calculate the price elasticity of demand for tickets. Show your working. [3 marks]
(b) Calculate the change in the theatre's weekly revenue. [2 marks]
(c) Explain why the theatre's revenue changed in this way. [2 marks]
(d) Analyse what would have happened to revenue if demand had been elastic. [3 marks]
Model answer
(a) Percentage change in price = 5 ÷ 20 × 100 = 25% (1). Percentage change in quantity = 40 ÷ 400 × 100 = 10% (1). PED = 10 ÷ 25 = 0.4 (1).
(b) Revenue before = $20 × 400 = $8,000. Revenue after = $25 × 360 = $9,000 (1). Revenue rises by $1,000 (1).
(c) Demand is inelastic because PED is less than 1 (1). The percentage fall in tickets sold is smaller than the percentage rise in price, so revenue rises (1).
(d) If demand were elastic, the percentage fall in quantity would be bigger than the percentage rise in price (1). Fewer tickets would be sold, so the revenue lost on the lost sales would be greater than the revenue gained from the higher price (1). Revenue would fall (1).
Exam tip
In a revenue question, write out both calculations in full (price × quantity before and after) and state the difference. Marks are given for the working, not just the final figure.