Elasticity and total revenue
Why raising a price can increase or decrease what sellers take in, and three of Mankiw's puzzles solved with elasticity.
FinanceA company's marketAbout 5 min: 3 reading, 2 practiceUpdated
General education, not financial advice.
- Predict how a price change affects total revenue from the elasticity of demand
- Explain why a better harvest can lower farm incomes
- Use elasticity to explain OPEC's experience and the effects of drug policies
Builds toward: Judge a company. Read a company's accounts, apply Graham's tests, and make a rough valuation.
A company's market: pricing power, taxes and trade: lesson 2 of 15
- A company's market
- Price elasticity of demand 6 min
- Elasticity and total revenue 5 min
- Consumer and producer surplus 4 min
- Market efficiency 5 min
- Price ceilings and floors 6 min
- Who really pays a tax 5 min
- Deadweight loss 5 min
- How tax size changes the loss 5 min
- Absolute and comparative advantage 5 min
- Why trade helps both sides 5 min
- Winners and losers from trade 5 min
- Tariffs and quotas 5 min
- What makes productivity grow 5 min
- Growth policy 5 min
- Why unemployment exists 6 min
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Pairs with any introductory economics textbook; for example N. Gregory Mankiw, Principles of Macroeconomics (6th ed.), chapter 5
What it is
Total revenue is what buyers pay and sellers receive: price × quantity sold.
When a seller raises the price, two things happen: each unit sold brings in more, but fewer units are sold. Which effect wins depends on the elasticity of demand:
| Demand | Price rises | Price falls |
|---|---|---|
| Inelastic (below 1) | Revenue rises | Revenue falls |
| Elastic (above 1) | Revenue falls | Revenue rises |
| Unit elastic (1) | Revenue unchanged | Revenue unchanged |
Mankiw's figures: with inelastic demand, a price rise from 4 to 5 cuts the quantity from 100 to 90, and revenue rises from 400 to 450. With elastic demand, the same rise cuts the quantity from 100 to 70, and revenue falls from 400 to 350.
Quick check
Tap an answer to check it.
A museum's demand is elastic. It wants more ticket revenue. Should it raise or lower the price?
- With elastic demand, a price rise loses proportionately more visitors
Show answer
Lower it: with elastic demand, the extra visitors more than make up for the lower price. When demand is elastic, price and revenue move in opposite directions.
Why it matters
Mankiw applies elasticity to three puzzles.
1. Can good news for farming be bad news for farmers? A new wheat hybrid raises yields by 20%. Supply shifts right, so the price falls and the quantity rises. But the demand for basic foods is usually inelastic, so the price falls proportionately more than the quantity rises, and total revenue falls. Each farmer gains by adopting the hybrid; farmers together may be worse off. Mankiw uses this to explain why farm incomes can fall as farming becomes more productive, and why some farm programmes try to help farmers by inducing them not to plant all their land, cutting supply to raise the price.
2. Why did OPEC fail to keep oil prices high? When OPEC cut supply in the 1970s, prices rose sharply, because in the short run both supply and demand for oil are inelastic. Over time, the market became more elastic: buyers drove less and switched to more efficient cars, and producers outside OPEC found more oil. Through the 1980s the price fell, and by 1990 it was back to its 1970 level.
3. Drug policy. Stopping drugs entering the country (interdiction) shifts supply left, so the price rises. If demand is inelastic, users' total spending rises, and the users who fund their habit by theft may steal more, so drug-related crime can rise in the short run. Policies that reduce demand, such as education, lower both the quantity and the price, and reduce total spending. Mankiw notes that, for this reason, some analysts argue for demand-side policies such as education instead.
Worked example
A wheat market: last year the price was 4 a bushel and farmers sold 100 million bushels. A good harvest raises supply, and the price falls to 3, at which buyers take 110 million.
- Revenue before: 4 × 100 = 400 million.
- Revenue after: 3 × 110 = 330 million.
- Midpoint elasticity: quantity change 10 ÷ 105 ≈ 9.5%; price change 1 ÷ 3.5 ≈ 28.6%; elasticity ≈ 9.5 ÷ 28.6 ≈ 0.33: inelastic.
Farmers grew more wheat and earned 70 million less: the price fell proportionately more than sales rose.
Text description
A steep, inelastic demand curve for wheat. The supply curve S1 crosses it at a price of 4 and 100 million bushels. A better harvest shifts supply right to S2, which crosses demand at a price of 3 and 110 million bushels. The quantity rises only 10% while the price falls 25%, so revenue falls from 400 million to 330 million.
Common mistake
Assuming that a higher price always means more revenue (or that selling more always means more revenue). It depends on elasticity: with elastic demand, a price rise reduces revenue; with inelastic demand, a bigger harvest can reduce it.
Key terms
- total revenue
- the amount buyers pay and sellers receive: price × quantity sold
- interdiction
- efforts to stop goods, here illegal drugs, entering a country
- short run
- here, a period too short for buyers and sellers to fully adjust
- long run
- a period long enough for buyers and sellers to adjust, so elasticities are usually larger
Practise the key terms
Tap a card to turn it over. 4 cards.
| Front | Back |
|---|---|
| total revenue | the amount buyers pay and sellers receive: price × quantity sold |
| interdiction | efforts to stop goods, here illegal drugs, entering a country |
| short run | here, a period too short for buyers and sellers to fully adjust |
| long run | a period long enough for buyers and sellers to adjust, so elasticities are usually larger |
Practice
Work it through
A cinema charges 10 and sells 300 tickets a night. At 8 it would sell 420.
- 10 × 300
- 8 × 420
- (120 ÷ 360) ÷ (2 ÷ 9) = 0.333 ÷ 0.222
Quick quiz
Tap an answer to check it.
In the last exercise, should the cinema cut its price to raise revenue?
- That holds only for inelastic demand
Show answer
Yes: demand is elastic (1.5), so revenue rises from 3,000 to 3,360. With elastic demand, a price cut raises revenue.
Why can a bumper harvest lower farmers' total revenue?
- They sell more, but at a much lower price
Show answer
Demand for food is inelastic, so the price falls proportionately more than quantity rises. With inelastic demand, price and revenue move in the same direction.
Why did OPEC's high prices fade over time, in Mankiw's account?
- Mankiw's explanation is the rising long-run elasticities
Show answer
Supply and demand are more elastic in the long run, as buyers and other producers adjust. Elasticities are larger in the long run.
In short
- Total revenue = price × quantity.
- Inelastic demand: price and revenue move together. Elastic demand: they move in opposite directions.
- A better harvest can lower farm revenue, because food demand is inelastic.
- OPEC's power faded because supply and demand are more elastic in the long run; interdiction can raise drug spending when demand is inelastic.
Mastery check
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Check yourself
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Demand is inelastic and the price falls. What happens to total revenue?
Show answer
It falls.
In Mankiw's elastic-demand figure, what happens to revenue when the price rises from 4 to 5?
Show answer
It falls from 400 to 350.
Which policy, in Mankiw's analysis, reduces both drug use and total spending on drugs?
Show answer
Policies that reduce demand, such as education.
Further reading
- N. Gregory Mankiw, Principles of Macroeconomics, 6th ed. (South-Western Cengage, 2012), chapter 5.
- On this site: Price elasticity of demand.
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