Question 2 (c)
Quantity halves while revenue rises by a quarter: is demand elastic or inelastic?
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (c) · 6 marksA change in price causes the quantity demanded of a good to fall by 50 percent, while the total revenue from those good rises by 25 percent. Is the demand curve being elastic or inelastic? Explain.
Reworded from the university paper; the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- ExplainA statement to explain: say what it means first, then build the answer around it.
What the paper leaves open
As printed, "those good" is singular after a plural determiner; the question asks whether the demand curve is elastic or inelastic over the price change described. "Is the demand curve being elastic or inelastic?" stands as printed.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 How the change in revenue reveals elasticity 2 marks 3 min
- 2 Price change implied by the figures 2 marks 3 min
- 3 Conclusion, inelastic, with the elasticity 2 marks 3 min
- Check: every ask answered, key terms underlined 2 min
Short on time? Trim steps 1–3 evenly rather than skip one: each is capped at its own marks.
Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Revenue as a test of elasticity. Revenue equals price multiplied by quantity. When a price change and the resulting change in quantity pull revenue in opposite directions, the larger percentage change wins:
- a price rise that raises revenue means quantity fell by a smaller percentage than price rose: demand is inelastic;
- a price rise that lowers revenue means quantity fell by a larger percentage: demand is elastic;
- unchanged revenue means unit elasticity.
The price change behind the figures. Quantity demanded falls, so the price must have gone up. Revenue still rises, by 25%, even though only half as much is sold, so the price must have risen a great deal:
(1 + price change) × 0.50 = 1.25, so the price rose by 1.25 ÷ 0.50 − 1 = 150% (it went up two and a half times).
The elasticity. eD = (% change in quantity demanded) ÷ (% change in price) = 50 ÷ 150 = 0.33, below 1. On the mid-point base (quantity 100 to 50, price 100 to 250) it is (50 ÷ 75) ÷ (150 ÷ 175) = 0.78, also below 1, so the conclusion does not depend on the method.
Answer. The demand curve is inelastic over this change: revenue rose with the price, so the 50% fall in quantity was smaller, in percentage terms, than the 150% rise in price. The elasticity is about 0.33 (0.78 by the mid-point method), less than 1.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | How the change in revenue reveals elasticity | 2 |
| 2 | Price change implied by the figures | 2 |
| 3 | Conclusion, inelastic, with the elasticity | 2 |
| Total | 6 |
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