Question 2 (a)
Quantity falls 20% while revenue rises 10%: elastic or inelastic demand?
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (a) · 6 marksA change in price causes the quantity demanded of a good to fall by 20 percent, while the total revenue from that good rises by 10 percent. Is the demand curve 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.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Revenue rule linking spending to 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.
Total revenue and elasticity. Total revenue is price times quantity. Because price and quantity demanded move in opposite directions, what happens to revenue after a price change shows which of the two percentage changes is larger:
- if revenue moves in the same direction as price (a price rise raises revenue), the quantity has changed by a smaller percentage than the price, and demand is inelastic;
- if revenue moves against the price, the quantity has changed by a larger percentage, and demand is elastic;
- if revenue does not change, demand is unit elastic.
What the figures imply about the price. The quantity demanded falls, so the price must have risen (along a demand curve the two move in opposite directions). Revenue still rises, by 10%, so the price must have risen by more than enough to make up for the 20% fall in quantity:
(1 + price change) × 0.80 = 1.10, so the price rose by 1.10 ÷ 0.80 − 1 = 37.5%.
The elasticity. eD = (% change in quantity demanded) ÷ (% change in price) = 20 ÷ 37.5 = 0.53, which is below 1. Measured instead on the mid-point base (quantity 100 to 80, price 100 to 137.5), it is (20 ÷ 90) ÷ (37.5 ÷ 118.75) = about 0.7, also below 1.
Answer. The demand curve is inelastic over this price change. A price rise that cuts quantity by 20% but raises revenue by 10% means quantity has fallen by a smaller percentage (20%) than price has risen (37.5%); the price elasticity is about 0.53 (about 0.7 by the mid-point method), less than 1.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Revenue rule linking spending to elasticity | 2 |
| 2 | Price change implied by the figures | 2 |
| 3 | Conclusion, inelastic, with the elasticity | 2 |
| Total | 6 |
Report a problemopens an email to admin@getkunji.com with the question ID2555-Q2aalready filled in.