Question 4 (b)
A price rise and total revenue under three elasticities of demand
6 marks
- Time to write
- About 12 minutes
Question
Question 4 (b) · 6 marksExplain how a rise in price affects the total revenue when the price elasticity of demand is
more than 1
lower than 1
equal to 1 (9,6)
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
- (i)–(iii)3 items, each marked on its own: give each its share.
What the paper leaves open
As printed, the marks (9,6) are written once, at the end of part (b), for parts (a) and (b): 9 and 6 marks. The elasticity cases (i) to (iii) are items of part (b).
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Total revenue, elasticity and the two opposing effects of a price rise 1½ marks 3 min
- 2 Case (i), elastic demand, with example 1½ marks 3 min
- 3 Case (ii), inelastic demand, with example 1½ marks 2 min
- 4 Case (iii), unit elastic demand, with example, and summary 1½ marks 2 min
- Check: every ask answered, key terms underlined 1 min
Short on time? Trim steps 1–4 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. The total revenue of sellers, which is the same as buyers' total expenditure on the good, is price × quantity. Price elasticity of demand measures how strongly quantity demanded responds to the good's own price: eD = (% change in quantity demanded) ÷ (% change in price), usually read without its minus sign. A price rise pulls total revenue two ways: each unit sold brings in more, but fewer units are sold. Which pull is stronger depends on whether the percentage fall in quantity is bigger or smaller than the percentage rise in price, which is exactly what elasticity measures. For small changes, the change in spending is approximately Δp × q × (1 + eD) with eD taken as negative, so its sign is fixed by whether eD is beyond, short of or equal to −1.
(i) Elasticity more than 1. Demand is elastic: the percentage fall in quantity is greater than the percentage rise in price, so the loss from selling fewer units outweighs the gain from the higher price. A rise in price lowers total revenue; spending moves opposite to price. Example (our own): a Bengaluru multiplex raises its ticket from ₹200 to ₹220 (+10%) and weekly tickets sold fall from 1,000 to 850 (−15%). eD = 15 ÷ 10 = 1.5. Revenue falls from ₹2,00,000 to ₹1,87,000.
(ii) Elasticity lower than 1. Demand is inelastic: the percentage fall in quantity is smaller than the percentage rise in price, so the higher price on each unit outweighs the units lost. A rise in price raises total revenue; spending moves with price. Necessities, for which buyers cut consumption little, tend to be like this. Example (our own): a brand of atta goes from ₹250 to ₹300 a 5 kg bag (+20%) and monthly sales in a town fall from 4,000 to 3,800 bags (−5%). eD = 5 ÷ 20 = 0.25. Revenue rises from ₹10,00,000 to ₹11,40,000.
(iii) Elasticity equal to 1. Demand is unit elastic: the percentage fall in quantity just equals the percentage rise in price, so the two pulls cancel. A rise in price leaves total revenue unchanged. A demand curve along which price × quantity is a constant (a rectangular hyperbola) has this property at every point. Example (our own): a household always spends ₹600 a month on mobile data packs. When the pack price goes from ₹200 to ₹300 it buys 2 packs instead of 3, so spending stays ₹600. Measured by the mid-point method, which uses the average price (₹250) and average quantity (2.5) as the base, eD = (1 ÷ 2.5) ÷ (100 ÷ 250) = 0.4 ÷ 0.4 = 1.
| Price elasticity of demand | % fall in quantity compared with % rise in price | Effect of a price rise on total revenue |
|---|---|---|
| More than 1 (elastic) | Larger | Falls |
| Lower than 1 (inelastic) | Smaller | Rises |
| Equal to 1 (unit elastic) | Equal | Unchanged |
Conclusion. A price rise lowers total revenue when demand is elastic, raises it when demand is inelastic, and leaves it unchanged when demand is unit elastic. This is why a seller facing inelastic demand gains revenue by raising price, while one facing elastic demand loses it.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Total revenue, elasticity and the two opposing effects of a price rise | 1.5 |
| 2 | Case (i), elastic demand, with example | 1.5 |
| 3 | Case (ii), inelastic demand, with example | 1.5 |
| 4 | Case (iii), unit elastic demand, with example, and summary | 1.5 |
| Total | 6 |
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