Question 2 (b)
How far the price of salt must rise to cut its consumption by a quarter
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (b) · 6 marksSuppose the price elasticity of demand for salt is roughly 0.5. If one kg of salt currently costs 60 and the government wants to reduce its consumption by 25 percent, by how much should it increase the price?
Reworded from the university paper: names and figures differ, 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
- how muchFormula first, then the working, then the answer with its unit (₹, %, units).
- should itEnd with a one-line decision that follows from your figures.
What the paper leaves open
As printed, the price of salt carries no currency sign.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Elasticity as the ratio of percentage changes, rearranged for the price change 2 marks 3 min
- 2 Required percentage rise in price 2 marks 3 min
- 3 New price and rise in rupees, with the inelastic-demand point 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
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.
The elasticity relation. Price elasticity of demand is eD = (% change in quantity demanded) ÷ (% change in price), read without its minus sign. The price of salt is read in rupees (the paper prints no sign). Rearranged, the price change needed for a given cut in quantity is:
% change in price = (% change in quantity demanded) ÷ eD.
Percentage rise in price. The government wants quantity to fall by 25%, and eD = 0.5:
% change in price = 25% ÷ 0.5 = 50%.
The new price. A 50% rise on ₹60 is 0.5 × 60 = ₹30, so the price must go up to ₹60 + ₹30 = ₹90 a kg.
Because demand for salt is inelastic (0.5 is below 1), the price has to rise by twice the percentage by which consumption is to fall: buyers cut back on salt only a little when it becomes dearer, so a large price rise is needed for a moderate fall in use.
The other reading. If both changes are measured on the mid-point base, a 25% fall from the starting quantity is a fall of 0.25 ÷ 0.875 = 28.57% on the average quantity; the price must then rise by 28.57% ÷ 0.5 = 57.14% on the average price, which takes it from ₹60 to ₹108. The question gives the change as a plain percentage of the present consumption, so the answer uses the simple method.
Answer. The government should raise the price of salt by 50%, that is by ₹30, from ₹60 to ₹90 a kg.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Elasticity as the ratio of percentage changes, rearranged for the price change | 2 |
| 2 | Required percentage rise in price | 2 |
| 3 | New price and rise in rupees, with the inelastic-demand point | 2 |
| Total | 6 |
Report a problemopens an email to admin@getkunji.com with the question ID2070-Q2balready filled in.