Question 3 (b)
Price elasticity of demand for tea by the mid-point method
6 marks
- Time to write
- About 12 minutes
Question
Question 3 (b) · 6 marksSuppose the price of tea increases from ₹60 to ₹75 per kilogram, the quantity demanded falls from 300 kilograms to 240 kilograms. Calculate the price elasticity of demand by the midpoint (arc elasticity) method.
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
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Mid-point formula and why it is used 1½ marks 3 min
- 2 Percentage change in quantity on the average base 1½ marks 3 min
- 3 Percentage change in price on the average base 1½ marks 2 min
- 4 Elasticity and its meaning unit elastic 1½ marks 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
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Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
The mid-point (arc) formula. Price elasticity of demand is eD = (% change in quantity demanded) ÷ (% change in price), read without its minus sign. Measured from the starting values, the result would differ according to whether the price rises or falls; the mid-point method measures each change against the average of the two values, so it gives one figure for the whole stretch of the curve:
eD = [ΔQ ÷ average Q] ÷ [ΔP ÷ average P].
Percentage change in quantity. Quantity falls from 300 kg to 240 kg: ΔQ = 60, average Q = (300 + 240) ÷ 2 = 270, so the change is 60 ÷ 270 = 22.22% (a fall).
Percentage change in price. Price rises from ₹60 to ₹75 a kg: ΔP = 15, average P = (60 + 75) ÷ 2 = 67.5, so the change is 15 ÷ 67.5 = 22.22% (a rise).
eD = 22.22% ÷ 22.22% = (60 ÷ 270) ÷ (15 ÷ 67.5) = 1.
Demand for tea is unit elastic over this range: quantity falls by the same percentage as price rises. Spending on tea therefore does not change: ₹60 × 300 = ₹18,000 before and ₹75 × 240 = ₹18,000 after, as unit elasticity implies.
Answer. By the mid-point method the price elasticity of demand for tea is 1 (unit elastic).
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Mid-point formula and why it is used | 1.5 |
| 2 | Percentage change in quantity on the average base | 1.5 |
| 3 | Percentage change in price on the average base | 1.5 |
| 4 | Elasticity and its meaning (unit elastic) | 1.5 |
| Total | 6 |
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