Question 3 (a)
How much the quantity of good X falls when its price rises from Rs. 10 to Rs. 15: short run and long run, by the mid-point method
6 marks
- Time to write
- About 12 minutes
Question
Question 3 (a) · 6 marksAssume the price elasticity of demand for good X is 0.3 in the short run and 0.6 in the long run. Suppose the price of Good X goes up from Rs. 10 per unit to Rs. 15 per unit, by how much will the quantity be altered
in the short run
in the long run
make use of the mid point method for your calculations.
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
- Assume the price elasticity of demand…The paper fixes this: use it as given, and say so in your answer.
- how muchFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
As printed, the sentence ends "change" without a question mark; read as asking by how much the quantity demanded changes, in the short run and in the long run, from the price rise.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 The mid-point formula and why it is used 1 mark 2 min
- 2 Percentage change in price by the mid-point method 1 mark 2 min
- 3 (i) Short-run change in quantity demanded 1½ marks 2 min
- 4 (ii) Long-run change in quantity demanded 1½ marks 2 min
- 5 Interpretation, short run against long run 1 mark 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 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 mid-point method. Price elasticity of demand is eD = (% change in quantity demanded) ÷ (% change in price), read without its minus sign. If the percentage changes are measured from the starting values, the answer depends on whether the price is rising or falling. The mid-point method avoids this by measuring each change against the average of the old and new values:
eD = [ΔQ ÷ average Q] ÷ [ΔP ÷ average P].
Rearranged, the percentage change in quantity demanded (on the mid-point base) = eD × the percentage change in price (on the mid-point base), with quantity moving opposite to price.
Percentage change in price. The price rises from Rs. 10 to Rs. 15, so ΔP = 5 and the average price is (10 + 15) ÷ 2 = 12.5.
% change in price = 5 ÷ 12.5 × 100 = 40%.
(i) In the short run. eD = 0.3.
% change in quantity demanded = 0.3 × 40% = 12%, a fall of 12%.
(ii) In the long run. eD = 0.6.
% change in quantity demanded = 0.6 × 40% = 24%, a fall of 24%.
| Elasticity | % change in price (mid-point) | % change in quantity demanded (mid-point) | |
|---|---|---|---|
| (i) Short run | 0.3 | +40% | −12% |
| (ii) Long run | 0.6 | +40% | −24% |
Illustration (our own base, to show what a mid-point percentage means in units): if 1,000 units a month were bought at Rs. 10, a 12% mid-point fall means (1,000 − Q2) ÷ [(1,000 + Q2) ÷ 2] = 0.12, so Q2 = 1,000 × 0.94 ÷ 1.06 = 886.79 units in the short run; in the long run Q2 = 1,000 × 0.88 ÷ 1.12 = 785.71 units.
Answer. By the mid-point method the price rises by 40%, so the quantity demanded of X falls by 12% in the short run and by 24% in the long run. Demand is inelastic in both periods (elasticity below 1), but the fall is twice as large in the long run: given time, buyers find substitutes and change their habits, so demand becomes more elastic.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | The mid-point formula and why it is used | 1 |
| 2 | Percentage change in price by the mid-point method | 1 |
| 3 | (i) Short-run change in quantity demanded | 1.5 |
| 4 | (ii) Long-run change in quantity demanded | 1.5 |
| 5 | Interpretation, short run against long run | 1 |
| Total | 6 |
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