Question 2 (a)
Elasticity of supply and income elasticity of demand
9 marks
- Time to write
- About 18 minutes
Question
Question 2 (a) · 9 marksFor the supply function x = 2 p² + 7, find the elasticity of supply when p = 4.
Demand x depends on income y through 40 x = 20 + 2 y. Calculate the value of the income elasticity of demand when y = 250.
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.
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Read off the question and its marks
Read from the question
- (i)–(ii)2 items, each marked on its own: give each its share.
- findFormula 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 Elasticity of supply 4½ marks 8 min
- 2 Income elasticity of demand 4½ marks 8 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 18 minutes for 9 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.
(i) Elasticity of supply of x = 2p² + 7 at p = 4
Elasticity of supply: eₛ = (dx/dp)(p/x). Here dx/dp = 4p (power rule).
At p = 4: x = 2(16) + 7 = 39 and dx/dp = 16.
eₛ = 16 × 4/39 = 64/39 = 1.64.
Supply is elastic at this price (eₛ > 1): a 1% rise in price raises the quantity supplied by about 1.64%.
(ii) Income elasticity of demand when y = 250
40x = 20 + 2y ⟹ x = 0.5 + 0.05y, so dx/dy = 0.05.
At y = 250: x = 0.5 + 12.5 = 13.
Income elasticity e_y = (dx/dy)(y/x) = 0.05 × 250/13 = 12.5/13 = 0.96 (= 25/26).
The income elasticity is positive and below 1: the good is a normal good and a necessity at this income (demand rises less than in proportion to income).
| Value at the point | Derivative | Elasticity | |
|---|---|---|---|
| Supply, p = 4 | x = 39 | dx/dp = 16 | 1.64 |
| Demand, y = 250 | x = 13 | dx/dy = 0.05 | 0.96 |
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Elasticity of supply | 4.5 |
| 2 | Income elasticity of demand | 4.5 |
| Total | 9 |
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