Question 2 (a)
Elasticities of demand and supply at the equilibrium of Qd = 96 – 6P and Qs = –12 + 3P
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (a) · 6 marksCalculate the elasticity of demand and the elasticity of supply at the equilibrium price for the demand and supply function given below:
Qd = 96 – 6P; Qs = – 12 + 3P
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).
What the paper leaves open
The paper prints the marks once, (6+6+6), at the end of part (c): 6 marks for each of (a), (b), (c). This part carries 6 marks. The functions are printed with plain letters and spaced minus signs.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Equilibrium price and quantity 2 marks 3 min
- 2 Price elasticity of demand at the equilibrium 2 marks 3 min
- 3 Price elasticity of supply at the equilibrium 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.
Equilibrium. The market is in equilibrium where the quantity buyers wish to buy equals the quantity sellers wish to sell:
96 – 6P = –12 + 3P, so 108 = 9P and P = 12.
Then Qd = 96 – 6 × 12 = 24 and Qs = –12 + 3 × 12 = 24, so Q = 24.
Elasticity of demand at the equilibrium. Price elasticity of demand is eD = (ΔQ / Q) ÷ (ΔP / P) = (ΔQ / ΔP) × (P / Q). On a straight-line demand curve q = a – bp, the change in quantity for each unit change in price is –b at every point, so eD = –b × (p / q). Here b = 6:
eD = –6 × (12 / 24) = –3.
Its absolute value, 3, exceeds 1, so demand is elastic at the equilibrium. This agrees with the rule for a straight-line demand curve: elasticity is 1 at the price a / 2b = 96 / 12 = 8 and greater than 1 at any higher price, and 12 is above 8.
Elasticity of supply at the equilibrium. Price elasticity of supply is eS = (ΔQ / ΔP) × (P / Q). From Qs = –12 + 3P, quantity supplied rises by 3 for each unit rise in price:
eS = 3 × (12 / 24) = 1.5.
Supply is elastic at the equilibrium. The geometry agrees: the supply line, extended, meets the quantity axis at –12, in its negative range, and a straight supply curve of that kind has elasticity greater than 1 at every point.
| Measure | Working | Value | Nature |
|---|---|---|---|
| Equilibrium price | 108 / 9 | 12 | |
| Equilibrium quantity | 96 – 72 | 24 | |
| Elasticity of demand | –6 × 12 / 24 | –3 | elastic (3 > 1) |
| Elasticity of supply | 3 × 12 / 24 | 1.5 | elastic (1.5 > 1) |
Answer. At the equilibrium price of 12 and quantity of 24, the price elasticity of demand is –3 (3 in absolute value, elastic) and the price elasticity of supply is 1.5 (elastic).
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Equilibrium price and quantity | 2 |
| 2 | Price elasticity of demand at the equilibrium | 2 |
| 3 | Price elasticity of supply at the equilibrium | 2 |
| Total | 6 |
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