Question 6 (a)
Equilibrium of Q = 360 − P and Q = 2P, with the elasticities of demand and supply at that point
8 marks
- Time to write
- About 16 minutes
Question
Question 6 (a) · 8 marksFor the demand and supply curves given below, find the equilibrium price and quantity, and the elasticity of demand and the elasticity of supply at the equilibrium point.
Demand curve Q = 360 – P
Supply curve Q = 2P
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
- findFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
As printed, the marks (4+4) are written once, after the supply curve: 8 marks.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Equilibrium condition and equilibrium price 2 marks 4 min
- 2 Equilibrium quantity, checked on both curves 2 marks 4 min
- 3 Elasticity of demand at the equilibrium point 2 marks 3 min
- 4 Elasticity of supply at the equilibrium point 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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 price and quantity. The market is in equilibrium at the price where quantity demanded equals quantity supplied:
360 − P = 2P 360 = 3P P = 120
Quantity: from demand, Q = 360 − 120 = 240; from supply, Q = 2 × 120 = 240. Both curves give the same quantity, so the market clears at P = 120 and Q = 240.
Elasticity at a point. Price elasticity is the percentage change in quantity divided by the percentage change in price, which at a point is (ΔQ ÷ ΔP) × (P ÷ Q). For a straight line, ΔQ ÷ ΔP is the constant coefficient of P; for a linear demand curve q = a − bp this gives eD = −b × p ÷ q.
Elasticity of demand at equilibrium. For Q = 360 − P, ΔQ ÷ ΔP = −1. At P = 120 and Q = 240:
eD = −1 × 120 ÷ 240 = −0.5, that is 0.5 in absolute value.
Demand is inelastic at the equilibrium point. This agrees with the position of the point on the line: the demand curve runs from P = 360 (Q = 0) to Q = 360 (P = 0), its mid-point is at P = 180, and any point below the mid-point has elasticity less than 1.
Elasticity of supply at equilibrium. For Q = 2P, ΔQ ÷ ΔP = 2. At P = 120 and Q = 240:
eS = 2 × 120 ÷ 240 = 1.
Supply is unit elastic. This is true at every point of this supply curve, because it is a straight line through the origin, and such a line has elasticity equal to 1 everywhere.
| Equation | ΔQ ÷ ΔP | P ÷ Q at equilibrium | Elasticity | |
|---|---|---|---|---|
| Demand | Q = 360 − P | −1 | 120 ÷ 240 | −0.5 (0.5 in absolute value) |
| Supply | Q = 2P | 2 | 120 ÷ 240 | 1 |
Answer. Equilibrium price 120, equilibrium quantity 240; at that point the elasticity of demand is −0.5 (inelastic, 0.5 in absolute value) and the elasticity of supply is 1 (unit elastic).
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Equilibrium condition and equilibrium price | 2 |
| 2 | Equilibrium quantity, checked on both curves | 2 |
| 3 | Elasticity of demand at the equilibrium point | 2 |
| 4 | Elasticity of supply at the equilibrium point | 2 |
| Total | 8 |
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