Question 2 (a)
Price elasticity versus cross price elasticity of demand
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (a) · 6 marksDifferentiative between the price elasticity of demand and the cross price elasticity of demand. Explain with an example.
Reworded from the university paper; 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
- exampleExamples are asked for: one short example with each point.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Price elasticity of demand: meaning, formula, sign and degrees 2 marks 3 min
- 2 Cross price elasticity: meaning, formula, sign for substitutes and complements 2 marks 3 min
- 3 Points of difference and a worked example 2 marks 3 min
- Check: every ask answered, key terms underlined 2 min
Easy marks
- Steps 1 and 2 opens with the meaning: a one-line definition, the quickest mark in each.
Short on time? Trim steps 1–3 evenly rather than skip one: each is capped at its own marks.
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Solution
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Price elasticity of demand. It measures how strongly the quantity demanded of a good responds to a change in that good's own price, other things (income, tastes, other prices) unchanged. It is the percentage change in the quantity demanded of the good divided by the percentage change in its own price:
e(d) = (% change in quantity demanded of X) / (% change in price of X) = (ΔQx / Qx) x (Px / ΔPx).
Because quantity demanded and own price move in opposite directions, the measure is negative; by convention its absolute value is used. Demand is called elastic when the value is greater than 1 and inelastic when it is less than 1, and unit elastic at exactly 1.
Cross price elasticity of demand. It measures how strongly the quantity demanded of one good responds to a change in the price of another, related good:
e(xy) = (% change in quantity demanded of X) / (% change in price of Y) = (ΔQx / Qx) x (Py / ΔPy).
Its sign tells us how the goods are related. For substitutes, a rise in the price of one raises the demand for the other, so the measure is positive; for complements, a rise in the price of one lowers the demand for the other, so it is negative. For unrelated goods it is zero.
| Basis | Price elasticity | Cross price elasticity |
|---|---|---|
| Price that changes | the good's own price | the price of a related good |
| Usual sign | negative (absolute value used) | positive for substitutes, negative for complements, zero for unrelated goods |
| What it tells us | how responsive buyers are to the good's price; elastic or inelastic | whether two goods are substitutes or complements, and how close |
| Effect on the demand curve | a movement along the good's own demand curve | a shift of the good's demand curve |
- Price elasticity: a neighbourhood shop raises the price of a kilogram of wheat flour from ₹40 to ₹50 (a 25% rise) and its weekly sales fall from 1,000 kg to 900 kg (a 10% fall). e(d) = 10 / 25 = 0.4 in absolute value: demand is inelastic.
- Cross price elasticity, substitutes: auto-rickshaw fares in a town rise by 20% and e-rickshaw rides rise from 1,000 to 1,080 a day (8%). e(xy) = +8 / 20 = +0.4: auto-rickshaw and e-rickshaw rides are substitutes.
- Cross price elasticity, complements: the price of petrol rises by 10% and sales of scooters fall by 3%. e(xy) = −3 / 10 = −0.3: petrol and scooters are complements.
Conclusion. Both measures divide a percentage change in the quantity demanded of a good by a percentage change in a price; they differ in whose price changes. Price elasticity concerns the good's own price and tells us how elastic its demand is; cross price elasticity concerns another good's price and, through its sign, tells us whether the two are substitutes or complements.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Price elasticity of demand: meaning, formula, sign and degrees | 2 |
| 2 | Cross price elasticity: meaning, formula, sign for substitutes and complements | 2 |
| 3 | Points of difference and a worked example | 2 |
| Total | 6 |
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