Question 2 (c)
Cross price elasticity of X with respect to Y by the mid-point method
6 marks
- Time to write
- About 12 minutes
Question
Question 2 (c) · 6 marksWith the information given in the table below, calculate the cross price elasticity of good X with respect to Y (by the mid-point method). How are these two goods related? Comment on it.
| BEFORE | AFTER | |||
|---|---|---|---|---|
| Price (□) | Quantity | Price (□) | Quantity | |
| X | 240 | 50 | 240 | 75 |
| Y | 480 | 36 | 600 | 24 |
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
- How…?Comment…Two asks in one question: answer both.
- Comment on itA statement to judge: take a stand on it in your first line, give your reasons, and come back to it at the end.
- Comment onThe comment carries marks too: say what the figures show, in two or three lines.
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
As printed, each price heading of the table shows an empty box where a rupee sign would stand; the table is kept exactly (heading cells BEFORE and AFTER, then Price and Quantity).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Meaning and formula of cross price elasticity 1½ marks 3 min
- 2 Mid-point percentage changes 1½ marks 3 min
- 3 Elasticity computed 1½ marks 2 min
- 4 The goods are substitutes, with comment 1½ marks 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.
Cross price elasticity. The cross price elasticity of demand measures how the quantity demanded of one good responds to a change in the price of a related good, a substitute or a complement:
Exy = (% change in quantity demanded of X) ÷ (% change in price of Y).
By the mid-point method each change is measured against the average of the before and after values. The prices in the table are read in rupees.
Percentage changes on the mid-point base.
- Quantity of X: rises from 50 to 75, a change of 25 on an average of (50 + 75) ÷ 2 = 62.5, that is 25 ÷ 62.5 = +40%.
- Price of Y: rises from ₹480 to ₹600, a change of 120 on an average of (480 + 600) ÷ 2 = 540, that is 120 ÷ 540 = +22.22%.
The price of X stays at ₹240, so the change in X's quantity is not due to its own price.
Exy = 40% ÷ 22.22% = (25 ÷ 62.5) ÷ (120 ÷ 540) = +1.8.
How X and Y are related. The cross elasticity is positive: a rise in the price of Y raises the quantity of X bought. That is the mark of substitutes: when one becomes dearer, buyers switch to the other, as with two brands of a similar product. For complements the sign would be negative, since a dearer Y would cut the demand for X as well.
Comment. The value 1.8 is well above 1, so X is a close substitute for Y: a 1% rise in Y's price raises the quantity of X demanded by about 1.8%. The table bears this out, since Y's own sales fall from 36 to 24 while X's rise from 50 to 75. A seller of X gains when Y's price goes up, without changing its own price.
Answer. The cross price elasticity of X with respect to Y is +1.8; being positive, it shows that X and Y are substitutes, and fairly close ones.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Meaning and formula of cross price elasticity | 1.5 |
| 2 | Mid-point percentage changes | 1.5 |
| 3 | Elasticity computed | 1.5 |
| 4 | The goods are substitutes, with comment | 1.5 |
| Total | 6 |
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