Question 2 (iii)
A change of taste to one-fourth of income: the demand curve and the elasticities
4 marks
- Time to write
- About 8 minutes
Question
Question 2 (iii) · 4 marks- Suppose Anita's taste changes and she decides to spend just one-fourth of her income on clothing. In what way does her demand curve change? What are her income and price elasticity now?
Reworded from the university paper; 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
- What…?Two asks in one question: answer both.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 Demand curve shifts to the left each price: three-quarters of the old quantity 2 marks 3 min
- 2 Income elasticity still 1 1 mark 2 min
- 3 Price elasticity still -1 1 mark 2 min
Short on time? Step 1 carries 2 of the 4 marks: guard its minutes.
Try it first. About 8 minutes for 4 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.
New demand. Anita now spends one-fourth of her income on clothing, so P x Q = M/4 and
Q = M / (4P).
Before the change of taste her demand was Q = M/(3P). At any given price and income, the new quantity is (M/4P) ÷ (M/3P) = 3/4 of the old one.
How the demand curve changes. A change in tastes is one of the other things held constant along a demand curve, so it shifts the curve rather than moving Anita along it. Her taste for clothing has weakened, so at every price she buys less: the demand curve shifts to the left (inwards), to three-quarters of its former quantity at each price. Example (our figures): with income ₹36,000 and a price of ₹600 per garment, she used to buy 36,000/(3 x 600) = 20 garments; now she buys 36,000/(4 x 600) = 15. The new curve is still a rectangular hyperbola, lying closer to the origin, with spending fixed at ₹9,000 instead of ₹12,000.
Income elasticity now. Quantity is still proportional to income (Q = M/4P), so a 10 per cent rise in income still raises the quantity by 10 per cent: income elasticity = 1.
Price elasticity now. Spending on clothing is still a fixed amount, M/4, whatever the price, so the demand curve is still a rectangular hyperbola with unitary elasticity at every point: price elasticity = -1.
Answer. The change of taste shifts Anita's demand curve to the left (each price now goes with three-quarters of the earlier quantity), but her income elasticity stays 1 and her price elasticity stays -1: any constant share of income, one-third or one-fourth, gives unit elasticities.
Where the 4 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Demand curve shifts to the left (each price: three-quarters of the old quantity) | 2 |
| 2 | Income elasticity still 1 | 1 |
| 3 | Price elasticity still -1 | 1 |
| Total | 4 |
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