Question 6 (ii)(c)
Ravi's optimal bundle when all prices and his income rise by the same percentage
3 marks
- Time to write
- About 6 minutes
Question
Question 6 (ii)(c) · 3 marksConsider that Ravi buys only milk and cookies.
How would Ravi's optimal combination of milk and cookies in year 2 compare with his optimal combination in year 1?
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
- (ii)–(c)2 items, each marked on its own: give each its share.
- compareCompare in a table, basis by basis.
Write it in this order
- 1 Budget lines of year 1 and year 2 compared 1 mark 2 min
- 2 Optimal combination unchanged, with the reason 1½ marks 3 min
- 3 Assumptions stated ½ mark 1 min
Short on time? Step 2 carries 1½ of the 3 marks: guard its minutes.
Try it first. About 6 minutes for 3 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.
Short answer. Ravi's optimal combination of milk and cookies in year 2 is the same as in year 1. When income and every price rise by the same 15 per cent, his budget line does not move, so the best bundle on it does not change.
The budget line in the two years. A consumer can buy the bundles whose cost does not exceed his income, and his budget line is the set of bundles that cost exactly his income. Using the figures of parts (a) and (b):
| Income | Price of milk (per quart) | Price of cookies (per dozen) | Milk if all income on milk | Cookies if all income on cookies | |
|---|---|---|---|---|---|
| Year 1 | $150 | $3 | $5 | 150 / 3 = 50 quarts | 150 / 5 = 30 dozen |
| Year 2 (all up 15%) | $172.50 | $3.45 | $5.75 | 172.50 / 3.45 = 50 quarts | 172.50 / 5.75 = 30 dozen |
Both intercepts are the same in the two years, and so is the slope (the price ratio 3 / 5 = 3.45 / 5.75 = 0.6: each quart of milk costs 0.6 dozen cookies in both years). Multiplying income and both prices by 1.15 leaves the budget line exactly where it was: a change in income shifts the line, and a change in a price turns it, but here the two changes cancel.
Why the optimal combination does not change. The optimal bundle is the point on the budget line that touches the highest indifference curve Ravi can reach. His tastes (indifference curves) are unchanged, and the budget line is identical, so the point of tangency is identical too. Ravi buys the same quarts of milk and the same dozens of cookies in year 2 as in year 1; only the money he spends on them is 15 per cent higher.
Assumptions. Ravi's preferences are the same in both years; he spends all his income on milk and cookies; the 15 per cent rise applies equally to his salary and to both prices; he does not suffer from money illusion (he looks at what his income can buy, not at its rupee or dollar figure).
Conclusion. A proportional rise in all prices and income leaves Ravi's real purchasing power and his budget line unchanged, so his optimal combination in year 2 is the same as in year 1.
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Budget lines of year 1 and year 2 compared | 1 |
| 2 | Optimal combination unchanged, with the reason | 1.5 |
| 3 | Assumptions stated | 0.5 |
| Total | 3 |
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