Question 4 (a)(iii)
Can Aditi and Kabir both gain by helping each other, and on what terms?
2 marks
- Time to write
- About 4 minutes
Question
Question 4 (a)(iii) · 2 marksAditi and Kabir are both students who work for the college fest. Aditi and Kabir are able to work for only 5 hours a day. The college President tells them that they must create 180 posters for display and call 240 companies to raise funds in next 10 days. The table below gives the numbers of posters and calls that Aditi and Kabir can work on in a given number of hours:
| Hours spent | Aditi (Poster) | Aditi (Calls) | Kabir (Poster) | Kabir (Calls) |
|---|---|---|---|---|
| 1 | 2 | 5 | 5 | 2 |
| 2 hours | 4 | 10 | 10 | 4 |
| 3 | 6 | 15 | 15 | 6 |
| 4 hours | 8 | 20 | 20 | 8 |
| 5 | 10 | 25 | 25 | 10 |
- Is it possible for both Aditi and Kabir to gain by helping each other? If so, what should their terms of trade be?
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
- Is…?What…?2 asks, each with its own marks below. Answer both.
Write it in this order
- 1 Opportunity costs and comparative advantage identified 1 mark 2 min
- 2 Specialisation, and the range of terms of trade in which both gain 1 mark 2 min
Try it first. About 4 minutes for 2 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.
Opportunity costs compared. From the table, one hour gives Aditi 2 posters or 5 calls, and Kabir 5 posters or 2 calls. The person with the lower opportunity cost of a task has the comparative advantage in it.
| Opportunity cost of 1 poster | Opportunity cost of 1 call | |
|---|---|---|
| Aditi | 5 ÷ 2 = 2.5 calls | 2 ÷ 5 = 0.4 poster |
| Kabir | 2 ÷ 5 = 0.4 call | 5 ÷ 2 = 2.5 posters |
Kabir has the comparative advantage in posters (0.4 call against Aditi's 2.5) and Aditi in calls (0.4 poster against Kabir's 2.5).
Who should do what. Yes, both can gain. Each should specialise in the task with the lower opportunity cost, and the two together then turn out more than when each splits time between both tasks. With 5 hours a day for 10 days, each has 50 hours: Kabir alone can make 5 × 50 = 250 posters (180 needed) and Aditi alone 5 × 50 = 250 calls (240 needed), so the whole target is met with time to spare.
The terms of trade. An exchange helps both only if each gets a task done for less than it would cost her or him to do it. Measured in calls per poster, Kabir will not supply a poster for less than 0.4 call (his own cost), and Aditi will not give more than 2.5 calls for one (her own cost). So the terms must lie between 0.4 and 2.5 calls for each poster (equivalently, between 0.4 and 2.5 posters for each call). For example, at 1 poster for 1 call, Kabir gives up 0.4 call to make a poster and gets 1 call for it, a gain of 0.6 call; Aditi gets for 1 call a poster that would have cost her 2.5 calls, a gain of 1.5 calls.
Answer. Yes. Kabir should make the posters and Aditi make the calls, and they gain from helping each other at any rate of exchange between 0.4 and 2.5 calls per poster, such as one poster for one call.
Where the 2 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Opportunity costs and comparative advantage identified | 1 |
| 2 | Specialisation, and the range of terms of trade in which both gain | 1 |
| Total | 2 |
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