Question 1 (b)(iv)
The new optimal number of burgers when the price rises to ₹84
2 marks
- Time to write
- About 4 minutes
Question
Question 1 (b)(iv) · 2 marksThe total benefits you get from consuming different quantities of burger each week are given in the table below.
| Burgers (per week) | Total benefit (equivalent in ₹) | Marginal Benefit |
|---|---|---|
| 0 | 0 | X |
| 1 | 180 | |
| 2 | 300 | |
| 3 | 384 | |
| 4 | 444 | |
| 5 | 480 | |
| 6 | 504 |
- If the prize of burger goes up to ₹84 then find the new optimal number of burgers to consume in a week.
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
- findFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
As printed, the word "prize" stands where "price" is meant. As printed, the price used in this part equals the marginal benefit of one of the burgers, so the consumer is indifferent about buying that burger; this copy keeps that.
Write it in this order
- 1 Each burger compared with the new price 1 mark 2 min
- 2 New optimal quantity, with the tie at the third burger 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.
The rule at the new price. The question's prize is read as the price. The consumer still buys a burger only if its marginal benefit, the change in total benefit it brings, is at least what it costs her, now ₹84.
| Burger | Marginal benefit (₹) | Price (₹) | Worth buying? |
|---|---|---|---|
| 1st | 180 | 84 | Yes: adds ₹96 more than it costs |
| 2nd | 120 | 84 | Yes: adds ₹36 more than it costs |
| 3rd | 84 | 84 | Neither gain nor loss: benefit equals price |
| 4th | 60 | 84 | No: costs ₹24 more than it adds |
The 5th and 6th burgers (marginal benefits ₹36 and ₹24) fall still further short of the price.
Check by totals. Net benefit (total benefit minus spending) is ₹180 − ₹84 = ₹96 for one burger, ₹300 − ₹168 = ₹132 for two, ₹384 − ₹252 = ₹132 for three and ₹444 − ₹336 = ₹108 for four. It is highest, ₹132, at 2 and 3 burgers.
Answer. At ₹84 a burger the optimal number falls to 3 burgers a week, the largest number at which the marginal benefit (₹84) is not below the price; 2 burgers give the same net benefit of ₹132, since the third burger is now the one she is indifferent about. The higher price cuts her consumption from 4 burgers at ₹60, the price given in part (ii) of this question, to 3 at ₹84.
Where the 2 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Each burger compared with the new price of ₹84 | 1 |
| 2 | New optimal quantity, with the tie at the third burger | 1 |
| Total | 2 |
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