Question 5 (i)(b)
Doubling the Manali room tax to Rs. 30: revenue and deadweight loss
6 marks
- Time to write
- About 12 minutes
Question
Question 5 (i)(b) · 6 marks- The rent of hotel rooms in Manali is for Rs.120 per night and 1,200 rooms are rented at this price.
- The mayor next decides to raise the tax to Rs.30 per room. As a result, the market price rises to Rs. 144, while the number of rooms rented falls to 800.
Compute the new tax revenue and the deadweight loss. State whether each of these values doubles, more than doubles, or less than doubles when compared with part (a), and briefly explain why?
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
- Compute…State…?Two asks in one question: answer both.
- ComputeFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 New revenue 1½ marks 3 min
- 2 New deadweight loss 1½ marks 3 min
- 3 Doubles / more / less than doubles for each 1½ marks 2 min
- 4 Explanation 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.
After the Rs. 30 tax. Guests now pay Rs. 144 a night and hotels keep 144 - 30 = Rs. 114; 800 rooms are rented, against 1,200 with no tax and 1,000 under the Rs. 15 tax.
New tax revenue. 30 x 800 = Rs. 24,000 a night.
New deadweight loss. The tax now stops 1,200 - 800 = 400 rooms from being rented. With straight-line curves the loss is the triangle over those rooms, with height equal to the tax: 1/2 x 30 x 400 = Rs. 6,000 a night.
| Rs. 15 tax (part a) | Rs. 30 tax (part b) | Ratio (b) / (a) | Verdict | |
|---|---|---|---|---|
| Tax revenue | Rs. 15,000 | Rs. 24,000 | 1.6 | less than doubles |
| Deadweight loss | Rs. 1,500 | Rs. 6,000 | 4 | more than doubles (it quadruples) |
- Revenue less than doubles because revenue is the tax per room times the rooms rented. The tax per room doubles, but the higher tax shrinks the market, from 1,000 rooms to 800, so the base on which the tax is collected falls: 2 x 0.8 = 1.6 times.
- Deadweight loss more than doubles because the deadweight loss is a triangle whose base (the rooms lost) and height (the tax) both grow with the tax. Doubling the tax doubles the height and, with straight-line curves, also doubles the rooms lost (200 to 400), so the area grows four times: the deadweight loss rises with the square of the tax. Each extra rupee of tax drives out rooms whose rental was worth more than the one before, so the cost to society grows faster than the revenue collected.
Answer. Revenue rises to Rs. 24,000 (less than doubles) and the deadweight loss to Rs. 6,000 (more than doubles, four times). Raising a tax brings in proportionately less revenue and costs proportionately more in lost surplus.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | New revenue | 1.5 |
| 2 | New deadweight loss | 1.5 |
| 3 | Doubles / more / less than doubles for each | 1.5 |
| 4 | Explanation | 1.5 |
| Total | 6 |
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