Question 5 (i)(a)

Tax revenue and deadweight loss of a Rs. 15 room tax in Manali

6 marks

Time to write: About 12 minutes
Topic: Tax incidence, deadweight loss and subsidies

Question

Question 5 (i)(a) · 6 marks

The rent of hotel rooms in Manali is for Rs.120 per night and 1,200 rooms are rented at this price.

In order to raise revenue, the mayor decides to levy a tax of Rs.15 per rented room on hotels. Once the tax is introduced, the market price of a room goes up to Rs.132, and the number of rooms rented falls to 1,000. Calculate the tax revenue collected by the Manali government and the resulting deadweight loss due to the tax.

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

12 minfor 6 marks

Read from the question

CalculateFormula 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 Prices paid and received, rooms rented 1½ marks 3 min
2 Tax revenue 2 marks 3 min
3 Deadweight loss, with the reason 2½ marks 4 min
Check: arithmetic, units (₹, %), final answer underlined 1 min

123

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Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Before and after the tax. The tax of Rs. 15 per room is levied on hotels. It drives a wedge between what guests pay and what hotels keep:

Item	Before the tax	After the tax
Price paid by guests (per night)	Rs. 120	Rs. 132
Price kept by hotels: 132 - 15	Rs. 120	Rs. 117
Rooms rented	1,200	1,000

Guests bear Rs. 12 of the tax (132 - 120) and hotels Rs. 3 (120 - 117), although the tax is collected from hotels.

Tax revenue. Revenue = tax per room x rooms rented after the tax = 15 x 1,000 = Rs. 15,000 a night.

Deadweight loss. The tax stops 200 rooms (1,200 - 1,000) from being rented. For each of those rooms a guest valued the room above what it cost a hotel to provide it, so the gains from those rentals are lost to everyone: they are not collected as revenue either. With straight-line demand and supply, this loss is the triangle between the two curves over the lost rooms, with base equal to the lost rooms and height equal to the tax:

Deadweight loss = 1/2 x 15 x (1,200 - 1,000) = 1/2 x 15 x 200 = Rs. 1,500 a night.

Answer. The Manali government collects Rs. 15,000 a night in tax, and the tax causes a deadweight loss of Rs. 1,500 a night, the surplus lost on the 200 rooms no longer rented. (We take the demand and supply curves to be straight lines between the before and after points, as is usual for such data.)

Where the 6 marks sit

#	Component	Marks
1	Prices paid and received, rooms rented	1.5
2	Tax revenue	2
3	Deadweight loss, with the reason	2.5
	Total	6

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