Question

Hotel rooms in Smalltown go for $100, and 1,000 rooms are rented on a typical day. a. To raise revenue, the mayor decides to charge hotels a tax of $10 per rented room. After the tax is imposed, the going rate for hotel rooms rises to $108, and the number of rooms rented falls to 900. Calculate the amount of revenue this tax raises for Smalltown and the deadweight loss of the tax. b. The mayor now doubles the tax to $20. The price rises to $116, and the number of rooms rented falls to 800. Calculate tax revenue and deadweight loss with this larger tax. Are they double, more than double, or less than double? Explain.

Answer 1

Answer:

a) Revenue generated = $9000

Deadweight loss = $500

b) Revenue generated = $16,000

Deadweight loss = $2000

Tax revenue doubles while the deadweight becomes more than double with the larger tax

Explanation:

Typical rent for a hotel room = $100

Typical rooms rented, R = 1,000

a) Tax charged = $10 per rented room

Going rate for hotel rooms = $108

number of rooms rented, R₁ = 900

Now,

Revenue generated = Size of tax × R₁

= $10 × 900

= $9000

Deadweight loss = $\frac{1}{2}$ × (R - R₁) × Size of tax

=  $\frac{1}{2}$ × (1000 - 900) × $10

= $500

b) Tax charged = $20 per rented room

Going rate for hotel rooms = $116

number of rooms rented, R₂ = 800

Now,

Revenue generated = Size of tax × R₂

= $20 × 800

= $16,000

Deadweight loss = $\frac{1}{2}$ × (R - R₂) × Size of tax

=  $\frac{1}{2}$ × (1000 - 800) × $20

= $2000

Tax revenue doubles while the deadweight becomes more than double