# Hotel rooms in Smalltown go for $100, and 1,000 rooms are rented on atypical day. a. To raise revenue, the mayor decides to charge

###### Question:

## Answers

doubling the size of the tax more than doubles the deadweight loss while less than doubles the revenue generated

Explanation:

(a)

The quantity of rooms rented before tax, Q1 = 1000 rooms.

The quantity of rooms rented after the imposition of tax Q2 = 900 rooms.

Size of the tax = $10

Price paid by buyer = $108

Price received by seller = $98

Deadweight loss = 1/2 x (Q2 — Q1) x (size of the tax)

Deadweight loss = 1/2 x (1000 — 900) x ($10) = $500

Tax revenue generated = size of tax * (Q2) = $10 x (900) = $9000

b)

The quantity of rooms rented before tax, Q1 = 1000 rooms

The quantity of rooms rented after the imposition of tax, Q2 = 800 rooms Size of the tax = $20

Price paid by buyer = $116

Price received by seller = $96

Deadweight loss = 1/2 x (Q2 — Q1) x (size of the tax)

New Deadweight loss = 1/2 x (1000 — 800) x ($20) = $2000

Thus, dead weight loss quadruples post doubling the size of tax. New Tax revenue generated = size of tax x (Q2) = $20 x (800) = $16000 Thus, revenue generated less than doubles post doubling the size of tax.

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 = [tex]\frac{1}{2}[/tex] × (R - R₁) × Size of tax

= [tex]\frac{1}{2}[/tex] × (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 = [tex]\frac{1}{2}[/tex] × (R - R₂) × Size of tax

= [tex]\frac{1}{2}[/tex] × (1000 - 800) × $20

= $2000

Tax revenue doubles while the deadweight becomes more than double