Hotel rooms in smalltown go for $100 and 1000 rooms are rented on a typical day.

a.To raise revenue the maypr decides to charge tax of $10 per rented room. After the tax is levied the going rate for hotel rooms rises to $108 and the number of rooms rentedfall to 900.Calculate the amount of revenue this rax raises for small town.and the deadweight loss of the tax.

b.The mayor now double the tax to $20.The price rises to $116 and the number of rooms rented fall to 800. Calculate the tax revenue and deadweight loss with this larger tax.Do they double or less than double.Explain.

a) Revenue = $9,000

Deadweight loss = $500

b) Revenue = $16,000

Deadweight loss = $2,000

Tax revenue rises by less than double while the deadweight loss rises by more than double.

Step-by-step explanation

a) Number of rooms rented before tax Q1 = 1000

Number of rooms rented after tax Q2 = 900

Tax amount = $10

Price paid per room = $108

Price received by seller = 108 - 10 = $98

Tax revenue generated = Tax amount x Q2

= $10 X 900 = $9000

Deadweight loss = 1/2(Q2 - Q1) x tax amount

= 1/2 (1000 - 900) x 10

= 50 x 10 = $500

b) Number of rooms before tax Q1 = 1000

Number of rooms after tax Q2 = 800

Amount of tax = $20

Price paid by buyer = $116

Price received by seller = 116 - 20 = $96

New tax revenue = Q2 x tax amount

= $800 x 20 = $16,000

Deadweight loss = 1/2(1000 -800) x tax amount

= 1/2( 200) x 20

= $2,000

When tax is doubled, tax revenue rises by less than double while the deadweight loss rises by more than double.