Question

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 hotels a tax of $10 perrented room. After the tax is imposed, the going rate for hotel roomsrises to $108, and the number of rooms rented falls to 900. Calculate theamount of revenue this tax raises for Smalltown and the deadweightloss of the tax. (Hint: The area of a triangle is l/2Xbase X height.)h. The mayor now doubles the tax to $20. The price rises to $116, andthe number of rooms rented falls to 800. Calculate tax revenue anddeadweight loss with this larger tax. Are they double, more thandouble, or less than double? Explain.

Answer 1

Answer:

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.