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.

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.  

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