   Chapter 8, Problem 9PA

Chapter
Section
Textbook Problem

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. (Hint: The area of a triangle is 1/2 × base × height.)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. Subpart (a): To determine The impact of tax on the market for hotel rooms. Explanation We have given that the equilibrium price of rooms in the town which is$100 and the equilibrium quantity is 1,000 without the tax and when the tax of $10 per room is imposed, the price increases to$108 and the quantity falls to 900 rooms. This can be illustrated as follows:

When the price is $108, the total rooms sold are 900. The tax revenue from the sale of a room to the government is$10 and thus, the total tax revenue of the government after the imposition of the tax can be calculated by multiplying the per room tax revenue with the total quantity of rooms sold after the tax which is equal to the area of A+B. It can be calculated as follows:

Total tax revenue=Tax revenue from each room×Total rooms demanded after tax=10×900=9,000

Thus, the total tax revenue from the rooms to the government is equal to \$9,000.

The total deadweight loss due to the tax is equal to the area of C+D which is the reduction in the total surplus of the economy

Sub part (b):

To determine
The impact of tax on the market for hotel rooms.

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