Question

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 3 base 3 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. Do

they double, more than double, or less than

double? Explain.

Answer 1

The tax revenue is calculated by :

Tax revenue = Tax Imposed $\times$ Quantity sold

Tax revenue = $10 $\times$ 900

= $ 9000

The deadweight loss is calculated as:

Deadweight loss = $\frac{1}{2}$ $\times$ Tax imposed $\times$ change in quantity sold

Deadweight loss = $\frac{1}{2}$ $\times$ $10 $\times$ (1000 - 900)

= $ 500

Hence,

Tax revenue = $ 9000

Deadweight loss = $ 500

PART(B):

Tax revenue = Tax imposed $\times$ quantity sold

= $ 20 $\times$ 800

= $ 16000

Deadweight loss = $\frac{1}{2}$ $\times$ Tax imposed $\times$ change in quantity sold

= $\frac{1}{2}$ $\times$ $ 20 $\times$ (1000 - 800)

= $ 2000

Therefore;

When a tax rate of $20 is imposed, it leads to the following:

Tax revenue rises to $ 16000

Deadweight loss becomes $ 2000

Tax revenue is less than double as it rises from $ 9000 to $ 16000

Deadweight loss is more than double as it rises from $ 500 to $ 2000.