Donna runs an inn and charges $300 a night for a room, which equals her cost. Sam, Harry, and Bill are three potential customers willing to pay $500, $325, and $250, respectively. When the government levies a tax on innkeepers of $50 per night of occupancy, Donna raises her price to $350. The deadweight loss of the tax is
a. $150
b. $100
c. $50
d. $25
Answer: d. $25
Donna charges $300 a night for a room, which equals her cost. This is the minimum price Donna can charge for a room and also this is the market price for a room in Donna's Inn. Sam, Harry, and Bill are three potential customers willing to pay $500, $325, and $250, respectively. For a room rate of $300, we can say that Bill whose reservation price is $250, won't be able to take a room in Donna's inn. So, there are only two potential customers, Sam and Harry, for Donna's inn.
Now, when the government levies a tax on innkeepers of $50 per night of occupancy, Donna raises her price to $350. At this time, Donna will lose one cutomer, i.e., Harry whose reservation price is $325. So, the number of customer Donna losses is one.
Before the imposition of tax, the market price of Donna's inn was $300. After the imposition of tax, the market price of Donna's inn is $350. Donna losses one customer.
The potential gain of business Donna losses, which is also the deadweight loss is as follows,
Deadweight Loss = 1/2 * 1 * ($350 - $300) = 1/2 * ($50)
Or, Deadweight Loss = 1/2 * ($50)
Or, Deadweight Loss = $25
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