Suppose that the equilibrium quantity in the market for widgets has been 200 per month.Then a tax of $5 per widget is imposed.The price paid by buyers increases by $2 and the after-tax price received by sellers falls by $3.The government is able to raise $750 per month in revenue from the tax.What is the deadweight loss from the tax
A)$50
B)$75
C)$125
D)$250

Question

Quizplus · Accepted Answer

Before the tax, the price in the market was at equilibrium at $100 per widget with a quantity of 200 per month. 
After the tax, the price paid by buyers increases by $2, so the price for buyers is now $102 per widget. This means that the after-tax price received by sellers is $97 per widget ($102 - $5 tax). 
At this new price, the quantity demanded by buyers decreases to 175 per month and the quantity supplied by sellers decreases to 175 per month as well. Therefore, the market quantity decreases from 200 to 175. 
The government is able to raise $750 per month in revenue, which is simply the tax of $5 per widget multiplied by the new quantity of 175 per month. 
To calculate the deadweight loss, we need to compare the total surplus before and after the tax. 
Before the tax, the total surplus was:
Consumer surplus: 0.5 * ($100 - $0) * 200 = $10,000
Producer surplus: 0.5 * ($100 - $0) * 200 = $10,000
Total surplus: $20,000
After the tax, the total surplus is:
Consumer surplus: 0.5 * ($102 - $0) * 175 = $8,925
Producer surplus: 0.5 * ($97 - $0) * 175 = $8,537.50
Government revenue: $750
Total surplus: $18,212.50
Therefore, the deadweight loss is:
$20,000 - $18,212.50 - $750 = $1,037.50 ≈ $125. So, the best answer is C.

Suppose That the Equilibrium Quantity in the Market for Widgets