Suppose that the equilibrium quantity in the market for widgets has been 300 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 1000 per month in revenue from the tax.What is the deadweight loss from the tax
A)$50
B)$100
C)$250
D)$500

Question

Quizplus · Accepted Answer

First, we need to use the information given to find the new equilibrium quantity after the tax is imposed.

- Price paid by buyers increases by $2, so the new price is $5 + $2 = $7.
- After-tax price received by sellers falls by $3, so the new price is $5 - $3 = $2.
- With a tax of $5, the effective price for buyers is $7 and sellers receive $2.
- We can use the supply and demand equations to solve for the new quantity:

Qd: a - bP = 300 - 3(7) = 279
        Qs: c + dP = 1000 + 2(279) = 1558
        Equilibrium: Q = 279

The new equilibrium quantity is 279 per month.

To find the deadweight loss, we need to compare the total surplus (consumer surplus + producer surplus) before and after the tax. We can use the original equilibrium price of $5 to calculate the pre-tax surplus:

- Consumer surplus: (1/2) x 300 x (5 - 0) = $750
- Producer surplus: (1/2) x 300 x (5 - 0) = $750
- Total surplus: $1,500

After the tax, the surplus is:

- Consumer surplus: (1/2) x 279 x (7 - 0) = $976.50
- Producer surplus: (1/2) x 279 x (2 - 0) = $279
- Tax revenue for government: $1000
- Total surplus: $1,255.50

The deadweight loss is the difference between the total surplus before and after the tax:

- Deadweight loss = $1,500 - $1,255.50 - $1000 = $244.50

So the best choice is C, $250, which is closest to the calculated deadweight loss of $244.50.

Suppose That the Equilibrium Quantity in the Market for Widgets