Suppose that a market is initially in equilibrium.The initial demand curve is The initial supply curve is Suppose that the government imposes a $3 tax on this market.What is the change in producer surplus due to the tax?

Question

Suppose that a market is initially in equilibrium.The initial demand curve is  The initial supply curve is  Suppose that the government imposes a $3 tax on this market.What is the change in producer surplus due to the tax?

Quizplus · Accepted Answer

To find the change in producer surplus due to the tax, we need to compare the original equilibrium price and quantity with the new equilibrium price and quantity after the tax is imposed. The original equilibrium price was $7, and the corresponding quantity was 5. At this price and quantity, the total surplus was:

- Consumer surplus: (1/2)(7-4)(5) = $7.50
- Producer surplus: (1/2)(7-2)(5) = $12.50
- Total surplus: $20.00

After the tax is imposed, the supply curve shifts leftward by $3, so the new equilibrium price is $8 and the corresponding quantity is 4. At this price and quantity, the total surplus is:

- Consumer surplus: (1/2)(8-4)(4) = $8.00
- Producer surplus: (1/2)(8-2-$3)(4) = $7.00
- Tax revenue: $3.00
- Deadweight loss: (1/2)(7-8)(1) = $0.50
- Total surplus: $18.50

Therefore, the change in producer surplus due to the tax is the difference between the original producer surplus ($12.50) and the new producer surplus ($7.00), which is $5.50.

Suppose That a Market Is Initially in Equilibrium