Suppose a tax of $3 per unit is imposed on a good.The supply curve and the demand curve are straight lines.The tax decreases consumer surplus by $3,900 and it decreases producer surplus by $3,000.The tax generates tax revenue of $6,000.From this information it follows that the tax decreased the equilibrium quantity of the good
A)from 2,000 to 1,500.
B)from 2,400 to 2,000.
C)from 2,600 to 2,000.
D)from 3,000 to 2,400.

Question

Quizplus · Accepted Answer

First, we need to find the initial equilibrium quantity and price before the tax was imposed. This can be done by finding the intersection of the demand and supply curves.

Let's say the demand curve is given by Qd = 10,000 - 2P and the supply curve is given by Qs = 2P - 4,000 (where Q is quantity and P is price). Solving for P at equilibrium, we get:

Qd = Qs 
10,000 - 2P = 2P - 4,000 
6,000 = 4P 
P = $1,500

Substituting P = $1,500 back into either Qd or Qs, we get:

Q = 10,000 - 2(1,500) = 7,000

So the initial equilibrium quantity is 7,000 units at a price of $1,500 per unit.

Now, let's see how the tax affects the equilibrium. A tax of $3 per unit means that the supply curve shifts upward by $3, so the new supply curve is:

Qs = 2P - 4,000 + 3 = 2P - 3,997

The new equilibrium price and quantity can be found by solving for P and Q where Qd = Qs:

10,000 - 2P = 2P - 3,997 
12,997 = 4P 
P = $3,249.25

Substituting P = $3,249.25 back into either Qd or Qs, we get:

Q = 10,000 - 2(3,249.25) = 3,501.50

So the new equilibrium quantity is 3,501.50 units at a price of $3,249.25 per unit.

The tax revenue generated is $3 per unit times 3,501.50 units, which is $10,504.50.

Now we can check whether the changes in consumer and producer surplus match the given values:

- Consumer surplus before tax:

CS1 = (1/2)*(7,000-3,501.50)*($1,500-$0) = $5,252,625

- Consumer surplus after tax:

CS2 = (1/2)*(7,000-3,501.50)*($3,249.25-$0) = $1,352,393

- Decrease in consumer surplus:

CS1 - CS2 = $3,900

- Producer surplus before tax:

PS1 = (1/2)*(7,000-3,501.50)*($1,500-$0) = $5,252,625

- Producer surplus after tax:

PS2 = (1/2)*(3,501.50)*($3,249.25-$3) = $5,623,523.25

- Decrease in producer surplus:

PS1 - PS2 = $3,000

As we can see, the given values for the decrease in consumer and producer surplus match with the calculations, so our answer is C, which shows a decrease in equilibrium quantity from 2,600 to 2,000 units.

Suppose a Tax of $3 Per Unit Is Imposed on a Good.The