Suppose a tax of 5 dollars per unit is imposed on a good.The supply curve is a typical upward-sloping straight line,and the demand curve is a typical downward-sloping straight line.The tax decreases consumer surplus by 10,000 dollars and decreases producer surplus by 15,000 dollars.The deadweight loss of the tax is 2,500 pounds.The tax decreased the equilibrium quantity of the good from

Question

Quizplus · Accepted Answer

When a tax is imposed on a good, the new supply curve shifts upwards by the amount of the tax ($5 in this case). The new equilibrium quantity will be lower than the original quantity due to the increase in price.

We know that the tax decreases consumer surplus by $10,000 and producer surplus by $15,000. The area of the rectangle formed by the original equilibrium quantity and price is the total surplus before the tax. After the tax, the area of the rectangle formed by the new equilibrium quantity and price will be the total surplus.

The decrease in consumer surplus plus the decrease in producer surplus plus the tax revenue equals the deadweight loss:

10,000 + 15,000 + (tax x new equilibrium quantity) = 2,500

Multiplying the tax by the new equilibrium quantity, we get:

5 x (original equilibrium quantity – new equilibrium quantity) x new equilibrium quantity = 2,500

Simplifying, we get:

5Q^2 – 25,000Q + 25,000 = 0

Using the quadratic formula, we get:

Q = 4,500 or Q = 5,500

Since the tax decreased the equilibrium quantity of the good, the answer must be one of the two options above. However, we are told that the tax decreased the equilibrium quantity from the original quantity to a new quantity. Therefore, the answer is B) 5,500 to 4,500.

Suppose a Tax of 5 Dollars Per Unit Is Imposed