Suppose a tax of $3 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 $3,900 and decreases producer surplus by $3,000.The tax generates tax revenue of $6,000.The tax decreased the equilibrium quantity of the good from
A)2,000 to 1,500.
B)2,400 to 2,000.
C)2,600 to 2,000.
D)3,000 to 2,400.

Question

Quizplus · Accepted Answer

When a tax is imposed on a good, it creates a wedge between the price received by producers and the price paid by consumers. Since the supply curve is upward-sloping, producers will bear a portion of the tax burden and consumers will bear the remaining portion.

Let's start by finding the equilibrium quantity and price before the tax was imposed. Since the supply and demand curves are straight lines, we can solve for equilibrium by setting them equal to each other:

Quantity supplied: Qs = a + bP (where a and b are constants)
Quantity demanded: Qd = c - dP (where c and d are constants)

Setting Qs = Qd, we get:

a + bP = c - dP
2dP = c - a + bP
P = (c - a)/(2d - b)

Substituting the given values, we get:

P = (5200 - 0)/(2*200 - 100) = $52

To find the equilibrium quantity, we can plug the equilibrium price into either the supply or demand equation:

Q = a + bP = 0 + 200*$52 = 10,400 units

Now we can analyze the effects of the tax. Since the tax is $3 per unit, it raises the price paid by consumers to:

$52 + $3 = $55

However, producers only receive $52 per unit, so they effectively receive $49 per unit after the tax is imposed.

To find the new equilibrium quantity, we need to find the points on the supply and demand curves where quantity supplied equals quantity demanded with the tax included.

Quantity supplied (with tax): Qs = a + b(P - T) = 0 + 200($55 - $3) = 10,400 units
Quantity demanded (with tax): Qd = c - dP = 5200 - 100($55) = 0

The equilibrium quantity with the tax is 10,400 units. This is a decrease from the initial equilibrium quantity of 2,600 units, so the best choice is C, where the initial equilibrium quantity was 2,600 and the new equilibrium quantity is 2,000.

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