The market for Good X can be depicted with the following demand and supply equations:

Question

The market for Good X can be depicted with the following demand and supply equations:

Demand: P = 50 – 1/2Q
Supply: P = 1/3Q
Where P is price per unit and Q represents quantity in units. Policy makers plan on imposing a $1 per unit tax on this good.
Question: ( Market for Good X) If this tax is imposed, the price of Good X will increase by:
A) $20.
B) $0.60.
C) $1.00.
D) $1.50.

I don't how to solve?

Answer 1

To solve this question, we need to find the new equilibrium price after the tax is imposed.

Step 1: Calculate the initial equilibrium price and quantity:
Set the demand and supply equations equal to each other to find the initial equilibrium:
50 - 1/2Q = 1/3Q

Step 2: Solve for the initial equilibrium quantity (Q):
Add (1/2Q) to both sides:
50 = 5/6Q

Multiply both sides by 6/5 to solve for Q:
Q = (6/5) * 50
Q = 60

Step 3: Calculate the initial equilibrium price (P):
Plug the equilibrium quantity (Q) back into the demand or supply equation:
P = 1/3 * 60
P = $20

So, the initial equilibrium price is $20.

Step 4: Calculate the new equilibrium price after the tax is imposed:
To find the new equilibrium price, we need to consider that the tax will be imposed on the buyers or sellers. In this case, the tax is imposed on the good itself, so it will affect the supply, not the demand.

The new supply equation will be: P (after tax) = 1/3Q + Tax

The tax is $1 per unit, so the new supply equation becomes:
P (after tax) = 1/3Q + 1

Now, set the new demand equation equal to the new supply equation:
50 - 1/2Q = 1/3Q + 1

Step 5: Solve for the new equilibrium quantity (Q):
Subtract (1/3Q) from both sides:
50 - 1 = 5/6Q

Simplify:
49 = 5/6Q

Multiply both sides by 6/5:
Q = (6/5) * 49
Q = 58.8

Step 6: Calculate the new equilibrium price (P):
Plug the new equilibrium quantity (Q) back into the demand or supply equation:
P = 1/3 * 58.8 + 1
P = $20 + 1
P = $21

So, the new equilibrium price (after the tax is imposed) is $21.

Step 7: Calculate the increase in price:
The increase in price is the difference between the new equilibrium price and the initial equilibrium price:
$21 - $20 = $1

Therefore, the price of Good X will increase by $1 if the tax is imposed.

The correct answer to the question is C) $1.00.