The demand curve for a good is given by the equation P = 200 - 1/4...

The demand curve for a good is given by the equation P = 200 - 1/4 Q and the supply curve is given by the equation P = 50 + 1/2 Q, where P represents the price of the good (measured in dollars per unit) and Q represents the quantity of the good (measured in units per week).

If the government imposes a sales tax of $9 per unit on this good. Find the new formula for the demand curve, the change in equilibrium quantity, the post-tax price received by suppliers, and the post-tax price paid by buyers. Illustrate graphically as well.

Expert Solution

The demand function is P = 200 - 0.25Q and supply function is P = 50 + 0.5Q. Before tax, the quantity at the equilibrium is found as:

200 - 0.25Q = 50 + 0.5Q

150 = 0.75Q

Q = 200 units and price P = 50 + 0.5*200 = $150 per unit

After tax the demand is unchanged because there is a sales tax imposed which will affect the supply function and not the demand. Hence new supply function is P = 50 + 0.5Q + 9 or P = 59 + 0.5Q.

New quantity at after tax equilibrium is

200 - 0.25Q = 59 + 0.5Q

141 = 0.75Q

Q = 188 units and

Price paid by buyers = 200 - 0.25*188 = $153

Price received by sellers = 50 + 0.5*188 = 144

Hence, the change in equilibrium quantity is (200 - 188) = 12 units, the post-tax price received by suppliers is $144 per unit, and the post-tax price paid by buyers is $153 per unit.

Rahul Sunny answered 4 months ago

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