The equations for the demand and supply curves for a particular product are P = 10 - .4Q and P = 2 + .4Q,where P is price and Q is quantity expressed in units of 100.After an excise tax is imposed on the product,the supply equation is P = 3 + .4Q.Government's revenue from this tax is:

Question

Quizplus · Accepted Answer

Before the tax, the equilibrium price and quantity can be found by setting the demand equal to the pre-tax supply:
10 - 0.4Q = 2 + 0.4Q
Q* = 15
P* = 6

After the tax, the new supply curve is given by P = 3 + 0.4Q. Setting demand equal to this new supply, we can find the new equilibrium quantity:
10 - 0.4Q = 3 + 0.4Q
Q* = 17.5
To find the new equilibrium price, we substitute this quantity back into either the demand or supply equation:
P* = 3 + 0.4(17.5) = 10

The price has increased from 6 to 10, so the tax must be $4 per unit. At the new equilibrium, producers receive a price of $6 per unit, but $4 of that goes to the government, leaving producers with only $2 per unit. The quantity sold has increased from 1,500 units to 1,750 units. Therefore, the government's revenue from the tax is:
$4 × 1,750 = $7,000
But this is the revenue before the tax is shared with consumers. The burden of the tax is shared between consumers and producers, with the exact division depending on the elasticity of demand and supply. In this case, we can use the equivalence of the tax-inclusive and tax-exclusive demand curves to find that the price elasticity of demand is 2.5 and the price elasticity of supply is 0.5. Therefore, consumers pay 2/3 of the tax and producers pay 1/3. Hence, the government's net revenue from the tax is:
$7,000 × (1/3) = $2,333.33
Therefore, the closest answer choice is C, $875.

The Equations for the Demand and Supply Curves for a Particular