(Advanced analysis) The equations for the demand and supply curves for a particular product are P = 10 − 0.4Q and P = 2 + 0.4Q, 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 + 0.4Q. Government's revenue from this tax is

Question

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Before the tax, the equilibrium is found by setting the demand and supply equations equal to each other, which gives:
10 - 0.4Q = 2 + 0.4Q
Solving for Q, we get Q = 20.
Substituting into either equation gives P = $6.
With the tax, the new supply equation is P = 3 + 0.4Q.
At the new equilibrium, demand equals supply, so we have:
10 - 0.4Q = 3 + 0.4Q
Solving for Q, we get Q = 14.
Substituting into the supply equation gives P = $8.60.
The tax revenue is equal to the difference in price before and after the tax, multiplied by the quantity sold:
($8.60 - $6) x 14 x 100 = $1,544
However, we have to account for the portion of the price increase due to the tax versus the portion due to the shift in the supply curve. To do this, we need to find the equilibrium price and quantity with just the shift in the supply curve (no tax):
10 - 0.4Q = 3 + 0.4Q
Solving for Q, we get Q = 17.5.
Substituting into the supply equation gives P = $6.50.
So, the portion of the price increase due to the tax is $8.60 - $6.50 = $2.10.
The tax revenue is equal to the tax per unit sold, multiplied by the quantity sold:
$2.10 x 14 x 100 = $2,940
However, the tax revenue does not go entirely to the government. Some of it is paid by consumers and some of it is paid by producers. The portion paid by consumers is equal to the area of the triangle formed by the original equilibrium price ($6), the new equilibrium price with the tax ($8.60), and the vertical intercept of the supply curve ($3):
(1/2) x ($8.60 - $6) x 14 x 100 = $1,960
The portion paid by producers is equal to the total tax revenue minus the portion paid by consumers:
$2,940 - $1,960 = $980
Therefore, the government's revenue from this tax is $980, or choice C.

(Advanced Analysis) the Equations for the Demand and Supply Curves