What is the government surplus with the optimal tax in place?

Question

Quizplus · Accepted Answer

The optimal tax will be achieved at the point where the marginal cost of providing public goods intersects with the demand curve. In this case, the optimal tax is $6 per unit. With this tax, the quantity demanded will be 27 units, which can be seen by finding the quantity demanded at a price of $8 (Qd = 36 - 2P = 36 - 2(8) = 20, and then adding the change in quantity from a $1 decrease in price, which is 7). Therefore, the government's total revenue will be $162 ($6 tax x 27 units). The cost of providing the public good at 27 units is $81 ($3 x 27 units). Therefore, the government surplus will be $81 (the difference between revenue and cost) + $567 (the surplus from the unconsumed units, which is 21 units x $3 each) = $648.

What Is the Government Surplus with the Optimal Tax in Place