Quantity effect of a specific tax. A regulator plans to impose a specific tax on a previously unregulated monopolist. Before imposing the tax, they want to know what the change in quantity produced will be from such a tax. The proposed specific tax is τ = 10 and the following are the inverse demand and total cost functions:
P(Q) = 100 − 1 8 Q
C(Q) = 20 + 10Q + 1 8 Q 2 .
Find the change in quantity from a $10 increase in the tax.