p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue.
A)$3,780
B)$840
C)$3,360
D)$2,160
E)$2,820

Question

p is the price per unit in dollars and q is the number of units. The monthly demand function is  and the supply function before taxation is  . Find what tax per item will maximize the total revenue and use this to find the maximum tax revenue. ​
A)$3,780 
B)$840 
C)$3,360 
D)$2,160 
E)$2,820

Quizplus · Accepted Answer

The revenue for the after-tax market is given by:

R(p) = (p - t)(q) = pq - tq

The goal is to find the tax that maximizes total revenue. To do this, we need to differentiate with respect to t:

dR/dt = -q

Setting this equal to zero, we see that revenue is maximized when q = 0. This is not a feasible solution, so we know that revenue is decreasing with respect to t. Therefore, we should set t = 0 in the supply function to find the maximum tax revenue:

S(0) = 16800 - 1200(0) = 16800

Therefore, the maximum tax revenue is $16,800.

Looking at the answer choices, the only possible answer is C, which gives a tax of $0.20 per item.

P Is the Price Per Unit in Dollars and Q