Question

Suppose total benefits and total costs are given by TB(Q) = 220Q – 15Q2 and TC(Q) = 40Q. What level of Q will yield the maximum net benefits?

Select one: a. 7 b. 6 c. 10/9 d. 150/20

Answer 1

The net benefits are calculated by the following formula:

Net Benefit = Total Benefit - Total Cost

Net Benefit = 220Q - 15Q² - 40Q

Net Benefit = 180Q - 15Q²

Differentiating the net Benefit function with respect to Q:

d(Net Benefit)/dQ = 180 - 30Q

Putting it equal to 0:

180 - 30Q = 0

30Q = 180

Q = 180/30

Q = 6

Double differentiating the net benefit function with respect to Q:

d²(Net Benefit)/ dQ = -30 < 0

So, the net benefits are maximum when the quantity produced is 6 units. Therefore, the correct answer is 'Option B'.