Use the following marginal benefit and marginal cost functions for activity A: MB = 100 - 5A
MC = 20 + 3A
The fifth unit of activity A will
A)increase net benefits by 75.
B)reduce net benefits by 35.
C)increase net benefits by 40.
D)decrease net benefits by 40.
E)reduce net benefits by 75.

Question

Quizplus · Accepted Answer

To determine the net benefits, we need to calculate the total benefit (TB) and total cost (TC) of activity A up to the fifth unit.
TB = ∫(0 to 5) MB dA = ∫(0 to 5) (100 F1S1 - 500) dA = 100 F1S1 A - 500A | from 0 to 5 = 500F1S1 - 2500
TC = ∫(0 to 5) MC dA = ∫(0 to 5) (20 + 3A) dA = 20A + 1.5A^2 | from 0 to 5 = 107.5

NB = TB - TC = 500F1S1 - 2607.5
To find the net benefit of the fifth unit, we need to subtract the net benefit of the fourth unit from the net benefit of the fifth unit:
NB5 - NB4 = (500F1S1 - 2607.5) - (500F1S1 - 2407.5) = -200
Since the net benefit of the fifth unit is negative, it means that the cost of the fifth unit exceeds the benefit, and it would reduce net benefits. Therefore, we should not choose the fifth unit of activity A. Any choice up to the fourth unit of activity A would increase net benefits.

Use the Following Marginal Benefit and Marginal Cost Functions for Activity