The equation for net benefits

a. The equation for net benefits (NB) can be obtained by subtracting the total cost (C) from the total benefit (B):

NB(Q) = B(Q) – C(Q)
= (100 + 36Q – 4Q^2) – (80 + 12Q)
= 20 + 24Q – 4Q^2

b. To find the net benefits when Q = 1 and Q = 5, substitute these values into the equation for NB:

Net benefits when Q = 1:
NB(1) = 20 + 24(1) – 4(1)^2
= 20 + 24 – 4
= 40

Net benefits when Q = 5:
NB(5) = 20 + 24(5) – 4(5)^2
= 20 + 120 – 100
= 40

c. The equation for marginal net benefits (MNB) can be obtained by taking the derivative of the net benefits equation with respect to Q:

MNB(Q) = d/dQ (NB(Q))
= d/dQ (20 + 24Q – 4Q^2)
= 24 – 8Q

d. To find the marginal net benefits when Q = 1 and Q = 5, substitute these values into the equation for MNB:

Marginal net benefits when Q = 1:
MNB(1) = 24 – 8(1)
= 24 – 8
= 16

Marginal net benefits when Q = 5:
MNB(5) = 24 – 8(5)
= 24 – 40
= -16

e. To find the level of Q that maximizes net benefits, we need to find the value of Q where MNB(Q) equals zero:

24 – 8Q = 0
-8Q = -24
Q = 3

Therefore, the level of Q that maximizes net benefits is Q = 3.

f. At the value of Q that maximizes net benefits (Q = 3), the value of marginal net benefits (MNB) can be found by substituting Q = 3 into the equation for MNB:

MNB(3) = 24 – 8(3)
= 24 – 24
= 0

Therefore, at the value of Q that maximizes net benefits, the value of marginal net benefits is zero.