Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations:
B(Q) = 100 + 36Q − 4Q2 and C(Q) =80 + 12Q.
(Note: MB(Q) = 36 − 8Q and MC(Q) = 12.)
Instructions: Use a negative sign (-) where appropriate.
a. Write out the equation for the net benefits.
N(Q) = + Q + Q2
b. What are the net benefits when Q = 1? Q = 5?
Net benefits when Q = 1:
Net benefits when Q = 5:
c. Write out the equation for the marginal net benefits.
MNB(Q) = + Q
d. What are the marginal net benefits when Q = 1? Q = 5?
Marginal net benefits when Q = 1:
Marginal net benefits when Q = 5:
e. What level of Q maximizes net benefits?
f. At the value of Q that maximizes net benefits, what is the value of marginal net benefits?