1. 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.]
a. Write out the equation for the net benefits
b. What are the net benefits when Q = 1? Q = 5?
c. Write out the equation for the marginal net benefits.
d. What are the marginal net benefits when Q = 1? 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?
2. Suppose the total benefit derived from a continuous decision, Q, is B(Q) = 20Q - 2Q2 and corresponding total cost is C(Q) = 4 + 2Q2 so that MB(Q) = 20 - 4Q and MC(Q) = 4Q.
a. What is total benefit when Q = 2? Q = 10?
b. What is marginal benefit when Q = 2? Q = 10?
c. What level of Q maximizes total benefit?
d. What is total cost when Q = 2? Q = 10?
e. What level of Q minimizes total cost?
f. What level of Q maximizes net benefits?