marginal product of capital and labor

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Your firms research department has estimated your total revenues to be: R (Q) = 3,000Q - 8Q2 and your total costs to be C (Q) = 100 + 2Q2.

Calculate the marginal benefit and marginal cost functions.
Marginal benefit =dR(Q)/dQ = 3000-16Q
Marginal cost = dC(Q)/dQ=4Q

a. What level of Q maximizes net benefits?
For maximization of net benefits (net profits), equate marginal benefits to marginal costs and solve for Q
3000-16Q=4Q
20Q=3000
Q=150

b. What is marginal benefit at this level of Q?
Marginal Benefit = 3000-16Q=3000-16*150=600

c. What is the marginal cost at this level of Q?
Marginal cost = 4Q = 4*150=600

d. What is the maximum level of net benefits?
=R(Q)-C(Q) = (3000*150-8*150*150) - (100+2*150*150)
=$224,900

e. What is another word for "Net benefits" in this example?
Profit is another word for net benefits.
GGH recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by GGH's leadership in this area. The costs of recycling include all the energy, labor, and space to do the recycling. Suppose these benefits and costs are given by: B (Q) = 100Q - 2Q2 and C (Q) = 2Q.

Calculate the marginal benefit and marginal cost functions.
a. What level of Q maximizes the total benefits of reclying?
Differentiate the total benefit equation wrt Q and equate to zero
dB(Q)/dQ = 100 - 4Q
Equating this to zero we have 100-4Q=0
Solving we get Q=100/4=25
The total benefits of recycling will be maximized at Q=25

b. What level of Q minimizes the total costs of recycling?
Differentiate the total cost equation wrt Q and equate to zero
dC(Q)/dQ = 2
There is no feasible solution.
Total cost function is a monotonous function and ever increasing, it will have the minimum value when Q=0.

c. What level of Q maximizes the net benefits of recycling?
For maximization of net benefits (net profits), equate marginal benefits to marginal costs and ...