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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 ...

Solution Summary

The marginal product of capital and labor is considered.

$2.19
See Also This Related BrainMass Solution

Labor, capital, & inputs & outputs

This is a 4 part question:

A manufacturer is hiring 20 units of labor and 6 units of capital (bundleA). The price of labor is $10 and the price of capital is $2 and at A the marginal products of labor and capital are both equal to 20.

1.Beginning at A if the manufacturer increases labor by 1 unit and decreases capital by 1 unit, what will happen to cost and output?

Cost remain constant & output rises by 20 units
Cost remain constant & output lowers by 20 units
Output remains constant & cost increase by $8
Output remains constant & cost lowers by $8
Both cost and output remain constant

2.Beginning at A, if the manufacturer raises expenses on labor by $1 and lowers expenses on capital by $1, which is True?

Output per $ spent will rise
Output per $ spent will lower
MP of labor will eventually rise and MP of capital will eventually fall
MP of labor will eventually rise and MP of capital will remain constant
Or none of these

3.The manufacturer

is using optimal combination of capital and labor
should use more labor and less capital
should use more capital and less labor
need more information to determine

4.In equilibrium

MPL will be less than 20
MPK will be more than 20
MPK=MPL
MPL will be 5 times MPK
Or the first 2 listed above

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