# marginal cost function for reducing pollution

Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is

MC = 40P

Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is

MR = 1,000 - 10P

How much pollution reduction should Appalachian Coal Mining undertake?

https://brainmass.com/economics/regression/marginal-cost-function-for-reducing-pollution-348037

#### Solution Preview

The installation of additional capital equipment will reduce pollution and increase the labor productivity..But look at the additional cost...It is not offsetting the benefit So fix the level of pollution reduction in an optimal manner...The optimal value P is Marginal cost = marginal revenue

Set MC = MR and solve for P

MC = 40P MR = 1000 -10P

That is 40P = 1000-10P

Take -10 p to that side... 40P + 10P = 1000

50P = 1000

P = 1000/50

P = 20

Chapter 3, Applied Problem 4

Twentyfirst Century Electronics has discovered a theft problem at its warehouse and

has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the

number of radios stolen per week.

Number of security guards Number of radios stolen per week

0 ............................. ............................. 50

1 ............................. ............................. 30

2 ............................. ............................. 20

3 ............................. ............................. 14

4 ............................. ............................. 8

5 ............................. ............................. 6

a. If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

b. If the cost of a stolen radio is ...

#### Solution Summary

The installation of additional capital equipment is advised in this case. References are also provided to further validate the findings.