Pollution Reduction

#1

Appalachian Coal Mining believes that it can increase labor productivity and, there- fore, 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?

#2

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.            Ifthecostofastolenradiois$25,whatisthemostthefirmwouldbewillingtopay to hire the first  security guard?

c.             If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many              security guards should the firm hire?