Bus. 640 Economics

Chapter 3: Problem 2: 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 marginalcost 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) isMR 1,000 10P How much pollution reduction should Appalachian Coal Mining undertake?
MC = MR and solve for P. That is 40P = 1000-10P
40P+10P=1000
50P=1000
P=20 units.

Problem 4:
Twenty first 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? 2 guards:
Number of Security Guards Number of radios stolen per week
0 50 (200 × 0) + (25×50)=1250

1 30 (200 x 1) + (25 x 30) =950
2 20 (200 x 2) + (25 x 20) = 900
3 14 (200 x 3) + (25 x 14) = 950
4 8 (200 × 4) +(25 × 8)=1000
5 6 (200 x 5) + (25 x 6) =1150

b. If the cost of a stolen radio is $25, what is the most the firm would be willing to pay to hire the first security guard?
50 – 30=20 * $25 = 500
So the maximum would be 500, anything over 500 would not be a benefit to the company.

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? 3 guards
Number of Security Guards Number of radios stolen per week
0 50 (200 × 0) + (50×50)=2500
1 30 (200 x 1) + (50 x 30) = 1700
2 20 (200 x 2) + (50 x 20) = 1400
3 14 (200 x 3) + (50