Bus640 Managerial Economics
Week 2 Assignment
Crystal G Tanner
BUS640: Managerial Economics
Brian Shaw
April 23, 2012
CH 3. 2. 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?
Set MC = MR and solve for P
40P = 1000-10P
40P + 10P = 1000
50P = 1000
P = 1000/50
P = 20 units of pollution reduction
MR = 1000 – 10(20)
MR = 1000 -200
MR = 800
MC = 40(20)
MC = 800
By installing additional capital equipment Appalachian Coal Mining can reduce the pollution by 20 units of pollution with the Marginal cost of 800. Therefore, the increase in capital will decrease the amount of pollution and will benefit both the company and the world with the reduction in pollution. Any company that invests capital to clean the environment is making the right choice no matter how much or how little it fixes, anything reduction is better than nothing.
CH 3. 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 Guards Number of radios
-------------------------------------------------
Security guards stolen per week 0 -------------------------------------------------
50
1 -------------------------------------------------
30
2 -------------------------------------------------
20
3
Crystal G Tanner
BUS640: Managerial Economics
Brian Shaw
April 23, 2012
CH 3. 2. 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?
Set MC = MR and solve for P
40P = 1000-10P
40P + 10P = 1000
50P = 1000
P = 1000/50
P = 20 units of pollution reduction
MR = 1000 – 10(20)
MR = 1000 -200
MR = 800
MC = 40(20)
MC = 800
By installing additional capital equipment Appalachian Coal Mining can reduce the pollution by 20 units of pollution with the Marginal cost of 800. Therefore, the increase in capital will decrease the amount of pollution and will benefit both the company and the world with the reduction in pollution. Any company that invests capital to clean the environment is making the right choice no matter how much or how little it fixes, anything reduction is better than nothing.
CH 3. 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 Guards Number of radios
-------------------------------------------------
Security guards stolen per week 0 -------------------------------------------------
50
1 -------------------------------------------------
30
2 -------------------------------------------------
20
3