# Week 2 Applied Problems Essay

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Chapter 3 Applied Problems
2. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in it 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?

If Appalachian Coal Mining decided to install additional capital equipment, they would decrease the amount of pollution that their company produces. This installation of additional capital
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 or 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?

In order to determine how many security guards Twentyfirst Century Electronics should hire, one must find the number of security guards in which the marginal benefit of having the security guards is greater than the marginal cost of the security guards. According to our text, “when a decision maker faces an unconstrained maximization problem and must choose among discrete levels of an activity, the activity should be increased if MB > MC and decreased if MB b= > c= 0 means that the advertising has a positive effect on their sales. c = -0.284. This is the slope parameter or Vanguard’s rivals advertising. c > 0 means that the advertising has a negative effect on the sales.
The regression output from the computer is as follows:
Dependent variable: S R-Square F-Ratio P- Value on F
Observations: 36 0.2247