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? 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
40P = 1000-10P
Take -10 p to that side...
40P + 10P = 1000
50P = 1000
P = 1000/50
P = 20
So 20 [ what unit would come here?]
pollution reduction must be undertaken by Appalachian Coal mining. (1) Appalachian coal mining believes that it can increase labor productivity and, therefore, net revenues 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 the marginal increase in revenue ( MR) is MR= 1,000- 10p
The costs are not greater than or equal to the benefits, thus offsetting any benefit from installing the equipment and the pollution reduction. In order to determine whether or not the cost of installing the capital equipment outweighs the benefits of the equipment, one must fix the level of pollution reduction and determine the optimal level of pollution reduction. According to our text, “the optimal level of the activity—the level that maximizes net benefit—is attained when no further increases in net benefit are possible for any changes in the activity, which occurs at the activity level for which marginal benefit equals marginal cost: MB = MC” (Thomas & Maurice, 2011, p. 97). In other words, the optimal value for pollution reduction is found when the marginal cost equals the marginal revenue. To find the optimal value, one would set the marginal cost equal to the marginal revenue and solve for P.
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
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
following rule: marginal benefit = marginal cost or MB=MC
MC=w=200, but MB from hiring second worker is:
with total benefit:
TB=(50-20)•25 - (200•2) = 750-400 = 350
So firm will hire two guards.
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.
Firm will be indifferent about hiring decision if benefit equals cost. Benefit from first guard is: B=(50-30)•25=20•25=500
so maximum payment to first guard firm will be willing to do is W=500
c. If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security...
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