: Managerial Economics
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
That is
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
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
That is
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