Applacian Coal Mine Co believes it can increase labor productivity and therefore, net revenue by reducing air pollution in its mines. It is estimated that the marginal cost for reducing pollution by installing additional capital equipment is MC = 40P....where P represents a reduction of one unit of pollution in the coal mines, the comapny feels that for every unit of pollution reduction the marginal increase in revenue (MR) is: MR=1,000 - 10P. How much pollution reduction should the coal mine company undertake?

Question

Applacian Coal Mine Co believes it can increase labor productivity and therefore, net revenue by reducing air pollution in its mines. It is estimated that the marginal cost for reducing pollution by installing additional capital equipment is MC = 40P....where P represents a reduction of one unit of pollution in the coal mines, the comapny feels that for every unit of pollution reduction the marginal increase in revenue (MR) is: MR=1,000 - 10P. How much pollution reduction should the coal mine company undertake?

Use algebra. Set MC=MR, then solve for P.

Answer 1

1000-10P=40P

1000=50P
P=20

Answer 2

To find out how much pollution reduction the coal mine company should undertake, we need to set the marginal cost (MC) equal to the marginal revenue (MR) and solve for P.

MC = MR

To do this, let's substitute the expressions for MC and MR:

40P = 1,000 - 10P

Now, let's solve for P.

First, we can combine like terms:

40P + 10P = 1,000

Simplifying further:

50P = 1,000

Divide both sides of the equation by 50:

P = 1,000 / 50

P = 20

Therefore, the coal mine company should undertake a pollution reduction of 20 units.