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 = 1000-10P.
How much pollution reduction should Appalachian Coal Mining undertake?
Marginal cost = MC = 40P
Marginal revenue = 1000 -10P
For optimal value we should have MC=MR
40P = 1000 -10P
50P = 1000
P = 1000/20
P = 50
Hope this helps!