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 addtional capital equipment is mMC=40p
where p represents a reduction of one unit of ppllution in the mines. It also feels that for every unit of pollution reduction the margiinal increase in revenue ( MR) is MR=1,000-10P. How much pollution reduction should Appalachina Coal Mining undertake?
Set MC = MR and solve for P. That is 40P = 1000-10P
To determine the optimal level of pollution reduction that Appalachian Coal Mining should undertake, we need to find the point where the marginal cost of reducing pollution equals the marginal increase in revenue.
Given:
Marginal cost of reducing pollution, mMC = 40p
Marginal increase in revenue, MR = 1,000 - 10P
To find the optimal level of pollution reduction, we equate mMC and MR:
40p = 1,000 - 10P
Let's solve this equation to find the value of p:
40p + 10P = 1,000
50p = 1,000
p = 1,000 / 50
p = 20
Therefore, the optimal level of pollution reduction that Appalachian Coal Mining should undertake is 20 units.