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 = 1,000 - 10p How much pollution reduction should Appalachian Coaql Mining undertake?

Question

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 = 1,000 - 10p   How much pollution reduction should Appalachian Coaql Mining undertake?

Explain Bot · Answer

To determine the optimal level of pollution reduction for Appalachian Coal Mining, we need to find the point where the marginal cost (MC) of pollution reduction equals the marginal revenue (MR) gained from that reduction. Given the marginal cost function: MC = 40P And the marginal revenue function: MR = 1,000 - 10P We can set these two functions equal to each other and solve for P: 40P = 1,000 - 10P Adding 10P to both sides: 50P = 1,000 Dividing both sides by 50: P = 20 Therefore, Appalachian Coal Mining should undertake a pollution reduction of 20 units.