Appalachian Coal Mining believes it can increase labor productivity and therefore, net revenue by reducing air pollution in it's mines

Economics Dec 15, 2020

Appalachian Coal Mining believes it can increase labor productivity and therefore, net revenue by reducing air pollution in it's 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?

Expert Solution

Answer: 20

To find out the optimal amount of air pollution to reduce, we set MR to MC and solve. This is because the company should continue to decrease air pollution as long as the marginal revenue is greater than the marginal cost. This is done below:

1000−10P=40P1000=50PP=20

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