Appalachian Coal Mining believes that it can increase labor productivity and, there-fore, 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 Coal Mining undertake?
To determine the optimal level of pollution reduction that Appalachian Coal Mining should undertake, we need to find the level of pollution reduction where the marginal cost equals the marginal revenue.
Given that the marginal cost (MC) of reducing pollution is given by MC = 40P, and the marginal revenue (MR) from reducing pollution is given by MR = 1,000 - 10P, we can equate MC and MR:
40P = 1,000 - 10P
To solve this equation, we can combine like terms:
40P + 10P = 1,000
Simplifying further:
50P = 1,000
To isolate P, the reduction in pollution, we divide both sides of the equation by 50:
P = 1,000 / 50
Thus, the optimal level of pollution reduction that Appalachian Coal Mining should undertake is P = 20 units.
Explanation of the process:
1. Identify the relevant marginal cost and marginal revenue functions for pollution reduction.
2. Set the marginal cost equal to the marginal revenue equation: MC = MR.
3. Simplify and solve the resulting equation to find the optimal level of pollution reduction.