Fixing optimum quantity by considering Marginal Cost and Marginal Revenue.
Appalachian Coal mining believes it can enhance 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 reduction of one unit of pollution in 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?