Appalachian Coal Mining believes that it can increase labor productivity and, th

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 Coal Mining undertake?

Explanation / Answer

In case if "Applachian Coal Mining" doesn't have any alternative investment opportunities with higher benefit - then investment optimality [maximization] condition is given by: MC=MR, thus: 1000-10P=40P 50P=1000 P=1000/50=20 [reduction of pollution units] So it will cost: TC=FC+?MC=FC+20P²= FC+20•20²=FC+8000 And revenue will be: TR=FR+?MR=FR+1000P-5P²= FR+20000-5•20²= =FR+20000-2000=FR+18000 With maximal total benefit: TR-TC=FR+18000-FC-8000= FR-TC+10000 Or assuming fixed revenue FR=0 and fixed costs FC=0 Net benefit from pollution limitation = TR-TC = 18000-8000 = +10000 With pollution reduction by P=20 units.

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