Chapter 3 Applied Problems
2. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in it 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?
If Appalachian Coal Mining decided to install additional capital equipment, they would decrease the amount of pollution that their company produces. This installation of additional capital equipment will also lead to an increase in labor productivity. However, when assessing the benefit that this equipment will produce, one must also take into consideration the additional costs of such activity. When assessing this situation, one must make sure that the costs are not greater than or equal to the benefits, thus offsetting any benefit from installing the equipment and the pollution reduction.
In order to determine whether or not the cost of installing the capital equipment outweighs the benefits of the equipment, one must fix the level of pollution reduction and determine the optimal level of pollution reduction. According to our text, “the optimal level of the activity—the level that maximizes net benefit—is attained when no further increases in net benefit are possible for any changes in the activity, which occurs at the activity level for which marginal benefit equals marginal cost: MB = MC” (Thomas & Maurice, 2011, p. 97). In other words, the optimal value for pollution reduction is found when the marginal cost equals the marginal revenue.
To find the optimal value, one would set the marginal cost equal to the marginal revenue and solve for P.
MC = 40P MR = 1000-10P
40P = 1000-10P
10P + 40P = 1000...
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