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?
Set MC = MR and solve for P 40P = 1000-10P 40P + 10P = 1000 50P = 1000 P = 1000/50 P = 20 units of pollution reduction MR = 1000 – 10(20) MR = 1000 -200 MR = 800 MC = 40(20) MC = 800 By installing additional capital equipment Appalachian Coal Mining can reduce the pollution by 20 units of pollution with the Marginal cost of 800. Therefore, the increase in capital will decrease the amount of pollution and will benefit both the company and the world with the reduction in pollution. Any company that invests capital to clean the environment is making the right choice no matter how much or how little it fixes, anything reduction s better than nothing.
Therefore Twenty-first Century Electronics should hire two guards b. If the cost of a stolen radio is $25,what is the most the firm would be willing to pay to hire the first security guard? Guard one = (50 – 30) * 25 Guard one = 20 * 25 Guard One = 500 The first security guard would be paid the maximum amount 500 c. If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire? MC = 200 Marginal Benefit (4) = (14-8)*50 MB = 6 * 50 MB = 300 TB = (50-8) * 50 – (4*200) = 1300
Therefore they should hire four guards @ $ 50 cost of stolen radio CH 4. . The director of marketing at Vanguard Corporation believes that sales of the company’s Bright Side laundry detergent (S) are related to Vanguard’s own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + cR where S, A, and R are measured in dollars per week. Vanguard’s marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better.