Question Week Two Exercises 2. Appalachian Coal Mining believes that it can increase labor productivity and, therefore,

Week Two Exercises

2. 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?

4. Twenty-first Century Electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week.

Number of Number of radios

security guards stolen per week

0 50

1 30

2 20

3 14

4 8

5 6

a. If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

b. Ifthecostofastolenradiois$25,what is the most the firm would be willing to pay to hire the first security guard?

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?

1. 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.

a. What sign does the marketing director expect a, b, and c to have?

b. Interpret the coefficients a, b, and c.

c. Does Vanguard’s advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value.

d. Does advertising by its three largest rivals affect sales of Bright Side detergent in a statistically significant way? Explain, using the appropriate p-value.

e. What fraction of the total variation in sales of Bright Side remains unexplained?

What can the marketing director do to increase the explanatory power of the sales equation?

What other explanatory variables might be added to this equation?

f. What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising 

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