BUS 640 Managerial Economics Week two Exercises

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 expenditures for the three rivals are $100,000 per week?