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ABC company believes that it can increase labor productivity and therefore net revenue by reducing waste in its factories

ABC company believes that it can increase labor productivity
and, therefore, net revenue by reducing waste in its factories. 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 waste at the
company. It also feels that for every
unit of pollution reduction the marginal increase in revenue (MR) IS
MR
= 1,000 – 10P

How much waste reduction should ABC company undertake?

Question #2

XYZ Manufacturing Inc. has discovered a theft problem at its
warehouse and has decided to here security guards. The manufacturing company wants to hire the
optimal number of security guards. The
following table shows how the number of security guards affects the number of
televisions stolen per week
Number
of Security Guards Number
of TVs 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 TV is $25, how many security guards should the firm hire?

b) If the cost of a stolen TV is $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 TV is $50, how many security guards should the firm hire?

Basic Estimation
Techniques

Question # 3 (see next page)
The director of Robinson Inc. believes that sales of the
company’s toothpaste (S) are related to Robinson’s own advertising expenditure
(A), as well as the combined advertising
expenditures of its three biggest rival toothpaste (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. Robinsons Inc.’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.

The regression output from the computer is as follows:

DEPENDENT VARIABLE : S R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS : 36 0.2247 4.781 0.0150

PARAMETER STANDARD
VARIABLE ESTIMATE ERROR T-RATIO P
– VALUE
INTERCEPT 175086.0 63821.0 2.74 0.0098
A 0.8550 0.3250 2.63 0.0128
R -0.284 0.164 -1.73 0.0927

c) Does Robinson Inc’s advertising expenditure have a statistically significant
effect on the sales of toothpaste?
Explain, using the appropriate p-value.

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

e) What fraction of the total variation in sales of
toothpaste 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
Robinsons Inc spends $40 000 per week and the combined advertising expenditure
for the three rivals are $100 000 per week?

Mar 17 2020 View more View Less

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