Marginal Analysis for Optimal Decisions
Question # 1
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
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?