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Dr. C. Chen
ECON 3305 Managerial Economics
Homework 2
Covers CH. 4~7. For each question, please show the necessary derivation (if applicable) and highlight
the answer. Limit your answers within 5 pages. No cover sheet is required.
Q1: 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 0.05 level or
better. The regression output from the computer is as follows:
DEPENDENT VARIABLE: S
OBSERVATIONS: 36
VARIABLE
INTERCEPT
A
R
R- SQUARE F- RATIO
P- VALUE ON F
0.2964
4.781
0.0150
PARAMETER
STANDARD
ESTIMATE ERROR
T- RATIO
P- VALUE
175086.0
63821.0
2.74
0.0098
0.8550
0.3250
2.63
0.0128
−0.284
0.164
−1.73
0.0927
a. Does Vanguard’s advertising expenditure have a statistically significant effect on the
sales of Bright Side detergent? Explain, using the appropriate p-value.
b. Does advertising by its three largest rivals affect sales of Bright Side detergent in a
statistically significant way? Explain, using the appropriate p-value.
c. What fraction of the total variation in sales of Bright Side remains unexplained
(undetermined)? What other explanatory variables might be added to this equation?
d. What is the expected level of sales each week when Vanguard spends $20,000 per
week and the combined advertising expenditures for the three rivals are $300,000 per
week?
Q2: Ch 5
Bridget has a limited income and consumes only wine and cheese; her current
consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is
$10 per bottle, and the price of cheese is $4 per pound. The last bottle of wine added 50
units to Bridget’s utility, while the last pound of cheese added 40 units.
a. Is Bridget making the utility- maximizing choice? Why or why not?
b. If not, what should she do instead? Why?
Dr. C. Chen
Q3: Ch 5
Suppose Bill is on a low- carbohydrate diet. He can eat only three foods: Rice Krispies,
cottage cheese, and popcorn. The marginal utilities for each food are tabulated below.
Bill is allowed only 167 grams of carbohydrates daily. Rice Krispies, cottage cheese, and
popcorn provide 25, 6, and 10 grams of carbohydrates per cup, respectively. Referring to
the accompanying table, respond to the following questions:
Units of food
(cups/day)
1
2
3
4
5
6
7
8
Marginal utility
of Rice Krispies
175
150
125
100
75
50
25
25
Marginal utility
of cottage cheese
72
66
60
54
48
36
30
18
Marginal utility
of popcorn
90
80
70
60
50
40
30
20
a. Given that Bill can consume only 167 grams of carbohydrates daily, how many cups of
each food will he consume daily? Show your work.
b. Suppose Bill’s doctor tells him to further reduce his carbohydrate intake to 126 grams
per day. What combination will he consume?
Q4: Ch 5
In terms of the consumer theory set forth in this chapter, can you explain the meaning of
the following statements?
a. “I think you get more for your money from Nike than from Reebok.”
b. “I wanted to buy a Boxster rather than a Malibu, but it just wasn’t worth it.”
c. “I’d like to go to Mexico over spring break, but I just can’t afford it,” said Don. Jill
asked, “Don’t you have enough money in your account?” Don replied, “Yeah, but I
can’t afford to go.”
d. “I’ll have to flip a coin to decide whether to buy chocolate chip or vanilla fudge ice
cream.”
Q5: Ch 6
Assume that the demand for cosmetic or plastic surgery is price inelastic. Are the
following statements true or false? Explain.
a. When the price of plastic surgery increases, the number of operations decreases.
Dr. C. Chen
b. The percentage change in the price of plastic surgery is less than the percentage change
in quantity demanded.
c. Changes in the price of plastic surgery do not affect the number of operations.
d. Quantity demanded is quite responsive to changes in price.
Q6: Ch 6 (10%)
The price elasticity of demand for imported whiskey is estimated to be −0.20 over a wide
interval of prices. The federal government decides to raise the import tariff on foreign
whiskey, causing its price to rise by 20 percent.
a. Will the quantity demanded on imported whiskey rise or fall, and by what percentage
amount?
b. What is the percentage change in the total revenue after the tariff increases?
Q7: CH 7
Wilpen Company, a price- setting firm, produces nearly 80 percent of all tennis balls
purchased in the United States. Wilpen estimates the U. S. demand for its tennis balls by
using the following linear specification:
Q = a + bP + cM + dPR
where Q is the number of cans of tennis balls sold quarterly, P is the wholesale price
Wilpen charges for a can of tennis balls, M is the consumers’ average household in-come,
and PR is the average price of tennis rackets. The regression results are as follows:
DEPENDENT VARIABLE: Q
OBSERVATIONS: 20
VARIABLE
INTERCEPT
P
M
PR
PARAMETER
ESTIMATE
455120.0
−37260.6
1.49
−1456.0
R- SQUARE
0.8435
F- RATIO
28.75
P- VALUE ON F
0.001
STANDARD
ERROR
220300.0
12587
0.3651
460.75
T- RATIO
1.93
−22.96
4.08
−3.16
P- VALUE
0.0716
0.0093
0.0009
0.0060
a. Discuss the statistical significance of the parameter estimates b, c, and d using the pvalues. Given the signs of c and d, please comment on the good category of tennis
ball and its relationship with tennis rackets.
Wilpen plans to charge a wholesale price of $1.65 per can. The average price of a tennis
racket is $110, and consumers’ average household income is $24,600.
b. What is the estimated number of cans of tennis balls demanded?
c. At the values of P, M, and PR given, what are the estimated values of the price (E),
income (EM), and cross- price elasticities (EXR) of demand?
d. What will happen, in percentage terms, to the number of cans of tennis balls demanded
if average household income increases by 20 percent?
e. What will happen, in percentage terms, to the number of cans of tennis balls demanded
if the average price of tennis rackets increases 25 percent?