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 R- SQUARE F- RATIO P- VALUE ON F OBSERVATIONS: 36 0.2964 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

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?

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 Marginal utility Marginal utility Marginal utility

(cups/day) of Rice Krispies of cottage cheese of popcorn

1 175 72 90

2 150 66 80

3 125 60 70

4 100 54 60

5 75 48 50

6 50 36 40

7 25 30 30

8 25 18 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.

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 R- SQUARE F- RATIO P- VALUE ON F OBSERVATIONS: 20 0.8435 28.75 0.001

PARAMETER STANDARD

VARIABLE ESTIMATE ERROR T- RATIO P- VALUE

INTERCEPT 455120.0 220300.0 1.93 0.0716

P −37260.6 12587 −22.96 0.0093

M 1.49 0.3651 4.08 0.0009

PR −1456.0 460.75 −3.16 0.0060

a. Discuss the statistical significance of the parameter estimates b, c, and d using the p-values. 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?