# Interpret the sign of coefficients a, b, and c.

The homework covers Ch 3 ∼ 6. It has to be your individual work. Copying answer from others will violate ACADEMIC HONESTY policy to cause a failing grade. For each ques- tion, please show the necessary derivation (if applicable) and highlight the answer. Limit your answers within 5 pages. No cover sheet is required.

Q1 (20%)
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 0.10 level or better. The regression output from the computer is as follows:

a. Interpret the sign of coefficients a, b, and c.
b. Does Vanguard’s advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value.
c. Does advertising by its three largest rivals affect sales of Bright Side detergent in a

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statistically significant way? Explain, using the appropriate p-value.
d. 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?
e. What is the expected level of sales each week when Vanguard spends \$30,000 per week and the combined advertising expenditures for the three rivals are \$200,000 per week?

Q2 (10%) Lorna consumes cans of anchovies, A, and boxes of biscuits, B. Each of her indif- ference curves reflects strictly diminishing marginal rates of substitution. If A = 2 and B = 2, her marginal rates of substitution between cans of anchovies and boxes of biscuits equals –1(= MUA/MUB). Will she prefer a bundle with three cans of anchovies and a box of biscuits to a bundle with two of each? Why?

Q3 (10%) a. Give as many reasons as you can why we believe that indifference curves are convex to the origin.

b. IfthebudgetlineisY =500=pBB+pZZ=5B+10Z,whatisthemarginalrate of transformation, MRT, between B (burritos) and Z (pizza)?

Q4 (10%) Using the information given in Table 5.2 (page 136), draw the isoquant correspond- ing to an output level of 20. Starting from L = 4 and K = 1, how much extra capital is needed to keep output constant if the labor is reduced by one unit to L = 3? How much extra capital is needed to keep output constant if the labor is reduced by one unit to L = 2?

Q5 (10%)

Michelle’s business produces ceramic cups using labor, clay, and a kiln. She produces cups using a fixed proportion of labor and clay, but regardless of how many cups she produces, she uses only one kiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process illustrate decreasing returns to scale or

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a diminishing marginal product of labor? What is the likely explanation for why output does not increase proportionately with the number of workers?

Q6 (10%)

a. When buying a piece of equipment, it is always best for the firm to pay cash instead of borrowing the funds since this renders the equipment less costly.
b. You have two career options. You can work for someone else for \$50,000 a year, or, you can run your own business, with an annual revenue of \$100,000, and explicit costs of \$40,000 annually. Explain which career option a profit-maximizer would select and why?

Q7 (10%) In the twentieth century, department stores and supermarkets largely replaced smaller specialty stores, as consumers found it more efficient to go to one store rather than many. Consumers incur a transaction or search cost to shop, primarily the oppor- tunity cost of their time. This transaction cost consists of a fixed cost traveling to and from the store and a variable cost that rises with the number of different types of items the consumer tries to find on the shelves. By going to a supermarket that carries meat, fruits and vegetables, and other items, consumers can avoid some of the fixed transaction costs of traveling to a separate butcher shop, produce mart, and so forth. Use math to explain why a shopper’s average costs are lower when buying at a single supermarket than from many stores. (Hint: define the goods as the items purchased and brought home.)

Q8 (20%)
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:

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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?

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