Managerial Economics

      Managerial Economics Homework 2 The homework covers Ch 4~7. It has to be your in" rel="nofollow">individual work. Copyin" rel="nofollow">ing answer from others will violate ACADEMIC HONESTY policy to cause a failin" rel="nofollow">ing grade. For each question, please show the necessary derivation (if applicable) and highlight the answer. Limit your answers within" rel="nofollow">in 5 pages. No cover sheet is required. Q1: Ch 4 (20%) The director of marketin" rel="nofollow">ing at Vanguard Corporation believes that sales of the company’s Bright Side laundry detergent (S) are related to Vanguard’s own advertisin" rel="nofollow">ing expenditure (A), as well as the combin" rel="nofollow">ined advertisin" rel="nofollow">ing expenditures of its three biggest rival detergents (R). The marketin" rel="nofollow">ing director collects 36 weekly observations on S, A, and R to estimate the followin" rel="nofollow">ing multiple regression equation: S = a + bA + cR where S, A, and R are measured in" rel="nofollow">in dollars per week. Vanguard’s marketin" rel="nofollow">ing director is comfortable usin" rel="nofollow">ing 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 0.4550 0.3250 2.63 0.0128 R −0.284 0.164 −1.73 0.0927 a. Does Vanguard’s advertisin" rel="nofollow">ing expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain" rel="nofollow">in, usin" rel="nofollow">ing the appropriate p-value. b. Does advertisin" rel="nofollow">ing by its three largest rivals affect sales of Bright Side detergent in" rel="nofollow">in a statistically significant way? Explain" rel="nofollow">in, usin" rel="nofollow">ing the appropriate p-value. c. What fraction of the total variation in" rel="nofollow">in sales of Bright Side remain" rel="nofollow">ins unexplain" rel="nofollow">ined (undetermin" rel="nofollow">ined)? 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 combin" rel="nofollow">ined advertisin" rel="nofollow">ing expenditures for the three rivals are $300,000 per week? Q2: Ch 5 (10%) Bridget has a limited in" rel="nofollow">income and consumes only win" rel="nofollow">ine and cheese; her current consumption choice is four bottles of win" rel="nofollow">ine and 10 pounds of cheese. The price of win" rel="nofollow">ine is $10 per bottle, and the price of cheese is $4 per pound. The last bottle of win" rel="nofollow">ine added 50 units to Bridget’s utility, while the last pound of cheese added 40 units. Dr. C. Chen a. Is Bridget makin" rel="nofollow">ing the utility- maximizin" rel="nofollow">ing choice? Why or why not? b. If not, what should she do in" rel="nofollow">instead? Why? Q3: Ch 5 (10%) Assume that Andy consumes two goods X and Y. His total utility (assumed measurable) of each good is in" rel="nofollow">independent of the rate of consumption of other goods. The prices of X and Y are, respectively, $5 and $10. Units of the Good Total Utility of X Total Utility of Y 1 2 3 4 5 6 7 8 50 95 135 170 200 225 245 260 400 750 950 1100 1220 1320 1400 1450 a. If Andy is given $65 to spend, how many X and Y will he consume daily? Show your work. b. If his budget in" rel="nofollow">increases to $110, what combin" rel="nofollow">ination will the person consume? Show your work. Q4: Ch 5 (10%) In terms of the consumer theory set forth in" rel="nofollow">in this chapter, can you explain" rel="nofollow">in the meanin" rel="nofollow">ing of the followin" rel="nofollow">ing statements? a. “I wanted to buy a Boxster rather than a Malibu, but it just wasn’t worth it.” b. “I’d like to go to Mexico over sprin" rel="nofollow">ing break, but I just can’t afford it,” said Don. Jill asked, “Don’t you have enough money in" rel="nofollow">in your account?” Don replied, “Yeah, but I can’t afford to go.” Q5: Ch 6 (20%) Assume that the demand for plastic (cosmetic) surgery is price in" rel="nofollow">inelastic. Are the followin" rel="nofollow">ing statements true or false? Explain" rel="nofollow">in. a. When the price of plastic surgery in" rel="nofollow">increases, the number of operations decreases. b. The percentage change in" rel="nofollow">in the price of plastic surgery is less than the percentage change in" rel="nofollow">in quantity demanded. c. Changes in" rel="nofollow">in the price of plastic surgery will affect the number of operations slightly. d. Quantity demanded is quite responsive to changes in" rel="nofollow">in price. Q6: Ch 6 (10%) The price elasticity of demand for imported whiskey is estimated to be −0.20 over a wide in" rel="nofollow">interval of prices. The federal government decides to raise the import tariff on foreign whiskey, causin" rel="nofollow">ing its price to rise by 30 percent. Dr. C. Chen a. Will the quantity demanded on imported whiskey rise or fall, and by what percentage amount? b. What is the percentage change in" rel="nofollow">in the total revenue after the tariff in" rel="nofollow">increases? Q7: CH 7 (20%) Wilpen Company, a price- settin" rel="nofollow">ing firm, produces nearly 80 percent of all tennis balls purchased in" rel="nofollow">in the United States. Wilpen estimates the U. S. demand for its tennis balls by usin" rel="nofollow">ing the followin" rel="nofollow">ing lin" rel="nofollow">inear 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" rel="nofollow">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 355120.0 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 usin" rel="nofollow">ing 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 in" rel="nofollow">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), in" rel="nofollow">income (EM), and cross- price elasticities (EXR) of demand? Round to hundredth. d. What will happen, in" rel="nofollow">in percentage terms, to the number of cans of tennis balls demanded if the average price of tennis rackets in" rel="nofollow">increases 25 percent?