1. 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 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 income, and PR is the average price of tennis rackets. The regression results are as follows:
Dependant Variable: Q R-Square F-Ratio P-Value on F
Observations: 20 0.8435 28.75 0.001
Variable Parameter Estimate Standard Error T-Ratio P-Value
Intercept 425120.0 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 a,b,c, and d using the p-values. Are the signs of b, c, and d consistent with the theory of demand?
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 $24,000.
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 the price of tennis balls decreases 15 percent?
e) What will happen, in percentage terms, to the number of cans of tennis balls demanded if average household income increases by 20 percent?
f) 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?
3. Rubax a US manufacturer of athletic shoes, estimates the following linear trend model for shoe sales.
Q1=a+bt+c1D1+c2D2+c3D3 where
Q1=sales of athletic shoes in the t-th quarter;
t=1,2,…,28{1998(I),1998(II),…2004(IV)}
D1=1if t is quarter I (winter);0 otherwise
D2=1 if t is quarter II (spring); 0 otherwise
D3= 1 if t is quarter III (summer); 0 otherwise
The regression analysis produces the following results:
Dependent Variable: QT
R-Square
F-Ratio
P-Value on F
Observations: 28
R-Square = 0.9651
F-Ratio = 159.01
P-Value = 0.0001
Variable Parameter Estimate Standard Error T-ratio P-value
Intercept 184500 10310 17.90 0.0001
T 2100 340 6.18 0.0001
D1 3280 1510 2.17 0.0404
D2 6250 2220 2.82 0.0098
D3 7010 1580 4.44 0.0002
a. Is there sufficient statistical evidence of an upward trend in shoe sales?
b. Do these data indicate a statistically significant seasonal pattern of sales
for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?
c. Using the estimated forecast equation, forecast sales of Rubax shoes for 2014
(III) and 2015 (II).
d. How might you improve this forecast equation?
Chapter 8
1. On the first day of the new year to get her business started, the owner of exquisite portraits inc. paid $200 for business cards, $1000 for a listing in yellow pages, and $250 for annual business license. She also leased a professional portrait camera and studio lighting equipment by signing an agreement to pay a monthly lease of $1000/month for the next 12 months. The lease is ironclad: She must pay for all 12 months and she cannot sublease to anyone else. She rents her office and studio for $1400 per month that must be paid at the beginning of each month. She does not have a lease on the office/studio, so she can vacate the office/studio at the end of any month should she decide to omve to a new location or to go out of business. After she opens the office on the first day of each month , her monthly cost of electricity for lighting the office and running her coffe machine is constant at $45 per month, because she always keeps the lights on in the office and drinks the same amount of coffee no matter how many photos she shhots each month. Additional electricity is required for the portrait studio lights, which varies directly with the number of hours the lights are used each month for photo sessions. Last year, before starting the business, the owner of Exquisite Portraits Inc. earned a salary of $5000 per month working at a bank. Answer the following questions.
A.) What are monthly fixed costs, quasi fixed costs, and variable costs for for the company.
B.)If the owner of the company wants to close her studio and go out of business at the end of August, identify her sunk costs and avoidable costs
C.) At the end of august, what role would the sunk costs play in the ownerrs decision to go out of business?
D.) In making her decision to start her own business, would her decision have been more or less difficult to make if sunk costs were zero at the company? Explain
2. At a management luncheon, two managers were overheard arguing about the following statement “A manager should never hire another worker if the new person causes diminishing returns”. Is this statement correct? If so, why? If not, explain why not.
3. Engineers at a national research laboratory built a prototype automobile that could be driven 180 miles on a single gallon of unleaded gasoline. They estimated that in a mass production the car would cost $60,000 per unit to build. The engineers argued that Congress should force U.S. automakers to build this energy-efficiency car.
a. Is energy efficiency the same thing as economic efficiency? Explain
b. Under what circumstances would the energy-efficient automobile described here be economically efficient?
c. If the goal of society is to get the most benefit from its limited resources, then why not ignore economic efficiency and build the energy-saving automobiles?
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