Question 1
Soft Drink Demand Estimation
Demand can be estimated with experimental data, time-series data, or cross-section data. Sara Lee Corporation generates experimental data in test stores where the effect of an NFL-licensed Carolina Panthers logo on Champion sweatshirt sales can be carefully examined. Demand forecasts usually rely on time-series data. In contrast, cross-section data appear in Table 1. Soft drink consumption in cans per capita per year related to six-pack rice, income per capita, and mean temperature across the 48 contiguous states in the United States.
Questions
Estimate the demand for soft drinks using a multiple regression program available on your computer.
Interpret the coefficients and calculate the price elasticity of soft drink demand.
Omit price from the regression equation and observe the bias introduced into the parameter estimate for income.
Now omit both price and temperature from the regression equation. Should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Why or why not?
TABLE 1 Soft Drink Demand Data
Table 1: Soft Drink Demand Data |
||||
State |
Cans /Capita /Yr |
6-Pack $ Price |
Income $ /Capita |
Mean Temp. Deg. F |
Alabama |
200 |
2.19 |
13 |
66 |
Arizona |
150 |
1.99 |
17 |
62 |
Arkansas |
237 |
1.93 |
11 |
63 |
California |
135 |
2.59 |
25 |
56 |
Colorado |
121 |
2.29 |
19 |
52 |
Connecticut |
118 |
2.49 |
27 |
50 |
Delaware |
217 |
1.99 |
28 |
52 |
Florida |
242 |
2.29 |
18 |
72 |
Georgia |
295 |
1.89 |
14 |
64 |
Idaho |
85 |
2.39 |
16 |
46 |
Illinois |
114 |
2.35 |
24 |
52 |
Indiana |
184 |
2.19 |
20 |
52 |
Iowa |
104 |
2.21 |
16 |
50 |
Kansas |
143 |
2.17 |
17 |
56 |
Kentucky |
230 |
2.05 |
13 |
56 |
Louisiana |
269 |
1.97 |
15 |
69 |
Maine |
111 |
2.19 |
16 |
41 |
Maryland |
217 |
2.11 |
21 |
54 |
Massachusetts |
114 |
2.29 |
22 |
47 |
Michigan |
108 |
2.25 |
21 |
47 |
Minnesota |
108 |
2.31 |
18 |
41 |
Mississippi |
248 |
1.98 |
10 |
65 |
Missouri |
203 |
1.94 |
19 |
57 |
Montana |
77 |
2.31 |
19 |
44 |
Nebraska |
97 |
2.28 |
16 |
49 |
Nevada |
166 |
2.19 |
24 |
48 |
New Hampshire |
177 |
2.27 |
18 |
35 |
New Jersey |
143 |
2.31 |
24 |
54 |
New Mexico |
157 |
2.17 |
15 |
56 |
New York |
111 |
2.43 |
25 |
48 |
North Carolina |
330 |
1.89 |
13 |
59 |
North Dakota |
63 |
2.33 |
14 |
39 |
Ohio |
165 |
2.21 |
22 |
51 |
Oklahoma |
184 |
2.19 |
16 |
82 |
Oregon |
68 |
2.25 |
19 |
51 |
Pennsylvania |
121 |
2.31 |
20 |
50 |
Rhode Island |
138 |
2.23 |
20 |
50 |
South Carolina |
237 |
1.93 |
12 |
65 |
South Dakota |
95 |
2.34 |
13 |
45 |
Tennessee |
236 |
2.19 |
13 |
60 |
Texas |
222 |
2.08 |
17 |
69 |
Utah |
100 |
2.37 |
16 |
50 |
Vermont |
64 |
2.36 |
16 |
44 |
Virginia |
270 |
2.04 |
16 |
58 |
Washington |
77 |
2.19 |
20 |
49 |
West Virginia |
144 |
2.11 |
15 |
55 |
Wisconsin |
97 |
2.38 |
19 |
46 |
Wyoming |
102 |
2.31 |
19 |
46 |
Question 2
THE PRODUCTION FUNCTION FOR WILSON COMPANY
Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data on 15 different plants that produce fertilizer (see the following table).
Questions
Estimate the Cobb-Douglas production function Q=αL^{β}_{1}K^{β}_{2}, where Q = output; L = Labor input; K = capital input; and α, β1, and β2 are the parameters to be estimated.
Test whether the coefficients of capital and labor are statistically significant.
Determine the percentage of the variation in output that is “explained” by the regression equation.
Determine the labor and capital estimated parameters, and give an economic interpretation of each value.
Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.)
PLANT |
OUTPUT (000 TONS) |
CAPITAL ($000) |
LABOR (000 WORKER HOURS) |
1 |
605.3 |
18,891 |
700.2 |
2 |
566.1 |
19,201 |
651.8 |
3 |
647.1 |
20,655 |
822.9 |
4 |
523.7 |
15,082 |
650.3 |
5 |
712.3 |
20,300 |
859 |
6 |
487.5 |
16,079 |
613 |
7 |
761.6 |
24,194 |
851.3 |
8 |
442.5 |
11,504 |
655.4 |
9 |
821.1 |
25,970 |
900.6 |
10 |
397.8 |
10,127 |
550.4 |
11 |
896.7 |
25,622 |
842.2 |
12 |
359.3 |
12,477 |
540.5 |
13 |
979.1 |
24,002 |
949.4 |
14 |
331.7 |
8,042 |
575.7 |
15 |
1064.9 |
23,972 |
925.8 |
Question 3
Reliability Exercise
Given the following reliabilities of components (Bridge will not collapse) in a series with reliabilities indicated. What is the probability someone can get from shore A to B using the bridges
B A
.996 |
.900 |
.860 |
2) Given the following reliabilities of components (Bridges), in parallel, determine the probability that someone can get from shore A to B.
3) Explain which bridges you would choose to attempt to use. (Assume you can put one foot on a bridge to see if it collapses before you attempt to cross.)
Note: Bridges in (1) and (2) above could be 3 components in a machine.
4) Assume you tested several automobile tires and recorded a Chi-sq. test, you decide that miles until failure are normally distributed, with mean failure of 50,000 miles and the standard deviation of failures was 10,000 miles.
a) Determine the reliability of the tires at 40,000 miles.
b) If you know one of these tires has been driven 20,000 miles (on a testing machine), what is its reliability at 60,000 miles?
5) Assume you are building a system (Aircraft, etc.) for a customer but using the best technology available. You cannot produce the reliability required. The customer requires reliability of .99 after the system (aircraft, etc.) has operated for 1000 hours. Your system (Aircraft, etc.) has a reliability of .80 after operating for 1000 hours. What can you do to meet the customers’ required reliability? Explain in detail.
Subject | Business |
Due By (Pacific Time) | 04/27/2015 12:00 pm |
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