Project #67506 - Economics Homework 3 questions

 

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

 

  1. Estimate the demand for soft drinks using a multiple regression program available on your computer.

  2. Interpret the coefficients and calculate the price elasticity of soft drink demand.

  3. Omit price from the regression equation and observe the bias introduced into the parameter estimate for income.

  4. 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

 

  1. Estimate the Cobb-Douglas production function Q=αLβ1Kβ2, where Q = output; L = Labor input; K = capital input; and α, β1, and β2 are the parameters to be estimated.

  2. Test whether the coefficients of capital and labor are statistically significant.

  3. Determine the percentage of the variation in output that is “explained” by the regression equation.

  4. Determine the labor and capital estimated parameters, and give an economic interpretation of each value.

  5. 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

 

  1. 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.

 

 

 

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Due By (Pacific Time) 04/27/2015 12:00 pm
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