ECO 740

CASE EXERCISE

SOFT DRINK DEMAND

ESTIMATION

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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 is appear in Table 1.

Soft drink consumption in cans per capita per year is related to six-pack price, income per capita, and mean temperature across the 48 contiguous in the United States.

Table 1

Alabama

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montan

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Cans/Capita 6-Pack $

Income

/Yr

Price

$/Capita

200

2.19

150

1.99

237

1.93

135

2.59

121

2.29

118

2.49

217

1.99

242

2.29

295

1.89

85

2.39

114

2.35

184

2.19

104

2.21

143

2.17

230

2.05

269

1.97

111

2.19

217

2.11

114

2.29

108

2.25

108

2.31

248

1.98

203

1.94

77

2.31

97

2.28

166

2.19

177

2.27

143

2.31

157

2.17

111

2.43

330

1.89

63

2.33

165

2.21

184

2.19

68

2.25

Mean

Temp. °F

13

17

11

25

19

27

28

18

14

16

24

20

16

17

13

15

16

21

22

21

18

10

19

19

16

24

18

24

15

25

13

14

22

16

19

66

62

63

56

52

50

52

72

64

46

52

52

50

56

56

69

41

54

47

47

41

65

57

44

49

48

35

54

56

48

59

39

51

82

51

Pennsylvania

Rohde Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Total

Mean

121

138

237

95

236

222

100

64

270

77

144

97

102

7594

158.208333

3

2.31

2.23

1.93

2.34

2.19

2.08

2.37

2.36

2.04

2.19

2.11

2.38

2.31

105.72

20

20

12

13

13

17

16

16

16

20

15

19

19

861

2.2025

50

50

65

45

60

69

50

44

58

49

55

46

46

2573

53.604166

67

17.9375

Question 1

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

Answer

QD = 514.267 – 242.971 Price + 1.224 Income – 2.931 Temp (4.120)

(0.804)

r2 =0.698

(-5.582)

SSE=38.261

SPSS result:

Coefficientsa

Unstandardized

Standardized

Coefficients

Coefficients

95% Confidence Interval for B

Std.

Model

1

B

(Constant)

Price

Error

Beta

t

514.267 113.332

Sig.

Lower Bound

Upper Bound

4.538

.000

285.862

742.672

-242.971

43.526

-.588

-5.582

.000

-330.692

-155.249

Income

1.224

1.523

.076

.804

.426

-1.844

4.293

Temp

2.931

.711

.402

4.120

.000

1.497

4.365

a. Dependent Variable: Can

EViews7 result:

Dependent Variable: CAN

Method: Least Squares

Date: 04/07/12 Time: 22:00

Sample: 1 48

Included observations: 48

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

PRICE

INCOME

TEMP

514.2669

-242.9708

1.224164

2.931228

113.3315

43.52628

1.522613

0.711458

4.537722

-5.582162

0.803989

4.120027

0.0000

0.0000

0.4257

0.0002

R-squared

Adjusted R-squared

S.E. of regression

Sum squared resid

Log likelihood

F-statistic

Prob(F-statistic)

0.698024

0.677435

38.26108

64412.06

-240.9536

33.90231

Mean dependent var

S.D. dependent var

Akaike info criterion

Schwarz criterion

Hannan-Quinn criter.

Durbin-Watson stat

158.2083

67.36719

10.20640

10.36233

10.26533

1.980543

0.000000

Question 2

Interpret the coefficients and calculate the price elasticity of soft drink demand. Mean P =105.72 / 48

= 2.2025

Mean Q = 7594 / 48

= 158.2083

dQ/dP = -242.97

Price elasticity ED = ( dQ/dP ) / (Mean P /Mean Q )

ED = (-242.97) / ( 2.2025 / 158.2083 )

ED = ( – 3.38 )

The price elasticity at the mean price and quantity across the states is in the elastic range, as expected. These are market-level price elasticity, so no firm behaviour is directly implied by this estimate. The elastic demand at the market level does imply elastic firm-level demand at comparable prices, comparable price sensitivity, and the smaller quantities facing each

firm.

Question 3

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

QD = -56.614 -2.054Y + 4.695F

Coefficientsa

Unstandardized

Coefficients

Model

1

Standardized

Coefficients

B

(Constan

t)

Income

Temp

Std. Error

–

Beta

t

63.117

56.614

-2.054

-.897 .375

1.815

4.695

Sig.

-.128

.824

1.132

.264

.644 5.699 .000

a. Dependent Variable: Can

Question 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 neighbourhoods? Why or why not?

ANSWER

QD = 254.563 – 5.372Y

Coefficientsa

Unstandardized Coefficients

Model

1

B

(Constant)

Std. Error

254.563

2.232

Beta

t

41.091

-5.372

Standardized Coefficients

Income

a. Dependent Variable: Can

Sig.

6.195

-.334

.000

-2.407

.020

No, a marketing plan should not be designed specifically to introduce canned soft drink machines to low-income neighbourhoods.