CASE 1 - DEMAND ESTIMATION and ELASTICITY: Soft Drinks in the U.S. Demand can be

Question

CASE 1 - DEMAND ESTIMATION and ELASTICITY: Soft Drinks in the U.S.

Demand can be estimated with experimental data, time-series data, or cross-section data. In this case, cross-section data appear in the Excel file. 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 states in the United States.

QUESTIONS

1. Given the data, please construct (a) a multiple linear regression equation and (b) a log-linear (exponential) regression equation for demand by MS Excel. (20%)

2. Given the MS Excel output in question 1, please compare the two regression equations coefficient of determination (R-square), F-test and t-test. Which equation is a good (better) fit? Which equation shows the stronger overall significance to predict the future demand? Which equation will you choose for a better demand estimation? Explain your answer in the language of statistics. (20%)

3. Given your choice of equation in question 2, please interpret each coefficient of independent variable in the soft drink demand estimated equation. (10%)

4. Given your choice of equation in question 2, how many cans/capita/year on soft drink should be for a state in which 6-pack price=$2.45, Income/Capita=$36,500, and Mean Temp= 68F? (20%)

5. Given your choice of equation in question 2 and the numbers in question 4, please calculate the price elasticity of demand and income elasticity. Comment on whether the demand is elastic or inelastic and whether soft drink is necessity, normal good or luxury good. (10%)

6. Now omit the price and temperature from the regression equation then run the regression again. Given the Excel output of only one independent variable, income, should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Please explain your answer in the language of economics. (20%)

TABLE 1. SOFT DRINK DEMAND DATA State Cans/Capita/Yr 6-Pack Price ($) Income/Capita ($1,000) Mean Temp. (F) Alabama 200 2.19 11.7 66 Arizona 150 1.99 15.3 62 Arkansas 237 1.93 9.9 63 California 135 2.59 22.5 56 Colorado 121 2.29 17.1 52 Connecticut 118 2.49 24.3 50 Delaware 217 1.99 25.2 52 Florida 242 2.29 16.2 72 Georgia 295 1.89 12.6 64 Idaho 85 2.39 14.4 46 Illinois 114 2.35 21.6 52 Indiana 184 2.19 18 52 Iowa 104 2.21 14.4 50 Kansas 143 2.17 15.3 56 Kentucky 230 2.05 11.7 56 Louisiana 269 1.97 13.5 69 Maine 111 2.19 14.4 41 Maryland 217 2.11 18.9 54 Massachusetts 114 2.29 19.8 47 Michigan 108 2.25 18.9 47 Minnesota 108 2.31 16.2 41 Mississippi 248 1.98 9 65 Missouri 203 1.94 17.1 57 Montana 77 2.31 17.1 44 Nebraska 97 2.28 14.4 49 Nevada 166 2.19 21.6 48 New Hampshire 177 2.27 16.2 35 New Jersey 143 2.31 21.6 54 New Mexico 157 2.17 13.5 56 New York 111 2.43 22.5 48 North Carolina 330 1.89 11.7 59 North Dakota 63 2.33 12.6 39 Ohio 165 2.21 19.8 51 Oklahoma 184 2.19 14.4 82 Oregon 68 2.25 17.1 51 Pennsylvania 121 2.31 18 50 Rhode Island 138 2.23 18 50 South Carolina 237 1.93 10.8 65 South Dakota 95 2.34 11.7 45 Tennessee 236 2.19 11.7 60 Texas 222 2.08 15.3 69 Utah 100 2.37 14.4 50 Vermont 64 2.36 14.4 44 Virginia 270 2.04 14.4 58 Washington 77 2.19 18 49 West Virginia 144 2.11 13.5 55 Wisconsin 97 2.38 17.1 46 Wyoming 102 2.31 17.1 46

Explanation / Answer

1. The linear demand estimation is as follows for the 48 contiguous states:

Coefficients

Standard Error

t Stat

Intercept

159.17

94.16

1.69

Price

-102.56

33.25

-3.08

Income

1.00

1.77

0.57

Temperature

3.94

0.82

4.83

Note that price and temperature are significant, but income is not significant.

Regression Statistics

Multiple R

0.736

R Square

0.541

Adjusted R Square

0.510

Standard Error

47.312

Observations

48

2. Both temperature and price are statistically significant with expected signs, whereas income is insignificant in its effect on soft drink demand. For the linear model, the price elasticity of demand is (

Coefficients

Standard Error

t Stat

Intercept

159.17

94.16

1.69

Price

-102.56

33.25

-3.08

Income

1.00

1.77

0.57

Temperature

3.94

0.82

4.83

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