CASE STUDY OF SOFT DRINK DEMAND ESTIMATIONDemand 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 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 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 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 25 2.698 (0.261 Where the numbers in parentheses are t-scores.19 2.31 2.37 2.93 2.21 2.804) SSE=38.224 Income – 2.9375 56 48 59 39 51 82 51 50 50 65 45 60 69 50 44 58 49 55 46 46 2573 53.2083333 2.72 15 25 13 14 22 16 19 20 20 12 13 13 17 16 16 16 20 15 19 19 861 158.931 Temp (4.19 2. (-5.6041666 7 QUESTION 1 Estimate the demand for soft drinks using a multiple regression program available on your computer.43 1.New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rohde Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Total Mean 157 111 330 63 165 184 68 121 138 237 95 236 222 100 64 270 77 144 97 102 7594 2.17 2.04 2.19 2.2025 17.36 2.33 2.23 1.34 2.08 2.582) .971 Price + 1.31 105.120) r2 =0.89 2. Estimated Demand for soft drink: QD = 514.267 – 242.11 2.38 2. 36719 10.0002 158.537722 -5.9708 1.4257 0.97 6 pack price + 1.2669 -242.0000 0.698024 0.2083 67.980543 .3315 43.22 income per capita + 2.93 mean.677435 38.711458 t-Statistic 4.20640 10. Prob. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.803989 4.931228 0.pack price + income per capita + mean temp +error : 514.D.26533 1.120027 Mean dependent var S.27 – 242.E.36233 10.0000 0.Multiple Regression : Demand of soft drink : constant + 6 .26108 64412. of regression Sum squared resid Log likelihood F-statistic Coefficient 514.522613 0.90231 Std.582162 0. Durbin-Watson stat QUESTION 2 Interpret the coefficients and calculate the price elasticity of soft drink demand. Error 113.9536 33.06 -240. 0.224164 2.52628 1.Temp Dependent Variable: CAN Method: Least Squares Sample: 1 48 Included observations: 48 Variable C PRICE INCOME TEMP R-squared Adjusted R-squared S. These are market-level price elasticities. comparable price sensitivity.2083 ∂Q/∂P = -242.97) / ( 2. 1) The coefficient for demand for soft drink and price of soft drink is inverse relationship. 2) The quantity demand for soft drink per capita will change in opposite direction as the price of soft drink change.97 Price elasticity ED = (∂Q/∂P) × (Mean P/Mean Q) ED = (-242.2025 Mean Q = 7594 / 48 = 158.2083 ) ED = ( .Both temperature and price are statistically significant with expected signs while income is insignificant in its effect on soft drink demand.72 / 48 = 2.2025 / 158. An elastic demand at the market level does imply elastic firm-level demand at comparable prices. for the log-linear model −3. and the smaller quantities facing each firm. as expected. This point elasticity at the mean price and quantity across the states is in the elastic range. Mean P =105. . so no firm behaviour is directly implied by this estimate. the consumption on soft drink is price elastic in nature. This means that for a 1% increase in price will result in more than 1% decrease in quantity demanded for soft drinks.12.38 ) elastic Interpretation on Price Elasticity: Based on the calculated price elasticity.3. QUESTION 3 Omit price from the regression equation and observe the bias introduced into the parameter estimate for income. So that.97 when price of soft drink change in the opposite direction or inverse direction.93 when mean temperature increase. and demand for soft drink also will increase by 2. 4) The coefficient for demand for soft drink and income and demand for soft drink and 5) mean temperature is positively relationship. demand for soft drink will increase by 1. .3) Demand for soft drink will reduce by 242. The quantity demand of soft drink will change in same direction as the income and mean temperature change.22 when income per capita increase. 06 .16 + 1.89 . Should a marketing plan for soft drinks be designed that relocates most canned drink machines into low –income neighborhoods? Why or why not? . the R-Squared value drops from 0.22LogY + 1.89/160.11LogT Income elasticity.22*(17.22 Interpretation on Income Elasticity: Based on the calculated income elasticity.49 (5.22Y + 2. log QD= − 0.242. QUESTION 4 Now omit both price and temperature from the regression equation.6).14 LogQ = 1.76) = 0.66 to 0. Thus the strength of correlation falls under moderate range (0. a positive income elasticity indicates that soft drink is a normal goods. Ey = δQ/δY x Y/Q = 1.152 log INCOME R2 = 0.92T Income elasticity. Ey = 0.88P + 1. The variables have a low association with the dependent variable as only 47% in quantity demanded are explained by the independent variables.137 When the independent variable of Price is removed from the equation.Income elasticity Q = 514.3.4 to 0.96) (− 0.73) SSE = 0.72 log TEMP − 0.19LogP + 0.47. E.47 − 0.20186 11.37 INCOME R2 = 0.3 -266.2 For the log-linear model.0202 158. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.552 INCOME R2 = 0.11) SSE = 64. .793010 0.09082 2.020162 Std.11 (− 2.18 No. Error 41.2083 67.6 − 5.092542 64. a marketing plan should not be designed specifically to introduce canned soft drink machines into low-income neighborhoods. And students should not offer the negative and significant income parameter estimate above as their reason.231815 t-Statistic 6.372Y QD = 254.23132 2.D. This illustrates the critical importance of using analytical reasoning and demand theory to correctly specify a regression model.0000 0.371683 R-squared Adjusted R-squared S.111849 0. Durbin-Watson stat Prob.8446 5.406867 Mean dependent var S.Dependent Variable: CAN Method: Least Squares Sample: 1 48 Included observations: 48 Variable C INC Coefficient 254.13) SSE = 0. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. 0. one obtains QD = 4.5629 -5.27983 11.313418 Omitting both price and temperature yields a linear model as follows: QD = 254. The above regression does NOT call for relocating canned soft drink machines away from low-income neighborhoods. The regression coefficient on income has been biased downward by the omission of price and temperature enough to make an insignificant factor appear negative and significant in its effect on demand.17440 189444.09 (− 2.195129 -2.563 – 5.36719 11. Thus. free one" (BOGO) promotions.e. it will not affect the quantity demanded that much.11 150 100 50 0 5 10 15 20 25 30 The graph above shows the weak relationship between Income and Quantity Demanded. Instead of wasting resources in trying to influence a variable that is weakly related to the dependant variable. In addition. as some variables i. the marketing plan should not be designed based on the income per capita factor as it does not strongly correlated with the demand of soft drink cans. it is unwise to rely solely on income factor to design on marketing plan as there exists a bias. price and temperature were removed from the equation.23x + 254.5. Since price is strongly related to Quantity Demanded. We strongly believe that the company should not design their marketing plan to relocate most canned drink machines into low-income neighbourhood. the company should focus on other variables such as pricing as the critical component of their marketing plan. the company can stimulate the demand for their soft drink by giving discounts and "buy one.INCOME 350 300 250 Q 200 Linear (Q) f(x) = .32 R² = 0. Whether they market the product at low income groups or otherwise. The ‘best’ demand specification . 1 2.4 2.5 2.3 2.2.23x + 254. INCOME 350 300 250 Q 200 Linear (Q) f(x) = .5.5683 which is within the 0.11 150 100 50 0 5 10 15 20 25 30 For Income.85x + 845.7 For Price.6 range. .67 R² = 0.9 2 2.57 200 Q Linear (Q) 150 100 50 0 1. the R-squared is 0.4 to 0.1094 which is within the range of 0 to 0.6 2.311.8 1.32 R² = 0. the R-squared is 0. This indicates a very weak correlation.2 2.PRICE 350 300 250 f(x) = . Hence it has moderately strong correlation. 4 to 0.TEMPERATURE 350 300 f(x) = 4. the R-squared is 0.4555 which is within the range of 0.104.91x .6. . Conclusion: The best demand specification is to remove income per capita from the regression equation as the variable has a low correlation to the equation. Hence it has moderate strong correlation.46 250 Q 200 Linear (Q) 150 100 50 0 30 40 50 60 70 80 90 For Temperature.03 R² = 0.
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