Demand can be estimated with experimental data, time-series data, or cross-secti

Question

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 the demand estimation for soft drink consumption in the United States by

(1) a multiple-linear regression equation and (2) a log-linear (exponential) regression equation

2. Given the log-linear equation, please provide the price elasticity of demand and income elasticity. Comment on whether the demand is elastic or inelastic and whether soft drink is a necessity, normal good or luxury good.

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. Below is the multiple linear regression:

2.

Below are regression results for  log-linear (exponential) regression equation

From the Log-linear regression results we can see that:

a. The coefficient of LN(Price) is -3.1955 which means that price elasticity of demand is - 3.1955. That is the softdrink consumption is highly elastic good i.e. if price of a soft drink declines by 1%, then its quantity demanded increases by 3.19%.

b. The coefficient of LN(Price) is 0.2205 which means that income elasticity of demand is 0.2205. That is, if the income increases by 1%, then the quantity demand increases by 0.2205%. The positive coefficient of ln(income) in the above regression means that it is a normal good.

Regression Statistics Multiple R 0.835478305 R Square 0.698023997 Adjusted R Square 0.677434724 Standard Error 38.26108281 Observations 48

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