Given the log-linear equation, please provide the price elasticity of demand and

Question

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

Below are regression results:

From the regression results we can see that:

1. Price elasticity of demand is - 3.1955. That is the softdrinks are highly elastic good i.e. if price of soft drinks fall by 1%, then quantity demanded increases by 3.19%.

2. The 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) implies that it is a normal good but its close to zero value means that the good itself is a necessary good.

Regression Statistics Multiple R 0.8194 R Square 0.6714 Adjusted R Square 0.6490 Standard Error 0.2563 Observations 48

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