Homework SourseGiven the loglinear equation please provide the price elasti
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 |
Solution
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 |
