Supermarket scanner data of prices and quantities for various types of beef and
ID: 2494521 • Letter: S
Question
Supermarket scanner data of prices and quantities for various types of beef and poultry are available in the accompanying Excel file. The monthly data from the Economic Research Center of the US Department of Agriculture in cooperation with the Livestock Marketing Information Center (LMIC) covers January 2001 to July 2005. The file includes quantity and price data for three cuts of beef (Chuck Roast, Porter House and Ribeye) plus data for chicken prices and disposable income. a. Using regression analysis, estimate the demand functions for Chuck Roast, Porter House, and Ribeye. Indicate significance of each coefficient and of each model citing the relevant test statistics. b. Estimate the own price elasticity, cross elasticity, and income elasticity for each cut of beef.
Year Month ChuckQ CkuckP PHQ PHP RibEQ RibEP ChickP DispInc 2001 1 120 $2.28 53 $6.04 74 $7.02 $1.61 8664.6 ChuckQ Qty of Ground Chuck 2001 2 76 $2.61 81 $5.37 79 $7.16 $1.68 8689.8 CkuckP Price of Ground Chuck 2001 3 102 $2.12 60 $5.74 71 $7.33 $1.57 8711.7 PHQ Qty of Porterhouse 2001 4 106 $2.41 65 $6.93 112 $7.38 $1.73 8710.7 PHP Price of Porterhouse 2001 5 87 $2.39 92 $5.95 113 $6.47 $1.74 8716.5 RibEQ Qty of Ribeye 2001 6 94 $2.11 157 $5.24 89 $7.14 $1.63 8732.4 RibEP Price of Ribeye 2001 7 97 $2.66 149 $5.39 146 $7.02 $1.69 8733.2 ChickP Chicken Prices 2001 8 79 $2.50 133 $5.54 120 $6.28 $1.71 8727.7 DispInc Consumer Disposable Income 2001 9 138 $2.39 97 $6.28 120 $7.57 $1.79 8738.5 2001 10 129 $2.30 113 $5.43 106 $6.72 $1.65 8743.1 2001 11 77 $2.69 78 $5.46 76 $7.73 $1.75 8751.7 2001 12 94 $2.44 123 $4.81 93 $7.71 $1.79 8769.6 2002 1 135 $2.23 87 $5.49 83 $6.74 $1.65 8789.9 2002 2 120 $2.45 73 $5.54 136 $6.87 $1.72 8814.2 2002 3 131 $2.24 88 $5.76 119 $7.11 $1.68 8840.2 2002 4 104 $2.41 108 $5.28 114 $7.00 $1.67 8879 2002 5 144 $2.24 82 $6.05 151 $6.70 $1.63 8889.3 2002 6 139 $2.08 148 $5.34 248 $7.08 $1.66 8907.6 2002 7 98 $2.42 155 $5.10 201 $6.54 $1.73 8894.8 2002 8 112 $2.47 45 $6.88 168 $6.46 $1.73 8892.7 2002 9 184 $2.34 97 $5.67 165 $6.72 $1.76 8898.8 2002 10 98 $2.33 82 $5.65 105 $6.89 $1.68 8910.3 2002 11 109 $2.35 65 $6.38 88 $7.69 $1.62 8920.8 2002 12 135 $2.35 53 $6.22 108 $7.44 $1.83 8945.3 2003 1 132 $2.22 63 $5.86 182 $6.65 $1.70 8976.3 2003 2 142 $2.38 59 $6.72 150 $6.72 $1.67 9011.5 2003 3 128 $2.45 55 $7.12 144 $7.51 $1.68 9053.2 2003 4 94 $2.53 49 $6.54 121 $7.80 $1.84 9067.9 2003 5 93 $2.34 92 $6.70 161 $7.40 $1.81 9124.5 2003 6 126 $2.48 88 $6.91 280 $6.64 $1.74 9163.4 2003 7 83 $2.40 65 $7.33 170 $6.68 $1.71 9188.2 2003 8 109 $2.54 92 $6.70 165 $7.73 $1.82 9214.2 2003 9 112 $2.46 41 $7.75 106 $8.20 $1.80 9243.7 2003 10 83 $2.86 42 $7.22 104 $8.32 $1.80 9271.7 2003 11 90 $2.90 56 $7.57 91 $9.74 $1.79 9339.4 2003 12 77 $3.03 30 $8.40 63 $9.87 $1.85 9374.8 2004 1 86 $2.83 41 $6.65 67 $9.92 $1.61 9435.9 2004 2 165 $2.55 51 $6.94 111 $8.48 $1.61 9487.9 2004 3 109 $2.25 25 $7.40 118 $7.51 $1.64 9530.7 2004 4 89 $2.37 34 $7.45 107 $8.27 $1.66 9571.8 2004 5 125 $2.27 54 $7.51 125 $8.27 $1.66 9628.3 2004 6 108 $2.28 33 $8.60 117 $8.86 $1.66 9642.8 2004 7 88 $2.52 34 $8.54 119 $8.55 $1.70 9689 2004 8 101 $2.64 41 $8.36 143 $8.87 $1.85 9739.8 2004 9 85 $2.64 51 $6.98 100 $7.48 $1.72 9759 2004 10 113 $2.61 45 $6.88 82 $8.20 $1.63 9858.4 2004 11 85 $2.69 27 $7.19 73 $8.59 $1.68 9924.9 2004 12 90 $2.67 31 $7.08 70 $8.10 $1.64 10291 2005 1 113 $2.62 38 $6.89 89 $8.34 $1.59 10025.2 2005 2 98 $2.70 39 $7.05 84 $7.90 $1.55 10072.9 2005 3 86 $2.82 30 $7.80 105 $7.88 $1.61 10122 2005 4 93 $2.66 38 $7.88 111 $8.92 $1.64 10145.1 2005 5 127 $2.51 55 $7.68 159 $7.60 $1.60 10180.6 2005 6 83 $2.47 40 $8.17 141 $7.99 $1.65 10231.5 2005 7 94 $2.44 39 $8.06 156 $7.18 $1.62 10268.8Explanation / Answer
(a)
(1) Ground Chuck: Regression summary output
(2) Regression (demand) equation: Ground Chuck
Q = 252 - 55.91 x ChuckP + 0.17 x ChickP - 0.0007 x DispInc
(3) Porter House: Regression summary output
(4) Regression (demand) equation: Porter House
Q = 173.69 - 26.23 x PHP + 58.75 x ChickP - 0.003 x DispInc
(5) Ribeye: Regression summary output
(6) Regression (demand) equation: Ribeye
Q = - 273.14 - 35 x RibEP + 205.15 x ChickP + 0.03 x DispInc
(b) We'll use the data for year 2005, month 7.
(1) Ground Chuck
Own price elasticity = (dChuckQ / dChuckP) x (ChuckP / ChuckQ)
= - 55.91 x (2.44 / 94) = - 1.45
Income elasticity = (dChuckQ / dDispInc) x (DispInc / ChuckQ)
= - 0.0007 x (10,268.8 / 94) = - 0.08
Cross price elasticity (with Chicken) = (dChuckQ / dChickP) x (ChickP / ChuckQ)
= - 0.17 x (1.62 / 94) = - 0.003
(2) Porter House
Own price elasticity = (dPHQ / dPHP) x (PHP / PHQ)
= - 26.23 x (8.06 / 39) = - 5.42
Income elasticity = (dPHQ / dDispInc) x (DispInc / PHQ)
= - 0.003 x (10,268.8 / 39) = - 0.79
Cross price elasticity (with Chicken) = (dPHQ / dChickP) x (ChickP / PHQ)
= 58.75 x (1.62 / 39) = 2.44
(3) Ribeye
Own price elasticity = (dRibEQ / dRibEP) x (RibEP / RibEQ)
= - 35 x (7.18 / 156) = - 1.61
Income elasticity = (dRibEQ / dDispInc) x (DispInc / RibQ)
= 0.03 x (10,268.8 / 156) = 1.97
Cross price elasticity (with Chicken) = (dRibEQ / dChickP) x (ChickP / RibEQ)
= 205.15 x (1.62 / 156) = 2.13
SUMMARY OUTPUT Regression Statistics Multiple R 0.497239885 R Square 0.247247503 Adjusted R Square 0.202967944 Standard Error 20.8225856 Observations 55 ANOVA df SS MS F Significance F Regression 3 7263.052733 2421.018 5.583784 0.00216943 Residual 51 22112.58363 433.5801 Total 54 29375.63636 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 252.417837 100.2506389 2.517868 0.014989 51.1562856 453.679388 CkuckP -55.91280225 17.14123351 -3.26189 0.001977 -90.325264 -21.500341 ChickP 0.172419479 43.11990783 0.003999 0.996825 -86.394406 86.7392448 DispInc -0.000753123 0.006999667 -0.10759 0.91474 -0.0148055 0.0132993Related Questions
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