In: Economics
Year | Q (millions of lbs) | P Beef Per Lb ($) | P Pork Per lb ($) | Disp Inc (millions $) | Pop (millions) |
1975 | 19295 | 1.9 | 1.864 | 517250 | 182.76 |
1976 | 17535 | 2.312 | 1.944 | 566500 | 185.88 |
1977 | 19520 | 2.208 | 1.972 | 708250 | 189.12 |
1978 | 25622.5 | 1.68 | 2.072 | 631500 | 192.12 |
1979 | 26530 | 1.68 | 2.128 | 643500 | 195.6 |
1980 | 27745 | 1.64 | 1.776 | 688250 | 199.08 |
1981 | 29805 | 1.568 | 1.732 | 733000 | 202.68 |
1982 | 28950 | 1.648 | 1.916 | 771250 | 206.28 |
1983 | 26932.5 | 1.868 | 2.092 | 796250 | 209.88 |
1984 | 27592.5 | 1.892 | 1.792 | 843250 | 213.36 |
1985 | 30162.5 | 1.804 | 1.884 | 875000 | 216.84 |
1986 | 31530 | 1.708 | 1.916 | 911000 | 220.44 |
1987 | 31397.5 | 1.856 | 1.9 | 963250 | 223.8 |
1988 | 34122.5 | 1.668 | 1.772 | 1011500 | 227.04 |
1989 | 39107.5 | 1.592 | 1.772 | 1095250 | 230.28 |
1990 | 39987.5 | 1.732 | 2.128 | 1183000 | 233.16 |
1991 | 41775 | 1.768 | 2.276 | 1279750 | 235.92 |
1992 | 43130 | 1.804 | 2.06 | 1365750 | 238.44 |
1993 | 45675 | 1.892 | 2.036 | 1477500 | 240.84 |
1994 | 47185 | 1.968 | 2.3 | 1586000 | 243.24 |
1995 | 48722.5 | 1.96 | 2.276 | 1729250 | 245.88 |
1996 | 49242.5 | 2.188 | 1.992 | 1866000 | 248.4 |
1997 | 51277.5 | 2.304 | 2.58 | 2006250 | 250.56 |
Assignment 4.2 Beef Demand Model
A meat packing company hires you to study the demand for beef. The
attached data are
supplied. Complete the following tasks, then open the quiz “4.2
Beef Demand” and
complete it.
1. Estimate the demand for beef as a function of the price of beef,
the price of pork,
disposable income, and population. Label this as Model 1. Which
independent
variables have a significant impact on the demand for beef?
2. The coefficient for the price of beef indicates that a
one-dollar increase in price
leads to how large a decrease in quantity demanded?
3. Estimate the demand for beef as a function of the price of beef,
the price of pork,
and per capita disposable income (per capita disposable
income=[disposable
income/population]; you have to create this variable from the
data). Label this as
Model 2. Which independent variables have a significant impact on
the demand
for beef?
4. Which Model fits the data better? Comment on why, using
statistics from the
regression model.
5. The meat packing company gives you the following assumptions:
Price of
beef=$2; price of pork=$2.50; disposable income=$1,000,000;
and
population=225. Given this information, use model 1 to complete the
following:
a. Estimate of beef demand and a 95% confidence interval around
this
estimate.
b. Estimate total revenue
c. Estimate the following elasticities: Price elasticity, Cross
elasticity (that
is, elasticity with respect to Pork price), income elasticity, and
population
elasticity.
d. Should the meat packing company increase or decrease the price
of beef?
Why or why not?
Multiple R | 0.99654 | |||||||
R Square | 0.993091 | |||||||
Adjusted R Square | 0.991556 | |||||||
Standard Error | 936.983 | |||||||
Observations | 23 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 4 | 2.27E+09 | 5.68E+08 | 646.8264 | 3.56E-19 | |||
Residual | 18 | 15802869 | 877937.2 | |||||
Total | 22 | 2.29E+09 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 22387.22 | 8795.19 | 2.545394 | 0.020294 | 3909.212 | 40865.23 | 3909.212 | 40865.23 |
P Beef Per Lb ($) | -12804.2 | 1369.294 | -9.35094 | 2.48E-08 | -15681 | -9927.4 | -15681 | -9927.4 |
P Pork Per lb ($) | 1608.836 | 1361.079 | 1.182029 | 0.252575 | -1250.69 | 4468.358 | -1250.69 | 4468.358 |
Disp Inc (millions $) | 0.022907 | 0.002125 | 10.78046 | 2.78E-09 | 0.018443 | 0.027371 | 0.018443 | 0.027371 |
Pop (millions) | 36.60052 | 37.47358 | 0.976702 | 0.341662 | -42.1285 | 115.3296 | -42.1285 | 115.3296 |
1) Model1
Q= 22387.22-12804.2*price of beef+1608.836 *price of pork+0.022907 Disp income+ 36.60052Pop
Price of pork has significant effect
2) The coefficient for the price of beef indicates that a
one-dollar increase in price
leads to 12804.2 decrease in quantity demanded.
3)
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.994732 | |||||||
R Square | 0.989491 | |||||||
Adjusted R Square | 0.987832 | |||||||
Standard Error | 1124.769 | |||||||
Observations | 23 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 3 | 2.26E+09 | 7.54E+08 | 596.3294 | 5.76E-19 | |||
Residual | 19 | 24036994 | 1265105 | |||||
Total | 22 | 2.29E+09 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 25433.41 | 2832.654 | 8.978653 | 2.9E-08 | 19504.6 | 31362.23 | 19504.6 | 31362.23 |
P Beef Per Lb ($) | -15007.6 | 1245.063 | -12.0537 | 2.4E-10 | -17613.6 | -12401.7 | -17613.6 | -12401.7 |
P Pork Per lb ($) | 941.0356 | 1579.913 | 0.595625 | 0.558455 | -2365.76 | 4247.832 | -2365.76 | 4247.832 |
per capita income | 7.363545 | 0.217049 | 33.92568 | 1.82E-18 | 6.909256 | 7.817834 | 6.909256 |
7.817834 |
Model 2-
Q= 25433.41-15007.6*price of beef+941.0356 *price of pork+ 7.363545Per capita income
4) Model 2 fits the data better as the number of variables are consolidated and brings out a better estimate as not single variable has significant effect on the quantity demanded for beef.
As the p values for model two close to each other except for price of pork so we can remove it