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=$1,000,000; and population=225. Given this information, use model 1 to complete the following:
a. Estimate of beef demand and a 95% confidence interval around this estimate.
b. Estimate total revenue
c. Estimate the following elasticities: Price elasticity, Cross elasticity (that is, elasticity with respect to Pork price), income elasticity, and population elasticity.
d. Should the meat packing company increase or decrease the price of beef?
Why or why not?
| |
Demand |
for |
Beef |
|
|
| |
|
|
|
|
|
| Year |
Q (millions of lbs) |
P Beef Per Lb ($) |
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 |