Question
In: Economics
. The meat packing company gives you the following assumptions: Price of beef=$2; price of pork=$2.50;...
. The meat packing company gives you the following assumptions: Price of beef=$2; price of pork=$2.50; disposable income=$1,000,000; and population=225. Given this information, use model 1 to complete the following: a. Estimate of beef demand and a 95% confidence interval around this estimate. b. Estimate total revenue c. Estimate the following elasticities: Price elasticity, Cross elasticity (that is, elasticity with respect to Pork price), income elasticity, and population elasticity. d. Should the meat packing company increase or decrease the price of beef? Why or why not?
| Year | Q (millions of lbs) | P Beef Per Lb ($) | P Pork Per lb ($) | Disp Inc (millions $) | Pop (millions) |
| 1975 | 19295 | 1.9 | 1.864 | 517250 | 182.76 |
| 1976 | 17535 | 2.312 | 1.944 | 566500 | 185.88 |
| 1977 | 19520 | 2.208 | 1.972 | 708250 | 189.12 |
| 1978 | 25622.5 | 1.68 | 2.072 | 631500 | 192.12 |
| 1979 | 26530 | 1.68 | 2.128 | 643500 | 195.6 |
| 1980 | 27745 | 1.64 | 1.776 | 688250 | 199.08 |
| 1981 | 29805 | 1.568 | 1.732 | 733000 | 202.68 |
| 1982 | 28950 | 1.648 | 1.916 | 771250 | 206.28 |
| 1983 | 26932.5 | 1.868 | 2.092 | 796250 | 209.88 |
| 1984 | 27592.5 | 1.892 | 1.792 | 843250 | 213.36 |
| 1985 | 30162.5 | 1.804 | 1.884 | 875000 | 216.84 |
| 1986 | 31530 | 1.708 | 1.916 | 911000 | 220.44 |
| 1987 | 31397.5 | 1.856 | 1.9 | 963250 | 223.8 |
| 1988 | 34122.5 | 1.668 | 1.772 | 1011500 | 227.04 |
| 1989 | 39107.5 | 1.592 | 1.772 | 1095250 | 230.28 |
| 1990 | 39987.5 | 1.732 | 2.128 | 1183000 | 233.16 |
| 1991 | 41775 | 1.768 | 2.276 | 1279750 | 235.92 |
| 1992 | 43130 | 1.804 | 2.06 | 1365750 | 238.44 |
| 1993 | 45675 | 1.892 | 2.036 | 1477500 | 240.84 |
| 1994 | 47185 | 1.968 | 2.3 | 1586000 | 243.24 |
| 1995 | 48722.5 | 1.96 | 2.276 | 1729250 | 245.88 |
| 1996 | 49242.5 | 2.188 | 1.992 | 1866000 | 248.4 |
| 1997 | 51277.5 | 2.304 | 2.58 | 2006250 | 250.56 |
Solutions
Expert Solution
The estimation results are as follows:
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 22387.22 | 8795.19 | 2.545394 | 0.020294 | 3909.212 | 40865.23 |
| P Beef Per Lb ($) | -12804.2 | 1369.294 | -9.35094 | 2.48E-08 | -15681 | -9927.4 |
| P Pork Per lb ($) | 1608.836 | 1361.079 | 1.182029 | 0.252575 | -1250.69 | 4468.358 |
| Disp Inc (millions $) | 0.022907 | 0.002125 | 10.78046 | 2.78E-09 | 0.018443 | 0.027371 |
| Pop (millions) | 36.60052 | 37.47358 | 0.976702 | 0.341662 | -42.1285 | 115.3296 |
Price of beef=$2; price of pork=$2.50; disposable income=$1,000,000; and population=225.
Estimated demand = 22387.22+2*-12804.2+0.022907*1000000
= 19685.82 (other variables are not significant as the
p-value<0.5)
Estimated Revenue = 19685.82*2 = 39371.64
Regress % unit change of quantity with P Beef Per Lb ($) for Price elasticity, P Pork Per lb ($) for Cross elasticity (that is, elasticity with respect to Pork price), Disp Inc (millions $) for income elasticity, and Pop (millions) for population elasticity.
New table:
| Year | Q (millions of lbs) | P Beef Per Lb ($) | P Pork Per lb ($) | Disp Inc (millions $) | Pop (millions) |
| 1975 | |||||
| 1976 | -0.09122 | 0.21684 | 0.04292 | 0.09522 | 0.01707 |
| 1977 | 0.1132 | -0.04498 | 0.0144 | 0.25022 | 0.01743 |
| 1978 | 0.31263 | -0.23913 | 0.05071 | -0.10837 | 0.01586 |
| 1979 | 0.03542 | 0 | 0.02703 | 0.019 | 0.01811 |
| 1980 | 0.0458 | -0.02381 | -0.16541 | 0.06954 | 0.01779 |
| 1981 | 0.07425 | -0.0439 | -0.02477 | 0.06502 | 0.01808 |
| 1982 | -0.02869 | 0.05102 | 0.10624 | 0.05218 | 0.01776 |
| 1983 | -0.06969 | 0.1335 | 0.09186 | 0.03241 | 0.01745 |
| 1984 | 0.02451 | 0.01285 | -0.1434 | 0.05903 | 0.01658 |
| 1985 | 0.09314 | -0.04651 | 0.05134 | 0.03765 | 0.01631 |
| 1986 | 0.04534 | -0.05322 | 0.01699 | 0.04114 | 0.0166 |
| 1987 | -0.0042 | 0.08665 | -0.00835 | 0.05735 | 0.01524 |
| 1988 | 0.08679 | -0.10129 | -0.06737 | 0.05009 | 0.01448 |
| 1989 | 0.14609 | -0.04556 | 0 | 0.0828 | 0.01427 |
| 1990 | 0.0225 | 0.08794 | 0.2009 | 0.08012 | 0.01251 |
| 1991 | 0.0447 | 0.02079 | 0.06955 | 0.08178 | 0.01184 |
| 1992 | 0.03244 | 0.02036 | -0.0949 | 0.0672 | 0.01068 |
| 1993 | 0.05901 | 0.04878 | -0.01165 | 0.08182 | 0.01007 |
| 1994 | 0.03306 | 0.04017 | 0.12967 | 0.07343 | 0.00997 |
| 1995 | 0.03258 | -0.00407 | -0.01043 | 0.09032 | 0.01085 |
| 1996 | 0.01067 | 0.11633 | -0.12478 | 0.07908 | 0.01025 |
| 1997 | 0.04133 | 0.05302 | 0.29518 | 0.07516 | 0.0087 |
| P Beef Per Lb ($) | -0.77871 |
| P Pork Per lb ($) | -0.0443 |
| Disp Inc (millions $) | -0.46249 |
| Pop (millions) | -0.02575 |
Increase the price of beef as the price elasticity of demand is less than 1, by increasing the price, the fall in quantity will be less than proportional, therefore revenue will increase
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