Case Exercise
CASE EXERCISE (PAGE 263)
THE PRODUCTION FUNCTION FOR WILSON COMPANY
Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data o 15 different plants that produce fertilizer. Plant | Output(000 tons) | Capital($000) | Labor(000 Worker Hours) | 1 | 605.3 | 18,891 | 700.2 | 2 | 566.1 | 19,201 | 651.8 | 3 | 647.1 | 20,655 | 822.9 | 4 | 523.7 | 15,082 | 650.3 | 5 | 712.3 | 20,300 | 859.0 | 6 | 487.5 | 16,079 | 613.0 | 7 | 761.6 | 24,194 | 851.3 | 8 | 442.5 | 11,504 | 655.4 | 9 | 821.1 | 25,970 | 900.6 | 10 | 397.8 | 10,127 | 550.4 | 11 | 896.7 | 25,622 | 842.2 | 12 | 359.3 | 12,477 | 540.5 | 13 | 979.1 | 24,002 | 949.4 | 14 | 331.7 | 8,042 | 575.7 | 15 | 1,064.9 | 23,972 | 925.8 |
1. Estimate the Cobb-Douglas production function Q = αLβ1Kβ2, where Q = output; L = labor input; K = capital input; and α, β1, and β2 are the parameters to be estimated.
The Cobb-Douglas production function is Q = -4.75L0.42K1.08.
2. Test whether the coefficients of capital and labor are statistically significant.
The t statistics for capital and labor exceed the value of three, meaning that there can be 99% confidence that capital and labor have an effect on output. The chance of observing such high t statistics for these two variables when in fact capital and labor have no effect on output is less than 1%. The probability for both capital and labor is less 0.05, which means the coefficients of capital and labor are statistically significant.
3. Determine the percentage of the variation in output that is “explained” by the regression equation.
The percentage of the variation in output that is “explained” by the regression equation is 94.8%.
4. Determine the labor and capital estimated parameters, and give an economic interpretation of each value.
The estimated parameters for labor and capital are 0.42 and 1.08. Therefore, 0.42% changes in output when 1%
THE PRODUCTION FUNCTION FOR WILSON COMPANY
Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data o 15 different plants that produce fertilizer. Plant | Output(000 tons) | Capital($000) | Labor(000 Worker Hours) | 1 | 605.3 | 18,891 | 700.2 | 2 | 566.1 | 19,201 | 651.8 | 3 | 647.1 | 20,655 | 822.9 | 4 | 523.7 | 15,082 | 650.3 | 5 | 712.3 | 20,300 | 859.0 | 6 | 487.5 | 16,079 | 613.0 | 7 | 761.6 | 24,194 | 851.3 | 8 | 442.5 | 11,504 | 655.4 | 9 | 821.1 | 25,970 | 900.6 | 10 | 397.8 | 10,127 | 550.4 | 11 | 896.7 | 25,622 | 842.2 | 12 | 359.3 | 12,477 | 540.5 | 13 | 979.1 | 24,002 | 949.4 | 14 | 331.7 | 8,042 | 575.7 | 15 | 1,064.9 | 23,972 | 925.8 |
1. Estimate the Cobb-Douglas production function Q = αLβ1Kβ2, where Q = output; L = labor input; K = capital input; and α, β1, and β2 are the parameters to be estimated.
The Cobb-Douglas production function is Q = -4.75L0.42K1.08.
2. Test whether the coefficients of capital and labor are statistically significant.
The t statistics for capital and labor exceed the value of three, meaning that there can be 99% confidence that capital and labor have an effect on output. The chance of observing such high t statistics for these two variables when in fact capital and labor have no effect on output is less than 1%. The probability for both capital and labor is less 0.05, which means the coefficients of capital and labor are statistically significant.
3. Determine the percentage of the variation in output that is “explained” by the regression equation.
The percentage of the variation in output that is “explained” by the regression equation is 94.8%.
4. Determine the labor and capital estimated parameters, and give an economic interpretation of each value.
The estimated parameters for labor and capital are 0.42 and 1.08. Therefore, 0.42% changes in output when 1%