PLANT OUTPUT (TONS) CAPITAL ($) LABOUR (HOURS) 1 605.3 18,891 700.2 2 566.1 19,201 651.8 3 647.1 20,655 822.9 4 523.7 15,082 650.3 5 712.3 20,300 859.0 6 487.5 16,079 613.0 7 761.6 24,194 851.3 8 442.5 11,504 655.4 9 821.1 25,970 900.6 10 397.8 10,127 550.4 11 896.7 25,622 842.2 12 359.3 12,477 540.5 13 979.1 24,002 949.4 14 331.7 8,042 575.7 15 1064.9 23,972 925.8 Estimate the Cobb-Douglas production function Q ¼ αLβ1Kβ2, where Q = output; L= labour input; K= capital input; and α, β1, and β2 are the parameters to be estimated. For the Cobb-Douglas production function, test whether the coefficients of capital and labour are statistically significant. For Cobb-Douglas production function, determine the percentage of the variation in output that is explained by the regression equation. For Cobb-Douglas production function, determine the labour and capital estimated parameters, and give an economic interpretation of each value. Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.
PLANT OUTPUT (TONS) CAPITAL ($) LABOUR (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 1064.9 23,972 925.8
- Estimate the Cobb-Douglas production function Q ¼ αLβ1Kβ2, where Q = output; L= labour input; K= capital input; and α, β1, and β2 are the parameters to be estimated.
- For the Cobb-Douglas production function, test whether the coefficients of capital and labour are statistically significant.
- For Cobb-Douglas production function, determine the percentage of the variation in output that is explained by the regression equation.
- For Cobb-Douglas production function, determine the labour and capital estimated parameters, and give an economic interpretation of each value.
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.
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