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Cobb Douglas Production

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Estimate the cobb Douglas production function Q = ΑL^B1K^Β2, where Q= out put, L labour input K= capital input and A,B1,B2 are parameters to be estimated.

test whether the coeficient of capital and labour are statistically significant.

Determine the percentage of the variation in output that is explained by the regression equation

Determine the labour and capital esitmated parameters and give an economic interpretation of each value. economical interpretation.

Determine whether this production funtion exhibits increasing, decresing, or constant returns to scale. Ignore the issue of statistical significant.

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Estimate the cobb Douglas production function Q = ΑL^B1K^Β2, where Q= out put, L labor input K= capital input and A,B1,B2 are parameters to be estimated.
Plant Output Capital Labor ln(Q) ln(L) ln(k)
1 605.3 18891 700.2 6.406 6.551 9.846
2 566.1 19201 651.8 6.339 6.480 9.863
3 647.1 20655 822.9 6.473 6.713 9.936
4 523.7 15082 650.3 6.261 6.477 9.621
5 712.3 20300 859 6.568 6.756 9.918
6 487.5 16079 613 6.189 6.418 9.685
7 761.6 24194 851.3 6.635 6.747 10.094
8 442.5 11504 655.4 6.092 6.485 9.350
9 821.1 25970 900.6 6.711 6.803 10.165
10 397.8 10127 550.4 5.986 6.311 9.223
11 896.7 25622 842.2 6.799 6.736 10.151
12 359.3 12477 540.5 5.884 6.292 9.432
13 979.1 24002 949.4 6.887 6.856 10.086
14 331.7 8042 575.7 5.804 6.356 8.992
15 1064.9 23972 925.8 6.971 6.831 10.085
Taking natural log on both sides of the Cobb Douglas production function, we get
ln(Q) = ln(ΑL^B1K^Β2)
ln(Q) = ...

Solution Summary

Cobb Douglas Production is estimated.

$2.19
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Labor/Capital Mix - Cobb Douglas:
Suppose a firm assumes the following production function:
Log Q=2 + .8 log K + .1 log L
a) Currently, the firm hires 10,000 workers and employs 50 units of capital. The "wage" of capital and labor are $500 and $800 respectively, what would you suggest would be the firm's mix of labor and capital if it produces 2,000,000 units?
b) Is this an example of a Cobb-Douglas Production function?
c) Would you suggest this firm merge with similar firms? Explain.

Suppose a firm assumes the following production function:
Log Q=2 + .8 log K + .1 log L
a) Currently, the firm hires 10,000 workers and employs 50 units of capital. The "wage" of capital and labor are $500 and $800 respectively, what would you suggest would be the firm's mix of labor and capital if it produces 2,000,000 units?
b) Is this an example of a Cobb-Douglas Production function?
c) Would you suggest this firm merge with similar firms? Explain.

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