1. Estimate the Cobb-Douglas production function Q = L1K2 where Q = output; L = labor input; K = capital input; and , 1, and

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.

2. Test whether 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.

4. Determine the labor and capital estimated parameters, and give an economic interpretation of each value.

5. Determine whether this production function exhibits increasing, decreasing, or constant returns to scale. (Ignore the issue of statistical significance.)

Economists at the Wilson Company are interested in developing a production function for fertilizer plants. They collected data on 15 different plants that producefertilizer.

LABOR (000 WORKER HOURS) 700.2 651.8 CAPITA (s000) 18,891 19.201 20,655 15,082 20,300 16,079 24,194 11,504 25,970 10,127 25,622 12,477 24,002 8,042 23,972 OUTPUT (000 TONS) 605.3 PLANT 647.1 523.7 712.3 487.5 761.6 442.5 821.1 397.8 896.7 359.3 979.I 331.7 1064.9 650.3 859.0 613.0 851.3 655.4 900.6 550.4 3 2 10 I1 12 540.5 949.4 575.7 925.8 14