Cobb-Douglas Production Function)
The Brady Corporation has eleven plants located around the world. In a recent year, the data for each plant gave the number of labor hours (in thousands), capital (total net plant assets, in $millions), and total quantity produced:
|
Labor
|
Capital
|
Actual Quantity
|
|
250
|
30
|
245
|
|
270
|
34
|
240
|
|
300
|
44
|
300
|
|
320
|
50
|
320
|
|
350
|
70
|
390
|
|
400
|
76
|
440
|
|
440
|
84
|
520
|
|
440
|
86
|
520
|
|
450
|
104
|
580
|
|
460
|
110
|
600
|
|
460
|
116
|
600
|
The plants all operate at a similar level of technology so a production function can be derived from the data.
a. Use a Cobb-Douglas production function t calculate a regression, and discuss the important characteristics of your results, such as the form of the equation, R2, and the statistical significance of the coefficients.
b. Does the result indicate constant, decreasing, or increasing returns to scale?
c. What are the elasticities of production of labor and of capital? What is the meaning of the elasticities?