Suppose you are given the following cross-section data on the production of a given good in a particular industry for 2010.
|
Company
|
Q
|
K
|
L
|
|
1
|
709
|
2400
|
59
|
|
2
|
650
|
2290
|
58
|
|
3
|
600
|
2150
|
58
|
|
4
|
180
|
570
|
44
|
|
5
|
300
|
900
|
51
|
|
6
|
345
|
1170
|
52
|
|
7
|
480
|
1740
|
53
|
|
8
|
540
|
2010
|
55
|
|
9
|
200
|
625
|
47
|
|
10
|
250
|
775
|
51
|
|
11
|
300
|
1020
|
50
|
|
12
|
370
|
1310
|
51
|
|
13
|
425
|
1600
|
53
|
|
14
|
500
|
1875
|
54
|
|
15
|
365
|
1300
|
55
|
|
16
|
700
|
2430
|
58
|
d. Now estimate the following function
Q = ALaKb ee
(i) Report the estimated function below.
(ii) Convert the estimated function to its original form
e. Evaluate the estimated function in terms the statistical significance of each coefficient and the overall significance of the regression equation. Use 5% level of significance.
f. Are the marginal products of L and K subject to diminishing marginal returns? Show why.
g. What is the output elasticity with respect to L and K? What is the degree of returns to scale?
h. How many units of output can be produced if K= 2,500 and L = 60?