A4 Industrial produces hydraulic pumps using a process that can be approximated
ID: 1113207 • Letter: A
Question
A4 Industrial produces hydraulic pumps using a process that can be approximated by a Cobb-Douglas production function. The production method uses tool shops that contain pieces of equipment that can be operated by a varying number of workers. The number of shops (units of variable capital) used during the month are given. The firm also hires skilled workers, and the number of full-time skilled workers hired for the month is given. The monthly output (number of pumps) produced is also given. The manager wants to estimate the Cobb-Douglas production function in order to determine the number of shops and number of workers required to achieve various levels of production.
The manager thus asks you to estimate a log-linear regression model based on the following monthly data over the last 2 years.
Q = quantity of boats produced per year
L = number of full-time workers per year
K = capital (number of shops) rented per year
P = average selling price per pump sold
Month
t
L
K
Q
P
Oct-15
1
120
25
1150
$438.93
Nov-15
2
122
25
1170
$437.88
Dec-15
3
118
26
1160
$438.46
Jan-16
4
110
26
1122
$440.14
Feb-16
5
116
24
1128
$439.96
Mar-16
6
120
24
1146
$439.01
Apr-16
7
124
27
1193
$436.90
May-16
8
125
27
1202
$436.38
Jun-16
9
130
28
1235
$434.92
Jul-16
10
127
28
1219
$435.58
Aug-16
11
128
27
1216
$435.85
Sep-16
12
136
27
1250
$434.09
Oct-16
13
140
27
1265
$433.54
Nov-16
14
135
28
1255
$433.85
Dec-16
15
130
28
1233
$435.05
Jan-17
16
135
29
1264
$433.43
Feb-17
17
128
29
1235
$434.95
Mar-17
18
138
30
1286
$432.39
Apr-17
19
145
30
1315
$431.19
May-17
20
141
28
1282
$432.58
Jun-17
21
134
29
1260
$433.78
Jul-17
22
140
29.0
1290
$432.20
Aug-17
23
142
30.0
1300
$431.89
Sep-17
24
146
30.0
1324
$430.72
2. Type the estimated Cobb-Douglas production function.
Round to 4 decimal places.
Q = # L #K #
Month
t
L
K
Q
P
Oct-15
1
120
25
1150
$438.93
Nov-15
2
122
25
1170
$437.88
Dec-15
3
118
26
1160
$438.46
Jan-16
4
110
26
1122
$440.14
Feb-16
5
116
24
1128
$439.96
Mar-16
6
120
24
1146
$439.01
Apr-16
7
124
27
1193
$436.90
May-16
8
125
27
1202
$436.38
Jun-16
9
130
28
1235
$434.92
Jul-16
10
127
28
1219
$435.58
Aug-16
11
128
27
1216
$435.85
Sep-16
12
136
27
1250
$434.09
Oct-16
13
140
27
1265
$433.54
Nov-16
14
135
28
1255
$433.85
Dec-16
15
130
28
1233
$435.05
Jan-17
16
135
29
1264
$433.43
Feb-17
17
128
29
1235
$434.95
Mar-17
18
138
30
1286
$432.39
Apr-17
19
145
30
1315
$431.19
May-17
20
141
28
1282
$432.58
Jun-17
21
134
29
1260
$433.78
Jul-17
22
140
29.0
1290
$432.20
Aug-17
23
142
30.0
1300
$431.89
Sep-17
24
146
30.0
1324
$430.72
Explanation / Answer
The log linear form of Cobb-Douglas production function will be -
log Q = A + B*log L + C*log K
Below are regression results -
Log Q = 1.7742 + 0.4668*Log K + 0.2279*Log L
Dependent var:Log Q Coefficients Standard Error t Stat P-value Intercept 1.7742 0.01 137.36 0.00 Log K 0.4668 0.01 45.40 0.00 Log L 0.2279 0.01 19.89 0.00Related Questions
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