***ONLY NEED ANSWER TO 11. OTHER QUESTIONS HAVE ALREADY BEEN SUBMITTED ON CHEGG.
ID: 1113216 • Letter: #
Question
***ONLY NEED ANSWER TO 11. OTHER QUESTIONS HAVE ALREADY BEEN SUBMITTED ON CHEGG.***
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
A4 Industrial hires labor and procures capital in competitive input markets. For that last two years, the input prices have been constant, and given as follows:
w = $2,400 = monthly wage rate per worker
r = $1,600 = monthly rental rate per shop
The firm also faces fixed cost (FC) of building rental, fixed capital, and overhead expenses given as follows:
f = $60,000
9.Now that you have computed the MC and MR, functions, the manager wants to know what the profit maximizing price and quantity are.
You can use rows 108 and 109 in the S-R Cost Function tab in order to find this answer. Make sure and enter the parameters for the inversed demand function in cells E66 and E67, and the MR function parameters in cells E69 and E70, before you begin.
P = $#
Q = # pumps
10.Refer to question 9. Which of the following gives the profit-maximizing (and, given the output from question 9, also cost-minimizing) levels of labor and capital? Also, state firm’s monthly total cost, total profit, and average profit. Note that you will have to include the fixed costs in the cost equation, which is given below.
(You will want to use the Excel tab called Cobb Douglas inputs for the calculations. The templates are consistent with Worksheet 3, questions 21 and 22.)
L = # full-time workers
K = # shops
C = w L + r K + FC
C = $#
p = $#
AC = $#
average p = $#
11. Refers to questions 9 and 10. State firm’s marginal cost, average total cost, and average profit.
MC = $#
AC = $#
average p = $#
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
11
t L K Q P TR MR VC TC AC MC Profit Averge Profit 1 120 25 1150 438.93 504769.5 328000 388000 337.3913 116769.5 101.5387 2 122 25 1170 437.88 512319.6 7550.1 332800 392800 335.7265 4800 119519.6 102.1535 3 118 26 1160 438.46 508613.6 -3706 324800 384800 331.7241 -8000 123813.6 106.7359 4 110 26 1122 440.14 493837.08 -14776.52 305600 365600 325.8467 -19200 128237.1 114.2933 5 116 24 1128 439.96 496274.88 2437.8 316800 376800 334.0426 11200 119474.9 105.9174 6 120 24 1146 439.01 503105.46 6830.58 326400 386400 337.1728 9600 116705.5 101.8372 7 124 27 1193 436.9 521221.7 18116.24 340800 400800 335.9598 14400 120421.7 100.9402 8 125 27 1202 436.38 524528.76 3307.06 343200 403200 335.4409 2400 121328.8 100.9391 9 130 28 1235 434.92 537126.2 12597.44 356800 416800 337.4899 13600 120326.2 97.43012 10 127 28 1219 435.58 530972.02 -6154.18 349600 409600 336.0131 -7200 121372 99.56687 11 128 27 1216 435.85 529993.6 -978.42 350400 410400 337.5 800 119593.6 98.35 12 136 27 1250 434.09 542612.5 12618.9 369600 429600 343.68 19200 113012.5 90.41 13 140 27 1265 433.54 548428.1 5815.6 379200 439200 347.1937 9600 109228.1 86.34632 14 135 28 1255 433.85 544481.75 -3946.35 368800 428800 341.6733 -10400 115681.8 92.17669 15 130 28 1233 435.05 536416.65 -8065.1 356800 416800 338.0373 -12000 119616.7 97.01269 16 135 29 1264 433.43 547855.52 11438.87 370400 430400 340.5063 13600 117455.5 92.92367 17 128 29 1235 434.95 537163.25 -10692.27 353600 413600 334.8988 -16800 123563.3 100.0512 18 138 30 1286 432.39 556053.54 18890.29 379200 439200 341.5241 25600 116853.5 90.86589 19 145 30 1315 431.19 567014.85 10961.31 396000 456000 346.7681 16800 111014.9 84.42194 20 141 28 1282 432.58 554567.56 -12447.29 383200 443200 345.7098 -12800 111367.6 86.87017 21 134 29 1260 433.78 546562.8 -8004.76 368000 428000 339.6825 -15200 118562.8 94.09746 22 140 29 1290 432.2 557538 10975.2 382400 442400 342.9457 14400 115138 89.25426 23 142 30 1300 431.89 561457 3919 388800 448800 345.2308 6400 112657 86.65923 24 146 30 1324 430.72 570273.28 8816.28 398400 458400 346.2236 9600 111873.3 84.49644 TR =P*Q Profit = TR-TC Average profit = Profit/QRelated Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.