Capital | labor | Output | MPk | APK | APL | VMPk |
0 | 20 | 0 | NA | NA | NA | NA |
1 | 20 | 50 | 50 | 50.0 | 2.5 | 200 |
2 | 20 | 150 | 100 | 75.0 | 7.5 | 400 |
3 | 20 | 300 | 150 | 100.0 | 15 | 600 |
4 | 20 | 400 | 100 | 100.0 | 20 | 400 |
5 | 20 | 450 | 50 | 90.0 | 22.5 | 200 |
6 | 20 | 475 | 25 | 79.2 | 23.75 | 100 |
7 | 20 | 475 | 0 | 67.9 | 23.75 | 0 |
8 | 20 | 450 | -25 | 56.3 | 22.5 | -100 |
9 | 20 | 400 | -50 | 44.4 | 20 | -200 |
10 | 20 | 300 | -100 | 30.0 | 15 | -400 |
11 | 20 | 150 | -150 | 13.6 | 7.5 | -600 |
Note: MPk = (Change in output) / (change in Capital)
APk = Output / Capital
APL = Output / Labor
VMPk = (Price of output) * (MPk)
(a) Labor is fixed input and capital is variable input
answer: Option (A)
(b) Wage rate is $30 per hour
labor is fixed at 20 hours
fixed cost = ($30) * (20)
Fixed cost = $600
Answer: $600
(c) 7 Units of capital are required to produce 475 units of output. The capital rental rate is $25.
The variable cost of producing 475 units of output = ($25) * (7)
The variable cost of producing 475 units of output = $175
Answer: $175
(d) the number of capital which maximizes the profit occurs at the point where MPk = rental rate
MPk = rental rate = $25 corresponding to 6 units of capital.
Answer: 6 units
(e) 6 units of capital with 20 units of labor are producing 475 units of output.
variable cost = ($25) (6) = $150
Fixed cost = $600
Total cost of producing 475 units = $150 + $600 = $750
Total revenue from 475 units = (475) * ($4) = $1900
Profit = TR -TC
Profit = $1900 - $600
Profit = $1300
answer: $1300
(f) Increasing marginal returns exist from 1 unit of capital to 4 units of capital.
the MPk is increasing between 1 unit to 4 units of capital
(g) decreasing marginal returns exist from 5 units of capiatl to 7 units of capital.
In this range, MPk is decreasing but remains positive.
e) 6 units of capital with 20 units of labor are producing 475 units of output.
variable cost = ($25) (6) = $150
Fixed cost = $600
Total cost of producing 475 units = $150 + $600 = $750
Total revenue from 475 units = (475) * ($4) = $1900
Profit = TR -TC
Profit = $1900 - $750
Profit = $1150
answer: $1150
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