Need help solving and explaining how to get to that answer.
We have the following information
Production function: q(L) = 10L^{1/2}
Labor (L) |
Output |
Average Product |
Marginal Product |
1 |
10.0 |
10.0 |
-- |
2 |
14.1 |
7.1 |
4.1 |
3 |
17.3 |
5.8 |
3.2 |
4 |
20.0 |
5.0 |
2.7 |
5 |
22.4 |
4.5 |
2.4 |
6 |
24.5 |
4.1 |
2.1 |
7 |
26.5 |
3.8 |
2.0 |
8 |
28.3 |
3.5 |
1.8 |
9 |
30.0 |
3.3 |
1.7 |
Average product (AP) of labor is total output divided by the total quantity of labor. Marginal product (MP) of labor is change in total output as the labor unit is increased by one.
It is given that the fixed cost is $100. Moreover, the price of labor is $20 which can be taken as the variable cost as well as the wage rate
Labor (L) |
Fixed Cost ($) |
Variable Cost ($) |
Total Cost ($) |
Marginal Cost ($) |
1 |
100 |
20 |
120 |
-- |
2 |
100 |
40 |
140 |
20 |
3 |
100 |
60 |
160 |
20 |
4 |
100 |
80 |
180 |
20 |
5 |
100 |
100 |
200 |
20 |
6 |
100 |
120 |
220 |
20 |
7 |
100 |
140 |
240 |
20 |
8 |
100 |
160 |
260 |
20 |
9 |
100 |
180 |
280 |
20 |
The equilibrium level of labor can be attained by equating the wage rate ($20) with the value of marginal product (VMP) of labor which marginal product of labor multiplied by the price of the output ($9)
Labor (L) |
Output |
Average Product |
Marginal Product |
Fixed Cost ($) |
Variable Cost ($) |
Total Cost ($) |
Marginal Cost ($)/Wage Rate |
Price ($) |
VMP |
1 |
10.0 |
10.0 |
-- |
100 |
20 |
120 |
-- |
9 |
-- |
2 |
14.1 |
7.1 |
4.1 |
100 |
40 |
140 |
20 |
9 |
37 |
3 |
17.3 |
5.8 |
3.2 |
100 |
60 |
160 |
20 |
9 |
29 |
4 |
20.0 |
5.0 |
2.7 |
100 |
80 |
180 |
20 |
9 |
24 |
5 |
22.4 |
4.5 |
2.4 |
100 |
100 |
200 |
20 |
9 |
21 |
6 |
24.5 |
4.1 |
2.1 |
100 |
120 |
220 |
20 |
9 |
19 |
7 |
26.5 |
3.8 |
2.0 |
100 |
140 |
240 |
20 |
9 |
18 |
8 |
28.3 |
3.5 |
1.8 |
100 |
160 |
260 |
20 |
9 |
16 |
9 |
30.0 |
3.3 |
1.7 |
100 |
180 |
280 |
20 |
9 |
15 |
From the table above one can see that the equilibrium level of labor is 5 units.
Need help solving and explaining how to get to that answer. 4. Suppose that your production...
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