Answer:
a. Therefore, the number workers the firm will hire is 12; and the amount of profit it will earn is $144.
b. Since the profit from when one fewer or more worker than L* workers is hired is equal to $143 which is lower than $144 profit from hiring L* workers, this implies that L* workers generate the most profit for the firm.
Explanation:
Note: There are some errors and omission in this question. These are therefore corrected by restating the complete question as follows:
A firm calculates that the marginal product of labor (MPL) can be found from the following equation:
MPL = 35 - 2L
where L is the number of workers hired.
The production function for this firm is as follows:
Q = 35L - L^2
The firm knows it can find profits with the following equation:
Profit = P * Q - W * L
where P stands for the selling price of the good, Q stands for total output, and W represents the wage. Price is equal to $1.
a. If the wage is $11, how many workers will the firm hire? How much profit will it earn?
b. Compare this level of profits to those earned by the firm if it hired one fewer worker than L* and one worker more than L* to demonstrate that L* workers generate the most profit for the firm.
The explanation of the answer is now given as follows:
a. If the wage is $11, how many workers will the firm hire? How much profit will it earn?
Given;
Profit = P * Q - W * L ………………………… (1)
Where;
P = 1
Q = 35L - L^2
W = 11
L = ?
Substitute the values above into equation (1), we have:
Profit = (1 * (35L - L^2)) - (11 * L)
Profit = 35L - L^2 - 11L …………………………. (2)
Taking the derivative of equation (2) with respect to L and equating to 0, we can then solve for L as follows:
35 - 2L - 11 = 0
2L = 24
L = 24 / 2
L = L* = 12
Substituting L = 12 into equation (2), we have:
Profit = (35 * 12) - 12^2 - (11 * 12)
Profit = 144
Therefore, the number workers the firm will hire is 12; and the amount of profit it will earn is $144.
b. Compare this level of profits to those earned by the firm if it hired one fewer worker than L* and one worker more than L* to demonstrate that L* workers generate the most profit for the firm.
<u>If it hired one fewer worker than L*</u>
This implies that L = 12 – 1 = 11
Using equation (2) from part a above and substitute L = 11, we have:
Profit = 35L - L^2 - 11L
Profit = (35 * 11) - 11^2 - (11 * 11)
Profit = 143
<u>If it hired one more worker than L*</u>
This implies that L = 12 + 1 = 13
Using equation (2) from part a above and substitute L = 13, we have:
Profit = 35L - L^2 - 11L
Profit = (35 * 13) - 13^2 - (11 * 13)
Profit = 143
Therefore, the profit from when one fewer or more worker than L* workers is hired is equal to $143.
Since the profit from when one fewer or more worker than L* workers is hired is equal to $143 which is lower than $144 profit from hiring L* workers, this implies that L* workers generate the most profit for the firm.
