(a)
Determine the number of workers of each race that a non-discriminating firm would hire and the amount of profit earned if there are no other costs.
(a)
Explanation of Solution
If a firm is non-discriminating, then it will hire all black workers as labor enters the function of the marginal product as a sum and black wage is lower than the white wage. Therefore, the firm will prefer to hire black workers Therefore, the number of worker can be calculated as follows:
Rearrange Equation 1 as follows:
Use Equation 2, to get the value of
Thus,
Substitute the value of
Since firm prefer black workers, it is assumed that
Therefore, the non-discriminate firm hires 15 black workers and 0 white workers. Substitute the value into the production Function (given in the question).
Thus, the output is approximately 111.
Therefore, the profit can calculate as follows:
Thus, the profit earned is $1,470.
(b)
Determine the number of workers of each race that a firm with discrimination coefficient of 0.6 against blacks would hire and the amount of profit earned if there are no other costs.
(b)
Explanation of Solution
Here, the discriminating firm is associated with a discrimination coefficient of 0.6. This coefficient will compare the white wage of $100 to the adjusted black wage of $80
Using the similar method explained in part “a”, the number of workers can be calculated as follows:
Rearrange Equation 3 as follows:
Use Equation 4, to get the value of
Thus,
Substitute the value of
For simplicity, it is assumed that
Therefore, the discriminate firm hires 9 black workers and 0 white workers. Substitute the value into the production Function (given in the question).
Thus, the output is approximately 88.
Therefore, the profit can be calculated as follows:
Thus, the profit earned is $1,310.
(c)
Determine the number of workers of each race that a firm with discrimination coefficient of 1.2 against blacks would hire and the amount of profit earned if there are no other costs.
(c)
Explanation of Solution
Here, the discriminating firm is associated with a discrimination coefficient of 1.2. This coefficient will compare the white wage of $100 to the adjusted black wage of $100
Using the similar method explained above, the number of workers can be calculated as follows:
Rearrange Equation 5 as follows:
Use Equation 6, to get the value of
Thus,
Substitute the value of
For simplicity, it is assumed that
Therefore, the discriminate firm hires 7 white workers and 0 black workers. Substitute the value into the production Function (given in the question):
Thus, the output is approximately 78.
Therefore, the profit can be calculated as follows:
Thus, the profit earned is $860.
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