(a)
Determine the number of workers of each race that a non-discriminating firm would hire and the amount of profit earned.
(a)
Explanation of Solution
According to the trend, there are no complementarities between the types of labor as the quantity of labor enters the production function as a sum
Rearrange Equation 1 as follows:
Substitute the respective values in Equation 2:
Since the market wage for blacks is $10, the value of
Therefore, the firm prefer 2,500 black workers and zero white workers.
Substitute the value into the production Function (given in the question).
Thus, the output is 500 units.
Therefore, the profit can calculate as follows:
Thus, the profit earned is $25,000.
(b)
Determine the number of workers of each race that a firm would hire with discrimination coefficient of 0.25
(b)
Explanation of Solution
Here, the discriminating firm is associated with a discrimination coefficient of 0.25. This coefficient will compare the white wage of $20 to the adjusted black wage of $12.5
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
The number of employees can derived e as follows:
Therefore, the firm prefer 1,600 black workers, and zero white workers.
Substitute the value into the production Function (given in the question).
Thus, the output is 400 units.
Therefore, the profit can calculate as follows:
Thus, the profit earned is $24,000.
(c)
Determine the number of workers of each race that a firm would hire with discrimination coefficient of 1.25
(c)
Explanation of Solution
Here, the discriminating firm is associated with a discrimination coefficient of 1.25. This coefficient will compare the white wage of $20 to the adjusted black wage of $22.5
Using the similar method explained above, the number of workers can be calculated as follows:
The number of employees can be derived as follows:
Therefore, the firm prefer 625 white workers, and zero black workers.
Substitute the value into the production Function (given in the question).
Thus, the output is 250 units.
Therefore, the profit can be calculated as follows:
Thus, the profit earned is $12,500.
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