Labor Economics
Labor Economics
7th Edition
ISBN: 9780078021886
Author: George J Borjas
Publisher: McGraw-Hill Education
Question
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Chapter 9, Problem 6P

(a)

To determine

Determine the number of workers of each race that a non-discriminating firm would hire and the amount of profit earned.

(a)

Expert Solution
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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 Ew+Eb. Moreover, the market wage for blacks is lower than the market wage for whites. Therefore, the firms are more interested to hire only black workers than white workers up to the point where the black wage equal the value of their marginal product. 

VMPE=WB        (1)

Rearrange Equation 1 as follows:

P×MPE=WB        (2)

Substitute the respective values in Equation 2:

$100×5Eb=WBWB=100(5)Eb

Since the market wage for blacks is $10, the value of Eb can calculate as follows:

$100×5Eb=1010=100(5)Eb10=500EbEb=50010Eb=50Eb=2,500.

Therefore, the firm prefer 2,500 black workers and zero white workers.

Substitute the value into the production Function (given in the question).

Q=10EbQ=10(2500)=10×50=500

Thus, the output is 500 units.

Therefore, the profit can calculate as follows:

Profit(π)=Total revenueTotal cost=(Price×output)(Number of employees×wage)=($100×500)(2,500×$10)=$50,000$25,000=$25,000

Thus, the profit earned is $25,000.

(b)

To determine

Determine the number of workers of each race that a firm would hire with discrimination coefficient of 0.25

(b)

Expert Solution
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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((1+0.25)×10). Still the adjusted black wage is lower than the white wage, the firm will prefer only to hire black workers. However, in the calculation the adjusted wage rate will include.

Using the similar method explained in part “a”, the number of workers can be calculated as follows:

VMPE=(1+d)×WB (3)                               

Rearrange Equation 3 as follows:

P×MPE=(1+d)×WB (4)                                   

Use Equation 4, to get the value of MPE, since Price is $12.50:

$100×5Eb=(1+0.25)×1012.5=100(5)Eb

The number of employees can derived e as follows:

12.50=100(5)Eb12.50=100(5)Eb12.50=500EbEb=50012.50Eb=40Eb=1,600.

Therefore, the firm prefer 1,600 black workers, and zero white workers.

Substitute the value into the production Function (given in the question).

Q=10EbQ=10(1,600)=10×40=400

Thus, the output is 400 units. 

Therefore, the profit can calculate as follows:

Profit(π)=Total revenueTotal cost=(Price×output)(Number of employees×wage)=($100×400)(1,600×$10)=$40,000$16,000=$24,000

Thus, the profit earned is $24,000.

(c)

To determine

Determine the number of workers of each race that a firm would hire with discrimination coefficient of 1.25

(c)

Expert Solution
Check Mark

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((1+1.25)×10). Here, the adjusted black wage is higher than the white wage. Therefore, the firm will prefer only to hire white workers

Using the similar method explained above, the number of workers can be calculated as follows:

P×MPE=Ww$100×5Ew=2020=100(5)Ew

The number of employees can be derived as follows:

20=100(5)Ew20=100(5)Ew20=500EwEw=50020Ew=25Ew=625.

Therefore, the firm prefer 625 white workers, and zero black workers.

Substitute the value into the production Function (given in the question).

Q=10EWQ=10(625)=10×25=250

Thus, the output is 250 units. 

Therefore, the profit can be calculated as follows:

Profit(π)=Total revenueTotal cost=(Price×output)(Number of employees×wage)=($100×250)(625×$20)=$25,000$12,500=$12,500

Thus, the profit earned is $12,500.

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