LABOR ECONOMICS
LABOR ECONOMICS
8th Edition
ISBN: 9781260004724
Author: BORJAS
Publisher: RENT MCG
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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Please answer questions D-H, I have already answered A , B,C but it may help you to still solve them yourself. Thank you!
2. A firm’s production function is given by:Q = 10KLThe unit capital and labour costs are 2 and 1 pounds respectively. The firm is contracted to produce2000 units.(a) Write out the optimisation problem of the firm. (b) Express this problem using a Lagrangian function. (c) Find values of K and L which fulfil the contract with minimal cost to the firm. (d) Calculate the total cost to the firm.
3. Consider the following estimated regression equation, estimated using a sample of firms, where RDis total firm spending on research and development in USD ($), Revenue is total firm revenuein USD ($), and W ages is the firms’ total spending on wages in USD ($) (standard errors inparentheses):RDd = 1000(600)+ 0.5(0.1)Revenue + 1.5(0.5)W ages,(a) Interpret the coefficients on each of the explanatory variables. (b) Which of the three coefficients are statistically significant at the 5% level of significance? Howdo you know? A researcher runs a two-sided statistical test of the null hypothesis that both the coefficients onthe explanatory variables above are jointly equal to 0.25 (mathematically, that β1 = β2 = 0.25),and reports a p-value of 0.045.(c) What does this p-value mean for the outcome of the test? (d) What would an appropriate two-sided alternative hypothesis look like?
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