Q 7. Please answer all the questions with steps, thank you !!!! 7. Suppose the f
ID: 1104196 • Letter: Q
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Q 7. Please answer all the questions with steps, thank you !!!!
7. Suppose the firm's production function is given by where Ew and E, are the number of whites and blacks employed by the firm respectively. Suppose the market wage for black workers is S10, the market wage for whites is $20, and the price of each unit of output is $100. a. Show that the marginal product of labor is-E5E5 b. How many workers would a firm hire if it does not discriminate? How much profit does this firm earn if there is no other cost? c. Consider a firm that discriminate against blacks with a discrimination coefficient equal to 0.25. How many workers does this firm hire? How much profit does it earn? d. Consider a firm that discriminate against blacks with a discrimination coefficient equal to 1.25. How many workers does this firm hire? How much profit does it earn?Explanation / Answer
a. Marginal product is the derivative of the production function. Thus, the derivative of q = 10 (Ew + EB)1/2 is taken as shown below:
dq/dE = [10] {1/2 * E1/2 - 1}
= [10/2 * E1/2]
= 5/ E1/2 (Where E = Ew +Eb)
= 5/ (Ew +Eb)1/2
NOTE: The derivative of the production function is done with respect to 'E' where E = Ew +Eb. The separate marginal products for both black and white workers can be calculated separately by putting the number of oppsite set of workers = 0)
MPEb = 5 / (0 + Eb)1/2
MPEw = 5 / (Ew +0)1/2
b. Let black workers be represented as Wb. The black workers employed in the firm can be shown as follows:
Wb = Q*MPE
Wb = (100*5) / Eb (where Ew = 0)
Equating the above mentioned euation to the wage rate of black workers,
10 = 500 / Eb
Eb = 500 / 10
=> Eb = 502 = 2500
Thus, the firm hires 2,500 black workers.
To calculate profit earned,
10 * 2500 = 10 * 50 = 500
Profit = (100*500) - (10*2500) = 50,000 - 25,000 = $25,000
Thus, the firm earns a profit worth $25,000.
c. Wb = Wb [1 + d] where d = discrimination
Wb = 10 (1.25)
Wb = $12.50
Now following the same to calculate the number of black workers hired by the firm,
12.50 = 100 (5) / Eb
12.50 = 500 / Eb
Eb = 500 / 12.5
Eb = 402 = 1,600
Thus, the firm will hire 1,600 black workers when discrimination is done.
10 * 1600 = 10 * 40 = 400
Profit = (100*400) - (10*1600) = 40,000 - 16,000 = $24,000
Thus, the firm earns a profit of $24,000 black workers are discriminated.
d. Wb = Wb [1 + d] = 10 [1 + 1.25]
Wb = 10 (2.25)
Wb = $22.50
20 = 100 (5) / Ew
20 = 500 / Ew
Ew = 500 / 20
Ew = 625
Therefore, the firm will hire 625 white workers.
10 * 625 = 10 * 25 = 250
Profit = 100 (250) - 20 (625) = 25,000 - 12,500 = $12,500
Therefore, the firm will earn a profit of $12,500.
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