3. Suppose a firm’s production function is given by Q = 10 (E w + E B ) 1/2 wher
ID: 2749859 • Letter: 3
Question
3. Suppose a firm’s production function is given by
Q = 10 (Ew + EB)1/2
where Ew and Eb are the number of white and black workers employed by the firm, respectively, and Q refers to the quantity of output produced. It can be shown that the marginal product of labor is given by:
MPE = 5 / (Ew + EB)1/2
Suppose the market wage for black workers is $10, the market wage for white workers is $20, and the price of each unit of output is $100.
a. How many workers does the firm hire if it does not discriminate (how many of each race…be specific)? How much profit does the firm make, assuming labor is the only cost of production?
b. Now assume that the firm discriminates against black workers with a discrimination coefficient of 0.25. (Hint: That is for every $1 the employer pays she interprets the cost as $1.25.) How many workers of each race does the firm hire? How much profit does it earn?
c. Finally, assume that the firm has a discrimination coefficient of 1.25. How many workers of each race would the firm hire and how much profit would it earn?
Explanation / Answer
a. Wb = 100(5) / Eb
10 = 500 / Eb
10 = 500 / 50 => 10 = 500 / 2500
The firm will hire 2500 black workers.
10 * 2500 = 10 * 50 = 500
100 (500) - 10 (2500) = 50000 - 25000 = $25000
The firm earns profit of $25000
b. Wb = Wb (1 + d)
Wb = 10 (1.25)
Wb = $12.50
12.50 = 100 (5) / Eb
12.50 = 500 / 40 => 12.5 = 500 / 1600
The firm hires 1600 black workers.
10 * 1600 = 10 * 40 = 400
100 (400) - 10 (1600) = 40000 - 16000 = $24000
The firm earns profits of $24000
c. Wb (1 + d)
Wb = 10 (2.25)
Wb = $22.50
20 = 100 (5) / Ew
20 = 500 / 25 => 20 = 500 / 625
The firm hires 625 white workers
10 * 625 = 10 * 25 = 250
100 (250) - 20 (625) = 25000 - 12500 = $12500
The firm earns profit of $12500
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