3. Suppose a firm’s production function is given by Q = , where E w and E b are

Question

3. Suppose a firm’s production function is given by

Q = ,

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 = .

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

Labor-market discrimination is a situation in which equally materially productive persons are treated unequally on the basis of an observable characteristic.The market wage for black workers is $ 10 and that for a white worker is $ 20. If the firm does not discriminate between the workers on the basis of their race it will certainly employ all black workers owing to their affordable rate of $10. The number of units of labour required to manufacture one unit of output are not given hence profit figure cannot be determined.

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