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(12 points) Suppose a firm’s production function is given by

q = 10 ∗

p

Ew + Eb

where Ew represents the number of white employee-hours and Eb represents the number of black

employee-hours. It can be shown that the marginal product of labor is

MPE =

5

√

Ew + Eb

Suppose the equilibrium market wage for black workers is $10 per hour, and the equilibrium

market wage for white workers is $15 per hour. The price of each unit of output is $60. Black

and white workers are substitutes in this production function, meaning that the quantity of output

only depends on the total quantity of labor (Ew + Eb). Note, Profits = Total Revenue − Total

Cost = P ∗ Q − (wb ∗ Eb + ww ∗ Ew).

(a) How many worker-hours of each type would a nondiscriminatory firm hire at the equilib-

rium wage rates listed above. How much profits does this nondiscriminatory firm earn,

assuming wages are the only cost incurred by this firm?

(b) Suppose a firm discriminates against blacks with an employer discrimination coefficient of

0.2. How many worker-hours of each type does this firm hire? How much profit does this

firm earn?

(c) Suppose a firm discriminates against blacks and has an employer discrimination coefficient

equal to 0.6. How many worker-hours of each type does this firm hire? How much profit

does it earn?

(d) Suppose a firm is nepotic and favors blacks so it has an employer nepotism coefficient of

0.4. (You can equivalently think of this as a discrimination coefficient equal to -0.4). How

many worker-hours of each type does this firm hire? How much profit does it earn?

(e) Based on your answers above, briefly discuss the long-run implications of discrimination

against or preferential treatment toward a specific racial group in a competitive labor mar-

ket?