5. (12 points) Suppose a firm’s production function is given by q = 10 Ew + Eb w

Question

5. (12 points) Suppose a firm’s production function is given by q = 10 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?

Explanation / Answer

Answer:

a) Wage rate for black workers is less than wagge rate for white workers. Then nondiscriminating firm hires only blackworker at the equilibrium where wage rate for black workers equals to value of marginal product of labour.

Therefore

Total cost (TC)=900*10=$9000

Total production would be

Total revenue (TR)=300*60=$18000

Therefore profit=18000-9000=$9000

b) Discrimination against black workers is represented on adjusted wage which is equal to wd(1+d).

Therefore adjusted wage rate would be 10*(1+0.2)=$12.

Now compare wage for white with adjusted wage for black. Still wage for black is lower than white. Firm only hires black workers at equilibrium

The profit would be

c. In this case adjusted wage for black workers would be

Now Firm only hire white workers at equilibrium

Therefore the profit would be

d. In this case adjusted wage for black would be 10*(1-0.4)=$6.

Firm only hires black workers at equilibrium

Therefore the profit would be

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