1) Suppose that an employer has a utility function, U (; R) where is profits

and R is the ratio of black to white workers. Assume that U1 > 0 and U2 < 0.

Let ww be the wage paid to whites and wb be the wage paid to blacks, ww > wb.

a) [15 points] Show the first order condition for the optimal number of blacks

and whites to hire.

b) [15 points] Let the supply of blacks be fixed at B and the supply of whites be

fixed at W. If there are n identical firms, how are equilibrium wages determined?

c) [10 points] Discuss in words how your answer in part (b) changes if supply

is a positive function of wage.

d) [15 points] What happens to your answer in part (b) if there are n=2 firms

with owners with utility function U (; R) and another n=2 firms with utility

function U ()?