Question

A competitive firm has the production function Q = (Lw + Lb) 1/2 , where Lw and Lb are the respective numbers of white and black workers employed. The price of output is constant at P = 36. The market wage is wb = 3 for black workers and ww = 9 for white workers. If a firm has a discrimination coefficient of d > 0, then it behaves as if the wage is wb(1 + d) for black workers and ww for white workers.

(a) How many white and black workers would a firm with a discrimination coefficient of 1 hire?

(b) How many white and black workers would a firm with a discrimination coefficient of 3 hire?

Answer 1

The production function is given as, “Q=(Lw+Lb)^0.5”, where “Lb = black workers” and “Lw = white workers”.

So, the production function is a positive monotonic transformation of “Lw+Lb”,

Hence, the production function is a “perfect substitute” type, with the marginal productivity “1” for both the inputs.

a).

Now, let us assume that the firms have a discrimination coefficient of “d > 0”, and given wb = 3

The black workers wage is given by “Wb*(1+d)”, where “d=1”,

=> Wb*2 = 3*2= 6 < Ww=9”.

Now, under the discrimination coefficient “black workers” are getting less than the “white workers” and both white and black workers have same marginal productivity

Therefore, firm will employ 0 white workers and all black worker.

b).

Here, let us assume that that the discrimination coefficient is “d=3”, given wb = 3

black workers wage is given by “Wb*(1+d)”, where “d=3”,

=> Wb*4 = 3*4= 12 > Ww=9”.

Now, under the discrimination coefficient “black workers” are getting more than that of the “white workers” and both white and black workers have same marginal productivity.

Therefore, firm will employ 0 black workers and all white worker.