Suppose a firm is a monopsonist in the labor market and faces separate labor supply functions for males and female workers.

The labor supply function for male workers is given by:
$L_m$= $w_m^k$
where $L_m$ is the amount of male labor available when the wage offered to male workers is $w_m$ and $k$ is a positive constant.

Analogously the labor supply function for females is given by:
$L_f =w_f$
Male and female workers are perfect substitutes for one another. The firm produces one unit of output from each unit labor it employs, and sells its output in a competitive market at price $p$ per unit. The firm can pay male and female workers differently if it chooses to. Suppose the firm decides to pay male workers more than female workers. Then answer the following questions.

  1. Which of the following must be true about the contant $k$?
    A) $k<1/2$
    B) $1/2<k<1$
    C) $k=1$
    D) $k>1$

2.Again, assume that the firm pays male workers more than the female workers, and the proce $p>2$. Then the firm must:
A) hire more male workers than females workers
B) Hire more female workers than male workers
C) Hire equal number of male and female workers
D) Hire more females than males if $2<p<4$, but more males than females if $p>4$

I only got this far: If male and female workers are perfect substitutes for the monopsonist then all that matters to him, is the total amount of labor employed. But then shouldn't it also be true that the monopsonist hires whichever worker costs him cheaper?
Why would he decide to pay male workers more than female workers? I'm struggling with the criteria one needs to use to find the values of $k$ for which monopsonist pays male workers more than the female workers.
How to find the MC and MRPL curves for the monopsonist here, so that we can equate the two for obtaining profit maximizing outcome?


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