Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 20

The Ajax Coal Company is the only employer in its area. It can hire any number of female workers or male workers it wishes. The supply curve for women is given by
Lf = 100w f
MEf = L f /50 and for men by Lm = 9w 2 m
where w f and wm are, respectively, the hourly wage rate paid to female and male workers. Assume that Ajax sells its coal in a perfectly competitive market at $5 per ton and that each worker hired (both men and women) can mine two tons per hour. If the firm wishes to maximize profits, how many female and male workers should be hired and what will the wage rates for these two groups be? How much will Ajax earn in profits per hour on its mining machinery? How will that result compare to one in which Ajax was constrained (say, by market forces) to pay all workers the same wage based on the value of their marginal products?Note: The following problems involve mainly the material from the Appendix to Chapter 13.