You are working for a government agency that wishes to know if a large employer ("ACME Corporation") discrimates between men and women when hiring for an entry level job on their production line. To formalize the notion of "discrimination", consider the following model. Mass 1 of men and women apply to ACME; men have continuously distributed productivity M~ f(OM), whereas women have continuously distributed productivity w ~ g(0w). These distributions may differ. ACME observes the productivity of each applicant, and hires men with productivity over and women with productivity over 0. Assume that the least productive agents of both genders are very bad, so not everyone is hired. We say there is no discrimination if 0 = 0w =:0*. a) Suppose ACME hires 50% of female applicants and 40% of male applicants. Does this mean ACME discriminates? b) Suppose we observe the average productivity of male and female employees, and Ow. We observe that the average woman is more productive than the average man. Does this mean ACME discriminates? c) Suppose we observe the productivity of each employee. We observe that the least productive man is less productive than the least productive women. Does this mean ACME discriminates? d) Suppose we only observe the average productivity of employees, as in (b). However, we observe the average in two periods. In period t = 1, ACME hires 50% of female applicants and 40% of male applicants. The average output is w = 104 for women and 0M 94 for men. In period t = 2, the company needs fewer employees so ACME hires 2 45% of female applicants and 36% of male applicants. The average output is w = 110 for women and M = 100 for men. Formally, we say there is no discrimination if ACME hires people with productivity above 0* in period 1 and above 0* +8 in period 2, where 6 > 0. Assume the distribution of applicants' productivity is constant over time. Do the above numbers mean ACME discriminates?