Suppose a worker's skill is captured by his efficiency units of labor s. The distribution of efficiency units in the population is distributed such that worker 1 has one unit, worker 2 has two and so on. There are 100 workers in the population. When deciding whether or not to obtain a certain diploma, worker compares her potential wage with the diploma (w_d(s)) minus the cost it takes to acquire the diploma (c(s)) to her potential wage without it. The two earnings relationships and the skill cost relationship are given by

w_d(s) = 100 + 0.5s

w_n(s) = w + 0.5s

c(s) = 25 - 0.1s

1. For what values of s will a worker acquire the diploma (as a function of w)?
2. How should a firm, who wants to be able to differentiate between workers with at least skill level 70 and (strictly) below 70 set w?
3. What if the firm wants to differentiate between workers with at least skill level 90 and (strictly) below 90?