Densities for unemployment ud and vacancies vd follow from the difference between supply and demand and actual employment:
ud[w] = s[w] - e[w] & vd[w] = d[w] - e[w]
The aggregate unemployment and vacancy are U and V, and their rates are:
u = (LS - LE) / LS = u[M] & v = (LD - LE) / LS = v[M]
Figure 23 gives the stylized fact that vacancies tend to occur at higher income brackets and unemployment at lower ones. The figure is quite stylized, since it is a difficult issue to construct plausible s[w] and d[w].
Figure 23: Supply and demand of labour
If labour supply LS was homogeneous, we would have difficulty explaining that u LS would be unemployed, since these persons are similar by assumption. Basically then u is a probability.