For heterogeneous labour we could use characteristics and a mechanism that explains why some are employed and others not. This mechanism could be related to the shift of the densities over time due to aggregate demand, inflation, technology, job changes and the like. In fact, we would use such methods to determine ud[w] and vd[w] in practice - and perhaps we would not start with w as the defining characteristic, but start with other characteristics and work towards the wage. However, we will not look into this deeply. We will use heterogeneity mainly to explain the effect of the minimum wage. For a level of income above the minimum wage we again assume some probability, quite analoguous to the homogeneous case. Basically, an agent has offers for various kinds of jobs and incomes, and associated probabilities (and one for unemployment). The s[w] and d[w] thus have a stochastic base.
Minimum wage unemployment differs from the ‘normal’ unemployment above the minimum. Thus:
u = um + un
Only part of um can be gainfully employed when the minimum wage would be abolished.
