The earnings distribution
Figure 5 gives an earnings distribution of a standard lognormal shape. The figure approximates the situation in Holland 2002, though without parttimers. With each level of income there is a number of ‘personsyears’ of people who earn that level. The earnings distribution can be used to compute how large unemployment will be below the minimum wage. Figure 6 gives the situation for the Dutch minimum wage of about € 18.3 thousand. Since Dutch unemployment is about 25% of a potential labour force of 8 million people, the graph conforms to the facts. [42]
Figure 6: Unemployment below the minimum wage
Analysing the minimum wage
We wonder how the minimum wage comes about. We see two terms in the minimum wage, as can be seen in equation (13.1a) and its explanation:
| M = minimum wage [43] B = subsistence [44] T = arbitrary tax function Bentham = Bentham tax function [45] y = an arbitrary level of income r = marginal rate x = exemption | (13.1a) M = B + T[M] (13.1b) Bentham[y] = r (y - x) for y > x, = 0 for y x (13.1c) Net[y] = y - T[y] |
The minimum wage provides subsistence and thus consists of that net minimum and the taxes at that minimum, which is expressed by (13.1a). Since net income must be larger than B, this means for the Bentham function: