Figure II: Possible Distribution of IncomeIn a world of full-time jobs only, where involuntary unemployment has come to stay and the unemployed receive a transfer income without supplying labour in exchange, four groups of labour market participants can be distinguished, represented in figure I.
| Voluntary | Involuntary | |
| Employed | A | C |
| Unemployed | B | D |
Figure I: Four groups of labour market participants
Group A is voluntarily employed, its members receive wages, and would not prefer to belong to any other group. Group B is voluntarily unemployed, its members receive a transfer income and would not prefer to belong to any other group. Group C is involuntarily employed, its members receive wages, but would prefer to belong to group B. Group D is involuntarily unemployed, its members receive a transfer income, but would prefer to belong to group A.
Let there be only two possible situations for any person p in a total number P of the population: Employment: having a job out of the limited total amount J of exactly identical jobs J� P, all yielding the very same wage w. Unemployment: not having a job, receiving a transfer income t.
We require jobs of an equal nature because we want to analyse personal preferences apart from differences in "job quality". This way preference for employment or unemployment can only be evaluated by the utility of having or not having a job (irrespective of its income ), and by comparing the incomes yielded by the alternative situations, that is, by what we shall call the relative wage w/t, in which w is income under employment (net wage) and t is transfer income under unemployment. Clearly, the idea is that a low value of w/t will lead a large proportion of the population to prefer unemployment, whereas a high value of w/t will lead a large proportion of the population to prefer employment. Then there must be a value of w/t which is such that the number of people preferring employment exactly equals the number of jobs J, which, with some reservation , could be called a state of equilibrium on the labour market. This state would be characterized by empty groups C and D in ourfigure I. And it would be an optimal distribution of labour (jobs) and income in the sense that no one in P would prefer to be in some different situation which he knows other people in P to be in.No one would like to exchange his situation with anyone else.
Since we wish to analyse the distribution of income, we assume a given gross wage sum W, to be distributed over the employed, all receiving the same wage w, and the unemployed, all receiving the same transfer income t. Thus the relative wage w/t will have to satisfythe following "budget restriction"
W=J.w+(P-J)
depicted in figure II.
Figure II: Possible Distribution of Income
Leaving the unemployed without income (point 1) would imply the maximum
wage w = W/J; leaving the employed without income (point 2) would imply the maximum
transfer income w = W/(P-J) Now we assign to every person p in population a critical value
(w/t)p, defined as the relative wage at which the person is indifferent to the
situations of employment and unemployment. Any w/t > (w/t)p
would lead p to prefer employment, any w/t < (w/t)p
would lead him to prefer unemployment. Persons with low job preference will have a high
critical value, persons with high job preference will have a low critical value. We shall
have to specify the shape of the distribution of critical values over the population. In
the absence of any further information, let us assume it to be normal in the usual sense: 
depicted in figure III. 
Figure III: A Distribution of Critical Values
Persons with extremely low job preference are found in the right extreme of the distribution, persons with extremely high job preference are found in the left extreme of the distribution.