This allows us to derive the supply of labour as a function of the relative wage.The cumulative normal distribution CNm _,s [(w/t)]_p:

is a supply curve of labour, as in the lower half of figure IV

Figure IV: Supply and Demand.

Since for the inverse function of CN , denoted by CN^-1 , the following holds

for every amount J of jobs, 0 < J < P

,it follows that if the demand for labour decreases, the equilibrium value of w/t, , CN^-1m _,s (J) decreases. That is: if unemployment rises, relative wages should go down if equilibrium is to be restored. This is not too surprising: if, starting from an optimal state with empty groups C and D, the number of jobs is reduced, then optimality requires that the resulting newly unemployed persons, who in the former conditions preferred employment, will now transcend their critical value downward, so as to come to prefer unemployment. This clearly requires a lowering of relative wage w/t. Keeping w/t high by exogenous means implies the creation of group D of involuntarily unemployed.

Similarly, if the demand for labour increases in the customary case where the unemployed are obliged to apply for jobs and to accept jobs offered (under pressure of the withdrawal of a transfer income), and if this is not accompanied by a rise of relative wages, a group C of involuntarily employed people comes into existence. Simultaneous existence of non empty groups C and D is impossible in our model since it presupposes the free exchangeability of jobs between members of group C and D.

Summarizing: with a number P of persons and a number J of jobs, J < P, there is a relative wage w/t such that exactly J persons prefer employment and P - J persons prefer unemployment. This value of w/t is called the equilibrium or optimal relative wage.