Q.E.D.
Remark: It stands to reason that if a change to full employment occurs, it is mainly because it is POC. This highlights the problem of wrong co-ordination.
Remark: In normal work-ethic conditions, the income-leisure utility considerations of the l low productivity workers improve too, when they move from forced leisure to a decent job. It is conceivable though, that the advance in net income does not compensate for the loss of leisure. Therefor, the concept of PPO is useful. In another respect, the voting power of l may be small, and when society decides that unemployment was a silly affair, the l may be said to have had an unintended bonus while it lasted. (Society might even try to recover that bonus.)
Remark: There is scope to define and judge PO from some fundamental rights rather than from the actual bureaucratic flux.
Remark: In an applied general equilibrium context we would have to deal with complexer aspects, like people fearing to lose their jobs, and the loss of income resulting from crowding out. Adding ‘approximately’ would help Lemma IV surviving.
The general theorem
Definition: There is wrong co-ordination if a SWF optimal change is blocked only by ‘lack of knowledge’ of the power elite while the information, though not yet available, still could be found rather quickly by not much effort. (Co-ordination can go wrong on other counts too.)
Theorem G.1: If full employment is a controlable dichotomous state for which sound compact information exists in principle, that also can become available rather quickly by not much effort, then:
(i) full employment results from conscious choice or chance
(ii) unemployment results from conscious choice or from wrong co-ordination
Proof:
Work along the proof of theorem BHL.2. Note that BHL.2 fills in the properties that are now provided by hypothesis: controlability, soundness, compactness, and availability. Note that controlability means that the information exists in principle, while it need not be available yet.