Theorem BHL.1 shows that full employment for the BHL welfare state is a controlable dichotomous state. The theorem is sound and compact. Thus Lemma III applies.
Possible states of sound compact knowledge and employment (I, t) are:
(1) (1, 1): having the knowledge, full employment results;
(2) (0, 1): lacking the knowledge, full employment results; thus there is a hidden cause; thus it is by chance;
(3) (1, 0): having the knowledge, unemployment results; thus, the explanation comes from the power distribution, so that full employment is not to the advantage of those in power, and the choice for unemployment is conscious;
(4) (0, 0): lacking the knowledge, unemployment results. Note that theorem BHL.1 is available knowledge (e.g. it was published by Colignatus (1992b, 1995a, or this book)). [118] Where we currently speak about ‘lack of knowledge’ then we mean the knowledge of the power elite, who do not fully use the knowledge budget set. Introduction of theorem BHL.1 into the knowledge bank of the power elite unveils two subcases:
(4.1) There is a switch to (1): optimal change was blocked only by lack of knowledge, while the information actually is available: hence wrong co-ordination;
(4.2.) There is a switch to (3): information doesn’t matter.
Q.E.D.
Remark: In both employment regimes we have ‘conscious maximizing behaviour subject to the state of information’, but the regimes cause different conditions. There is little use in subdividing case (2). If more information is introduced, then the power distribution may cause unemployment. This effect however has already been covered in (3). See the note “more on chance”.
Remark: Cases (3) and (4.2) give the situation where the possibility of full employment merely is logical but not empirical. It is conceivable that power parameters and political reaction patterns are such that the economy remains in a state of unemployment forever.