The well-known w–r relation results from the price equation system and the normalisation equation, that is, the equalisation of price of the normalisation commodity (numéraire) with a positive constant. In this article, we show that the w–r relation is neither that of the given technique nor that of the given production system, but that of the normalisation subsystem, that is, the subsystem which, using the above-mentioned technique, produces the normalisation commodity as its own net product. So, the maximum nominal wage rate, the slope and the maximum profit rate of the w–r relation vary with the normalisation commodity and the above constant. In inference of them, (a) the comparison and the ranking of given techniques concerning our profitability as the choice of the most profitable of them too is in reality a comparison, a ranking and a choice of the corresponding normalisation subsystems; (b) the phenomena of re-switching appear and disappear due to the change of the normalisation commodity; and (c) the comparison, the ranking, the choice of techniques and the ascertainment of the re-switching phenomenon are impossible. Finally, the normalisation subsystem tenders an index magnitude to solving the as yet unsolved problem of how the prices change with income distribution.
