86

A TREATISE ON MONEY

BK. II

prices, round which are scattered the moving price-levels of individual things. There are all the various,quite definite, conceptions of price-levels of compositecommodities appropriate for various purposes andinquiries which have been scheduled above, and manyothers too. There is nothing else. Jevons was pur-suing a mirage.

What is the flaw in the argument ? In the firstplace it is assumed that the fluctuations of individualprices round the “ mean ” are “ random ” in thesense required by the Theory of the Combination ofIndependent Observations. In this theory the di-vergence of one “ observation ” from the true positionis assumed to have no influence on the divergences ofother “ observations ”. But in the case of prices amovement in the price of one commodity necessarilyinfluences the movement in the prices of other com-modities , 1 whilst the magnitudes of these compensa-tory movements depend on the magnitude of thechange in expenditure on the first commodity as com-pared with the importance of the expenditure on thecommodities secondarily affected. Thus, instead of“ independence ”, there is between the “ errors ” inthe successive “ observations ” what some writers on'Probability have called “ connexity ”, or, as Lexis ■expressed it, there is “ sub-normal dispersion ”.

We cannot, therefore, proceed further until wehave enunciated the appropriate law of connexity.But the law of connexity cannot be enunciated with-out reference to the relative importance of the com-modities affected—which brings us back to the problemthat we have been trying to avoid, of weighting the

1 Divisia (“ L’Indice monetaire ”, Revue d'Economic politique, 1925, p.S58) has been one of the very few writers to point this out quite clearly.See also Olivier, Les Nombres Indices, pp. 106, 107. M. Divisia shows,not only that the non-independence of relative price changes is conclusiveagainst the applicability of the Gaussian Law of Error, but also that it is agratuitous assumption that a so-called “ monetary ” cause, however defined,will affect all prices equally.