CH. 8 COMPARISONS OF PURCHASING POWER 97

of utility. The problem, therefore, is to find thecriterion of “ equivalence ” for this purpose.

Our task in such a case is, not to prove something,but to elucidate by means of reflection a precise defini-tion which shall correspond as closely as possible towhat we really mean by a term in common use.On reflection it seems to me—and I hope the readerwill agree—that the criterion of equivalence is to befound as follows. Two collections of commoditiesare “ equivalent ” if they represent the commodity-incomes, i.e. the things which are purchased by themoney-incomes, of two persons of equal sensitiveness 1and possessed of equal real-incomes of utility . 2 Letus call such persons similar persons. If, then, we saythat the purchasing power of money in position A isr times what it is for similar persons in position B, wemean that similar persons will have r times the money-income in B that they have in A. Thus comparisonsof the purchasing power of money are the same thingas comparisons of the amounts of the money-incomesof similar persons.

There remains, however, a further serious difficulty.On the above definition it is fundamental to the mean-ing of a comparison between the purchasing powers ofmoney in two positions that it should be related toindividuals who have equal real-incomes. It does notenable us to make the comparison for communities asa whole, which are comprised of individuals havingvarious levels of real-income, unless the change in thepurchasing power of money, as given by the abovedefinition, is uniform for all the different levels of real-income. Yet, conceivably, it might have doubled forthe working-classes, trebled for the middle-classes, andquadrupled for the very wealthy. By how much, in

1 In what follows I shall, to avoid unnecessary complications, assumethat the condition of equal sensitiveness is fulfilled.

2 The importance for the Theory of Price Index-Numbers of the tripledistinction between money-incomes, commodity-incomes, and real-incomes,is well brought out by Haberler in his Der Sinn der Indexzahlen, p. 81.

VOL. I H