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A TKEATISE ON MONEY

BK. II

substitution 1 —as we shall call it—we are in effectincreasing the field of a, i.e. that part of the consump-tion that is common to, or strictly comparable in, bothpositions, and diminishing the fields of b x and b 2 . Letus, therefore, in what follows include in a those itemsof consumption for which we are in a position toestablish ratios of equivalence when one is substitutedfor another.

There will generally remain, nevertheless, a numberof intractable articles comprised in b x and b 2 , for whichit is beyond our power to apply the method of equiva-lent substitution. We are not in a position to weighthe satisfactions for similar persons of Pharaoh ’s slavesagainst Fifth Avenue’s motor-cars, or dear fuel andcheap ice to Laplanders against cheap fuel and dearice to Hottentots.

We are left, therefore, with a + b x and a + b 2 asrepresentative of average consumption in the twopositions respectively. Now since a has been assumedto be identical in its power of yielding satisfaction toany pair of similar persons in the two positions, wecould, if a represented the whole of consumption,compare purchasing powers in the two positionsmerely by comparing the prices of a. But the residualsb l and b 2 , which we cannot equate in this way orotherwise compare, cut us off from so simple a method.We have no right to assume that b r and b 2 are equiva-

1 I think that Edgeworth probably had this method in mind in thefollowing somewhat confusing passage, Economic Journal , vol. xxxv. p. 380 :“ We may indeed construct a ‘ cargo ’ of goods definite in quantity andquality, the varying values of which from time to time shall constitute aseries of index-numbers. But even in starting with such a cargo we are nolonger on the terra firma of perfectly objective quantity. Eor in the selec-tion of the assortment forming the cargo there must be some regard toutility. At any rate, to continue the metaphor, when we have put out tosea, the composition of the cargo suffering a sea-change, we have to abandonthe prima facie exact method of comparing prices and to substitute the moreindefinite procedure of comparing amounts of satisfaction. So ProfessorBowley, with reference to a period in which there had occurred considerablechanges in the prices and quantities of commodities, would then compare the‘ satisfaction ’ obtainable from different combinations of commodities atgiven prices.”