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A TREATISE ON MONEY

BK. II

showing the proportion of total expenditure in eachyear which is common to all the years. At any rateI see no advantage, but on the other hand much dis-advantage, in the usual procedure of using a + bythroughout as compared with the method, not adoptedhitherto, of using a throughout.

The value as an approximation of using a through-out generally diminishes as the proportion of commonexpenditure becomes smaller. But if we want some-thing better than this, we must seek it by developingour opportunities to make more use of the methodof the substitution of equivalents, thereby increasingthe proportion of the field covered by a, rather thanby employing some intermediate formula such as

- 1 * 2 or any other. In practice, however, the

Cl +

substitution of equivalents has not been applied hither-to on scientific lines except in the case of certaininquiries into the comparative cost of living of theworking classes in different centres. In these inquiriesan attempt has sometimes been made to deal with theproblem of changes in the conventional diet of theworking man by working out a system of assumedequivalents . 1

In certain historical inquiries the “ highest commonfactor ” method may be better than any feasiblealternative, even though a is no longer large comparedwith by and b 2 . If, for example, we are trying to makea very rough comparison between widely separatedepochs—so widely separated that the substitution ofequivalents is impracticable—there is nothing to bedone except to take some small number of importantcommodities for which comparable price quotationsare obtainable which are common to both positions.If we want to compile a Consumption Index-Number

1 According to Edgeworth (op. cit. p. 213) Drobisch was the first topropose a formula of equivalent substitution, though based on a veryunsatisfactory, indeed an absurd, criterion (namely avoirdupois).