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A TREATISE ON MONEY

BK. U

tastes have changed and of everything else. It leadsto just as good a result where it is obvious to commonsense that no intelligible comparison is possible at all,as in cases where the strictly appropriate compositesare so nearly similar that any compromise inter-mediate between them will yield a very tolerableapproximation.

The oldest formula of this type—though this is acase of what Professor Fisher calls “ crossing theweights ”, not “ crossing the formulae ”—which wasproposed independently many years ago both byMarshall and by Edgeworth (see Edgeworth, Papersrelating to Political Economy, vol. i. p. 213), is notless objectionable. This method of approximation

compares the prices in the two positions of ?-i-,

i.e. it assumes that a third composite intermediatebetween the two composites strictly appropriate tothe two positions is approximately appropriate toboth of them. This amounts (in the above notation)

to taking . q as the measure of the change in the

price-level. 1

It may be of interest, before we conclude thisdiscussion, to show by an example that, when tastesand environment are not constant, p and q are notreliable guides to the change in the value of money,even when p = q.

Suppose that in the first position Beef and Whisky(one unit of each) are the predominant objects ofexpenditure, and in the second position Rice andCoffee (one unit of each) ; suppose further that unitsof beef and coffee are 50 per cent cheaper in thesecond position than in the first, whilst units of whisky

1 Dr. Bowley has given ingenious reasons, in his “ Notes on IndexNumbers ” (Economic Journal, June 1928), for preferring this formula toany other, subject to certain assumptions as to continuity and as to whatquantities can be regarded as small enough to be neglected.