84
A TREATISE ON MONEY
BK. II
We mean by the rise or fall “ in the value of money ”the hypothetical movement which would have beenbrought about if the “ changes on the side of money ”,i.e. the changes which tend to affect all prices equally,had been the only changes operating and there hadbeen no forces present “ on the side of the things ”tending to change their prices relatively to oneanother.
The problem being of this character, it is supposedthat what we need as a sound scientific basis for ourcalculations are numerous observations of individualprices, particularly of prices which are subject to“ independent ” influences, though we may, if welike, indulge in some rough weighting, to counter-balance a possible want of a full measure of independ-ence. Such weighting can do no harm, but will, onthe other hand, if our observations are a numerousand random selection, make but little difference tothe final result, and is therefore, on the whole, moretrouble than it is worth. Having obtained a numerousand random selection of individual prices, our nexttask is to determine the most appropriate methodof combining them. What is the law according towhich the relative movements are most likely todistribute themselves round the bull’s eye ? Will itbe such that the geometrical average of the individualprices will be nearest to the mark, as Jevons believed ?Or is the arithmetical average good enough, as mostcomputers have supposed, for no better reason, per-haps, than that it is easier to add than to multiply ?Or is the mode on the whole preferable, as Edgeworthinclined to think ? Or are there good arguments for“ fancy ” formulae like the harmonic average, or theroot of the mean square, or another ? 1
1 Some authors have tried to settle this question by observing whetherthe dispersions of individual prices which actually occur distribute them-selves along the Gaussian curve corresponding to the arithmetic mean oralong the curve corresponding to the geometric mean, and so forth. Fora good account of the results of this method see Olivier, Lea Nombres