112

A TREATISE ON MONEY

BK. II

in effect, an attempt to carry the Method of Limitssomewhat further—further, in my opinion, than islegitimate.

The reasoning employed is of the followingcharacter. As before, let P be the composite com-modity appropriate to the first position (of time, placeor class), and p the price in the second position of aunit of P which costs £l in the first position ; andlet Q be the composite appropriate to the second

position, and - the price in the first position of a

unit of Q which costs £l in the second position.Then, as we have seen above, the true measure ofcomparison—assuming that tastes, etc., are constantand that only relative prices are changed—betweenthe price-levels in the two positions necessarily liessomewhere between p and q. Professor Fisher (amongstothers) concludes from this that there must be somemathematical function of p and q which will afford usthe best possible estimate of whereabouts between pand q the true value lies. Setting out on these lines,he has proposed and examined a great variety offormulae with the object of getting the best possibleapproximation to the true intermediate position.

Now, to my way of thinking, the proportion betweenthe price-levels under comparison is not, in general,any definite algebraic function of these two ex-pressions. We can concoct all sorts of algebraicfunctions of p and q as determining the point’sposition, and there will not be a penny to choosebetween them. We are faced with a problem inprobability, for which in any particular case we mayhave relevant data, but which, in the absence of suchdata, is simply indeterminate.

For this reason I see no real substance in ProfessorFisher’s long discussion, by which, after examining avast number of formulae, he arrives at the conclusionthat V pq (in my notation) is theoretically ideal—if,