98

A TREATISE ON MONEY

BK. II

such a case, has it changed for the community as awhole ?

There is, in my opinion, no satisfactory answer tothis question — for the reason that we can give nomeaning to a numerical comparison between the pur-chasing power of money to a poor man and its pur-chasing power to a rich man, the two things being, soto speak, in different dimensions. Any attempt tostrike an average for the amount by which purchas-ing power has changed for a community as a wholenecessarily involves equating the purchasing powerof money for one class to its purchasing power fora different class, which cannot be done except by anarbitrary assumption. For example, let us supposethat the income of the community is equally dividedbetween three classes, and that purchasing powerdoubles in position B as compared with position A forthe lower class, trebles for the middle class, and quad-ruples for the upper class. Then, if we assume thatthe purchasing power of money was equal for all threeclasses in position A, we find that the average rise inposition B is 3 times ; but if we assume that it wasequal for the three classes in position B, then we findthat the average rise in position B is 2]4| times. 1 Notonly is there no means of reconciling these conclusions,but I see no meaning in an assumption to the effectthat the purchasing power of money is equal for differ-ent classes of the community.

When, therefore, the change in the purchasingpower of money is different for different ranges ofreal-income, the best we can do is to neglect thoseranges in which comparatively few persons are to befound, and to say that the change in purchasing powerfor the community as a whole lies between the largestand the smallest change shown when the changes forthose ranges of real-income, which include the bulk

1 In effect we are taking the arithmetic mean of 1, 2, 3 in the first caseand the inverse of their harmonic mean in the second case.