OH. 8 COMPARISONS OP PURCHASING POWER 117

Thus the final result is reached by comparing eachposition with its neighbours in two ways, and thenassuming that these two alternative measurements ofthe same thing are approximately equal. In otherwords :

if n-L is the price-level strictly appropriate to the firstposition;

if n 2 is the price-level strictly appropriate to thesecond position;

if n' 2 is the price-level in the second position obtainedby assuming that the composite appropriate tothe first position is also appropriate to the second;if n’ z is the price-level in the third position measuredby assuming that the composite appropriate tothe second position is also appropriate to thethird,

then n' 3 =^-n 2 ,

?*

n' 2 th,

p i

so that, assuming n 2 =n' 2 , we have

n' 3 = 2? • — ; and so on.

?* Pi

Let us analyse the validity of the above procedurein the light of the preceding argument. In the firstplace it is clear that it assumes constancy of tastes,etc. ; on the other hand, it permits not only changesin relative prices but also the introduction in the laterpositions of new objects of expenditure which werenot available to the consumer in the earlier positions(whilst ass umin g, however, that any objects of ex-penditure on the market in one position are still onthe market and have not dropped out in the nextposition). In the second place it is assumed that n 2 = n\approximately ; which is only justifiable if we haveapplied the method of limits to the comparison between