118 



Transactions. — Miscellaneous. 



It will be noticed that from 1880 to 1896 prices, as 

 measured by these numbers, steadily declined, with the ex- 

 ception of an interruption which culminated about 1890. 

 The decline for the whole period, as represented by the first 

 and last of the index numbers — viz., 88 and 61 — is one of 

 nearly 31 per cent., and this is equivalent to an increase in 

 the purchasing-power of money in the ratio of 61 to 88. or 

 some 44 per cent. In 1896, however, there set in a rapid 

 rise in prices and consequent fall in the purchasing-power of 

 money, which continued to 1900. 



Index numbers are calculated by different authors in 

 various ways and from different data with different results, 

 and no one set of index numbers can be regarded as being 

 exact. Indeed, they are intended to represent the average 

 prices of commodities, the very idea of which is more or less 

 indefinite. But, though differing somewhat in the magnitudes 

 of the changes in prices and purchasing-power of money 

 which they indicate, it is remarkable how concordant are 

 the index numbers of different statisticians in indicating 

 always the same tendency to rise or fall. These remarks 

 should be carefully borne in mind in the following application 

 of Sauerbeck's index numbers. 



Application of Index Numbers. 



We propose to take the exports, imports, and public debt 

 of New Zealand for the vears 1880-1900, and to calculate 

 their values in terms of the pound of the year 1880 — i.e., to 

 find how many pounds would have been required in the year 

 1880 to have the same purchasing-power as the various sums 

 concerned in the several years. The values thus calculated 

 we shall call the " general exchange values expressed in the 

 pound of 1880 " — (1880)£. By comparing these values we 

 shall be able, notwithstanding the roughness of the method, 

 to form a better idea of the course of trade and of the burden 

 of debt than we could from the ordinary statistics, as the 

 general exchange values thus calculated will represent the 



