INDEX NUMBERS. An index number is a method adopted by statistical and economic writ ers to exhibit. the course of prices of a group of commodities or of commodities generally.
A crude method of attaining this result is to add the prices of the various commodities togeth er. The defects of such a procedure are apparent from the following simple illustration: In this comparison, where each article has an equal weight in determining the result, there :appears to have been a fall in price of tia; per cent.; while in the first statement, where pig iron predominated. a rise in price c 1 1.2 per cent. ap peared, and in the second statement, where flour predominated, the fall in price appeared to be 7.2 per cent. It is obvious that the third state numt or simple index number is a far better in i:ication of the course of prices of these articles than the other two, where one article or the other dominates the result simply by reason of the fortuitous eircumstance that its unit. of in•asnre fluent is rebitivelv large.
The third statement is not, however, an abso hitely exact measme of the twat price change, since it is not equal significative that flour falls and that pig iron rises. To the individual consumer no doubt a slight fall in flour is more important than an equal rise in pig iron. It. may readily be assumed that he buys for his daily needs 10 times as many things afTeeti•il by the of cotton as are affected by that of pig iron, and perhaps. four times as many affected by the price of flour as are affected by that of cotton. lfis relative consumption might be: pig iron, 1; cotton. 10; flour, 40. hence the price changes noted affect him in varying measure, and this must be accounted for in estimating the significance of the total change. The calcula tions are as follows: If the sum be a criterion, it appears that there has on lho un ;111V:1111bl' in price of the group despite the fall in cotton and flour. A little reflection will show that had pig iron been quoted by the pound instead of by the ton the result would have been different, a, follows: (In the other hand, ill the aggregate consump tion of the nation the proportions of the differ ent. articles might be quite different, and hence
also the significance of these combined eliang(s in the wholesale market. 1,et us assume them to be: pig iron I, cotton 2, and flour 4. We then have the following ealeulation: But even here there are still great differences in the initial prices and the variations are meas ured on very different scales.
The index number avoids this difficulty by re ducing the initial prices to common terms. It establishes the variation of eaeli price from its own starting-point, and then determines the aver age variation. The 'assumed figures above given will serve the purpose of demonstration, and the following statement of relative prices is true for either of the series: We have now determined by these slightly different methods the price of the group to have been at the second date, compared with the first, as 94.4, 92.0, and 92.8 respectively are to $100, and we have in these results from assumed figures a fair illustration of the methods of index num ber calculations, and the problems to which they give rise.
The problems of a general index number are not dissimilar. The first is the choice of articles whose prices are to he ineluded. No definite statement of what articles should or should not be comprised in the index can be made except that they should he staple articles of general use. It would defeat the object of an investigation aiming to determine the course of general prices, to include specialties, or rarities, or objects of such restricted use as not to be subject to the ordinary influences affecting prices.
The character of the component price series being thus stated, how shall the number be fixed? It must evidently be large enough to in clude all the more important lines of staple commodities. No precise limit can be fixed. While it would seem obvious that in any effort to determine general prices, the greater the num ber of commodities embraced in the comparison, the more accurate the result, such is not the case, since, as the number multiplies, the propor tion of articles of limited demand which are more or less removed from the primary influences af fecting prices generally increases.