160 



SCIENCE 



[N. S. Vol. XXXVIT. No. 944 



combine in some rational way the general 

 concepts of the cost of living and of the 

 average rates of income may lead eventu- 

 ally to many interesting conclusions, but 

 this problem at the present time is ex- 

 tremely difficult. 



In this paper, which is divided into three 

 parts, I shall present, first, the results of 

 original computations of two series of in- 

 dex numbers for American prices. Hitherto, 

 the purpose of index numbers has been 

 chiefly to measure the changing cost of liv- 

 ing in order to compare the relative condi- 

 tions of successive years for the same coun- 

 try. 



In the second part of this paper, I have 

 endeavored to present some comparative 

 measurements of the changing cost of liv- 

 ing for various countries at the same time, 

 and, incidentally, to devise an interna- 

 tional index number, based on some index 

 numbers of the United States, England 

 and France. In the third part, it is inter- 

 esting to consider briefly various remedies 

 for the instability of the price level, and to 

 inquire whether a society has not within 

 its control indirect methods of reducing ab- 

 solutely the cost of living — methods which 

 may prove more fruitful than some of the 

 direct methods which have been suggested 

 from time to time in order to secure a rela- 

 tive rather than an absolute reduction. 



It is unnecessary to present a technical 

 description of my two series of index num- 

 bers for American prices which have been 

 described in the Quarterly Journal of Eco- 

 nomics,- and elsewhere.^ Suffice it to state 

 that the general method of the Sauerbeck 

 system has been adopted along with certain 

 modifications, some of which were sug- 

 gested by Forbes and others occurred as 

 practical necessities of the computation. 



'Quarterly Journal of Economics, August, 1910. 

 ° Pamphlets on Index Numbers, published by 

 the Gibson Publishing Co., 1910-11. 



The two index numbei-s may be described 

 as the averages of the percentages of the 

 prices of fifty important commodities ex- 

 pressed in terms of the average prices of 

 the years, 1890 to 1899, so that the aver- 

 age price level of the years 1890 to 1899 is 

 the base or one hundred per cent. Two 

 systems of weighting have been used. My 

 firet series follows Sauerbeck in the use of the 

 simple arithmetical average. The second se- 

 ries was intended as an approximate con- 

 tinuation of the Dun index numbers which 

 ended in 1907, and which have been pub- 

 lished since 1910 as the Gibson index num- 

 ber. The same arbitrary weighting is used 

 in the two series, although the Dun num- 

 bers were based on three hundred and fifty 

 commodities and the Gibson on fifty lead- 

 ing commodities. Mitchell'' has shown that 

 my method of continuing the Dun num- 

 bers by using fifty primary commodities 

 rather than three hundred and fifty com- 

 modities, many of which are derivative, 

 produces an average difference on the 

 basis of past years approximately of two 

 per cent. The fifty commodities consist of 

 the leading articles of commerce which are 

 most capable of accurate grading. 



In the succeeding table, ^ the relative 

 weighting of the various groups, such as 

 foods, clothing, minerals and other com- 

 modities, is presented in contrast for various 

 index numbers, in order to suggest the 

 cause of the slight differences which occur 

 in the results reached by the various num- 

 bers. 



The more heavily the food group is 

 weighted, the more the total index number 

 of all commodities tends to advance. This 



* Quarterly Journal of Economics, November, 

 1910. 



' ' ' How Index Numbers are Made, " by F. C. 

 Croxton, Journal of Commerce, June 2, 1910, and 

 Norton, "Weighting of Index Numbers," June 

 9, 1910. 



