but changes in the prices of individual goods, due to causes affecting demand and supply, may be sharp and sudden. Even when the fact of a rise or a fall in prices is evident, the extent of the change is difficult to measure.

To observe and register changes in the general trend of prices "index numbers" are used. An index number represents the price of a group of commodities, or the average price during a given period, which is used as a basis or standard with which to compare the price of these commodities at other dates. Suppose, for example, that the average price per bushel of barley for the period 18901899 was 48 cents, while the average for 1910 was 60 cents; then if the average price for the earlier period be represented by 100, called the "base," it will be seen that the relative price for 1910 is 125, that is, the index number shows a rise in price of 25 per cent. By grouping and comparing the prices of a large number of representative commodities, so that the influences affecting the value of different groups will counterbalance each other, a means is obtained of indicating the changes in the purchasing power of money from period to period.

The following simple example illustrates one method of constructing price tables and index numbers:

100

In this table we have two sets of hypothetical prices, one for 1900, the other for 1917. The prices for 1900 have been taken as the basis at 100 per cent and the changes in prices in 1914 calculated with reference to this base. Reduced to the simple arithmetical mean, the index number for 1900 is 100; that for 1917 is 112. It appears that while some prices have advanced and others have fallen, the general level of the commodities considered has risen 12 per cent. This rise of prices of 12 per cent indicates a decline in the value of money with respect to the commodities included in the table. It means that the purchasing power of the dollar in 1917 is 119, or 89 per cent of its purchasing power in 1900. In other words, a rise of 12 per cent in the general price level is equivalent to a fall of 11 per cent in the value of money. The general law may be expressed thus: Changes in the index number show direct variations in the general price level; changes in its reciprocal show variations in the value of money. If, instead of the five commodities used in the illustration, a table could be constructed including the prices of all commodities we should be able to derive index numbers which would register changes in the purchasing power of money. Most systems of price tables include a sufficiently large number of representative articles to show that though the prices of some articles may have declined while others have advanced, yet the general movement of prices has been in the direction indicated by the change in the index number.

The method of obtaining index numbers by the simple arithmetical average is open to the objection that it tends to exaggerate the influence of rising prices. Suppose, for example, that within a given period the price of a pȧrticular article has doubled while the price of another article has fallen by one-half. The index number after the change would be 125, indicating a decline of 80 per cent in the value of money, whereas it would appear that the value of money had not changed, since it had gained as much in the one case as it had lost in the other. To overcome this

defect various methods have been suggested in computing index numbers, as, for example, the geometric mean, which is the square root of the product of two prices, the cube root of the product of three commodity prices, and so on for any number of articles. Another method uses the median, in which price quotations for a given period are arranged in numerical order and the figure which has an equal number of quotations above and below it is taken as the mean. Still another method is based on the harmonic mean, which is computed from the reciprocals of a series of index numbers. These methods are intended to offset the effect on the index number of a very high or low price of a single article or a small number of articles. In general, however, these various methods yield substantially the same results.

The method of the arithmetical mean is open to the objection, also, that it gives equal importance to all articles included in the price tables, whereas we know that our family budgets are much more seriously affected by an increase of fifty per cent in the price of wheat or coal than by a similar increase in the price of cutlery or silks. To correct this defect a system has been devised of "weight. ing" the articles according to their relative importance as determined by total consumption or production. The results obtained, however, by the weighting of price tables, especially where these embrace a large number and a wide range of commodities, are not materially different. from those obtained by the simple or unweighted method. At best, price tables can only be approximate, indicating the general trend of prices.

48. Different types of price tables.-The most familiar price tables are those of Jevons, Palgrave, Sauerbeck, and the London Economist in England; Soetbeer and Conrad in Germany; and Falkner-Bureau of Labor, Dun's Review and Bradstreet's in the United States.1 One of the oldest

1 For a full statement of price tables, with diagrams and bibliography, see Laughlin: Principles of Money, Ch. VI; Bulletin of U. Š. Bureau of Labor Statistics, Whole Number 173, July, 1915.

and best known tables of index numbers is that published by the London Economist. Starting with the base period, 1845-1850, this price table has been published annually (except for 1852 and 1854–1856) down to the present. It includes only twenty-two articles and is based on the unweighted arithmetical principle. Adopting 100 as the average price of each of the twenty-two articles, the basic index number for 1845-1850 is 2,200 and the index number for succeeding years must be compared with that number rather than with 100, as in most other price tables. The Economist table is criticized on the grounds that, since it is based on a small number of articles, a large increase in the price of any one article causes an excessive change in the index number; and that the commodities are badly chosen, there being, out of the twenty-two, four in which cotton is the principal element.

Professor Jevons published his notable study of prices in 1863. He based his calculations upon the prices of thirty-nine articles during the period 1845-1850, and worked out index numbers on the geometric average for the period 1844-1862 to show the effect on prices of the new gold from California and Australia. Another wellknown table of English prices is that of Mr. Augustus Sauerbeck, published annually in the Journal of the Royal Statistical Society since 1886. He uses as the base line the average prices of the years 1867-1877 and computes his index numbers by a simple unweighted arithmetical average. The Sauerbeck index number is criticized because it includes only thirty-seven articles,1 and these are all staple raw products, such as wheat, coal and iron. The Soetbeer index number was made from the commodities entering the port of Hamburg and covered the period from 1847 to 1891. Soetbeer took the total quantity and price of each article and computed the average price on a simple arithmetical basis.

The most important table of American prices is that

1 The Sauerbeck index number as continued in the London Statist is based on 45 commodities.

prepared by Dr. Roland P. Falkner for the Senate Committee on Finance in 1893.1 In compiling this table ninety commodities were used for the period 1840-1891 and between 1860 and 1891 two hundred and twenty-three commodities were included. Prices for the year 1860 were selected as the base and by using the method of the arithmetical mean, tables were made both from weighted and unweighted prices. The principal groups included in the two hundred and twenty-three articles were: food, cloths and clothing, fuel and lighting, metals and implements, lumber and building materials, drugs and chemicals, house furnishing goods, and miscellaneous articles such as powder, rubber, soap and starch. To show the effect of price changes upon the working classes Dr. Falkner compiled price tables in which various articles were weighted according to their importance in the average family budget. It will be remembered that from 1862 to 1879 the standard money of this country was not gold, but the depreciated greenback. In order to show what the index number would have been if gold had been the actual standard, Falkner in his table reduced the greenback prices for the years 1862-1879 to the gold standard, using the premium on gold as the measure of the depreciation of paper money.1

The price tables of the Falkner Report extended only to 1891, but the Department of Labor subsequently issued a series of wholesale prices from 1890 to 1899. In 1902 that Department began a new series, based upon the period 1890-1899, which with some modifications has been continued by the Bureau of Labor Statistics. In 1914, however, the Bureau adopted a new computation, using as the base (100) for its index numbers the wholesale prices of the latest year. The Bureau explains that this change was made "for the purpose, first, of utilizing the latest and most trustworthy price quotations as the base from which price fluctuations are to be measured, and, second, to 1 Compare the second and third columns of the table on next page.

2 See Bureau of Labor Statistics (1915), Bulletin 181, p. 239.