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Rh by the total sum spent on them in a period or some other criterion, and each price ratio is multiplied by the corresponding factor, the sum of the products is divided by the sum of the factors and the resulting quotient is the index number of wholesale prices for that year; or the more important commodities are represented by two or more price quotations and the resulting price ratios are simply averaged to obtain the index number. There are many variants of method and there has been much controversy on every detail of the process; in fact, however, the precision of the result depends not to any great extent on the particular method followed, but principally on (i.) the number of independent prices included and (ii.) on the dispersion of the various price ratios in the year to which the index number refers, so that when prices are moving on the whole in the same proportion the index number is more accurate than when some are moving rapidly upwards and others are stationary or falling. In normal times when changes are moderate it has been shown both from theoretical considerations and by comparing the numbers obtained by various methods that the precision of the method is high, but during the war period the movements were rapid and unequal, the conditions of accuracy were lost and no very precise measurement could be obtained. The object of the method of index numbers is to average away the variations due to the special conditions of supply and demand of particular commodities, and to obtain a resultant which measures the effect on prices of general causes, such as the supply of currency.

It is found in practice that the necessity for restricting price quotations to those of commodities for which the same grade and quality is in the market in large quantities through a long period of years restricts the choice greatly, and limits it to raw materials or articles in an elementary state of manufacture. In some cases the price used is based on the average value of all grades of the commodities (e.g. of wheat, of tea, of coal), imported or exported, but this introduces a possibility of error since the average may change owing to a change in the relative quantities of high and low grades independently of any change in price. The three index numbers of wholesale prices in use in the United Kingdom are the Board of Trade's, the Economist's, and the Statist's (formerly Sauerbeck's); the first uses average values to some extent and applies factors to the price ratios to allow for the relative importance of commodities, the second and third use market quotations of definite qualities of goods and take a simple average of the price ratios.

Table I. exhibits the general movement in the twelve years before the World War, and shows how little the variation of method affects the result in this period. The year 1903 is taken as the starting point, since it is after the great fall of prices ending in 1896 and the subsequent rise and the inflation of 1900-1, and may be regarded as a normal year.

Sauerbeck's index numbers for 1903 on the same basis for separate groups of commodities were:—Vegetable food 90; animal food 85; sugar, tea, coffee, 86; minerals 74; textiles 79; sundry materials 83. Wholesale prices had therefore been rising from 1902-13 (with a short inflation and depression in 1906-8), but tended downwards in the first half of 1914.

Immediately after the declaration of war in 1914 prices began to rise, and with certain interruptions continued to mount up till the spring of 1920, when the index numbers reached their maximum (Statist 323, end of April; Economist 326, end of March; Board of Trade 357, average of July). Till Oct. 1917 the increases showed a remarkable regularity averaging 2% monthly, equivalent cumulatively to 27% per annum; on this scale the index in the successive Octobers would reach in 1914 106, in 1915 135, in 1916 171, in 1917 217 and in 1918 258, numbers which (except the last) are in close agreement with those shown in the table. This was, however, a definite seasonal movement superimposed on this regularity; in the first three or four months of each year prices moved up with special rapidity, while in the summer the increase was slackened and in some cases was replaced by a fall. The check in the increase in the summer of 1917, following a specially rapid rise, is attributable to the control of prices which by that date was general. From Aug. 1917 prices continued to rise in spite of control till Sept. 1918, but the rise in these 13 months aggregated to only 13% (239 against 213). After the Armistice prices fell slowly for five months, during the season in which in previous years the increase had been specially rapid, but expectations of a permanent fall were not realized; in the year beginning April 1919 the index rose from 224 to 323 or 44%.

From the beginning of the war till July 1919 the Statist and Economist index numbers are in close agreement, except that the Economist shows a more rapid rise for twelve months from Oct. 1916 and less increase in the late autumn of 1917, but there is disagreement as to the dates and amount of the increase after July 1919. At that date the three index numbers agree in estimating the whole increase in five years at 148, 149 or 150%. The following table shows the divergence in subsequent months:—

The earlier agreement is more remarkable than the later discrepancies, for the conditions of accuracy named above were not present during the war when prices were moving rapidly and quotations for the usual qualities of goods were often