2. The Commodities Used. As it is impossible to include all commodities in the preparation of an index number, only the principal ones arc used; but the more the better, for the index is then the more representative. If, for example, the index is to be used to determine the variations in the cost of living for a particu lar class of workmen, the commodities used should be those that compose his budget. A wider use requires a larger and more general list of goods.
3. The Base Prices Used. Care is necessary lest the base year be a year of exceptionally high or low prices, and the percentage of increase or decrease be thereby vitiated. To overcome this danger, it is best to use as the base the average prices for a decade; the Sauerbeck index number, for instance, uses the average prices for the decade 1858-1867.
4. The Kind of Average Used. Of the common methods of averaging a series of numbers the following four may be noted: (a) One method is to arrange the numbers in a series accord ing to their magnitude and choose the middle figure, which is called the "median." It is the easiest of all methods to calculate and does not attach undue importance to very high and very low numbers; on the other hand, it pairs numbers regardless of the relative quantities sold at the respective prices.
(b) A second method, the "geometrical" average, is to take the nth root of the product of the n prices or of the prices of n commodities, n signifying any given number. The chief criticism of this is the difficulty of its calculation, as it requires the use of logarithms.
(c) A still more awkward average to calculate is the "simple harmonical" average, which is the reciprocal of the sum of the reciprocals of the prices.
(d) By far the most common average is the "simple arith metical" average which is the quotient of the sum of n prices divided by n. To make the average more exact the prices are "weighted" by using as the multiplier numbers which indicate the relative quantities of the commodities sold at the respective prices, and the sum of these products is then divided by the sum of the weights. This "weighted arithmetical average" is quite generally used and it has the advantage of being fairly easy to calculate.
Another common form of index number is to state the sum of values of the same quantities of goods at their respective prices prevailing at different dates.
Whatever form of average is used, the results are approxi mately the same; exactitude is not expected, for the numbers are , but indexes of price changes.
Useful index numbers are those of the London Economist, Sauerbeck, Dun, Bradstreet, Gibson, the United States Bureau of Labor Statistics, the Canadian Department of Labor, and the Annalist. The following table gives some of these numbers for recent years: Inflation and Its Effects According to the quantity theory of money, most exactly stated in Professor Fisher's "equation of exchange," an increase in money and bank credit beyond the needs of trade at a given price level tends to raise that price level. Such is the common concep tion of inflation. The equal and simultaneous movements of total purchasing power and trade would result in a stable price level. Total purchasing power has been shown to be the sum of two products, namely, the quantity of money in circulation multiplied by its efficiency (or velocity of circulation) and the quantity of bank deposits multiplied by their efficiency. If this total purchasing power remains the same but the quantity of trade declines, there will be inflation. If the quantity of trade remains the same, then inflation may be caused by increases in the quantity of money or of bank credit, or in their efficiencies. There can be gold inflation as well as paper money inflation or bank credit inflation.
It is quite impossible to determine the actual volume of goods that enter into trade during a certain period in a complex coun try like ours. The relative increase or decrease may, however, be approximated from certain indexes. The best barometers of trade, measured in physical units and not in dollars of value, are the production of the basic materials, such as coal, iron, petroleum, copper, silver, the production of agricultural commodities, the tonnage of the railroads, the tonnage of vessels entered and cleared at lake ports and seaports, the number of building permits, and the number of shares traded on the stock exchanges.