The price level is calculated and estimated in terms of an index number, which is some form of average of prices of representative commodities. When the price level rises or falls the prices of all commodities do not rise or fall together or in the same degree or direction. The index number is simply an average of prices, or of the percentages of increase or decrease of prices, of a selected list of commodities.

In the preparation of index numbers there are many considerations which vitally affect their usefulness, among which are the following:

1. The Prices Used. What prices should be used is governed by the purposes to which the index number is devoted. If the index is to be used over a broad area, the prices should be those prevailing in a central, organized, competitive market. If the price movement in a limited locality is to be studied only prices obtaining in that locality should be used.

Wholesale prices fluctuate more widely and are more quickly responsive to changes in supply and demand than retail prices. An index number based upon wholesale prices is therefore a better barometer of business conditions for manufacturers, jobbers, large credit-grantors, and the like, but an index number based upon retail prices measures better the changes in the cost of living and the proper adjustment of wages thereto. In any case, the average price for the day, week, or month is better for purposes of comparison than the prices on the market at a certain instant.

2. The Commodities Used. As it is impossible to include all commodities in the preparation of an index number, only the principal ones are 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 particullar 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 according 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 arithmetical" 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 approximately 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:

Index Numbers Table