index number

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index number in econometrics, a figure reflecting a change in value or quantity as compared with a standard or base. The base usually equals 100 and the index number is usually expressed as a percentage. For example, if a commodity cost twice as much in 1970 as it did in 1960, its index number would be 200 relative to 1960. Index numbers are used especially to compare business activity, the cost of living, and employment; one of the most influential indexes in the United States is the Consumer Price Index (see under cost of living ). Index numbers enable economists to reduce unwieldy business data into easily understood terms.

Bibliography: See R. Marris, Economic Arithmetic (1958).

index number A number used to represent the changes in a set of values between a base year and the present. If the index reflects fluctuations in a single variable, such as the price of a commodity, the index number can be calculated using the formula: 100 (p_n/p\0),
where p\0 represents the price in the base year and p_n represents the price in the current year. In practice many indices reflect variations in a combination of variables, such as the raw materials required to manufacture a product. In this situation it is necessary to produce an index that weights the important variables, e.g. labour costs. These are known as weighted aggregate indices. If both costs and quantities have varied over a period, it is further necessary to find a way of using the same quantities for the numerator and denominator of the index. When the calculation uses base-year quantities as the fixed point, the resultant index is a base-weighted (or Laspeyres') index, i.e.: 100(total cost of base year quantities at current prices/total cost of base year quantities at base year prices),
or 100(∑p_nq\0/∑p\0q\0),
where p represents the price and q represents the quantity. When the calculation uses current year quantities, it is known as a current-weighted (or Paasche's) index, i.e.: 100(total cost of current quantities at current prices/total cost of base year quantities at current prices),
or 100(∑p_nq_n/∑p\0q_n).
See also Financial Times Share Indexes; Retail Price Index.