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/p₀), where p₀ represents the price in the base year and p₀ 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_nq₀/∑p₀q₀), 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-∑p₀q_n). See also Financial Times Share Indexes; Retail Price Index