Mean Value Properties of the Weights of Linear Price Indices

Abstract

Often a price index is taken as a ratio of two price levels which are linear functions of prices. For calculating the nominator a linear function is applied to the vector of the current year prices and for calculating the denominator the same function is applied to the vector of the base year prices. Usually the weights (or coefficients) of such a linear level function are interpreted as a vector of quantities which represents the so-called basket of goods. Commonly one requires this basket of goods to be some average of the two baskets of goods, the one stated for the base year and the other stated for the current year. Obviously, this requires mean value properties for the weights of a linear price index. For example, such mean value properties are fulfilled for the well-known indices of Laspeyres and Paasche in a weak sense and for the indices of Edgeworth-Marshall and Walsh in a strict sense.