Price Indices Depending only on Prices
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In this section, we only consider price indices which depend on the prices of a ‘base year’ and a ‘comparison year’, respectively. For technical reasons, we further assume that the domain of definitionof all price indices is always restricted to the positive orthant, i.e., only positive components of the various vectors are admitted. This requirement is especially necessary for price indices which depend on both prices and quantities, since even classical price indices such as Laspeyres’ or Paasche’s index (see (3.1.7), (3.1.8)) cannot properly be defined for certain points of the non-negative orthant. This restriction can be eased by imposing a condition stating the behavior of a price index as any scalar argument (price or quantity of a commodity) tends to zero. This condition is introduced in section 3.2 (see the Determinateness Test (3.2.3)).
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