Jointly consistent price and quantity comparisons and the geo-logarithmic family of price indexes’’,

This paper addresses the issue of decomposing the value index into the product of a price and a quantity index, both satisfying proportionality, commensurability and homogeneity axioms. In fact, classical index number theory deals primarily with axiomatic properties of price indexes, irrespective of the properties of the implied implicit quantity index (the cofactor). Unfortunately, cofactors of axiomatically compliant price indexes need not satisfy even essential axioms, like proportionality. As a result, just focusing on axiomatic properties of price indexes may result in inconsistent value index decompositions. The paper shows that a sufficient condition for proportionality, commensurability and homogeneity of both the price index and its cofactor is that the price index belongs to a parametric class known as geo-logarithmic family. Some properties of this family are discussed and original results pertaining to monotonicity are also provided. Finally, a way to extend the geo-logarithmic family is proposed.