Axiomatic properties of geo-logarithmic price indexes

The geo-logarithmic family of price indexes constitutes an interesting parametric class of index numbers for price comparison, due to the properties satisfied by its members, together with their cofactors. The family was introduced in the early ’90s, as a generalization of the Sato-Vartia price index, but a consistent study of its properties still lacks. The present paper aims at filling this gap. It contains both a review of already existing material, arranged in an original and consistent way, and a comprehensive treatment of the axiomatic properties of the geo-logarithmic family. New results are derived and some mistakes that can be found in other references are also fixed. The paper ends discussing some open issues, needing further research.