This paper establishes a basis in economic theory for solving the problem of how to make comparisons of aggregate quantities and price levels across two or more geographic regions. Two new classes of relative purchasing power measures are set out and the dual relationships between them are explored. The first is a many-household analogue of the (single-household) cost-of-living index and, as such, is rooted in the theory of group cost-of-living indexes. The second is motivated by a generalization of the cost-of-living index and consists of sets of (nominal) expenditure-share deflators. A particular set of these deflators and the associated system of (real) consumption shares are shown to have definite bounds, and the latter is shown to provide rigorous exact index-number interpretations for a trio of axiomatic quantity indexes. Journal of Economic Literature Classification Numbers: C43, C81, F31, 018, 057.

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Keywords Economic approaches to index-number theory, Index numbers, Multilateral comparisons, Purchasing power parities
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Journal Journal of Economic Theory
Armstrong, K. (2001). Microeconomic foundations for the theory of international comparisons. Journal of Economic Theory, 101(2), 585–605. doi:10.1006/jeth.2000.2767