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The chapter reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer's cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences, and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

The theoretical base for cost‐of‐living comparisons between geographical areas is examined and developed. The interpretation of bilateral comparisons is discussed within a framework of a matrix of cost‐of‐living comparisons with all countries being listed in both columns and rows. The use of multilateral comparisons is questioned.