Index Number Theory Using Differences Rather Than Ratios

Abstract

A bstract Traditional index number theory decomposes a value ratio into the product of a price index times a quantity index. The price (quantity) index is interpreted as an aggregate price (quantity) ratio. The present paper takes an alternative approach to index number theory, started by Bennet and Montgomery in the 1920s, which decomposes a value difference into the sum of a price difference plus a quantity difference. Axiomatic and economic approaches to this alternative branch of index theory are considered in the present paper. The analysis presented has some relevance to accounting theory in which revenue, cost, or profit changes need to be decomposed into price quantity components or where standard or budgeted performance is compared with actual performance (variance analysis). The methodology presented in the paper is also relevant for consumer surplus analysis.