Invariance Axioms and Economic Indexes

Abstract

exhibited. We present axiom systems for indexes of several economic variables: inputs, outputs, prices, wages, inflation, and technological change. In addition to conventional smoothness and proportionality conditions, in each case an Invariance Axiom is proposed. For technological change this says, in a sense, that when there is no technological change there is no change in the index. One can prove that in each case there is a unique index satisfying the axioms, and this is a Divisia index.2 Since these continuous indexes are not generally independent of the path, the problem of how often to change index weights may be viewed in the light of a choice between invariance and independence. We show that the unique invariant measure of technological change is a natural generalization of Solow's measure to the case of many commodity types.

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