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Invariance Axioms and Economic Indexes

Marcel K. Richter

Abstract

Our main objective is to demonstrate that there is only one "nice" way to measure technological change. Along the way, the unique "nice" measures of several other economic variables will be 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. 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.