Monotonicity in price relatives: A price index paradox

Abstract

A new axiom for price indexes is proposed, referred to here as monotonicity in price relatives. This axiom requires that if prices of all goods and services rise more in country A than in country B, then the price index for A must exceed that for B. Although monotonicity in price relatives seems fundamental, all the main weighted price index formulae (including all known superlatives) and even some elementary price indexes violate it. The implications of this somewhat paradoxical finding for the index number literature are explored. It is shown that violation of monotonicity in price relatives is only a concern for elementary price indexes, thus strengthening the case for Jevons over Dutot, since the latter violates this axiom.