The Index Number Problem
Sydney N. Afriat · Oxford University Press eBooks · 2014
A theft amounting to £1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since £1 was no longer what it was. Such association of money with a date is well recognized for its importance in very many connections. Thus arises the need to know how to convert an amount at one date into the right amount at another date. In other words, a price index. The longstanding question concerning how such an index should be constructed is known as ‘The Index Number Problem’. The ordinary consumer price index or CPI represents a practical response to the need. The truth of a price index is an issue giving rise to extensive thought and theory to which an impressive number of economists have each contributed. However, there have been hold-ups at a basic level. The approach brings the subject into involvement with constructions on the basis of finite data, in particular of price indices, and of utility, already well known in a form usually referred to as ‘Afriat's Theorem’. But utility is subject to constant returns, also possibly approximate. Despite a general importance for economic life and decades of outstanding professional attention, there had been no resolution of the Index Number Problem, nor had there been a real idea what could be meant by such a resolution. However, the method now proposed does convey what could be meant, and it undoubtedly represents the resolution.