The price index, a pervasive long established institution for economics, is a number issued by the Statistical Office that should tell anyone the ratio of costs of maintaining a given standard of living in two periods where prices differ. For a chain of three periods, the product of the ratios for successive pairs must coincide with the ratio for the endpoints. This is the chain consistency required of price indices. A usual supposition is that the index is determined by a formula involving price and quantity data for the two reference periods, as with the one or two hundred in the collection of Irving Fisher, joined with the question of which one to choose and the perplexity that chain consistency is not obtained with any. Hence finally they should all be abandoned. This situation reflects ‘The Index Number Problem’. Now with any number of periods consistent prices indices are all computed together to make a resolution of the ‘Problem’, proved unique and hence never to be joined by others to make a Fisher-like proliferation
