A Note on the Interpretation of Index Numbers

Given that the p's refer to market prices, and the q's to the aggregate quantities of the different goods, what does the formula Zp2q2 7/ Ep2q tell us ? On the above assumptions, as Mr. Hicks has shown,2 it tells us that no redistribution of the goods consumed in the first period could have sufficed to make everyone as 'well off' then, as they in fact were in the second period. (More precisely, Zp2q2 ,7/ 'p2q implies that, given every 'individual's' second period consumption, the distribution of the quantities of the first period could conceivably have been such that the formula Zp2q2 ,/ Zp2q would have held for every 'individual '-or it is inconceivable that it should have been such that ZpPq2< Zp2ql for every ' individual '.) Mr. Hicks considered that this fact sufficed for one to say that real social income had increased. In the article cited, and for the reasons given, I found cause to reject this criterion

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