§ 3. General Meanings of p's and Q's

We may here pause to point out that the whole present discussion relates purely to the form of an index number of p's and Q's without reference to the meaning to be assigned to these p's and Q's. These meanings may be far wider than simply the prices and quantities in the equation of exchange. For example, an index number of prices may be constructed with reference to the purchasing power of a workman's wages. In this case, the same formula as before, Sp1Q1, may be employed, but the terms have different meanings. The p's now relate to the prices of goods entering into the workmen's budgets, and the Q's to the quantities of workmen's goods entering into their consumption. In this case, the price index, P, indicates the price level of workmen's consumption, and the index, T, means an index for workmen's real-wages. Any special form of price index now implies a correlative special form of real-wages index.

Again, if we are studying statistics of capital such as in Giffen's Growth of Capital, we have SpQ as the value of capital, the p's being the prices of different forms of capital and the Q's, their quantities. For every special form of price index number, P, representing the price level of capital, there will be a correlative special index of capital showing the real "growth of capital" as distinct from its mere money value. Such an index seems seldom to have been employed.Yet it is evidently advisable to distinguish between an apparent increase of capital due to inflated prices and a real increase, as would be shown by such an index as here suggested.

We see, therefore, that wherever prices and quantities are united, we have the requisite conditions for constructing correlative pairs of index numbers, one index in each pair relating to prices, and the other to quantities.

We shall, however, for convenience, continue to employ the magnitude T, rather than Q, and to refer to it as a "trade" index.