238

A TREATISE ON MONEY

BK. Ill

That is to say, the Cash-balances Price-level, whichwe have designated P 1} is not identical with the Cash-transactions Price-level, which we have designated P 2 .This is evident when we remember that the date andthe amount of some types of cheque transactions canbe foreseen or can be provided against more accuratelythan others, so that of two cheque transactions ofequal amount one may have led to a greater amount (intime multiplied by quantity) of anticipatory holding ofcash-balances than the other. Furthermore the pricequotations appropriate to the former index are notthe same as those appropriate to the latter, inasmuchas the price-quotations which affect the face-value ofthe cheques being cleared at any time relate on theaverage to an earlier date than the price-quotationswhich affect the amount of cash-balances required tobe held. This point is particularly important whenprices are changing. Thus when prices are falling,the proportion P x to P 2 will be lowered. Understable conditions, however, the proportion will be amore or less constant one.

Now Quantity Equations of the “ Cambridge ”type lead up, as we have seen, to the Cash-balancesPrice-level, whilst Equations of the “ Fisher ” typelead up to the Cash-transactions Price-level. Thusthe relationship between the two types of Equation isthe same as between the two Price-levels.

Let us write P x = P 2 . /; so that we have

P M ,_MY rPi = Q -Pa •/- qi .W.f.

Thus if we define the Price -level by reference to thequantity of money in demand, rather than by referenceto the quantity of money turnover or cash-transactions(as Professor Irving Fisher has done), we have to intro-duce this additional element /, representing the pro-portion of Pj to P 2 , into the final result of the “ Fisher ”Equation. It is particularly important not to over-