ch. i 4< ALTERNATIVE QUANTITY EQUATIONS 237

(3) Let V = the velocity of circulation of theCash-deposits, i.e. the ratio of thetotal volume of money paymentsto the total volume of Cash-deposits, and V' = the velocity ofcirculation of cash-facilities,

so that B = MVw = MV'w(l +w'), where B isthe total turnover of cash trans-actions.

Then we have

or

P 2 T = B = MVw = MV'w(l + w')

MV'

T

w(l + w').

This equation, like the Fisher Equation, is merelyan amplification of the statement that the total cashfacilities multiplied by their velocity of circulationequal the bank clearings.

Where there are no overdraft facilities andno savings - deposits, i.e. where iv = 1 and w' = 0,

equation (ii.) reduces to the form P 2

MVT ’

which is

identical with the Fisher equation.

Where there are no deposits and nothing but over-drafts, i.e. where M = 0, it reduces to the formM'V'

P 2 = — ip—, where M' is the volume of unused overdraft

facilities.

(iv.) The Relationship between the “ Cam-bridge ” and the “ Fisher ” Equations

We have seen in Chapter 6 (pp. 76-78) that therelative importance of different articles of exchange isnot necessarily the same in respect of the volume ofcheque transactions to which they give rise as inrespect of the balances which they cause to be held.