150

A TREATISE ON MONEY

BK. Ill

money, we can proceed as follows : Let M ls M 2 , andM 3 be the totals of the income-deposits, the business-deposits, and the savings-deposits respectively, and Mthat of the total deposits, so that M = M x + M 2 + M 3 .Therefore

Let w be the proportion of the cash - deposits tothe total deposits and Y the average velocity of thecash-deposits where V 3 and V 2 are the velocities of theincome-deposits and of the business-deposits respect-ively, so that

evidently bears a family relationship to ProfessorIrving Fisher ’s familiar equation

except that 0 represents current output whereas T isthe volume, not of output, but of transactions, andthat M l5 V x represent the income-deposits and theirvelocity, whereas M, V are the cash-deposits and theirvelocity. 1

1 We shall consider further Professor Fisher ’s type of Quantity Equationin Chapter 14.

■d Vj(M -M 2 -M 3 )0

Mi +M 2 =wM,

MjVj + M 2 V 2 = ic . M . Y ;

and

so that

The equation

then

w(V 2 -V)

M 1= M

V 2 -V :

wVi(V 2 -V)

M x Vi = M-

V s -V;

M wY t { y 2 - Y)

V a -V,

P. 0=M 1 V 1

P . T = M . V,