CH. 15 INCENTIVES TO LIQUIDITY 201

by changing Y and therefore M1 . The division of theincrement of cash between M1 and M2 in the newposition of equilibrium will depend on the responsesof investment to a reduction in the rate of interest andof income to an increase in investment.1 Since Y partlydepends on r, it follows that a given change in Mhas to cause a sufficient change in r for the resultantchanges in M1 and M2 respectively to add up to thegiven change in M.

(ii) It is not always made clear whether the income-velocity of money is defined as the ratio of Y to M oras the ratio of Y to M1 . I propose, however, to takeit in the latter sense. Thus if V is the income-velocityof money, L1(Y) = Y/V = M1.

There is, of course, no reason for supposing that V isconstant. Its value will depend on the character ofbanking and industrial organisation, on social habits,on the distribution of income between different classesand on the effective cost of holding idle cash. Never-theless, if we have a short period of time in view andcan safely assume no material change in any of thesefactors, we can treat V as nearly enough constant.

(iii) Finally there is the question of the relationbetween M2 and r. We have seen in Chapter 13 thatuncertainty as to the future course of the rate of interestis the sole intelligible explanation of the type ofliquidity-preference L2 which leads to the holding ofcash M2 . It follows that a given M2 will not have adefinite quantitative relation to a given rate of interestof r \—what matters is not the absolute level of r but thedegree of its divergence from what is considered afairly safe level of r, having regard to those calculationsof probability which are being relied on. Never-theless, there are two reasons for expecting that, in

1 We must postpone to Book V. the question of what will determine thecharacter of the new equilibrium.