I have occasionally seen some confusion between money velocity and the Keynesian multiplier. The basic formula of the quantity theory of money, from which money velocity comes is:
M x V = P x Y
M is defined as the money supply, which can be expressed in different terms, like MB (monetary base), M1 or M2. Usually either M1 or M2 are used. P is the "price level" and Y is real output and both together are equivalent to Nominal Gross Domestic Product. V, money velocity is equivalent to Nominal Gross Domestic Product divided by the quantity of money.
The Keynesian multiplier is derived from an equation which shows the progression of expenditures, as follows:
ΔY = ΔC + c1∙ΔC + . . . + cn∙ΔC
What this indicates is that an initial change in consumption of (C) will cause additional spending of, for example, 100 in the first round of expenditures, if c, which is the marginal rate of consumption, is 0.5 (which would mean an additional dollar in income would lead to an additional $0.50 in expenditures), then by the second round of consumption, total expenditures would have increased by another 50, and by the third round another 25, until the total change in expenditures reaches a cumulative ΔY, which, in this case, would be 200. The expression above can be simplified to give a multiplier of
In a simple Keynesian formula of aggregate demand in a closed economy, aggregate demand is given by the equation:
Y = C + I + G
In this simple model, m can be multiplied by any change in the components of aggregate demand to give the total change to expenditures. In any case, it is very clear that the Keynesian multiplier is a very different thing from money velocity. Money velocity is about how many times a unit of currency is spent on average, while the Keynesian multiplier is about how a change in a component of aggregate demand affects total expenditure. Further caution must also be employed because what I have set out above is does not account for taxes or imports (although a modification does). Additionally, "the" multiplier is generally not the same for all types of consumption. I might also add that this does not account for the complexity inherent even in the IS/LM model, where the effective multiplier (so we might call it) is affected by the elasticity of the IS and LM curves.
I discussed some of the issues with the multiplier, more briefly, in the post Fiscal policy in the states, although I touched on it from a different perspective.