With the development of national accounts the QTM equation has been as follows:
M.V = P.Q ..... (i)
M is the total amount of money in circulation;
V is the velocity of circulation or the average frequency across all transactions in final expenditures.
P is the price level associated with transactions in the period under consideration;
Q is an index of the real value of final expenditures.
The economists Marshall, Pigou & Keynes, all associated with Cambridge University, reasoned that the application of money was more significant than the supply, in that a certain proportion of nominal income (designated as k in the short run) is not be used for transactions but it will be saved or held as cash. So the so-called Cambridge equation is as follows:
M = k . P. Y ..... (ii)
P is the price level
Y real income
k is savings
The problem with this equation or identity is that it is wrong in the sense that savings are not a multiplier2
but rather a component of the money supply that is not circulating and therefore this should be added to the remaining P.Y quantity as follows:
M = k + (P.Y) ..... (iii)
However, the economists involved considered wealth to have some influence, but unfortunately and for simplicity's sake, this element was omitted from the widely circulating QTM identity.
The last decade has shown that these economsts were correct, but at that time, based on experience, the wealth or asset class were generally not considered to be a significant determinant in the QTM. Adding wealth in the form of assets
In the shadow of the evidence generated following a decade of quantitative easing (QE) has demonstrated that it is important to add to the equation assets as well as savings in order to reflect the effect of the diversion of the flow of monetary expansion into assets. This is not a theoretical notion, it is what has happened. Thus designating "a" as asset holdings, that is, money not circulating but invested in assets such as land, shares and stocks, both the Cambridge equation and the QTM need tobe substituted by a more realistic identity, herein referred to as the the Real Money Theory (RMT)
which takes the following form:M = (a + k) + (P.Y) ..... (iv)
P is the price level and Y real income, a is assets and k is savings. Under QE k is virtually zero as a result of close-to-zero interest rates.
As "k" (savings and cash) has been driven down by QE to close to zero, real incomes and prices (P and Y) fall to the degree that "a" (asset holdings) increase. This is exactly what QE has accomplished. As can be seen that the QTM equation (i) as applied has little relationship to reality, it is flawed as is the Cambridge equation in its application of the wrong operator to savings (multiplication instead of addition).
To see this in graphic form see "The outcome of quantitative easing on real incomes - summary note"
if k is a savings rate the and then expressed as (1-k) where k is a percentage decimal then the Cambridge equation would make more sense but then this loses the absolute value of savings from the identity. This is important in policy terms and even more important when the signifiant impact of monetary flows into assets, as experienced under QE, need to be taken into account.