The equation for aggregate demand in the Keynesian system is as follows: C + I +(G-T) +(X-M) = D (Aggregate demand).C is consumption,I is investment, G is government expenditures, T is taxes, X is exports, and M is imports. Note that the equation does not specify the rate of interest that prevails nor the the ratio of monetized debt in relation to the broadly defined money stock M2B. This is because aggregate demand is usually thought of in the context of fiscal policy whereas the bank rate and debt monetization are part of monetary policy. But in fact the the two are both integral in shaping the macro-economic environment. Other things being equal it matters what interest rates prevail and therefore how much treasury debt in comparison to the broadly defined money stock the central bank is holding. The values for I and C will be partly functions of these variables. So these equations are actually at a specific interest rate and a specific tax regime and a specific value for central bank holding of debt.
On the other side of the argument the monetarist school which is best identified with Milton Friedman who taught at the University of Chicago relies on a variant of the classical quantity theory of money. That is MV = PO where M is the money stock. V is the velocity of money in other words how many times the money stock circulates in a given time period P the price level and O the level of output. Because monetarists believe that the income velocity of money or the transactions velocity of money tends to be predictable and not vary much it can be treated as a constant. They also believe in Say’s law of markets that supply creates its own demand and hence involuntary unemployment is not possible since markets always clear hence O is always at the full employment level. In such circumstances they argue that changes in the money stock affect prices. Hence their concern with controlling the growth of the money stock over time to target low inflation. The Keynesian school denies this argument arguing Says law does not hold, involuntary unemployment is very possible and the velocity of money can vary and that there is a real demand in certain circumstances for cash balances.
Modern monetarism from Friedman forward have attempted to integrate the quantity theory with Keynesian demand for money notions.Individuals hold their wealth in different forms according to Binhammer in his text on Money, Banking and the Canadian Financial system.These forms are: money; bonds and other interest bearing financial assets;equities;physical capital such as houses, automobiles; and human capital.The demand for money can be expressed as follows (Binhammer, p412)
Md/P = f(Yp, rm, rb, re (dP/P), h, u) where Md/P is the real demand for money, Yp is permanent income, rm is money’s own rate of return, rb is the rate of return from bonds and other fixed income financial assets, re the return from equities including dividends and capital gains, dP/P the expected rate of inflation, h the ratio of human wealth to total wealth, and u is tastes and preferences. Permanent income is defined as the average level of income expected to prevail over a long period of time. (Binhammer p412)
Monetarists like Friedman believe that the nominal demand for money is directly proportional to the price level and controversially that the data support his argument.