Concepts and measures of money supply relate to the supply of ordinary money (M), referring to money, as people generally understand it. Monetarists often distinguish it from what they call the high-powered money (H) while discussing the theories of money supply.
According to them, the single-most factor determining money supply is the high-powered money (H), defined as money produced by the central bank and the government and held by the public and the banks. It consists of
(i) Currency, C, including coins and notes in circulation with the public;
(ii) Cash reserves, R, held by commercial banks as vault cash;
(iii) Other Deposits, OD, of the central bank High-power money (H) can thus be expressed as
Money supply is thus directly proportional to the high-powered money, H. Differentiating the expression for M with respect to H, we have (dM/dH) = m, defined as the ratio of increase in money supply (M) per unit increase in high-powered money (H) and known as the money multiplier.
In short run analysis, TD may be treated as insignificant. Expression for money supply can now be expressed as
M = (1 + c) / (c + r) × H
Expression for money multiplier would then change to
dM / dH = m = (1 + c) / (c + r)
In either case, when increase in H is not infinitesimally small, increase in M may be given as
∆M = (m) × ∆H
This shows that change in money supply (∆M) is directly proportional to the change in high-powered money (∆H).
Inferences drawn from Equations 7.13 and 7.14 support the statement that high- powered money (H) is the single-most determinant of money supply (M), given c, r and t. It is for this reason that high-powered money (H) is at times called the money base.
Equilibrium of the market of high-powered money refers to equilibrium of demand and supply of high-powered money.
At a given stock of high-powered money, its supply,
Hs = H
In the same way, demand for high-powered money can be expressed as
HD = CD + Rd
HD can thus be obtained by vertical summation of CD and RD, where CD and RD represent demands for currency and cash reserves. Fig. 7.1 demonstrates the equilibrium of the H-market.
To demonstrate the money multiplier process, let us have an illustration.
Government purchases goods and services from public worth Rs. 90.00 crores. Currency-deposit ratio is 0.50 and reserve-deposit ration is 0.10. Determine deposit and money multipliers and hence calculate the additional volumes of deposits and money created in consequence of an increase in high-powered money by Rs. 90.00 crores.
The mechanism can also be explained without the use of the formulae developed above.
As soon as public receives the cheque of Rs. 90.00 crores from government for goods and services sold by it and deposits the same with its bank, the cheque is sent for collection by the bank.
The amount becomes available to the public in a few days’ time. Currency deposit ratio being 0.50, public divides the amount between currency held and deposit made in such a way that 50% of the deposit forms the currency withdrawn by the public. As result, C = 30 crores and D = 60 crores so that C/D = 1/2. Thus bank deposits increase by Rs. 60 crores in consequence.
As soon as the bank of deposit comes to know of it, reserve-deposit ratio being 0.10, it holds 10% of the deposit (Rs. 6.00 crores) as vault cash and lends out the rest (Rs. 54.00 crores) to borrowers, who in turn split it between cash held and deposit made in the ratio 1:2. That is, the borrowers withdraw Rs. 18 crores leaving Rs. 36 crores by way of deposits with the bank.
In the next round, the bank holds back 10% of the new deposits, that is, Rs. 3.60 crores as vault cash and lends out the remainder, that is, Rs. 32.40 crores to the borrowers. The borrowers divide Rs. 32.40 between cash held and deposits made in the ratio of 1:2 as C/D = 0.50. As a result, they withdraw Rs. 10.80 crores and leave the rest, Rs. 21.60 crores as deposits with the bank.
The process continues indefinitely until nothing is left with the bank to lend. Deposits in respective rounds increase by Rs. 60, 36, 21.60, …crores while currency held by public increases by Rs. 30, 18, 10.80, …crores and that held as vault cash by the bank increases by Rs. 6.00, 3.60, 2.16, … crores.
Total additional deposits work out at Rs. 150.00 crores and total additional currency held by the public and the bank works out at Rs. 75.00 crores. Addition money pumped into the economy increases by Rs. 225.00 crores.