High-powered money is the sum of commercial bank reserves and currency (notes and coins) held by the public. High-powered money is the base for the expansion of bank deposits and the creation of the money supply. The supply of money varies directly with changes in the monetary base, and inversely with the currency and reserve ratios.
The use of high-powered money consists of the demand of commercial banks for the legal limit or required reserves with the central bank and excess reserves and the demand of the public for currency. Thus high-powered money:
Where, C represents currency, RR the required reserves and ER the excess reserves.
A commercial bank's required reserves depend upon its deposits. But a bank usually holds reserves in excess of its required reserves. In fact, banks do not advance loans up to the legal limits but precisely less than that. This is to meet unanticipated cash withdrawals or adverse clearing balances. Hence the deed arises for maintaining excess reserves by them. The money supply is thus determined by the required reserve ratio and the excess reserve ratio of commercial banks. The required reserve ratio (RRr) is the ratio of required reserves to deposits (RR/D), and the excess reserve ratio (ERr) is the ratio of excess reserves to deposits (ER/D).
Currency held by the public is another component of high-powered money. The demand for currency by the public is expressed as a proportion of bank deposits. Thus the currency ratio Cr=C/D, where C is the currency and D is the deposits. The currency ratio is influenced by such factors as changes in income levels of the people, the use of credit instruments by the public, and uncertainties in economic activity.
The formal relation between the money supply and high-powered money can be stated in the form of equations as under:
The money supply (M) consists of deposits of commercial banks (D) and currency (C) held by the public. Thus the supply of money
High-powered money (H) (or monetary base) consists of currency held by the public (C) plus required reserves (RR) and excess reserves of commercial banks. Thus high-powered money
The relation between M and H can be expressed as the ratio of M to H. So divide equation (1) by (2):
Dividing the numerator and denominator of the right-hand side of equation (3) by D:
By substituting Cr for C/D, RRr for RR/D, and ERr for ER/D. equation (4) becomes
Thus, high-powered money:
And money supply:
Equation (7) defines money supply in terms of high-powered money. It expresses the money supply in terms of four determinants, H, Cr, RRr and ERr. The equation states that the higher the supply of high powered money, the higher the money supply. Further, the lower the currency ratio (Cr), the reserve ratio (RRr), and the excess reserve ratio (ERr) the higher the money supply, and vice versa.
The relation between the money supply and high-powered money is illustrated in the figure. The horizontal curve 
shows the given supply of high powered money. The curve 
shows the demand for high-powered money associated with each level of money supply and represents equation (6). The slope of the curve is equal to the term 
. Given Cr, RRr and ERr and the high-powered money , the equilibrium money supply is 
. If the money supply is larger than this, say 
, there will be excess demand for high-powered money. On the contrary, a less than money supply will mean less demand for high-powered money.
If there is an increase in any one of the ratios Cr or RRr or ERr, there would be an increase in the demand for high-powered money. This is shown by the 
curve in the figure where the increase in the demand for high-powered money leads to a decline in the money supply to 
.
The quotient 
is the money multiplier 
. Thus
Now the relation between the money supply and high-powered money of equation (7) becomes
Equation (9) expresses the money supply as a function of m and H. In other words, the money supply M is determined by high powered money (H) and the money multiplier (m). The size of the money multiplier is determined by the currency ratio (Cr) of the public, the required reserve ratio (RRr) at the Central bank, and the excess reserve ratio (ERr) of commercial banks. The lower these ratios are, the larger the money multiplier is. If m is fairly stable, the central bank can manipulate the money supply (M) by manipulating H. The central bank can do so by open market operations. But the stability of m depends upon the stability of the currency ratio and the reserve ratios RRr and ERr. Or, it depends upon off-setting changes in RRr and ERr ratios. Since these ratios and currency with the public are liable to change, the money multiplier is quite volatile in the short run. Given the division of high-powered money between currency held by the public, the required reserves at the central bank, and the excess reserves of commercial banks, the money supply varies inversely with Cr, RRr and ERr. But the supply of money varies directly with changes in the high-powered money.
Additional notes:
The supply of money varies directly with changes in the high-powered money:
This is shown in the figure.
An increase in the supply of high-powered money by 
shifts the curve upward to 
. At E, the demand and supply of high-powered money is in equilibrium and the money supply is . With the increase in the supply of high-powered money to , the supply of money also increases to at the new equilibrium point 
. Further, the figure reveals the operation of the money multiplier. With the increase in the high-powered money by , the money supply increases by 
. An increase in high-powered money by Re 1 increases by a multiple of Re 1.
Reading List:
1. Jhingan, M.L. (2012), Micro Economic theory (12th edition). Vrinda Publications Pvt. Ltd, Delhi.
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