The money supply is determined not only by Bank of Canada policy, but also by the
behaviour of households that hold money and of banks in which money is held.
Money Supply = Currency + Deposits ... M = C + D
To understand money supply, we must understand the interaction between currency and
deposits and how Bank of Canada policy influences these two components of money
100-percent-reserve banking: the deposits that banks have received but have not lent out
are called reserves. Some reserves are held in the vaults of local banks throughout the
country, but most are held at a central bank such as the Bank of Canada. 100-percent-
reserve banking means that all bank deposits are held as reserves: banks simply accept
deposits, place the money in reserve, and leave the money there until the depositor makes
a withdrawal or writes a cheque against the balance. If banks hold 100 percent of
deposits in reserve, the banking system does not affect the supply of money.
Fractional-reserve banking: now imagine banks start to use some of their deposits to
make loans. The banks must keep some reserves on hand so that reserves are available
whenever depositors want to make withdrawals, but as long as new deposits equals the
amount of withdrawals, a bank need not keep all its deposits in reserve. Fractional-
reserve banking means that banks keep only a fraction of their deposits in reserve. The
reserve-deposit ratio is the fraction of deposits kept in reserve. After a loan is made with
the fraction of deposits not kept in reserve, the money supply has increased by the
amount that the bank loaned out. Thus, in a system of fractional-reserve banking, banks
The person who received the loan goes and deposits the money in their bank, and that
bank loans out a fraction of that deposit, and so on and so forth. With each new deposit
and loan, more money is created. Letting rr denote the reserve-deposit ratio: Total
Money Supply = (1/rr) x Original Deposit. Banks’ ability to create money separates
them from other financial institutions. Financial markets serve the purpose of financial
intermediation; they transfer funds from savers to borrowers. Financial intermediaries
include the stock market, the bond market, mortgage loan companies, credit unions, and
the banking system. Note that the creation of money by the banking system increases the
economy’s liquidity, not its wealth, since borrowers are undertaking a debt obligation to
the bank, so the loan does not make them wealthier.
A model of the money supply under fractional reserve banking
The model has three exogenous variables:
The monetary base (B) is the total number of dollars held by the public as currency C
and by banks as reserves R. It can be directly controlled by the Bank of Canada.
The reserve-deposit ratio rr is the fraction of deposits that banks hold in reserve. It is
determined by the business policies of banks, and used to be regulated by law in the past.
It is R/D, reserves/deposits.
The currency-deposit ratio cr is the amount of currency C people hold as a fraction of
their holdings of deposits D. It reflects the preferences of households about the form of
money they wish to hold. It is C/D, currency/deposits.
Our model shows how the money supply depends on these three. We begin with
Money Supply = Currency + Deposits ... M = C + D
Monetary Base = Currency + Bank Reserves ... B = C + R
Divide the first equation by the second and then divide all terms by D. Rearrange to
𝑐𝑟 + 1
𝑀 = ∗ 𝐵
𝑐𝑟 + 𝑟𝑟
This equation shows how the money supply depends on the three exogenous variables
above. We can now see that the money supply is proportional to the monetary base. The
factor of proportionality, (cr + 1)(cr + rr), is denoted m and is called the money
multiplier. We can then write: 𝑀 = 𝑚 ∗ 𝐵. Each dollar of the monetary base produces
m dollars of money. Because the monetary base has a multiplied effect on the money
supply, the monetary base is sometimes called high-powered money.
We can see how changes in the three exogenous variables – B, rr, and cr – cause the
money supply to change:
1. The money supply is proportional to the monetary base. Thus, an increase in the
monetary base increases the money supply by the same percentage.
2. The lower the reserve-deposit ratio, the more loans banks make, and the more
money banks create from every dollar of reserves. Thus, a decrease in the
reserve-deposit ratio raises the money multiplier and money supply.
3. The lower the currency-deposit ratio, the fewer dollars of the monetary base the
public holds as currency, the more base dollars banks hold as reserves, and the
more money banks can create. Thus, a decrease in cr raises the money multiplier
and money supply.
However, this does not mean that central bankers can control the value of the money
supply precisely. They cannot for two reasons.
1. Officials at the Bank of Canada do not know what reserve-deposit ratio will be
chosen by the chartered banks. Years ago when it was regulated by law, Banks
chose the lowest reserve-deposit ratio allowable (so they could loan out more and
make money), so the money multiplier was predictable. Now that those
regulations are removed it is harder to estimate it.
2. The public’s currency-deposit ratio, the other component of the multiplier, is a
matter of choice and beyond the control of the Bank.
The Bank of Canada controls the money supply indirectly by alterin