ECON 2000 Chapter Notes - Chapter 18: Fractional-Reserve Banking, Monetary Base, Money Multiplier
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
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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
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:
. 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 altering the monetary base.
To do this, the bank of Canada has at its disposal two instruments of monetary policy:
1. Open-market operations are the purchases and sales of federal government bonds by
the Bank of Canada. When it buys bonds, the dollars it pays for the bonds increase the
monetary base and thereby the money supply. When it sells bonds to the public, the
dollars it receives reduce the monetary base and thus reduce the money supply. Open-
market operations are also carried out in the foreign exchange market. To keep the
Canadian dollar high when market pressure is pushing it down, the Bank buys lots of
Canadian dollars by selling some of Canada’s foreign exchange reserves, which are held
by the Bank of Canada. Since the Canadian dollars bought by the bank are no longer in
private use, the monetary base is reduced. To keep the Canadian dollar from rising in
value, the Bank sells lots of Canadian dollars by using the currency to purchase foreign
exchange. The new currency that is used to pay for the foreign exchange forms part of
the domestic monetary base. As a result, buying foreign exchange causes a multiple
expansion in the money supply, just like buying bonds does. We cannot fix both the
quantity and the price of our currency. A fixed exchange rate is inconsistent with
independent monetary policy. A floating exchange rate is what permits independent
2. Deposit-switching is the switching of federal government deposits between the Bank
of Canada and the chartered banks for the purposes of regulating the money supply. If
the government holds some deposits in chartered banks, they will be loaned out and the
money supply increases, while if they are at the Bank of Canada the money supply will
not increase. A switch of government deposits away from chartered banks depletes their
reserves, including a contraction of loans and so a decrease in the money supply.
The Bank Rate is the interest rate that the Bank of Canada uses to determine how much
it charges if it ever has to lend reserves to chartered banks. Because an increase in the
bank rate is interpreted as an increase in chartered bank costs, it is taken as a signal that
banks will be cutting back loans and that the money supply is shrinking. A decrease in
the bank rate is expansionary monetary policy. However, since Canada has so few banks
and they all have many branches, they simply borrow from each other on the “overnight”
market and rarely need to borrow reserves from the Bank of Canada.
Individuals write cheques to each other which represent instructions for a bank to transfer
funds to another bank. Banks make these transfers on a net basis by writing cheques to
each other against their own deposit accounts at the Bank of Canada. The total of these
accounts is known as the quantity of settlement balances. Banks are not allowed to end
the day with a negative balance in their settlement account.
The overnight lending rate is the rate at which chartered banks and other money market
participants borrow from and lend to each other one-day funds. The Bank of Canada
establishes a range, called the operating band, in which the overnight lending rate can
move up or down. The Bank Rate is set at the upper limit of this band, which is half a
percentage point wide. The Bank of Canada commits to lend out reserves at a rate given
by the upper limit of the band, and to pay interest on the deposits of private financial
institutions at the Bank at the lower limit of the band. These commitments ensure that the
overnight rate stays within the band. By changing the operating band and thus the
overnight lending rate, the Bank of Canada sends a clear signal about the direction in
which interest rates will be moving.
A summary indicator that the Bank of Canada has published in its semi-annual Monetary
Policy Report is the Monetary Conditions Index (MCI). It is a weighted average of the
interest rate and the exchange rate. Researchers at the Bank have estimated that it takes
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