# Money and Banking

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Money & Banking ­ MGT411
VU
Lesson 35
MONEY MULTIPLIER
Remember, we discussed that
Assuming
No excess reserves are held
There are no changes in the amount of currency held by the public,
The change in deposits will be the inverse of the required deposit reserve ratio (rD) times the
change in required reserves, or ĆD = (1/rD) ĆRR
Alternatively
RR = rDD  or ΔRR = rDΔD
For every dollar increase in reserves, deposits increase by 1/ rD
The term (1/rD) represents the simple deposit expansion multiplier.
A decrease in reserves will generate a deposit contraction in a multiple amount too
The money multiplier shows how the quantity of money (checking account plus currency) is
related to the monetary base (reserves in the banking system plus currency held by the Nonbank
public)
Taking m for money multiplier and MB for monetary base, the Quantity of Money, M is
M = m x MB
(This is why the MB is called High Powered Money)
Consider the following relationships
Money = Currency + Checkable deposits
M=C+D
Monetary Base = Currency + Reserves
MB = C +R
Reserves = Req. Res. + Exc. Res
R = RR + ER
The amount of excess reserves a bank holds depends on the costs and benefits of holding them,
The cost is the interest foregone
The benefit is the safety from having the reserves in case there is an increase in withdrawals
The higher the interest rate, the lower banks' excess reserves will be; the greater the concern
over possible deposit withdrawals, the higher the excess reserves will be.
Introducing Excess Reserve Ratio {ER/D}
R = RR + ER
= rDD + {ER/D} D
= (rD + {ER/D}) D
The decision of how much currency to hold depends on the costs and benefits, where the cost is
the interest foregone and the benefit is the lower risk and greater liquidity of currency.
As interest rates rise cash becomes less desirable, but if the riskiness of alternative holdings
rises or liquidity falls, then it becomes more desirable
Now taking Currency Ratio as {C/D}
MB = C + R
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Money & Banking ­ MGT411
VU
= {C/D} D + (rD + {ER/D}) D
= ({C/D} + rD + {ER/D}) D
This shows that monetary base has three uses
Required reserves
Excessive reserves
Cash in the hands of nonbank public
Deposit Expansion with Excess Reserves and Cash Withdraws
1
D=
x MB
{C/D} + rD + {ER/D}
{C / D} +1
M =
x MB
{C/D} + rD + {ER/D}
The Quantity of Money (M) Depends on:
The Monetary base (MB), Controlled by the central bank
Reserve Requirements
Bank's desired to hold excess reserves
The public's demand for currency
The quantity of money changes directly with the base, and for a given amount of the base, an
increase in either the reserve requirement or the holdings of excess reserves will decrease the
quantity of money.
But currency holdings affect both the numerator and the denominator of the multiplier, so the
effect is not immediately obvious. Logic tells us that an increase in currency decreases reserves
and so decreases the money supply.
Table: Factors Affecting the Quantity of Money
Factors
Who controls it
Change
Impact on M
Monetary Base
Central bank
Increase
Increase
Required reserve-to-deposit ratio
Bank regulators
Increase
Decrease
Excess reserve-to-deposit ratio
Commercial banks
Increase
Decrease
Currency-to-deposit ratio
Nonbank public
Increase
Decrease
The Central Bank's Monetary Policy Toolbox
Central bank controls the quantity of reserves that commercial banks hold
Besides the quantity of reserves, the central bank can control either the size of the monetary
base or the price of its components
The two prices it concentrates on are
Interest rate at which banks borrow and lend reserves overnight (the federal funds rate)
Interest rate at which banks can borrow reserves from the central bank (the discount rate)
The central bank has three monetary policy tools, or instruments:
The target federal funds rate,
The discount rate, and
The reserve requirement
The Target Federal Funds Rate and Open Market Operations
The target federal funds rate is the central bank's primary policy instrument.
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Money & Banking ­ MGT411
VU
The federal funds rate is determined in the market, rather than being controlled by the central
bank.
The name "federal funds" comes from the fact that the funds banks trade their deposit balances
at the federal reserves or central bank.
Central bank holds the capacity to force the market federal funds rate to equal the target rate all
the time by participating directly in the market for overnight reserves, both as a borrower and as
a lender.
As a lender, the central bank would need to make unsecured loans to commercial banks, and as
a borrower, the central bank would in effect be paying interest on excess reserves
The central bank chooses to control the federal funds rate by manipulating the quantity of
reserves through open market operations: the central bank buys or sells securities to add or drain
reserves as required.
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