MONEY MULTIPLIER:The Quantity of Money (M) Depends on

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Money & Banking MGT411

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

= {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

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

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

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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