DEPOSIT CREATION IN A SINGLE BANK:Types of Reserves

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Money & Banking MGT411

Lesson 34

DEPOSIT CREATION IN A SINGLE BANK

If the central bank buys a security from a bank, the bank has excess reserves, which it will seek

to lend

The loan replaces the securities as an asset on the bank's balance sheet

Table: Change in First Bank's Balance Sheet following Central Bank's purchase of a Treasury

bond

Assets

Liabilities

Reserves

+$100,000

Securities

-$100,000

Assuming First bank has granted a loan of $100,000 to Office Builders Incorporated (OBI)

Table: Change in First Bank's Balance sheet following Central Bank's purchase of a Treasury

bond and Extension of a loan

Assets

Liabilities

Reserves

+$100,000

OBI Checking account

+$100,000

Securities

-$100,000

Loans

+$100,000

OBI paid off its employees and suppliers through checks worth $100,000

Table: Change in First Bank's balance sheet following Central Bank's purchase of a Treasury

Bond, Extension of a loan, and withdrawal by the borrower

Assets

Liabilities

Reserves

Checkable deposits

Securities

-$100,000

Loans

+$100,000

Deposit Expansion in a System of Banks

The loan that the First bank made was spent and as the checks cleared, reserves were transferred

to other banks

The banks that receive the reserves will seek to lend their excess reserves, and the process

continues until all of the funds have ended up in required reserves

Types of Reserves

Actual Reserves (R)

Required Reserves (RR=rDD)

Excess Reserves (ER)

Assume

Bank holds no excess reserves.

The reserve requirement ratio is 10%

Currency holding does not change when deposits and loans change.

When a borrower writes a check, none of the recipients of the funds deposit them back in the

bank that initially made the loan.

Let's say, OBI uses the $100,000 loan to pay its supplier American Steel Co (ASC), which it

deposits in its bank the Second bank.

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Money & Banking MGT411

Table: Change in Second Bank's Balance sheet following American Steel's Deposit

Assets

Liabilities

Reserves

+$100,000

American Steel's checking

+$100,000

account

Table: Change in Second Bank's Balance sheet following a Deposit and Extension of a loan

Assuming a 10% reserve requirement, banks hold no excess reserves, and there are no changes in

currency holdings.

Assets

liabilities

Reserves

+$10,000

American Steel's Checking

+$100,000

Loan

+$90,000

account

Table: Change in Third Bank's Balance Sheet following a Deposit and Extension of a loan

Assuming a 10% reserve requirement, banks hold no excess reserves, and there are no changes in

currency holdings.

Assets

Liabilities

Reserves

+$9,000

Checking account

+$90,000

Loan

+$81,000

106

Money & Banking MGT411

Multiple Deposit Creation

Assuming a 10% reserve requirement, banks hold no excess reserves and there are no

changes in currency holdings.

Central Bank

$100,000 Reserves

$100,000 Securities

First Bank

$100,000 Loan

Office Builders lnc.

$100,000 Payment

American Steel Co.

$100,000 Deposit

Second Bank retains $10,000 in reserves

$90,000 Loans

Third Bank retains $90,000 in reserves

$81,000 Loan

Fourth Bank retains $8,100 in reserves

$72,900 Loan

Fifth Bank retains $7,290 in reserves

$65,610 Loan

And so on

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Money & Banking MGT411

Table: Multiple Deposit Expansion following a $100,000 Open Market Purchase Assuming a 10%

reserve requirement

Bank

Increase in Deposits

Increase in Loans

Increase in Reserves

First bank

$100,000

Second bank

$100,000

$90,000

$10,000

Third bank

$90,000

$81,000

$9,000

Fourth bank

$81,000

$72,900

$8,100

Fifth bank

$72,900

$65,610

$7,290

Sixth bank

$65,610

$59,049

$6,561

The Banking System

$1,000,000

$100,000

Deposit Expansion Multiplier

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

So for every dollar increase in reserves, deposits rise 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

RD=10% (0.10), and ΔRR=$100,000

$ 100 , 000

ΔD=

ΔD= $1,000,000

Deposit Expansion with Excess Reserves and Cash Withdrawals

The simple deposit expansion multiplier was derived assuming no excess reserves are held and

that there is no change in currency holdings by the public.

These assumptions are now relaxed as

5% withdraw of cash.

Excess reserves of 5% of deposits

Continuing with our previous example, if American Steel Co (ASC) removes 5% of its new

funds in cash, which leaves $95,000 in the checking account and $95,000 in the Second bank's

reserve account

Bank wishes to hold excessive reserves of 5% of deposits, it would keep reserves of 15% of

$95,000 or $14,250 and making a loan of $80,750

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Money & Banking MGT411

Table: Change in Second Bank's Balance sheet following a Deposit and Extension of a Loan

Assuming excess reserves and cash holdings. Note: American Steel also has $5,000 in cash.

Assets

Liabilities

Required reserves

+$9,500

American Steel's checking

+$95,000

Excess reserves

+$4,750

account

Loan

+$80,750

The desire of banks to hold excess reserves and the desire of account holders to withdraw cash

both reduce the impact of a given change in reserves on the total deposits in the system.

The more excess reserves banks desire to hold, and the more cash that is withdrawn, the smaller

the impact.

Money Multiplier

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

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