MGT411 - Money & Banking - Lecture Handout 34

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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
Securities -$100,000
Loans +$100,000
OBI Checking account +$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 $0
Securities -$100,000
Loans +$100,000
Checkable deposits $0

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.
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
Loan +$90,000
American Steel’s Checking +$100,000
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
Loan +$81,000
Checking account +$90,000

Multiple Deposit Creation

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 $0 $100,000 $0
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 $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
  • ΔD = (1/rD) ΔRR
  • 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

Deposit Expansion Multiplier

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
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
Excess reserves +$4,750
Loan +$80,750
American Steel’s checking +$95,000
account
  • 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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