Chapter 17 – The Central Bank Balance Sheet and the Money Supply Process
III. The Deposit Expansion Multiplier
A. Deposit Creation in a Single Bank
1. If the Fed buys a security from a bank, the bank has excess reserves, which it
will seek to lend.
2. The loan replaces the securities as an asset on the bank’s balance sheet.
B. Deposit Expansion in a System of Banks
1. However, the loan that the bank made was spent and as the checks cleared,
reserves were transferred to other banks.
2. 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.
3. Assuming no excess reserves are held and that 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 ∆D = (1/rD) ∆RR
4. The term (1/rD) represents the simple deposit expansion multiplier.
5. A decrease in reserves will generate a deposit contraction in a multiple amount
too.
IV. The Monetary Base and the Money Supply
A. Deposit Expansion with Excess Reserves and Cash Withdrawals
1. 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.
2. 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 two factors operate in the same way as an
increase in the reserve requirement.
B. The Arithmetic of the Money Multiplier
1. The amount of excess reserves a bank holds depends on the costs and benefits
of holding them, where the cost is the interest foregone and the benefit is the
safety from having the reserves in case there is an increase in withdrawals.
2. 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.
3. Similarly, 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.
4. As interest rates rise cash becomes less desirable, but if the riskiness of
alternative holdings rises or liquidity falls, then it becomes more desirable.
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