### 17. Multiple Deposits Creation and Contraction Chapter 17 : main menu 17.1 Assumptions of deposits creation Concept Explorer 17.1 The process of multiple deposits 17.2 creation Concept.

```17. Multiple Deposits Creation
and Contraction
1
17.1 Assumptions of deposits creation Concept Explorer 17.1
The process of multiple deposits
17.2
creation
Concept Explorer 17.2
Progress Checkpoint 1
17.3 Limitations of credit creation
Theory in Life 17.1
Progress Checkpoint 2
17.4 Multiple contraction of credit
Progress Checkpoint 3
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Concept Explorer 17.1

The balance sheet of banks

What does the balance sheet of banks show?
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Concept Explorer 17.1

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
Banks own assets (資產). These can be in the forms of cash reserves,
bank loans to borrowers, shares, foreign currency and bonds
purchased, furniture and computers used in a bank office. Some of
them are liquid, e.g. cash reserves, while some are illiquid, e.g. bank
loans, furniture, etc.
Banks accept deposits from the public. This is one of the banks’
liabilities ( 負 債 ). Liabilities can be in the forms of deposits,
certificate of deposits held by public, loan borrowed from the
government, etc.
A balance sheet (資產負債表) is used to present the data of banks’
assets and liabilities. Owing to double entry booking (復式記帳), the
total assets must equal total liabilities.
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Concept Explorer 17.1
The following shows a typical balance sheet of a bank:
The balance sheet of a bank
Assets (\$)
Reserves
Liabilities (\$)
500 Deposits
Loan
1,500
Total
2,000 Total
2,000
2,000
If the bank holds no excess reserves, its actual reserves equals required reserves.
\$500_ x 100% = 25%
The minimum reserve ratio is
\$2000
The bank loan lent out is \$1,500.
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Concept Explorer 17.2

Maximum change in deposits Vs maximum
change in money supply

In the above example, the maximum change in deposits
is \$40,000 while the maximum change in money supply
is only \$30,000. Why are they different?
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Concept Explorer 17.2
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Before the \$10 000 is deposited by Patrick in HSBC,
Ms = Cp + Dd
Dd = \$0 (i.e. no deposits)
= \$10,000 + \$0= \$10,000
When the \$10 000 is deposited by Patrick in HSBC,
Ms = Cp + Dd
Dd = \$ 10,000 (i.e.newly accepted deposits)
= \$0 + \$10,000
= \$10,000
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Concept Explorer 17.2


Thus, the first round change in Ms is \$0, because
there is only a redistribution of the component in
money supply from cash in public circulation to
deposits by \$10,000.
However, the first round change in deposits is
\$10,000, because initially the \$10,000 cash is not a
part of deposits. Hence the maximum change in
deposits is greater than that of money supply by the
amount of initial deposits.
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Concept Explorer 17.2


The formula on finding the maximum change in money supply is
applicable to the cases where the new deposits come from the cash
component of money supply. If the newly accepted deposits come
from :
- the issuing of new currency from the government, or
- remittance overseas,
then the maximum change in deposits and money supply will be the
same. This is because the initial cash deposit is not originally included
in the money supply. When the newly printed or remitted cash is
deposited, both deposits and money supply rise by the same amount.
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Progress Checkpoint 1
Q17.1 Suppose the deposits in a bank is \$5,000 and the
required reserves is \$1,000. What is the implied
minimum reserve ratio?
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Progress Checkpoint 1
\$1,000 x 100%
Minimum reserve ratio = \$5,000
= 20%
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Progress Checkpoint 1
Q17.2 The following shows the consolidated balance sheet of a bank:
Assets (\$)
Reserves
Liabilities (\$)
600 Deposits
Loan
3,400
Total
4,000 Total
4,000
4,000
Suppose the minimum reserve ratio is 10%.
If Tom deposits \$2,000 into the bank, find the amount of excess reserve
of the bank immediately after Tom’s deposits.
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Progress Checkpoint 1

If Tom deposits \$2,000 into the bank, deposits will become
\$6,000 while actual reserves will become \$2,600. Required
reserves is \$6,000 x 10% = \$600. Excess reserves is \$2,600 \$600 =\$2,000.
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Progress Checkpoint 1
Q17.3 Suppose in a certain economy all the banks keep no excess reserves,
and their balance sheet is as follows:
Assets (\$)
Reserves
Liabilities (\$)
500 Deposits
Loan
1,500
Total
2,000 Total
2,000
2,000
Suppose someone deposits \$1,000 cash into his bank.
(a) Calculate the minimum reserve ratio.
(b) Calculate the maximum change in deposits (including the initial deposit).
(c) Calculate the maximum change in money supply.
(d) Are the maximum change in deposits and maximum change in money supply the same?
(e) Explain.
(e) Calculate the maximum change in bank loan.
(f) Show how the balance sheet of the whole banking system will be after the multiple
(g) deposit creation process is completed.
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Progress Checkpoint 1
required reserves x 100%
total deposits
\$500_ x 100%
=
\$2,000
(a) Minimum reserve ratio (ra) =
=
(b) Maximum change in deposits =
25%
Initial change in deposits x
= 1000 x
1_
rm
1__
25%
= \$4,000
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Progress Checkpoint 1
(c) Maximum change in money supply = Initial change in excess reserves x
= 750 x
1_
rm
1__
25%
= \$3,000
(d) No, they are not the same. Before the initial deposit was made, the \$1,000 cash was
included in money supply but not in deposits. When the deposit was made, deposits
immediately increased by \$1,000 while money supply did not change.
Hence the total change in deposits is greater than that of money supply.
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Progress Checkpoint 1
(e) Maximum change in bank loan =
Initial change in bank loan x
= 750 x
1_
rm
1__
25%
= \$3,000
(f) The balance sheet of the banking system will become:
Assets (\$)
Liabilities (\$)
Reserves
1,500 Deposits
Loan
4,500
Total
6,000 Total
6,000
6,000
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Theory in Life 17.1
Actual banking multiplier
Suppose a banking system accepts an initial deposits of \$2,000m, and
keeps a required reserve of \$200m. Then :
Minimum reserve ratio (ra) =
required reserves x 100%
total deposits
=
\$200m_ x 100%
\$2,000m
=
10%
Maximum banking multiplier =
1_ = 1_ = 10
rm
10%
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Theory in Life 17.1
Maximum change in deposits = Initial change in deposits x
= \$2,000m x
1_
rm
1_
= \$20,000m
10%
The banking system can at maximum create a total deposits of \$20,000m, 10 times the
amount of initial deposits. The balance sheet of the banking system will be:
Assets (\$)
Reserves
Liabilities (\$)
2,000 Deposits
Loan
18,000
Total
20,000 Total
20,000
20,000
Table 17.1 The balance sheet of a banking system without excess reserves
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Theory in Life 17.1
However, if the banking system keeps an actual reserves of \$800m
(i.e. excess reserves = \$800m - \$200m = \$600m), then we can define the
actual reserve ratio (ra) (實際儲備率):
Actual reserve ratio (ra) =
=
actual reserves x 100%
total deposits
\$800m_ x 100% = 40%
\$2,000m
The actual reserve ratio shows the ratio of total deposits that a banking system
actually holds as reserves.
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Theory in Life 17.1
We can find the actual banking multiplier (實際銀行乘數):
Actual banking multiplier =
1_ = 2.5
1_
=
ra
40%
The actual banking multiplier shows the actual change in deposits resulting from an
initial change in deposits in the banking system.
Actual change in deposits = Initial change in deposits x
= 2,000m x
1_
40%
1_
ra
= \$5,000m
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Theory in Life 17.1
The banking system can actually create a total deposits of \$5,000m, just 2.5 times the
amount of initial deposits. Hence, we can see that if banks keep excess reserves,
the credit creation ability of the banking system will be reduced.
The balance sheet of the whole banking system will be:
Assets (\$)
Liabilities (\$)
Reserves
2,000 Deposits
Loan
3,000
Total
5,000 Total
5,000
5,000
Table 17.2 The balance sheet of a banking system with actual reserve ratio equals 40%.
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Theory in Life 17.1
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Reminder :
The maximum banking multiplier varies inversely with
the minimum reserve ratio.
Reminder :
Even if banks keep excess reserves, so long as the actual
reserve ratio is not 100%, they can still create money.
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Progress Checkpoint 2
Q17.4 Given the following consolidated balance sheet of a certain bank:
Assets (\$)
Reserves
Liabilities (\$)
5,000 Deposits
Loan
15,000
Total
20,000 Total
20,000
20,000
Suppose the required reserves of the bank is \$4,000 only. Find
(a) the minimum reserve ratio,
(b) the maximum banking multiplier,
(c) the actual reserve ratio, and
(d) the actual banking multiplier.
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Progress Checkpoint 2
(a) Minimum reserve ratio (ra) =
minimum reserves x 100%
total deposits
=
(b) Maximum banking multiplier =
\$4,000_ x 100%
= 20%
\$20,000
1_
1_
= 5
=
rm
20%
actual reserves x 100%
total deposits
\$5,000_ x 100% = 25%
=
\$20,000
1_
1_ =
= 4
(d) Actual banking multiplier =
ra
25%
(c) Actual reserve ratio (ra) =
25
Progress Checkpoint 2
Q17.5 If a banking system does not keep excess reserve, then
the maximum banking multiplier is equal to the actual
banking multiplier. Do you agree?
Yes. If no excess reserve is kept, the minimum reserves
equals actual reserves. Then the minimum reserve ratio
equals the actual reserve ratio, and the maximum
banking multiplier equals the actual banking multiplier.
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Progress Checkpoint 2
Q17.6 Which of the following is true? Why?
(a) A bank-run may occur because banks’ total assets is
less than their total liabilities.
(b) A bank-run may occur because banks’ liquid assets is
less than their total liabilities.

(a) This statement is false. This is because banks’ total assets
(e.g. reserves, loans, investment, etc.) must equal their total
liabilities.
(b) This statement is true. This is because banks’ assets like
reserves or short-term loan may be less than their liabilities,
and if they have insufficient cash reserves to support
withdrawals, a bank-run may occur.
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Progress Checkpoint 2
Q17.7 If banks keep excess reserves, can they create money?
So long as the actual reserve ratio is less than 100%,
they can still create money.
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Progress Checkpoint 3
Q17.8 The following shows the balance sheet of Bank A on a certain date:
Assets (\$)
Reserves
Liabilities (\$)
3,000 Deposits
Loan
13,000
Total
16,000 Total
16,000
16,000
Suppose the minimum reserve ratio is 20%. Calculate how much
shortage of reserve is if a customer withdraws \$1,000 from the bank.
Show how the resulting balance sheet of Bank A will change.
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Progress Checkpoint 3
If a customer withdraws \$1,000, the balance sheet of the bank will immediately become:
Assets (\$)
Reserves
Liabilities (\$)
2,000 Deposits
Loan
13,000
Total
15,000 Total
15,000
15,000
The minimum reserve is \$15,000 x 20% = \$3,000. As the actual reserves is only \$2,000,
the shortage of reserves is \$1,000.
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Progress Checkpoint 3
Q17.9 Given the following balance sheet of a fully loaned up banking system:
Assets (\$)
Liabilities (\$)
Reserves
2,000 Deposits
Loan
3,000
Total
5,000 Total
5,000
5,000
If the public withdraws \$400 from the banking system,
(a) calculate the maximum change in deposits
(b) calculate the maximum change in money supply
(c) calculate the maximum change in bank loan, and
(d) show how the balance sheet of the banking system will become after
deposit contraction has completed.
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Progress Checkpoint 3
(a) Maximum change in deposits
= Initial change in deposits
x
_1_
rm
= -\$400 x
(b) Maximum change in money supply
1__
40%
= -\$1,000
= Initial change in excess reserves
x
_ 1_
rm
= -\$240 x
(c) Maximum change in bank loan
1__
40%
= -\$600
= Initial change in bank loan
x
_1_
rm
= -\$240 x
1__
40%
= -\$600
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Progress Checkpoint 3
(d) The balance sheet of the banking system will become:
Assets (\$)
Liabilities (\$)
Reserves
1,600 Deposits
Loan
2,400
Total
4,000 Total
4,000
4,000
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End of Chapter 17
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