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Bank-a-mythica is unlikely to be happy with the situation illustrated in Table 2, for it is
holding $80,000 in excess reserves on which it earns no interest. So as soon as possible, it
will lend out the extra $80,000”let us say to Hard-Pressed Construction Company. This
loan leads to the balance sheet changes shown in Table 3: Bank-a-mythica™s loans rise by
$80,000 while its holdings of cash reserves fall by $80,000.

TA BL E 3
Changes in Bank-a-mythica™s Balance Sheet, January 3“6, 2008

Assets Liabilities
Loans outstanding +$80,000 No change
Reserves “$80,000

Addendum: Changes in Reserves
Actual reserves “$80,000
Required reserves No change
Excess reserves “$80,000


By combining Tables 2 and 3, we arrive at Table 4, which summarizes the bank™s trans-
actions for the week. Reserves are up $20,000, loans are up $80,000, and, now that the bank
has had a chance to adjust to the inflow of deposits, it no longer holds excess reserves.
Looking at Table 4 and keeping in mind our specific definition of money, it appears at first
that the chairman of Bank-a-mythica is right when he claims not to have engaged in the
nefarious-sounding practice of “money creation.” All that happened was that, in exchange
for the $100,000 in cash it received, the bank issued the widower a checking balance of
$100,000. This transaction does not change M1; it merely converts one form of money (cur-
rency) into another (checking deposits).

TA BL E 4
Changes in Bank-a-mythica™s Balance Sheet, January 2“6, 2008

Assets Liabilities
Reserves +$20,000 Checking deposits +$100,000
Loans outstanding +$80,000

Addendum: Changes in Reserves
Actual reserves +$20,000
Required reserves +$20,000
Excess reserves No change



In all such tables, which are called T accounts, the two sides of the ledger must balance. This balance is required
4

because changes in assets and changes in liabilities must be equal if the balance sheet is to balance both before
and after the transaction.



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Part 3
254 Fiscal and Monetary Policy



But wait. What happened to the $100,000 in cash that the eccentric man brought to the
bank? The table shows that Bank-a-mythica retained $20,000 in its vault. Because this cur-
rency is no longer in circulation, it no longer counts in the official money supply, M1.
(Notice that Figure 2 included only “currency outside banks.”) But the other $80,000,
which the bank lent out, is still in circulation. It is held by Hard-Pressed Construction
Company, which probably will redeposit it in some other bank. But even before this new
deposit is made, the original $100,000 in cash has supported an increase in the money
supply. There is now $100,000 in checking deposits and $80,000 of cash in circulation, mak-
ing a total of $180,000”whereas prior to the original deposit there was only the $100,000
in cash. The money-creation process has begun.


Multiple Money Creation by a Series of Banks
By tracing the $80,000 in cash, we can see how the process of money creation gathers mo-
mentum. Suppose that Hard-Pressed Construction Company, which banks across town at
the First National Bank, deposits the $80,000 in its bank account. First National™s reserves
increase by $80,000. But because its deposits rise by $80,000, its required reserves increase by
20 percent of this amount, or $16,000. If First National Bank behaves like Bank-a-mythica,
it will lend out the $64,000 of excess reserves.
Table 5 shows the effects of these events on First National Bank™s balance sheet. (We do
not show the preliminary steps corresponding to Tables 2 and 3 separately.) At this stage
in the chain, the original $100,000 in cash has led to $180,000 in deposits”$100,000 at
Bank-a-mythica and $80,000 at First National Bank”and $64,000 in cash, which is still in
circulation (in the hands of the recipient of First National™s loan”Al™s Auto Shop). Thus,
instead of the original $100,000, a total of $244,000 worth of money ($180,000 in checking
deposits plus $64,000 in cash) has been created.

TA BL E 5
Changes in First National Bank™s Balance Sheet

Assets Liabilities
Reserves Checking deposits +$80,000
1$16,000
Loans outstanding 1$64,000

Addendum: Changes in Reserves
Actual reserves 1$16,000
Required reserves 1$16,000
Excess reserves No change

But, to coin a phrase, the bucks do not stop there. Al™s Auto Shop will presumably de-
posit the proceeds from its loan into its own account at Second National Bank, leading to
the balance sheet adjustments shown in Table 6 when Second National makes an addi-
tional loan of $51,200 rather than hold on to excess reserves. You can see how the money
creation process continues.

TA BL E 6
Changes in Second National Bank™s Balance Sheet

Assets Liabilities
Reserves Checking deposits +$64,000
1$12,800
Loans outstanding 1$51,200

Addendum: Changes in Reserves
Actual reserves 1$12,800
Required reserves 1$12,800
Excess reserves No change



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Chapter 12 255
Money and the Banking System



Figure 3 summarizes the balance sheet changes of the first five banks in the chain (from
Bank-a-mythica through the Fourth National Bank) graphically, based on the assump-
tions that (1) each bank holds exactly the 20 percent required reserves, and (2) each loan
recipient redeposits the proceeds in the next bank. But the chain does not end there. The
Main Street Movie Theatre, which received the $32,768 loan from the Fourth National
Bank, deposits these funds into the Fifth National Bank. Fifth National has to keep only
20 percent of this deposit, or $6,553.60, on reserve and will lend out the balance. And so
the chain continues.
Where does it all end? The running sums on the right side of Figure 3 show what even-
tually happens to the entire banking system. The initial deposit of $100,000 in cash is ulti-
mately absorbed in bank reserves (column 1), leading to a total of $500,000 in new deposits
(column 2) and $400,000 in new loans (column 3). The money supply rises by $400,000
because the nonbank public eventually holds $100,000 less in currency and $500,000 more
in checking deposits.
As we see, there really is some hocus-pocus. Somehow, an initial deposit of $100,000 leads
to $500,000 in new bank deposits”a multiple expansion of $5 for every original dollar”and
a net increase of $400,000 in the money supply. We need to understand why this is so. But
first let us verify that the calculations in Figure 3 are correct.
If you look carefully at the numbers, you will see that each column forms a geometric
progression; specifically, each entry is equal to exactly 80 percent of the entry before it. Recall
that in our discussion of the multiplier in Chapter 9 we learned how to sum an infinite



F I GU R E 3
Running Sums
The Chain of Multiple
(1) (2) (3)
Deposit Creation
Reserves Deposits Loans

$100,000 deposit $100,000


$20,000 on reserve $80,000 lent out $20,000 $80,000



$80,000 deposit $180,000


$16,000 on reserve $64,000 lent out $36,000 $144,000
SOURCE: This schematic diagram was suggested to us by Dr. Ivan K. Cohen, whom we thank.




$64,000 deposit $244,000


$12,800 on reserve $51,200 lent out $48,800 $195,200



$51,200 deposit $295,200


$10,240 on reserve $40,960 lent out $59,040 $236,160



$40,960 deposit $336,160


$8,192 on reserve $32,768 lent out $67,232 $268,928



And so on . . . • • •
• • •
• • •
$100,000 $500,000 $400,000




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Part 3
256 Fiscal and Monetary Policy



geometric progression, which is just what each of these chains is. In particular, if the com-
mon ratio is R, the sum of an infinite geometric progression is:
1
1 1 R 1 R2 1 R3 1 . . . 5
12R
By applying this formula to the chain of checking deposits in Figure 3, we get:
$100,000 1 $80,000 1 $64,000 1 $51,200 1 . . .
5 $100,000 3 ( 1 1 0.80 1 0.64 1 0.512 1 . . . )
5 $100,000 3 ( 1 1 0.80 1 0.80 2 1 0.80 3 1 . . . )
$100,000
1
5 $100,000 3 5 $500,000
5
1 2 0.80 0.20
Proceeding similarly, we can verify that the new loans sum to $400,000 and that the new
required reserves sum to $100,000. (Check these figures as exercises.) Thus the numbers in
Figure 3 are correct. Let us, therefore, think through the logic behind them.
The chain of deposit creation ends only when there are no more excess reserves to be
loaned out”that is, when the entire $100,000 in cash is tied up in required reserves. That
explains why the last entry in column (1) of Figure 3 must be $100,000. But, with a reserve
ratio of 20 percent, excess reserves disappear only when checking deposits expand by
$500,000”which is the last entry in column (2). Finally, because balance sheets must bal-
ance, the sum of all newly created assets (reserves plus loans) must equal the sum of all
newly created liabilities ($500,000 in deposits). That leaves $400,000 for new loans”which
is the last entry in column (3).
More generally, if the reserve ratio is some number m (rather than the one-fifth in our
example), each dollar of deposits requires only a fraction m of a dollar in reserves. The com-
mon ratio in the preceding formula is, therefore, R 5 1 2 m, and deposits must expand by
1/m for each dollar of new reserves that are injected into the system. This suggests the
general formula for multiple money creation when the required reserve ratio is some num-
ber m:
OVERSIMPLIFIED MONEY MULTIPLIER FORMULA

If the required reserve ratio is some fraction, m, the banking system as a whole can con-
vert each $1 of reserves into $1/m in new money. That is, the so-called money multiplier
The money multiplier is
the ratio of newly created is given by:
bank deposits to new
Change in money supply = (1/m) 3 Change in reserves
reserves.
Although this formula correctly describes what happens in our example, it leaves out an
important detail. The initial deposit of $100,000 in cash at Bank-a-mythica constitutes $100,000
in new reserves (see Table 2 on page 253). Applying a multiplier of 1/m 5 1/0.20 5 5 to this
$100,000, we conclude that bank deposits will rise by $500,000”which is just what happens.
But remember that the process started when the eccentric widower took $100,000 in cash and
deposited it in his bank account. Thus the public™s holdings of money”which includes both
checking deposits and cash”increase by only $400,000 in this case: There is $500,000 more in
deposits, but $100,000 less in cash.


The Process in Reverse: Multiple Contractions
of the Money Supply
Let us now briefly consider how this deposit-creation mechanism operates in reverse”as
a system of deposit destruction. In particular, suppose that our eccentric widower returned
to Bank-a-mythica to withdraw $100,000 from his checking account and return it to his
mattress, where it rightfully belongs. Bank-a-mythica™s required reserves would fall by
$20,000 as a result of this transaction (20 percent of $100,000), but its actual reserves would
fall by $100,000. The bank would be $80,000 short, as indicated in Table 7(a).

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