If you once forfeit the confidence of your fellow citizens, you can never regain their respect and esteem.  It is true that you may fool all the people some of the time;  you can even fool some of the people all the time;  but you can't fool all of the people all the time.

— Abraham Lincoln, to a caller at the White House
from Lincoln's Yarns and Stories [1904], Alexander K. McClure

Money

An understanding of money is a prerequisite to understanding fractional reserve banking.  Such an understanding must begin with the rules of money.  To work well as money, a thing must be durable, portable, divisible without loss, available in limited quantity, generally accepted as money, and it must have intrinsic value as money.¹  Nothing in use today satisfies those rules very well.  Much of what passes for money doesn't satisfy them at all and, therefore, isn't money.  Throughout this essay, I've tried to avoid the word money.  Instead, I've used the word dollars.  Even that isn't quite right because a dollar is a unit of measure of money.  A transaction might involve a certain number of dollars of money just like it might involve a certain number of gallons of ice cream.  If the ice cream melted on the way home and I say that I brought home some gallons because the ice cream went away, that's pretty much like talking about dollars in today's economy.

The Model Bank

In my analysis of fractional reserve banking, I've treated the banking system as if it was a single bank.  That model simplifies the essay, which is already complicated enough without worrying about which bank is which.  One bank is a reasonable model for understanding fractional reserve banking and illustrates the dynamics of the process very nicely.  When I refer to "the bank" in this essay, then I'm talking about the model.  When I talk about a bank as a part of the banking system that exists in the real world, and if I think that my meaning might not be clear, then I refer to it as a "real bank."

There are only two relevant locations for dollars in this analysis:  in the bank or not in the bank.  I've therefore considered all of the rest of the economy to behave as a unit with regard to its interaction with the bank.  In terms of the consequences of fractional reserve banking, it doesn't matter what the dollars do while they're out of the bank.  What matters is the consequences of their leaving the bank and entering the bank.

Page 1

When someone makes a deposit into a real bank, the real bank must be prepared to return the same amount of the same thing that was deposited.  If the deposit is cash, then the real bank must be prepared to return the same amount of cash.  The real bank assumes that people won't all want their cash at the same time and keeps in its possession only a fraction of the cash that was actually deposited.  That cash is called the fractional reserve, which is a subtle deception.  It should more properly be called the cash reserve.

When someone deposits cash into a real bank, a record of the deposit is made.  The real bank then uses most of the deposited cash for some purpose of its own and keeps on hand only the cash reserve.  The record of deposit isn't changed when the dollars are used for something else.  That is, the real bank has a few dollars on hand (the cash reserve) but a record indicating that it has many more dollars on deposit.  The cash on hand is real, tangible cash.  I call those cash dollars.  The dollars on deposit are mostly not really there.  I call those deposit dollars.  They're only the record of the cash dollars that were deposited and then mostly used for something else.

When someone deposits a check into a real bank, cash doesn't cross the counter.  Cash doesn't enter the vault.  The checks are all processed through a clearing house, a correspondent bank (real bank), or a Federal Reserve Bank (real bank again), and net settlement is made not by transferring cash but by electronic messages in deposit balances.  That means that when a deposit is made by check, it's impossible for a real bank to keep a cash reserve because the real bank doesn't receive cash as a result of the deposit.  The very concept of a cash reserve requires that deposits be made in cash, of which a fraction can be kept on reserve.  Checks do not deposit cash.  That's why it's deceptive to refer to the cash reserve as a fractional reserve.  The real bank can measure a fraction of anything, but it can keep a cash reserve only if it receives a cash deposit.
0

Page 2

In this essay, I've illustrated the dynamics of fractional reserve banking with a model of the process of deposits, loans, and redeposits.  The model cycle is as follows:

1.		Some number of cash dollars, in circulation in the economy, is available for deposit in the bank.
2.		The available cash dollars are deposited in the bank.
3.		The required number of cash dollars is held in reserve by the bank.
4.		The difference between the number of cash dollars deposited and the number of cash dollars held in reserve is loaned by the bank, as cash, and again enters the economy.
5.		The loaned cash dollars, circulating in the economy, are then available to be redeposited in the bank.

A series of such cycles is an idealization of the process of fractional reserve banking as it would happen in a real fractional reserve banking system.  It illustrates the ideal performance to be expected from such a system.  I've used a variety of examples to investigate the consequences of several such cycles.  Those examples are shown in detail in Appendix 1.  The various tables and figures that I've used throughout this essay are based on those examples.

Calculations

The quantities in appendix 1, and in the various tables shown in this essay, can be calculated by equations which will yield the accumulated total for any combination of parameters.  Appendix 2 contains examples of such equations, as well as their derivations.  Those equations are academically correct and should impress my critics, but there are easier ways to do the calculations.  I used a Hewlett-Packard HP-25 programmable calculator.  The calculator programs are presented in Appendix 3.

Fractional Reserve Banking

I believed, when I began this essay, that cycles of fractional reserve deposits and loans greatly increase the number of cash dollars in circulation, thereby contributing to inflation.  I'd heard that claim from various folks who believed it to be one of the banking system's evils.  It seemed reasonable and I believed it.  However, Table 1 shows that I was mistaken.  The number of cash dollars placed in circulation by fractional reserve banking, in that example, will never equal the initial deposit, by which cash was removed from circulation.  The example is shown graphically in Figure 1.
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Page 3

Deposits and Loans

It's interesting to look at the number of dollars recorded as on deposit in the bank.  I call those deposit dollars.  The number of deposit dollars increases with successive deposit and loan cycles, as shown in Table 4.  In that example, 1818.18 deposit dollars accumulate from an original deposit of only 1000 cash dollars.  That happens when the bank loans cash dollars out of someone's account and then receives them back again as a deposit of cash dollars into another account.  Although they're the same cash dollars, they're on deposit in two accounts.  That happens over and over again, creating a record of deposits of cash dollars that are not really there.  It might seem superfluous to make a distinction between cash dollars and deposit dollars, but the distinction is important because of a third kind of dollars.  Those are deposit dollars that don't correspond to anything.  I call them fictional dollars.  At first, this might not be obvious.  Here's what happens.  When the bank receives the initial deposit, those are cash dollars.  They exist physically, even if they are only green paper.  When the bank makes its first loan, it loans a portion of those cash dollars and no longer has them in its possession.  After the first loan, the bank has (see the first example in Appendix 1) 100 cash dollars, but it still claims 1000 deposit dollars.  The difference between those two amounts represents fictional dollars, which the bank says that it has on deposit but which it really doesn't have.  When the bank receives the second deposit (the previously loaned cash dollars being redeposited), there are 550 cash dollars in the bank (450 from the new deposit + 100 held on reserve from the first deposit).  Also, the bank claims 1450 deposit dollars (450 from the new deposit + 1000 from the first deposit).  The second deposit thus causes an increase in both cash dollars and deposit dollars.  After the second loan, however, the number of cash dollars in the bank decreases but the number of deposit dollars doesn't.  Thus, the number of fictional dollars (deposit dollars — cash dollars) changes

Page 4

Obviously, deposit dollars cannot be loaned by the bank.  They're nothing more than the record of deposits, and the bank can't arbitrarily reduce the depositors' records of deposits.  Neither can fictional dollars be loaned.  Their existence is even more abstract than that of deposit dollars.  When the bank loans dollars, within the context of fractional reserve lending, it can loan only cash dollars.³
0

During cycles of fractional reserve deposits and loans, an indebtedness to the bank accumulates.  Tables 5, 6, and 7 reveal several interesting features of that debt.  First (Table 5), the fewer dollars the bank holds on reserve, the greater will be the eventual indebtedness to it.  That gives the bank an incentive to lower the cash reserve requirement.  Second (Table 6), the more times the bank re-loans the same dollars, the greater will be the indebtedness to the bank.  That gives the bank an incentive to make loans.  And finally (Tables 5 and 7), the more conscientiously people deposit their cash dollars in the bank, the more they enable it to make them indebted to it.

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The growing predominance of checkbook transactions and electronic transactions, and the fear of using cash, verify the tendency toward a cashless economy.  That economy will, I believe, be inherently more vulnerable to instability than a cash economy.⁵  However, to understand the implications of a cashless economy requires more than arithmetic.  Its undesirability derives not only from economic considerations, but from political ones.

•		Cash accepted from another party is good regardless of his character, but the integrity of a cashless transaction depends upon the integrity of the parties to the transaction.  Therefore, a cashless economy creates an identity requirement whereby the parties to a transaction must prove themselves prior to the transaction.  That principle is already in force.  Government ID is a prerequisite for participation in today's banking system and in most of the rest of the economy.
•		In a cashless economy, the identities and activities of all participants in a transaction are visible to the government.  There can't be any privacy.6  That principle of a cashless economy is in force today.  Banks will reveal any financial record to a government agency upon request without any need for the consent of the customer.  In fact, the customer might not even be informed.
•		In a cashless economy, the banking system doesn't serve its customers, but its master.  Today, the banking system routinely reports to government agencies, enforces government policies, and complies with government regulations.  The system's response to a customer objection can be accurately summarized by "love it or leave it".

Someone who thinks that he has little to hide might belittle the importance of a loss of privacy.  That is a naive attitude.  Whether or not a person has something to hide might have less to do with that person's activities than it does with other people's attitudes toward those activities.  We don't have any control over those attitudes and

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The present political system claims to derive its just powers from the consent of the governed but remains mute with regard to the pedigree of its unjust powers.  The most noteworthy result of that claim is to place upon the governed a responsibility for the actions of government, just or otherwise.  There's enough truth to the theory to make it barely plausible.  In this particular case, the banks can't make loans unless people borrow from the banks.  Checkbook transactions will not occur unless people write checks.  If enough people demand their dollars in cash, then they'll get them that way, at least until the banks are bankrupt.⁷  And most important of all, the banks couldn't function AT ALL if people would refuse to deposit their cash in the banks.  The entire banking system as it exists today rests upon the solid support of the people.

No one has yet determined if it's possible to fool all of the people all of the time but the Federal Reserve System has shown that it can fool too many of them too much of the time.  Whatever happens, the people will be getting exactly what they deserve.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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I did these calculations by bringing forward for each deposit and loan cycle the complete history of previous cycles and updating each item for the current cycle according to the transaction taking place.  It's tedious and it used a lot of paper but it has the virtue of being unambiguous.  You can see the current total for each item at the end of each cycle.  You can also see, at each total, the entire history of the cycles that got you there.

Fraction withheld from initial deposit = 0
Fraction held on reserve = 10%
Fraction withheld from redeposit = 50%
Fraction redeposited = 50%
0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
Initial Condition    ^	$0.00	$0.00	$0.00	$1000.00

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
Deposit Number 1    ^	$1000.00	$1000.00	$0.00	$0.00

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
Loan Number 1    ^	$1000.00	$100.00	$900.00	$900.00

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
Deposit Number 2    ^	450.00	450.00	0.00	0.00
	$1450.00	$550.00	$900.00	$450.00

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
Loan Number 2    ^	450.00	45.00	405.00	405.00
	$1450.00	$145.00	$1305.00	$855.00

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
	450.00	45.00	405.00	202.50
Deposit Number 3    ^	202.50	202.50	0.00	0.00
	$1652.50	$347.50	$1305.00	$652.50

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
	450.00	45.00	405.00	202.50
Loan Number 3    ^	202.50	20.25	182.25	182.25
	$1652.50	$165.25	$1487.25	$834.75

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
	450.00	45.00	405.00	202.50
	202.50	20.25	182.25	91.13
Deposit Number 4    ^	91.13	91.13	0.00	0.00
	$1743.63	$256.38	$1487.25	$743.63

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
	450.00	45.00	405.00	202.50
	202.50	20.25	182.25	91.13
Loan Number 4    ^	91.13	9.11	82.01	82.01
	$1743.63	$174.36	$1569.26	$825.64

0

	Deposits Recorded (Deposit Dollars)	Cash Dollars in the Bank	Debt to the Bank	Cash Dollars in Circulation
	$1000.00	$100.00	$900.00	$450.00
	450.00	45.00	405.00	202.50
	202.50	20.25	182.25	91.13
	91.13	9.11	82.02	41.01
Deposit Number 5    ^	41.01	41.01	0.00	0.00
	$1784.64	$215.37	$1569.27	$784.64

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