4. The Effects Produced by Bankers' Use of Demand Deposits: The Case of an Individual Bank

Nevertheless, as we saw in chapter 2, bankers were soon tempted to violate the traditional rule of conduct requiring them to maintain the tantundem of monetary irregular deposits continuously available to depositors, and they ended up using at least a portion of demand deposits for their own benefit. In chapter 3 we covered the comments of Saravia de la Calle with respect to this human temptation. Now we must stress how overwhelming and nearly irresistible it is, given the huge profits that result from yielding to it. When bankers first began using their depositors' money, they did so shamefacedly and in secret, as shown by chapter 2's analysis of different historical cases. At this time bankers were still keenly aware of the wrongful nature of their actions. It was only later, after many centuries and vicissitudes, that bankers were successful in their aim to openly and legally violate the traditional legal principle, since they happily obtained the governmental privilege necessary to use their depositors' money (generally by granting loans, which initially were often given to the government itself.)⁷ We will now consider the way bankers record the appropriation of demand deposits in their account books. Our study will begin with the case of an individual bank and will later extend to the banking system as a whole.

THE CONTINENTAL ACCOUNTING SYSTEM

Two accounting systems, the continental and the Anglo-Saxon, have traditionally been used to document the phenomenon we are studying. The continental system is based on the false notion that for the depositor, the irregular deposit contract is a true deposit contract, while for the banker it is a loan or mutuum contract. In this case, Mr. X makes a “demand” deposit of 1,000,000 m.u. in Bank A, and Bank A receives the money not as a deposit, but as a loan it can freely use, considering the depositor will not be aware of this use nor be affected by it. Moreover, while keeping only a portion of deposits on hand as a security reserve, the bank estimates it will be able to comply with depositors' withdrawal requests. These expectations are especially strong, given that under normal circumstances it is highly unlikely customers will attempt to withdraw an amount exceeding the security margin or reserve ratio. Experience appears to show this is true, and the trust the bank has earned through years of properly safeguarding clients' deposits contributes to the unlikelihood of such a predicament, as does the fact that many withdrawals are offset by new deposits. If we suppose the banker considers a 10-percent security reserve (also called a “reserve ratio”) sufficient to satisfy possible demands for deposit withdrawals, then the other 90 percent of demand deposits, or 900,000 m.u., would be available to him to use to his own benefit. Using the European accounting system, this economic event would be represented in the following way:⁸

When Mr. X makes the demand deposit, a book entry identical to number (7) is made, though this time it is not considered a memorandum entry.

Once the bank yields to the temptation to appropriate most of the tantundem, which it should keep on hand and available to the depositor, the following entry is made:

At the moment the banker appropriates the money and loans it to Z, an economic event of great significance occurs: 900,000 m.u. are created ex nihilo, or out of nothing. Indeed, Mr. X's essential motive for making a demand deposit of 1,000,000 m.u. was the custody and safekeeping of the money, and with good reason he subjectively believes he retains the complete availability of it, just as if he had it in his pocket, and in a sense better. To all intents and purposes, Mr. X still has 1,000,000 m.u. in cash as if the money were physically “in his possession,” since according to his contract it remains fully available to him. From an economic standpoint, there is no doubt the 1,000,000 m.u. Mr. X deposited in Bank A continue to contribute to his cash balances. However, when the bank appropriates 900,000 m.u. from deposits and loans them to Z, it simultaneously generates additional purchasing power from nothing and transfers it to Z, the borrower, who receives 900,000 m.u. It is clear that, both subjectively and objectively, Z enjoys the full availability of 900,000 m.u. beginning at that point and that these monetary units are transferred to him.⁹ Therefore, there has been an increase in the amount of money in circulation in the market, due to beliefs held simultaneously and with good reason by two different economic agents: one thinks he has 1,000,000 m.u. at his disposal, and the other believes he has 900,000 m.u. at his disposal. In other words, the bank's appropriation of 900,000 m.u. from a demand deposit results in an increase equal to 900,000 m.u. in the aggregate balances of money existing in the market. In contrast, the loan or mutuum contract covered earlier involves no such occurrence.

We should also consider the location of the existing money in the market from the time the banker appropriates the deposit. The number of monetary units in the market has clearly grown to 1,900,000, though these units exist in different forms. We say there are 1,900,000 m.u. because different economic agents subjectively believe they have at their disposal 1,900,000 m.u. to exchange in the market, and money consists of all generally-accepted mediums of exchange. Nevertheless the form of the money varies: Borrower Z possesses it in a different form from Mr. X, who made the deposit. Indeed, Z has available to him 900,000 physical monetary units (which we could call commodity money or, nowadays, paper money or fiat money), while Depositor X has a checking account containing a deposit of 1,000,000 m.u. Considering the bank has kept 100,000 m.u. in its vault as a security reserve or reserve ratio, the difference between 1,900,000 m.u. and the 1,000,000 m.u. existing in physical form is equal to the amount of money the bank created from nothing. (A total money supply of 1,900,000 m.u. minus 900,000 physical m.u. in Z's possession and 100,000 physical m.u. in the bank's vault equals 900,000 m.u. which do not physically exist anywhere.) As this money lacks the corresponding backing and exists due to the confidence Depositor X has in Bank A, it is called fiduciary money (or, better, fiduciary media). It is important to emphasize that to all intents and purposes demand deposits are like physical units; that is, they are perfect money substitutes. The depositor can use them to make payments at any time by issuing a check on which he writes the sum he wishes to pay and giving instructions to the bank to make the payment. The portion of these perfect money substitutes, or demand deposits, which is not fully backed by physical monetary units in the bank's vault (the 900,000 m.u. not backed by reserves in the present example) is called fiduciary media. ¹⁰

Demand deposits backed by cash reserves at the bank (100,000 m.u. in our example) are also called primary deposits, while the portion of demand deposits not backed by the bank's reserves (fiduciary media) is also called a secondary deposit or derivative deposit. ¹¹

Once banks had violated the legal principle that no one may appropriate a deposit made with them for safekeeping, and had ceased to guard 100 percent of the tantundem, it was natural for them to try to justify their activity and defend themselves with the argument that they had actually received the money as if it were a loan. In fact, if a banker considers the money received a loan, then there is nothing improper in his conduct, and from the economic and accounting viewpoint described in the previous section, he is only playing the legitimate, necessary role of intermediary between lenders and borrowers. Nonetheless, an essential difference arises here: the money is not handed over to the bank as a loan, but as a deposit. In other words, when Mr. X made his deposit, he did not have the slightest intention of relinquishing the availability of present goods in exchange for a somewhat higher figure (considering interest) of future goods. Instead, his only desire was to improve the custody and safekeeping of his money and to receive other peripheral services (cashier and bookkeeping services), while at all times retaining the full, unaltered availability of the tantundem. This absence of an exchange of present goods for future goods is precisely what indicates we are faced with a radically different economic event, one that involves the creation ex nihilo of 900,000 m.u. of fiduciary media or derivative deposits when the bank loans 90 percent of the money it has in its vault.

In addition it is important to understand clearly that if the bank uses the money to grant a loan to Z, as we have supposed in our example and is usually the case, this loan does entail the exchange of present goods for future goods, though it is not backed anywhere in the market by a necessary, previous increase of 900,000 m.u. in voluntary saving. Indeed, the bank creates from nothing money it loans to Z in the form of present goods, while no one has been first obliged to increase his savings by the amount of the loan. Mr. X, the original depositor, continues to subjectively believe he possesses the full availability of the 1,000,000 m.u. he deposited in the bank; that is, he thinks he has at his disposal 1,000,000 m.u. of a completely liquid asset (money). At the same time, Borrower Z receives for his investments 900,000 m.u. of new liquidity which has not come from anyone's savings. In short, two different people simultaneously believe they have at their full disposal the same liquid asset of 900,000 m.u., which correspond to the portion of the deposit of 1,000,000 m.u. which the bank loaned to Z (derivative deposit). At this point it is obvious banks generate liquidity which is invested without any prior saving. This phenomenon constitutes the main cause of recurring economic crises and recessions, and we will examine its crucial economic importance in the following chapters.

Once the bank has given the loan to Z, the bank's balance sheet appears as follows:

Clearly, the banker will tend to deceive himself, thinking he has received his depositors' money as a loan. Furthermore, it will never occur to him that by granting the loan to Business Z he has created 900,000 m.u. ex nihilo, nor much less that he has granted a loan without the prior backing of an actual increase in saving by anyone. Moreover, the banker will consider the natural counteraction between withdrawals and new deposits, and in accordance with his “experience,” he will deem his decision to maintain a cash or security reserve of 10 percent adequate and the resulting cash reserve of 100,000 m.u. more than sufficient to satisfy requests for normal deposit withdrawals by customers.¹² The whole structure is made possible by customers' faith that the bank will honor its future commitments. The bank must build up this faith through the impeccable custody and safekeeping of the money for an extended period of time, without any misappropriation.¹³ It is understandable that a banker may not be familiar with economic theory and therefore not recognize the fundamental economic events we have just described. It is more difficult to excuse the fact that his misappropriation of deposits constitutes a violation of traditional legal principles which, in the absence of a theory to explain the social processes involved, serve as the only safe guide to follow in order to avoid severe social damage. However, any intelligent person, banker or not, would surely be able to see some signs of what is really happening. Why is it necessary for the banker to maintain any reserve ratio? Does he not realize that when he acts legitimately as true intermediary between lenders and borrowers he need not maintain any? Does he not understand, as Röpke states, that his bank is “an institution which, finding it possible to hold less cash than it promises to pay and living on the difference, regularly promises more than it could actually pay should the worse come to the worst”?¹⁴ In any case, these are simply indications which any practical person could understandably interpret in a wide variety of ways. Legal principles exist for precisely this reason. They act as an “automatic pilot” for behavior and facilitate cooperation between people, though given the abstract nature of these principles, we may not be able to identify their exact role in the processes of social interaction.

As Mises correctly indicates, as long as confidence in the bank is preserved, the bank will be able to continue using the majority of deposited funds, and customers will remain unaware that the bank lacks the necessary liquidity to meet all of its commitments. It is as if the bank had found a permanent source of financing in the creation of new money, a source it will continue to tap as long as the public retains its faith in the bank's ability to fulfill its commitments. In fact, as long as these circumstances last, the bank will even be able to use its newly created liquidity for covering its own expenses or for any other purpose besides granting loans. In short, the ability to create money ex nihilo generates wealth the banker can easily appropriate, provided customers do not doubt his good conduct. The generation of this wealth is detrimental to many third parties, each of whom suffers a share of the damage caused by the banker's activities. It is impossible to identify these individuals, and they are unlikely to recognize the harm they suffer or to discover the identity of the perpetrator.¹⁵

Though private bankers may often be unaware that their ability to create new money ex nihilo (by using customers' deposits to grant loans) constitutes a source of huge profits, and although they may naively believe they are merely loaning a part of what they receive, the majority of their profits still derive from a general process in which they are immersed and the implications of which they do not completely comprehend. We will see this point confirmed later when we study the effects of fractional-reserve banking in terms of the entire banking system. One thing bankers understand perfectly, however, is that by loaning most of the funds clients deposit, they make a much larger profit than they would if they acted only as legitimate intermediaries between lenders and borrowers—entries (1) to (6)—or as mere providers of bookkeeping and cashier services—entries (8) and (9). In fact on the loan made to Z, Bank Awill earn an interest rate of 15 percent of the amount of the loan; that is, 135,000 m.u. The entry is as follows:

If we suppose the bank performs the cashier and bookkeeping services described earlier, which are typical of checking accounts and generate an operating cost of 20,000 m.u. in our example, then by covering these costs with interest income it is even able to provide these services free of charge. The following entry is made to record the operating costs:

Although the bank would be completely justified in continuing to charge 30,000 m.u. (3 percent of the amount deposited) for its services, and although it may offer these services free to its depositors to attract more deposits and to pursue the more or less covert objective of using these deposits to grant loans, it still makes a very large profit, equal to the 135,000 m.u. it receives in interest, minus the 20,000 m.u. it pays in operating costs.

In fact the bank's profit of 115,000 m.u. is more than double the legitimate profit it would make as a mere financial intermediary between lenders and borrowers and more than ten times what it would bring in by charging its customers for cashier and bookkeeping services.¹⁶ The bank's income statement would hence appear as follows:

After carrying out all of the operations, the bank's balance sheet would appear as follows:

ACCOUNTING PRACTICES IN THE ENGLISH-SPEAKING WORLD

English banking practices reflect fewer reservations about plainly recording in the accounts the creation ex nihilo of fiduciary media. Indeed, as Hayek states, “English banking practice credits the account of the customer with the amount borrowed before the latter is actually utilized.”¹⁷

In English-speaking countries, when a customer makes a demand deposit of 1,000,000 m.u. at a bank, the first account entry made corresponds exactly to that made in the continental system:

The difference between the Anglo-Saxon and the continental system lies in the entry the English-speaking banker makes upon deciding to grant a loan to Z, and hence to make self-interested use of 900,000 m.u. the banker holds in his vault in excess of his security reserve. In Anglo-Saxon banking practices, an entry is made to record the loan under Assets, and at the same time a checking account in favor of the borrower is opened under Liabilities for the sum of the loan (900,000 m.u.). The entry looks like this:

Thus, in this respect the English custom is much more straightforward and appropriate to the actual economic events than the continental custom. Anglo-Saxon accounting practices distinctly reflect the ex nihilo creation of 900,000 m.u. which results when demand deposit funds are loaned to Z. After the loan is granted, the bank's balance sheet appears as follows:

In keeping with the English custom, this balance sheet clearly reveals that the moment the bank grants a loan of 900,000 m.u., it simultaneously generates deposits ex nihilo for the sum of 900,000 m.u. In other words, the bank places at the disposal of the borrower up to 900,000 m.u., which raises the balance of demand deposits to 1,900,000 m.u. Of this amount, 1,000,000 m.u. correspond to physical monetary units; that is, to primary deposits. The other 900,000 m.u. reflect fiduciary media created from nothing; in other words, derivative or secondary deposits.

If we again suppose for the sake of argument that the banker regards as a loan the money placed with him on demand deposit, then because this loan derives from a monetary irregular-deposit contract, which by definition stipulates no term for the return of the money (as it is “on demand”), the “loan” in question would clearly have no term. Furthermore, if the depositors trust the bank, the banker will rightly expect them to withdraw only a small fraction of their deposits under normal conditions. As a result, even though the “loan” he has supposedly received from his depositors is “on demand,” the banker may with good reason consider it a “loan” he will never have to return, since it ultimately lacks a term. Obviously if the banker receives a loan believing he will never have to return it (and in most cases he does not even have to pay interest on it, though this is not fundamental to our argument), then rather than a loan, we are dealing with a de facto gift the banker gives himself and charges to the funds of his depositors. This means that although for accounting purposes the bank recognizes a debt (parallel to the loan granted) in the form of “demand deposits” (derivative or secondary deposits for the sum of 900,000 m.u.), under ordinary circumstances what the bank actually does is to create from nothing a perennial source of financing which the banker supposes he will never have to return. Therefore, despite the impression the account books give, the banker ultimately appropriates these funds and considers them his property. In short, banks amass tremendous wealth, mainly by generating means of payment to the detriment of third parties. The harm done is very generalized and diluted, however, and takes the form of a gradual relative loss of purchasing power. This phenomenon occurs constantly and stems from the banking system's ex nihilo creation of means of payment. This continuous transfer of wealth to bankers persists as long as the banking business suffers no disruptions and assets keep increasing bankers' balances in the form of loans and investments backed by the corresponding deposits created from nothing. The full recognition of this never-ending source of financing and of the enormous wealth banks have accumulated to the detriment of other citizens (money which still contributes to the banks' balances, disguised as active investments backed by “deposits”) will prove very important in the last chapter, when we propose a model for changing and reforming the current banking system. Though these funds in fact only benefit banks and governments, and though from an economic and accounting standpoint they belong to alleged depositors, in all reality they do not belong to anyone, since these depositors view their deposits as perfect money substitutes. Therefore, as we will see when we study the process of banking reform, these resources could be used to pursue important goals in the public interest. Such goals might include eliminating the remaining public debt or even financing a process of social-security reform to accomplish a transition from a pay-as-you-go public system to an entirely private system based on investment.

Let us return now to our example. As Borrower Z gradually uses his money by writing checks on the account opened for him by the bank, the two banking systems, the Anglo-Saxon and the Continental, would begin to reflect the bank's account records in an increasingly similar way. Let us suppose the borrower withdraws his loan in two portions, one on each of two separate, consecutive occasions. On the first occasion (t1) he withdraws 500,000 m.u., and on the second (t2), 400,000 m.u. The accounting entries would appear as follows:

After the borrower withdraws the entire loan, the bank's balance sheet looks like this:

This balance sheet corresponds exactly with balance sheet (12), which we obtained using continental accounting methods and which comprises demand deposits of 1,000,000 m.u. made by customers and backed by 100,000 m.u. in cash (the reserve ratio or requirement) and 900,000 m.u. in loans granted to Z. Therefore once the borrower withdraws his entire loan, the accounting records of both systems are identical: 1,900,000 m.u. exist in the market, of which 900,000 m.u. correspond to fiduciary media (the portion of demand deposits which are not backed by cash balances at the bank, in this case 1,000,000 m.u. minus 100,000 m.u.) and 1,000,000 m.u. are physical monetary units (the 100,000 m.u. in the bank's vault and the 900,000 m.u. that have been handed over to Borrower Z and which he has already used for his own purposes).¹⁸

The main advantage of the Anglo-Saxon accounting system is that it demonstrates, as Herbert J. Davenport pointed out in 1913, that banks “do not lend their deposits, but rather, by their own extensions of credit, create the deposits.”¹⁹ In other words, banks do not act as financial intermediaries when they loan money from demand deposits, since this activity does not constitute mediation between lenders and borrowers. Instead banks simply grant loans against deposits they create from nothing (fiduciary media) and which therefore have not first been entrusted to them by any third party as deposits of physical monetary units. Not even under the continental accounting system are banks financial intermediaries, since true original depositors turn their money over for custody and safekeeping, not as a loan to the bank. Furthermore we have already shown that by reducing to a fraction the number of monetary units they keep on hand (reserve ratio), banks create fiduciary media in proportion to the total sum of their unbacked deposits. Thus, by a somewhat more abstract analysis, the continental accounting system leads us to the same conclusion as the Anglo-Saxon system: rather than credit intermediaries, banks are creators of loans and deposits, or fiduciary media. Nevertheless, the process is much more obvious and easier to understand when evaluated according to Anglo-Saxon accounting criteria, because from the beginning this method reflects the fact that the bank creates deposits ex nihilo and grants loans against them. Therefore, no abstract intellectual exercise is required to understand the process.

From the perspective of economic theory, the chief disadvantage of both accounting systems is that they reflect a much lower volume of deposit creation and loan concession than truly exists. That is, they reveal only a fraction of the total volume of deposits and loans which the banking system as a whole is capable of creating. Only when we consider the effects of fractional-reserve banking from the standpoint of the overall banking system will this important fact be confirmed. However, first it is necessary to identify the limits to deposit creation and loan concession by an isolated bank.

AN ISOLATED BANK'S CAPACITY FOR CREDIT EXPANSION AND DEPOSIT CREATION

We will now consider the limits to an isolated bank's capacity to create loans and expand deposits from nothing. The following variables are involved:

d: the money originally deposited in the bank's vault;

d₁: the money or reserves which leave the bank as a result of loans it grants;

x: the bank's maximum possible credit expansion starting from d;

c: the cash or reserves ratio maintained by the bank, in keeping with the banker's experience and his careful judgment on how much money he needs to honor his commitments; and

k: the proportion of loans granted which, on average, remain unused by borrowers at any given time.

From the above definitions it is clear that the reserves which leave the bank, d₁, will be equal to the loans granted multiplied by the percentage of these loans which is used by borrowers; that is:

[1] d₁ = (1 - k)x

In addition, if we consider that the money which leaves the bank, d₁, is equal to the amount originally deposited, d, minus the minimum amount kept on reserve, cd, in relation to the money originally deposited, plus ckx, in relation to the percentage of loans which on average remains unused, then we have:

[2] d₁ = d - (cd + ckx)

If we now replace d₁ in formula [2] with the value of d₁ in [1], we have:

(1 - k)x = d - (cd + ckx)

Next we work to solve the equation, factor out common factors and isolate x:

(1 - k)x = d - cd - ckx

(1 - k)x + ckx = d - cd

x(1 - k + ck) = d(1 - c)

Therefore the maximum credit expansion, x, an isolated bank could bring about ex nihilo would be:²⁰

Or to put it another way:

As formula [3] makes clear, the reserve ratio, c, and the average percentage of loans which remain unused, k, have opposite effects on an isolated bank's capacity to create loans and deposits. That is, the lower c is and the higher k is, the higher x will be. The economic logic of formula [3] is therefore very plain: the higher the reserve ratio estimated necessary by the bank, the fewer the loans it will be able to grant; in contrast, if the reserve ratio or requirement remains unchanged, the fewer the loaned funds the bank believes, on average, will be withdrawn by borrowers, the more money it will have available for expanding loans.

Up until now we have assumed k to be the average percentage of loans unused by borrowers. However, according to C.A. Phillips, k can include other phenomena which have the same ultimate effect.²¹ For instance, k can stand for the very great likelihood that, in a market where few banks operate, a borrower will make payments to some other customers of his own bank. It is assumed that when this happens, these customers will deposit their checks in their own accounts at the same bank, thus keeping money from leaving the bank. This phenomenon has the same ultimate effect as an increase in the average percentage of loans unused by borrowers. The fewer the banks operating in the market, the higher k will be; the higher k is, the less money will leave the bank; the less money leaves the bank, the greater the bank's capacity for expanding loans. One of the strongest motivations behind the trend toward bank mergers and acquisitions which has always been obvious in fractional-reserve banking systems is precisely the desire to increase k. ²² In fact, the more banks merge and the larger their subsequent market share, the greater the possibility that the citizens who receive the banks' fiduciary media will be their own customers. Therefore both k and the corresponding capacity to create loans and deposits from nothing will be increased and the resulting profit much greater. The value of k is also increased when monetary deposits are made in other banks, which in turn expand their loans, and their borrowers ultimately deposit in the original bank a significant portion of the new money they receive. This phenomenon also causes an increase in the bank's monetary reserves and therefore in its capacity for credit expansion.

For example, if we suppose that the reserve ratio or requirement, c, is 10 percent; that the proportion of loans which remain unused, k (which also includes the effects of a larger number of bank customers, as well as other factors), is 20 percent; and that the sum of the original deposits, d, made in the bank is equal to 1,000,000 m.u.; then, by substituting these values into formula [3] we obtain:

Therefore we see that a bank which accepts 1,000,000 m.u. in demand deposits, and which maintains a reserve ratio of 10 percent and a k of 20 percent will be able to grant loans not only for the sum of 900,000 m.u., as we assumed for the purpose of illustration in entries (18) and following, but for a considerably larger amount, 1,097,560 m.u. Hence, even in the case of an isolated bank, the capacity for credit expansion and ex nihilo deposit creation is 22 percent greater than we initially supposed in entries (18) and following.²³ As a result, we should modify our earlier accounting entries to reflect that, in keeping with the Anglo-Saxon accounting system, when c =0.1 and k =0.2, the bank will be able to expand its credit by 1,097,560 m.u., instead of the 900,000 we assumed before (that is, the bank's capacity for credit expansion is 22 percent greater). The modified journal entries and corresponding balance sheet would appear as follows (compare with initial entries 18 and 19):

These entries correspond to an original deposit of 1,000,000 m.u. and an isolated bank's ex nihilo creation of loans and deposits for the sum of 1,097,560 m.u. The value of k (0.2) indicates that, on average, borrowers only withdraw 80 percent of the funds they are lent. When this withdrawal is made (and even if a greater amount is withdrawn, when some of the final recipients of the money are also customers of the original bank and deposit their money there), the following entry is recorded:²⁴

The bank's balance sheet would appear as follows:

THE CASE OF A VERY SMALL BANK

Let us now consider a particular type of isolated bank: a very small or “Lilliputian” bank; that is, one in which k =0.

This means borrowers immediately withdraw the entire amount of their loans, and those to whom they make payments are not customers of the same bank as the borrowers. If k =0, then by substituting this value into formula [3] we obtain formula [5]:

[5] x = d(1 - c)

And since in our example d = 1,000,000 m.u. and c = 0.1, then:

x = 1,000,000(1 - 0.1) = 1,000,000 . 0.9 = 900,000 m.u.

This is precisely the sum of deposits or fiduciary media created ex nihilo which appears in entries (11) and (18). Nevertheless, we saw in the last section that in practice, even if k is only slightly larger than 0, an isolated bank can create a considerably larger amount of fiduciary media. (If k = 0.2, it can create 22 percent more, or 1,097,560 m.u. instead of the 900,000 m.u. in the first example.) This is true whether the bank uses the continental accounting system or the Anglo-Saxon system, and the sum created may even exceed the total of original deposits in the isolated bank.

With this in mind, it is easy to understand why banks compete as fiercely as they do to attract the largest possible number of deposits and customers. Bankers try to obtain as much money as possible in the form of deposits, because they are capable of expanding credit for an even greater amount than the volume of their deposits. Thus, the greater the volume, the more the bank will be able to expand the corresponding credit. Bankers try to attract as many customers as they can, because the more customers they have, the larger k will be; and the larger k is, the greater their capacity to expand loans and generate deposits. Most importantly, bankers are technically unable to discern whether their growth policies lead to a broadening of their individual spheres of activity at the expense of other banks, or whether their policies ultimately result in a generalized increase in credit expansion involving the entire banking system, or whether both occur at once. Banks expand credit and deposits on their own and also participate in processes which bring about even greater credit and deposit expansion in the banking system as a whole. Moreover, in this process banks strive to play an increasingly important role with respect to other banks, and as a result they continually provide fresh impetus to credit expansion on the level of individual banks and in the banking system as a whole. In any case, k is a crucial factor in determining a bank's earning power. Competition between banks keeps k significantly below 1, however each bank fights to continually raise the value of its k factor. To do so banks take advantage of their opportunities (with respect to geographic expansion, the ability to exclude or take over competitors and the development of competitive advantages).²⁵ Though a k factor equal to one is impossible for an isolated bank (except in the case of a monopolistic bank), k values significantly greater than zero are very common, and under almost all circumstances, banks make a supreme effort to increase k. Among other phenomena, this explains the constant pressure they face to merge with other banks.

For illustrative purposes, we have compiled the following table of different combinations of reserve ratios, c, and percentages of loans unused or customers banking with the same institution, k, which allow an isolated bank to alone double its money supply (by substituting these values into formula [3], we obtain x =d).

CREDIT EXPANSION ANDEX NIHILO DEPOSIT CREATION BY A SOLE, MONOPOLISTIC BANK

Let us now suppose that k =1. We are dealing either with a sole, monopolistic bank in which borrowers are obliged, because there is no other, to maintain as deposits all funds they are lent; or a situation exists in which all final recipients of payments made by borrowers of the bank are also clients of the bank. (This “ideal” goal would be reached at the merger of all remaining megabanks.) When we substitute the value k =1 into formula [3], we obtain:

Returning to our example in which d =1,000,000 m.u. and c =0.1, if we substitute these values into the formula, we obtain:

In this case, the bank could alone create ex nihilo loans and deposits or fiduciary media for the sum of 9,000,000 m.u., which means it could multiply its total money supply by ten (1,000,000 m.u. originally deposited, plus 9,000,000 m.u. in the form of fiduciary media or deposits created from nothing to back the loans granted by the bank).

Following the example of Bresciani-Turroni,²⁶ and assuming all payment transactions are carried out between customers of the same bank (given that it is monopolistic, or because certain circumstances exist which produce this situation), we will now use accounting records to show the process leading to this result.

We will now follow the traditional continental system (as opposed to the Anglo-Saxon) in which all payments are registered in the cash account. The following represents the journal at moments t₁, t₂, t₃,... t₉, etc., and reflects the bank's practice of repetitively granting its own clients loans for an amount equal to 90 percent of the funds it receives in cash. The clients withdraw the full amount of the loan, but because they have no account in any other bank (or there is no other bank in society), they ultimately deposit the money they receive back into the same bank. This permits the bank, in turn, to grant new loans and generate new deposits, and the process is repeated again and again:

Let us suppose that U withdraws the entire amount of his loan and pays his creditor, A. A is also a customer of U's bank and deposits the 900,000 m.u. he receives. The following entries result:

We will assume that Borrower V withdraws his money and pays Creditor B, who is also a customer of the bank and deposits his money back into it. This repetitive process continues, producing the following journal entries:

This occurs again and again, until at the end of the year the bank's total deposits equal:

The above expression represents the sum of the terms in a geometrical progression. The terms increase and have a common ratio of 0.9.²⁷

In our example, r =0.9 and a =1,000,000 m.u., and hence the sum of the terms would be equal to:

If we keep in mind that d represents the 1,000,000 m.u. originally deposited, and that r =1-c ; that is, r =1-0.1=0.9, then clearly the sum of all the bank's deposits (original and secondary) would be:

Thus, the total volume of deposits in a monopolistic bank (or in a bank where all those who receive money from the bank's borrowers also ultimately have their accounts) would be equal to the value of the original deposits, d, divided by the reserve ratio, c.

Formula [14] is the simplest version of the so-called bank multiplier, and it is identical to formula [27], which yields the same result for a banking system of multiple small banks and appears to have been worked out for the first time by Alfred Marshall in 1887.²⁸

We could use the following formula to calculate the net credit expansion the bank brings about ex nihilo (in other words, the deposits or fiduciary media generated from nothing to make the credit expansion possible):

Now we factor out common factors:

The above formula coincides with [6].

In fact, when d =1,000,000 m.u. and c =0.1, in the case of a monopolistic bank, the net credit expansion would be equal to:

Therefore the balance sheet of Bank A, a monopolistic bank, would ultimately appear as follows:

With only 1,000,000 m.u. in original deposits safeguarded in its vault, Bank A, a monopolist, has expanded credit by granting loans for the sum of 9,000,000 m.u. and creating from nothing 9,000,000 m.u. in new deposits or fiduciary media to back these loans.²⁹