Banks and Money Multipliers

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money: An item is considered to be money if it serves as (a) a medium of exchange, (b) a standard unit of account (or measure of value), and (c) a store of value.

monetary base (MB): The monetary base (sometimes called “high-powered money”) is the total of bank reserves plus currency held by the nonbanking public.

demand deposits: Demand deposits are funds kept in a financial institution that by law must be available immediately in response to the depositor’s request. Checking accounts are examples.

reserve requirement ratio (rr): The fraction of a bank’s deposit liabilities that it legally must hold in reserves is the reserve requirement ratio.

potential money multiplier: The potential money multiplier (mp) equals the monetary base (MB) times the reciprocal of the required reserve ratio (rr): mp = MB × 1/rr.

actual money multiplier: The actual money multiplier (ma) equals the monetary supply (MS) divided by the monetary base (MB):  ma = MS / MB.

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Banks and the Creation of Money

 

Where does money come from? We know that U.S. currency is printed by the Federal Reserve System (bills) or minted by the Treasury (coins). But demand deposits (checking accounts) are the largest component of our money supply. Currency is little more than convenience money—less than 30 percent of the M1 money supply. How do demand deposits originate?

 

The Origin of Fractional Reserve Banking

 

Several centuries ago, money consisted primarily of gold coins. Wealthy people found the amounts of gold they accumulated quite heavy. (Gold is only semi-portable.) An even bigger drawback is that thieves love gold. Gold pieces (or modern coins for that matter) are rarely identifiable as stolen. Looking around for safe places to store their wealth, people in medieval Europe thought of goldsmiths. Goldsmiths made jewelry, gold statues, and other precious goods. Most also had some excess space in their heavily guarded vaults.

Most goldsmiths were willing to store valuables for a small fee and issued receipts for the gold deposited with them. Buyers found it convenient to exchange these receipts instead of physically getting the gold, and sellers were happy to take the receipts because they knew they could redeem them for gold whenever they wished. This was the beginning of checking accounts – the receipts issued by the goldsmiths were primitive demand deposits.

Goldsmiths observed that they stored nearly all of a community’s coins and that the gold in their vaults fluctuated little. When a buyer paid for a purchase with a gold receipt, sellers typically were content to leave the gold in the vault. After all, receipts could be used for purchases as readily as gold. One depositor’s withdrawal was just another customer’s deposit. The goldsmiths began lending some of the gold on deposit to borrowers who would pay interest. In fact, they seldom physically relinquished much gold – just like depositors, most borrowers preferred receipts to the actual gold. This was the origin of modern fractional reserve banking.

 

Demand Deposit Expansion

 

People sometimes physically withdrew gold, so the total value of receipts that could be written as loans was limited. Goldsmiths kept reserves in their vaults to meet withdrawals of deposits.

Banks keep reserves on hand to meet withdrawals by depositors.

Suppose a goldsmith observed that, although deposits and withdrawals were sporadic, the amount of gold in the vault varied less than 10 percent annually. How much might a prudent goldsmith loan from a given deposit of gold?

For simplicity, consider a monopolist who owns the only local vault. (We look at a multi-bank world in a bit.) This goldsmith cautiously stops lending when the value of receipts (demand deposits) issued is five times larger than the gold on deposit. That is, reserves equal 20 percent of deposits – twice the observed variation in deposits (10 percent), and solid insurance against excessive deposits being withdrawn simultaneously.

Fractional reserve banking legally permits financial institutions to hold less than 100 percent of their deposits as currency in their vaults.

We also assume the goldsmith already has many deposits and loans outstanding prior to the transactions we will consider and views “the bank” as fully loaned up[1] (reserves equal 20 percent of earlier deposits). Finally, we initially assume that no one actually withdraws any gold during the period considered; receipts for gold are perfectly acceptable as money.

Suppose Allen, a gold miner, deposits $1,000 worth of newly mined gold in Goldsmith’s bank. This deposit and issuance of a receipt are written in the bank’s “T-account” shown in Table 1. T-accounts statements represent partial balance sheets for the bank. The left-hand and right-hand entries must balance, and reflect only changes in the accounts following the new $1,000 deposit. The $1,000 recorded on the right side (credit) represents a liability or debt of the bank – Goldsmith owes Allen $1,000 on demand. The left side (debit) shows an increase of $1,000 in the bank’s reserves, which is Goldsmith’s new asset.

 

 

Table 1: Initial Deposit of $1,000 in a New Account in Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

+$1,000 Reserves (Gold)

   $   200 Planned reserves (RR)

   $   800 Excess reserves (XR)

+$1,000 (Demand Deposit — Allen)

 

 

When Bob, a local customer, wants to borrow, Goldsmith is happy to lend him as much as $800. How did we arrive at $800? Goldsmith calculates: 20 percent times $1,000 equals $200, which is planned for reserves (RR). Actual reserves of $1,000 minus $200 in planned reserves equal $800 in excess reserves (XR) available for the loan. When Bob borrows the full $800, the bank deposits $800 to Bob’s account, and the bank’s accounts change as shown in the T-account of Table 2. When you borrow money from a bank, the standard practice is to credit your account instead of handing you cash. The bank’s assets are increased by an $800 IOU from Bob; its new liability is Bob’s demand deposit for $800.

 

 

Table 2 First-Round Lending: Changes in Accounts in Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

+$800 (IOU – Bob)

    +$800 (Demand Deposit — Bob)

 

 

Notice that the $1,000 in gold reserves now “backs” $1,800 in demand deposit money. This may sound like a magician’s trick, but it is the way banks operate. Suppose Bob writes Carol a check for $800 – he did intend to spend the money he borrowed. Table 3 shows the bank’s view of this exchange. Bob’s $800 demand deposit simply becomes Carol’s demand deposit. In fact, because all deposits stay in this bank, we can ignore further transactions between the bank’s customers. Such transactions are irrelevant for the bank’s asset/liability position and for the amount of money in circulation.

 

 

Table 3: A Transaction Between Two of Goldsmith’s Depositors

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

(No change)

     – $800 (Demand Deposit— Bob)

     + $800 (Demand Deposit— Carol)

 

 

When Deirdre wants to borrow money, Goldsmith can still lend up to $640, because actual reserves of {$1,000 – 0.20  ($1,000+ $800) = $640 (excess reserves available to lend her). Alternatively, 80 percent of Carol’s deposit (0.80 × $800) is $640. Her IOU and the loan that is deposited to Deirdre’s account are shown in the T-account in Table 4.

 

 

Table 4:  Second-Round Lending: Changes in Accounts in Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

+$640 (IOU—Deirdre)

     +$640 (Demand Deposit — Deirdre)

 

 

When Ed comes in to borrow money, Goldsmith offers a loan of as much as $512 because $1,000 – [0.20 × ($1,000 + $800 + $640)] = $512. Again, 80 percent of Deirdre’s $640 deposit is $512 and is available to loan. Table 5 depicts this loan and demand deposit (DD).

 

 

Table 5:  Third-Round Lending: Changes in Accounts in Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

+$512 (IOU—Ed)

     +$512 (Demand Deposit — Ed)

 

 

At this point, the $1,000 the bank holds as reserves supports $2,952 in demand deposits ($1,000 + $800 + $640 + $512). How much longer can this process continue? The answer is that the bank can make more loans as long as 20 percent times all demand deposits is less than the $1,000 held in reserve. To spare you further agony, all possible subsequent loans and demand deposits (dd) are summarized in table 6.

 

 

Table 6:  All Remaining Rounds:  Changes in Accounts in Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

+$2,048 (IOU – All others)

+$2,048 (Demand Deposit – All others)

 

 

How did we know how large this entry would be? Well, the bank will continue to make loans until 0.20 × (DD) = $1,000. If both sides of this equation are multiplied by five, we get: DD = 5($1,000) = $5,000. The $1,000 held in bank reserves will support up to $5,000 in DD, regardless of whether these dds are based on loans or not. In fact, the original $1,000 in new money deposited by Allen allowed the creation of an additional $4,000 in demand deposits generated as loans. Table 7 summarizes all these transactions.

 

 

Table 7:  Summary of Transactions at Goldsmith’s Bank

 

 

 

Assets (debits)

Liabilities (credits)

 

 

 

1            +$1,000 Reserves

2            +800 (IOU – Bob)

3               No change

 

4            +640 (IOU – Deirdre)

5            +512 (IOU – Ed)

6            +2,048 (IOU – All others)

Total      +$5,000  ($1,000  gold reserves + $4,000  IOUs)

    + $1,000 (Demand Deposit – Allen)

    +      800 (Demand Deposit – Bob)

    –      800 (Demand Deposit – Bob)

    +      800 (Demand Deposit – Carol)

    +      640 (Demand Deposit – Deirdre)

    +      512 (Demand Deposit – Ed)

    +    2,048 (Demand Deposit – All others)

    +  $5,000 (Total new Demand Deposits)

 

 

It is not absolutely necessary for Goldsmith, as a monopoly banker, to go through all these lending rounds. After experimenting a bit, Goldsmith would learn that Allen’s $1,000 deposit could be translated directly into an immediate $4,000 loan to Bob. We have gone through each step of this loan-money creation process because of its relevance for a multiple-bank financial system.  In a multi-banking system, many of these transactions would have taken place in different banks – the banks into which deposits were made after the borrowers made purchases.

 

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Author: Ralph Byrns

 

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