How To Calculate Total Money Supply When All Banks Have The Same Reseve Ratio

Learning Objectives

• Explain and testify how banks create money
• Use the money multiplier formula to calculate how banks create coin

Money Cosmos by a Single Bank

Banks and coin are intertwined. Information technology is not only that about money is in the form of depository financial institution accounts. The cyberbanking system can literally create money through the process of making loans. Let's see how.

Showtime with a hypothetical bank called Singleton Bank. The bank has $10 million in deposits. The T-account balance sheet for Singleton Depository financial institution, when it holds all of the deposits in its vaults, is shown in Figure 1. At this stage, Singleton Banking concern is simply storing coin for depositors; information technology is not using these deposits to brand loans, so information technology cannot pay its depositors interest either.

Figure 1. Singleton Banking company's Balance Canvass: Receives $x million in Deposits.

Singleton Bank is required by the Federal Reserve to go along 10% of total deposits, or  $ane million, on reserve to encompass withdrawals. It will loan out the remaining $9 million. Past loaning out the $ix million and charging interest, it volition exist able to make interest payments to depositors and earn involvement income for Singleton Banking company and make involvement payments to depositors (for now, nosotros will proceed it simple and not put interest income on the rest sail). Instead of becoming just a storage place for deposits, Singleton Bank can become a financial intermediary between savers and borrowers.

This change in business programme alters Singleton Bank'south rest sheet, as shown in Effigy 2. Singleton's assets have changed; it at present has $1 million in reserves and a loan to Hank's Auto Supply of $nine 1000000. The depository financial institution even so has $10 million in deposits.

Effigy 2. Singleton Banking company's Balance Sheet: 10% Reserves, One Round of Loans

Singleton Bank lends $9 one thousand thousand to Hank's Auto Supply. The bank records this loan past making an entry on the balance sheet to indicate that a loan has been made. This loan is an asset, because it will generate interest income for the bank. Of course, the loan officer is not going to let Hank walk out of the bank with $9 million in cash. The banking company issues Hank'due south Auto Supply a cashier's bank check for the $9 million. Hank deposits the loan in his regular checking account with Start National. The deposits at Kickoff National rise by $ix million and its reserves also ascent past $9 one thousand thousand, equally Figure 3 shows. First National must hold 10% of boosted deposits as required reserves but is free to loan out the rest.

Effigy iii. First National Bank'due south Balance Sheet: Required 10% Reserves

Since the loan to Hank was deposited into a need eolith account (Hank'south checking account), the loan increases the M1 money supply. Making loans that are deposited into a demand deposit account increases the M1 money supply. Remember the definition of M1 includes checkable (demand) deposits, which can be easily used as a medium of exchange to buy goods and services. Notice that the money supply is now $xix million: $x million in deposits in Singleton banking company and $9 million in deposits at Commencement National. Apparently these deposits will exist fatigued down equally Hank's Auto Supply writes checks to pay its bills, but as long every bit those checks are deposited in other checking accounts, the consequence is the aforementioned. The bottom line is that a bank must hold enough money to meet its reserve requirement; the rest the bank loans out, and those loans, when deposited, add to the coin supply. In this case then far, banking concern lending has expanded the money supply by $9 1000000.

At present, Outset National must hold but 10% as required reserves ($ninety,000) but can lend out the other 90% ($viii.i meg) in a loan to Jack's Chevy Dealership as shown in Figure 4.

Figure four. First National Rest Sheet

If Jack's deposits the loan in its checking business relationship at Second National, the money supply just increased past an additional $8.i million, as Figure 5 shows.

Effigy v. Second National Banking company's Balance Sheet

How is this money creation possible? It is possible because there are multiple banks in the financial organization, they are required to hold only a fraction of their deposits, and loans end up deposited in other banks, which increases deposits and, in essence, the money supply.

Endeavor It

Sentry It

This video explains how banks use deposits and loans to create money.

You lot can view the transcript for "How Banks Create Coin – Macro Topic four.4" here (opens in new window).

The Money Multiplier in a Multi-Bank Arrangement

In a system with multiple banks, the initial excess reserve corporeality that Singleton Banking company decided to lend to Hank's Auto Supply was deposited into Get-go National Bank, which is gratis to loan out $eight.i million. If all banks loan out their excess reserves, the money supply will aggrandize. In a multi-banking company organization, the amount of money that the system can create is found by using the money multiplier. The coin multiplier tells us by how many times a loan will be "multiplied" through the process of lending out backlog reserves, which are deposited in banks every bit demand deposits. Thus, the coin multiplier is the ratio of the change in money supply to the initial change in bank reserves.

Fortunately, a formula exists for calculating the full of these many rounds of lending in a banking system. Themoney multiplier formula is:

[latex]\displaystyle\frac{1}{\text{Required Reserve Ratio}}[/latex]

USING THE Coin MULTIPLIER FORMULA

Using the money multiplier for the example from Singleton Bank higher up in this text:

Step one. In this example, the reserve requirement is x% (or 0.10), and then the coin multiplier is one divided by 0.ten, which is equal to 10.

Footstep 2. Since Singleton Bank initially has reserves of $10 million, using the formula we can determine the potential amount of new money created past that deposit:

[latex]\displaystyle\text{Total M1 Money Supply Supported by Singleton Bank's Reserves}=\frac{one}{\text{Required Reserve Ratio}}\times\text{Bank Reserves}[/latex]

[latex]\displaystyle\text{Total M1 Money Supply Supported past Singleton Depository financial institution'south Reserves}=\frac{one}{0.10}\times{ten}\text{ meg}[/latex]

[latex]\displaystyle\text{Total M1 Money Supply Supported by Singleton Banking concern'southward Reserves}=x\times{10}\text{ 1000000}[/latex]

[latex]\displaystyle\text{Total M1 Money Supply}=100\text{ million}[/latex]

Step iii. Thus, we tin can say that, in this example, subsequently all rounds of lending are completed, Singleton Bank's initial reserves of $x million will back up $100 million in M1 Money Supply.

Step four. Since initially Singleton Bank started with $10 one thousand thousand in need deposits (which means that $10 one thousand thousand was already counted in the money supply), we subtract that initial amount from the total.

[latex]\displaystyle\text{Change in M1 Money Supply}=\frac{1}{\text{Required Reserve Ratio}}\times\text{Bank Reserves} - \text{Initial Deposit}[/latex]

[latex]\displaystyle\text{Full M1 Money Supply Supported by Singleton Bank's Reserves}=10\times{10}\text{ meg} -{10}\text{ million}=90\text{ million}[/latex]

And then the loan expansion procedure from Singleton Bank's Deposit was able to create $90 meg in new deposits/coin supply.

Notation that when we talk near changes in the M1 money supply, it makes a divergence whether the modify in deposits comes from people depositing currency or from the Federal Reserve.

If a person takes currency and deposits information technology into their checking account, their bank holds the required reserves and and then lends out the rest, spurring the loan expansion procedure. The change in the coin supply needs to take into business relationship that the currency was already part of M1 and shouldn't be counted again.

Thus, the change in the M1 money supply will exist the change in deposits multiplied by the money multiplier minus the decrease in currency held that was deposited in the bank (as shown in this example with Singleton Banking concern).

Let's look at another instance. Suppose Carla deposits $fifty in cash into her checking account. The $l cash was already role of the coin supply. If the required reserve ratio is 10%, the money multiplier will be one/x% = i/0.ten = 10. Carla's banking concern keeps $5 of her eolith as required reserves and loans out the rest. When the loan expansion procedure in the banking organization is complete, the total alter in the M1 money supply is 10 times $50 minus the $50 currency that Carla moved from currency to her depository financial institution account.

Modify in M1 Coin Supply = 10 x $50 = $500 – $l = $450

In the module on monetary policy, nosotros volition explain how when the Federal Reserve conducts expansionary budgetary policy (ie. purchasing Treasury bonds), the change in deposits comes from outside the financial organization. In that case, the change in the money supply volition equal the change in deposits times the coin multiplier. Since there is no change in currency holdings, we don't subtract the amount of the initial eolith.

Cautions about the Money Multiplier

The coin multiplier will depend on the proportion of reserves that banks are required to concur past the Federal Reserve Banking concern. Additionally, a banking concern can also choose to hold extra reserves. Banks may make up one's mind to vary how much they agree in reserves for two reasons: macroeconomic weather and government rules. When an economic system is in recession, banks are likely to hold a higher proportion of reserves because they fright that loans are less probable to be repaid when the economic system is deadening. The Federal Reserve may also raise or lower the required reserves held by banks as a policy motion to bear upon the quantity of money in an economy, equally we will discuss in more depth in the module on monetary policy.

The process of how banks create coin shows how the quantity of money in an economy is closely linked to the quantity of lending or credit in the economy. Indeed, all of the coin in the economy, except for the original reserves, is a effect of banking company loans that are re-deposited and loaned out, again, and once again.

Finally, the money multiplier depends on people re-depositing the money that they receive in the banking system. If people instead store their greenbacks in rubber-deposit boxes or in shoeboxes hidden in their closets, and then banks cannot recirculate the money in the form of loans. Indeed, central banks accept an incentive to assure that banking company deposits are safe because if people worry that they may lose their bank deposits, they may start property more money in cash, instead of depositing it in banks, and the quantity of loans in an economy will refuse. Low-income countries have what economists sometimes refer to as "mattress savings," or coin that people are hiding in their homes because they practice not trust banks. When mattress savings in an economy are substantial, banks cannot lend out those funds and the coin multiplier cannot operate as effectively. The overall quantity of money and loans in such an economy volition decline.

Try It

Watch information technology

This video explains how money is created and reviews the concepts you simply learned about the money multiplier. It besides explains a little flake nearly the Federal Reserve'due south involvement in creating new coin to buy financial assets, thereby adding reserves to the banking system.

If banks concur the minimum corporeality of money required by the 10% reserve ratio, then they would lend out 90% of their reserves, and the multiplier would go on to stay around 10. This does not happen in practice, and the multiplier remains closer to 3. When nosotros talk about monetary policy in more depth later, yous'll acquire more most other ways that the Federal Reserve may cull to increase the coin supply.

You can view the transcript for "The Money Multiplier" here (opens in new window).

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These questions allow y'all to become as much practice as you need, as you can click the link at the top of the starting time question ("Try another version of these questions") to go a new set of questions. Practise until y'all experience comfortable doing the questions.

Glossary

money multiplier:

ratio of total money in the economic system divided by the corporeality of reserves, or the ratio of modify in the total money in the economic system divided past a change in the amount of reserves; formula for the money multiplier is 1/(required reserve ratio)

required reserve ratio:

percentage of full deposits a bank must hold every bit reserves

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Source: https://courses.lumenlearning.com/wm-macroeconomics/chapter/how-banks-create-money/

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