The Money Multiplier (Formula & Simple Example)

The money multiplier is the standard economics textbook explanation of how money is created in a fractional reserve banking system. In the traditional model, a central bank supplies base money, commercial banks hold a fraction of their deposits as reserves at the central bank, and the remainder is lent out, generating a multiple expansion of the money supply.

This relationship between reserves and deposits is known as the money multiplier.

While the money multiplier still appears in economics textbooks, it no longer provides an accurate explanation of how modern fiat-based banking systems function. The core problem is not merely that reserve ratios are flexible these days (rather than fixed as in the traditional model) or that banks can acquire reserves after lending (which is not possible in the traditional model).

The deeper issue is that the money multiplier treats central bank reserves as the source of liquidity, when in reality liquidity in modern financial systems is created elsewhere. If that sounds unclear then don’t worry, all is explained in simple terms below.

A Simple Money Multiplier Example

There’s a great deal of confusion circling around the meaning of bank reserves, so keep in mind that this does not refer to regular money, it is a special type of money that commercial banks and the government hold in their accounts at the central bank i.e., in the U.S. the central bank is called the Federal Reserve Bank (commonly referred to as the Fed).

These reserves are assumed, by the traditional money multiplier theory, to be the foundation upon which regular money circulating in the economy is built.

For example, imagine that $100 is added to the money supply via a government welfare payment to someone. That $100 is paid from the government’s Treasury General Account (TGA) at the Fed.

It works as follows – the person never receives actual cash from the government; it’s always a deposit that’s paid into a commercial bank. When the commercial bank credits the person’s bank account with $100, it also receives a payment from the government i.e., the Fed transfers reserves from the government’s TGA into the commercial bank’s account at the Fed.

This, however, is not the end of the story.

With an extra $100 of reserves, the commercial bank can increase the amount of loans that it makes by a multiple of that $100. How large that multiple will be depends on the Fed’s required reserve ratio (RRR). That can easily be explained with the money multiplier formula.

The Money Multiplier Formula

The money multiplier formula can be expressed as one of the simplest equations in Economics:

Money Multiplier = 1/r

(Where r is the banking system RRR expressed as a decimal)

So, if the banking sector has an RRR of 8%, the multiplier would be 1 divided by 0.08, which equals 12.5. But, if the Fed then lowered its RRR to 4%, the money multiplier would double to 25, and the economy's money-supply would also double! In a nutshell, commercial banks will create new credit/loans equal to the initial increase in its reserves multiplied by the money multiplier.

With the $100 example given above and an RRR of 8%, the money supply would increase by:

$100/0.08 = $1,250

Under this framework, the Fed controls the money supply by controlling the monetary base, and bank lending expands as a predictable multiple of reserves.

This view implies a simple causal chain i.e., that more reserves lead to more lending, and less reserves lead to less lending. The RRR therefore appears synonymous with liquidity, and changes in reserves are assumed to directly affect credit expansion.

However, in modern fiat banking systems, this causal chain does not hold.

Why the Money Multiplier Fails in Practice

The failure of the money multiplier is about causality. Banks do not make lending decisions by first assessing how many reserves they have at the Fed, or how close they are to a required reserve ratio set by the Fed.

In reality, lending decisions are driven by expected profitability, risk assessment, regulatory capital requirements, and borrower demand.

Once lending occurs, reserves are required only to settle interbank payments. Central banks supply these reserves elastically to preserve payment system stability and to maintain control over short-term interest rates. This elastic supply can take several forms:

Open market operations (OMO): Buying or selling government securities to inject or drain reserves.
Standing lending facilities / discount window: Banks can borrow reserves at a penalty rate.
Reverse repos: The Fed absorbs excess reserves by selling securities with an agreement to repurchase them, helping control short-term rates.

As a result, the reserve ratio becomes an outcome of credit conditions rather than a constraint on them, meaning that it is not a tool to control the money supply at all.

When reserve ratios are allowed to vary like this, the money multiplier ceases to function as a theory of money creation. It becomes an ex-post description of how deposits and reserves happen to relate after balance sheets have already expanded.

A better explanation of how money is created in the fiat based fractional reserve system is offered by:

Credit Creation Theory; How Money Is Actually Created

Central Bank Reserves and the Illusion of Liquidity

A key reason the money multiplier has remained influential is that it implicitly treats central bank reserves as a measure of liquidity. To understand why this is misleading, it helps to clarify exactly what liquidity means in modern banking and financial markets.

Liquidity is the ability to meet payment obligations on time without incurring significant loss or disruption. It is not simply a question of holding cash or reserves. In practice, liquidity has several dimensions:

Settlement liquidity refers to the availability of assets that can be immediately used to settle obligations with other banks – this is where central bank reserves are important. Reserves allow banks to clear interbank payments efficiently and ensure that the payment system continues to operate smoothly.
Market liquidity, on the other hand, refers to the ability to quickly convert assets into cash or other usable forms of payment at predictable prices. This type of liquidity depends on the quality of a bank’s balance sheet, the value and acceptability of its assets as collateral, and the willingness of counterparties to lend or trade.

In modern banking, market liquidity is the more fundamental constraint because banks can only lend, roll over debt, or fund themselves as long as they have collateral that others are willing to accept.

Moreover, shortages of central bank reserves rarely constrain lending. The availability of reserves does not determine whether a bank can create new credit; it merely ensures that the banking system can settle obligations safely once lending occurs.

In short, treating central bank reserves as synonymous with liquidity, as the traditional money multiplier does, leads to the illusion that lending is mechanically constrained by the monetary base. In reality, liquidity is endogenous and largely collateral-dependent, and credit creation operates according to these deeper balance-sheet and market considerations.

Financial booms are characterized by abundant collateral, narrow haircuts, and easy funding. Financial crises occur when collateral values fall, margins rise, and confidence evaporates. These are liquidity crises in a meaningful economic sense, even when reserves are plentiful.

Reinterpreting the Money Multiplier in Modern Banking

Seen through this lens, the money multiplier is not so much wrong as misleading. The ratio between deposits and reserves does change, but it changes in response to credit conditions, collateral valuations, and funding markets. The multiplier does not cause credit expansion; it reflects it.

Focusing on the money multiplier directs attention toward reserve quantities and away from balance-sheet dynamics, leverage, and asset prices. This explains why policies aimed at controlling reserves have repeatedly failed to control credit cycles, asset bubbles, or financial instability.

Modern central banks implicitly recognize this reality.

Rather than targeting reserve quantities, they focus on interest rates, capital regulation, stress testing, and collateral policy. During crises, they expand the range of assets eligible as collateral, acknowledging that liquidity problems arise from balance-sheet stress, not reserve scarcity.

Implications for Monetary Policy and Financial Stability

The instability of modern fiat-based fractional reserve banking is largely a feature of the system itself. By allowing banks to create deposits through lending while relying on central banks to supply reserves elastically, the system encourages cyclical expansions of credit and leverage that are inherently procyclical.

Asset bubbles, financial crises, and boom-bust cycles are built into the design, rather than being anomalies or failures of policy.

Monetary policy in such a system can at best mitigate the symptoms of instability, but it cannot eliminate the underlying structural vulnerabilities. Tools like interest rate adjustments, quantitative easing, or reserve management can stabilize liquidity temporarily, yet they cannot prevent the recurrence of credit-driven cycles or the accumulation of systemic risk. In practice, central banks are repeatedly forced to intervene, expanding collateral acceptance and balance sheets to prevent collapse, illustrating the fragility embedded in the system.

By contrast, a sound money framework such as full reserve banking fundamentally limits endogenous credit creation by tying deposits to actual, fully backed reserves. While this would reduce the amplitude of credit cycles and constrain the short-term expansion of lending, it would eliminate the structural instability that fractional reserve systems generate. From the perspective of financial stability, the key lesson is that repeated crises are not accidents; they are an inevitable consequence of an inherently flawed monetary and banking architecture.

FAQs

How do primary dealers interact with the central bank in modern monetary operations?

Primary dealers are the only institutions that transact directly with central banks in open market operations. They buy and sell government securities, settle with reserve balances, and redistribute Treasuries to other market participants.

What is the difference between base money and broad money?

Base money includes currency in circulation and reserves held at the central bank, while broad money encompasses all bank deposits and other liquid assets created through lending in the banking system.

Why did the money multiplier collapse after the 2008 financial crisis?

After 2008, banks prioritized capital preservation and liquidity over loan expansion. Regulatory changes (like Basel III) tightened capital adequacy rules, and public demand for safe deposits rose. As a result, even though the Federal Reserve expanded reserves dramatically, banks’ effective reserve ratios increased, shrinking the multiplier.

How is the money multiplier related to inflation?

If banks aggressively expand credit and reduce their reserve ratios, the multiplier rises and money supply grows faster than goods production, leading to inflationary pressure. Conversely, if credit contracts, the multiplier falls, reducing spending power and often contributing to disinflation or deflation.

What is the difference between the simple money multiplier and the real-world multiplier?

The simple money multiplier uses the formula 1/r, assuming a fixed reserve ratio. The real-world multiplier is endogenous, shaped by banks’ preferences, central bank policy, and loan demand. It’s not a constant — it expands and contracts based on incentives, regulation, and market confidence.

How do interest rates influence the money multiplier?

Lower interest rates make borrowing more attractive and reduce the opportunity cost of holding fewer reserves, increasing the multiplier. Higher interest rates have the opposite effect: they discourage borrowing, tighten liquidity, and often lead banks to maintain higher reserve ratios, reducing the multiplier’s strength.

Conclusion

The money multiplier endures in economic teaching because it offers a simple and intuitive narrative linking central bank reserves to the expansion of money and credit. However, this simplicity obscures how modern fiat banking systems actually function. In practice, reserves do not drive lending decisions, reserve ratios do not represent meaningful liquidity constraints, and the monetary base does not mechanically determine the size of the money supply.

A more accurate understanding recognizes that credit creation precedes reserves, and that liquidity is not defined by reserve quantities but by balance-sheet strength, collateral quality, and access to funding markets. The relationship between deposits and reserves is therefore an outcome of credit conditions rather than their cause. When viewed through this lens, the money multiplier becomes a descriptive ratio observed after the fact, not a theory of money creation.

Replacing the multiplier framework with a collateral and balance-sheet-based understanding of liquidity clarifies why credit cycles, asset booms, and financial crises recur despite stable reserve management. Once this distinction is understood, the limitations of the money multiplier are no longer technical curiosities, but fundamental flaws in how money and banking have traditionally been explained.

Data Sources:

Garfinkel & Thornton - Multiplier Approach to the Money Supply

Related Pages:

Monetary Transmission Mechanism – explains how policy decisions affect credit creation, asset prices, and economic activity beyond reserve levels.
Quantity Theory of Money – shares the money multiplier’s assumption that money supply changes drive prices, an idea challenged by modern banking realities.
Loanable Funds Theory – like the money multiplier, assumes lending is constrained by prior savings rather than bank balance-sheet capacity.
Liquidity Preference Theory – helps explain why banks and markets value safe, liquid assets during periods of financial stress.
Debt Deflation Theory – illustrates how falling asset prices and collapsing collateral can amplify financial instability and economic downturns.
Types of Money – clarifies the difference between central bank reserves, bank deposits, and settlement balances.

About the Author
Steve Bain is an economics writer and analyst with a BSc in Economics and experience in regional economic development for UK local government agencies. He explains economic theory and policy through clear, accessible writing informed by both academic training and real-world work.
Read Steve’s full bio

The Money Multiplier (Formula & Simple Example)

A Simple Money Multiplier Example

The Money Multiplier Formula

Why the Money Multiplier Fails in Practice

Central Bank Reserves and the Illusion of Liquidity

Reinterpreting the Money Multiplier in Modern Banking

Implications for Monetary Policy and Financial Stability

FAQs

Conclusion

Recent Articles

What Happens to House Prices in a Recession?

Does Government Spending Cause Inflation?

What Happens to Interest Rates During a Recession

Circular Flow Diagram in Economics: How Money Flows

What Happens to House Prices During Stagflation?