AP MACROECONOMICS • FINANCIAL SECTOR

Banking and the Expansion of Money Supply

How fractional-reserve banking transforms a single deposit into a multiple expansion of the nation's money supply.

Historical Context & Motivation

The modern banking system did not emerge overnight; it evolved from centuries of experimentation with money, credit, and trust. Early goldsmiths in medieval Europe discovered that depositors rarely reclaimed all of their gold simultaneously, which meant a portion of deposits could be lent out to generate interest income. This practice—holding only a fraction of deposits in reserve while lending the rest—became the foundation of fractional-reserve banking. The resulting ability of banks to create money through lending is one of the most powerful mechanisms in macroeconomics, directly affecting aggregate demand, interest rates, and economic growth. Understanding how this process works—and how it can be controlled—is essential for grasping monetary policy on the AP Macroeconomics exam.

1609
Bank of Amsterdam
The Bank of Amsterdam (Wisselbank) was established as a public deposit bank, standardizing currency and pioneering the concept of centralized reserves for commercial deposits.
1694
Bank of England Founded
Created to fund government debt, the Bank of England became a model for central banking, issuing banknotes backed by fractional reserves and acting as a lender of last resort.
1913
Federal Reserve Act
The United States established the Federal Reserve System to provide elastic currency, supervise banks, and set reserve requirements—formalizing control over money supply expansion.
1933
Glass-Steagall & FDIC
In response to the Great Depression's bank runs, Congress created the FDIC to insure deposits and separated commercial and investment banking, stabilizing the fractional-reserve system.
2008–2020
Quantitative Easing Era
The Fed purchased trillions in assets to inject reserves into the banking system, demonstrating the modern tools central banks use to influence lending, money creation, and aggregate demand.

A central question animates this entire topic: if the government prints only a limited amount of currency, how does the total money supply in the economy end up being several times larger than the monetary base? The answer lies in the mechanics of bank lending and the money multiplier process, a chain reaction in which a single dollar of new reserves can support many dollars of new deposits across the banking system.

Core Principles & Definitions

Before tracing the step-by-step expansion of the money supply, several foundational concepts must be firmly established. Each of the principles below plays a distinct role in the money creation process, and the AP exam frequently tests your ability to distinguish among them with precision.

1

Required Reserve Ratio (rr)

The fraction of each deposit a bank must hold as reserves, set by the central bank. If the required reserve ratio is 10%, a bank receiving $1,000 must keep $100 and may lend the remaining $900.
2

Excess Reserves

Any reserves a bank holds beyond the required amount. Excess reserves represent the bank's lending capacity—the maximum new loans it can issue. Excess reserves = Total reserves − Required reserves.
3

Money Multiplier

The simple money multiplier equals 1 / rr. It indicates the maximum amount the money supply can expand from an initial change in reserves, assuming banks lend all excess reserves and no cash leaks from the system.
4

T-Account (Balance Sheet)

A simplified accounting tool showing a bank's assets (reserves, loans) on the left and liabilities (deposits) on the right. T-accounts are the standard AP Macroeconomics method for tracing money creation step by step.
5

Monetary Base vs. Money Supply

The monetary base (MB) is currency in circulation plus bank reserves. The money supply (M1) includes currency in circulation plus checkable deposits. Because deposits are multiplied through lending, M1 is much larger than MB.
KEY TAKEAWAY
Think of the banking system like a series of connected water tanks. The central bank pours water (reserves) into the first tank. That tank keeps a required fraction and lets the overflow (excess reserves) pour into the next tank, which again keeps its fraction and releases the rest. By the time the water has passed through many tanks, the total amount of water held across all tanks far exceeds the original pour. In the same way, a single deposit cascades through the banking system, generating new deposits at each stage until the total expansion is a multiple of the original injection.

The Money Multiplier Process — Visual Explanation

The diagram below illustrates how a single $1,000 deposit cascades through a banking system operating with a 20% required reserve ratio. At each round of lending, the bank retains the required reserves and lends out its excess reserves. The borrower spends the loan proceeds, which are deposited in another bank, restarting the cycle. Notice how each successive round of new deposits shrinks geometrically, and the cumulative total converges toward the theoretical maximum predicted by the money multiplier.

The left column traces loans moving from Bank A to Bank B to Bank C and beyond. The right panel shows how cumulative new deposits grow with each round, converging toward the maximum expansion of $5,000 predicted by the simple money multiplier (1/rr).

Several features of this diagram deserve emphasis. First, each round of new deposits is exactly 80% of the previous round, reflecting the fact that 20% is set aside as required reserves. Second, the cumulative total approaches $5,000 but never exceeds it—this maximum represents the theoretical ceiling that holds only when every bank lends out all of its excess reserves and borrowers redeposit every dollar. In practice, the actual expansion is often smaller because banks may hold excess reserves voluntarily and some money leaks out of the banking system as cash held by the public.

Mathematical Framework

The money multiplier process can be expressed in compact algebraic form. These equations are essential tools on both the multiple-choice and free-response sections of the AP Macroeconomics exam. The derivation begins with the geometric series that describes successive rounds of deposit creation and then simplifies to the familiar multiplier formula.

SIMPLE MONEY MULTIPLIER
Money Multiplier = 1 / rr
where rr = the required reserve ratio (expressed as a decimal). For example, if rr = 0.10, the multiplier is 1 / 0.10 = 10.
MAXIMUM CHANGE IN MONEY SUPPLY
ΔMS = (1 / rr) × ΔExcess Reserves
The maximum possible change in the money supply (ΔMS) equals the money multiplier times the initial change in excess reserves, not total reserves. If someone deposits $1,000 in cash and rr = 0.20, the initial excess reserves are $800 (since $200 must be held), and ΔMS = 5 × $800 = $4,000 in new money created through lending.
MAXIMUM CHANGE IN TOTAL DEPOSITS
ΔDeposits = (1 / rr) × ΔInitial Deposit
When tracing the total change in checkable deposits system-wide (including the original deposit), multiply the initial deposit by the full multiplier. A $1,000 deposit with rr = 0.20 produces a maximum total deposit change of $5,000.
GEOMETRIC SERIES DERIVATION
ΔDeposits = D + D(1−rr) + D(1−rr)² + D(1−rr)³ + … = D / rr
Each round's new deposit is (1 − rr) times the previous round. This infinite geometric series with common ratio (1 − rr) converges to D / rr, confirming the multiplier formula. The convergence requires 0 < rr ≤ 1.
⚠️ AP EXAM TIP
A common FRQ error is confusing the change in the money supply with the change in deposits. When someone deposits existing cash into a bank, the initial deposit itself does not change M1 (cash decreases, checkable deposits increase by the same amount—it's a swap). The new money created equals the multiplier times the initial excess reserves. However, when the Fed injects new reserves (e.g., through open-market purchases), the entire injection is new money in the system.

T-Account Analysis — Step-by-Step Balance Sheets

The AP Macroeconomics exam frequently requires students to construct or interpret T-accounts (simplified balance sheets) showing how a bank's assets and liabilities change following a deposit, loan, or open-market operation. The left side of a T-account lists assets—reserves and loans—while the right side lists liabilities, primarily demand deposits owed to customers. Because every loan eventually becomes a deposit somewhere in the system, T-accounts provide a transparent way to track each round of money creation.

With rr = 10%, a $1,000 initial deposit generates $900 in excess reserves at Bank A. After all rounds of lending, total deposits expand to $10,000, total loans reach $9,000, and total required reserves equal the original $1,000. The change in the money supply is $9,000 (the new money created by lending).

Notice the critical accounting identity in the T-accounts: at every bank, assets (reserves + loans) equal liabilities (deposits). Also observe that the system-wide required reserves ultimately absorb the entire original deposit of $1,000. This is the mathematical reason the expansion cannot be infinite—each round siphons off a fraction of reserves until there are no more excess reserves left to lend.

Worked Example — Open-Market Purchase

The most common AP Macroeconomics scenario involves the Federal Reserve conducting an open-market purchase of government bonds. When the Fed buys bonds from commercial banks or the public, it injects new reserves into the banking system, triggering the money multiplier process. Let us work through a complete example.

Open-Market Purchase of $5,000 in Bonds (rr = 20%)
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Step 1 — Identify the InjectionThe Federal Reserve purchases $5,000 worth of government bonds from a commercial bank. The Fed credits the bank's reserve account with $5,000. Since the bank did not receive a new deposit from a customer, these $5,000 are entirely excess reserves—no required reserves need to be set aside at this stage.
Initial ΔExcess Reserves = $5,000
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Step 2 — Calculate the Money MultiplierApply the simple money multiplier formula: Multiplier = 1 / rr = 1 / 0.20 = 5.
Money Multiplier = 5
3
Step 3 — Calculate Maximum ΔMoney SupplyThe maximum change in the money supply is the multiplier times the initial excess reserves: ΔMS = 5 × $5,000 = $25,000. This means the banking system can create up to $25,000 in new checkable deposits through successive rounds of lending.
Maximum ΔMS = $25,000
4
Step 4 — Trace the First Two RoundsRound 1: The bank lends $5,000. The borrower spends it, and the recipient deposits $5,000 at Bank B. Bank B sets aside 20% ($1,000) as required reserves and lends the remaining $4,000. Round 2: That $4,000 is deposited at Bank C, which holds $800 in required reserves and lends $3,200. The pattern continues, with each round's loanable amount equal to 80% of the previous round.
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Step 5 — Verify with the Total Deposit FormulaTotal new deposits = $5,000 + $4,000 + $3,200 + $2,560 + … = $5,000 / 0.20 = $25,000. The total new loans across the system equal $25,000 − $5,000 = $20,000, and total required reserves across all banks equal $25,000 × 0.20 = $5,000, exactly matching the original injection.
Total New Deposits = $25,000 ✓ | Total New Loans = $20,000 | Total New Req. Reserves = $5,000

Ideal Model vs. Real-World Complications

The simple money multiplier provides a clean, testable model, but the actual expansion of the money supply is almost always smaller than the theoretical maximum. Several real-world frictions reduce the effective multiplier, and understanding these limitations is important both for the exam and for genuine macroeconomic reasoning.

Comparison of simple money multiplier assumptions vs. real-world frictions
FactorSimple Model AssumptionReal-World Reality
Excess reservesBanks lend all excess reserves immediately.Banks may hold excess reserves for precautionary reasons, especially during recessions or financial crises (e.g., 2008–2015).
Cash drainBorrowers redeposit 100% of loaned funds into the banking system.Some borrowers hold cash outside banks, reducing the deposit base available for further lending.
Borrower demandThere are always creditworthy borrowers ready to take loans.During downturns, fewer borrowers qualify or desire loans, limiting money creation even when reserves are plentiful.
Reserve requirementsA single, fixed rr applies to all deposits.In many countries (including the U.S. since March 2020), reserve requirements have been reduced to 0%, and monetary control relies on interest on reserves instead.
KEY TAKEAWAY
The simple money multiplier is analogous to the theoretical maximum efficiency of a heat engine in thermodynamics: it establishes an upper bound, but real-world frictions (cash drains, voluntary excess reserves, weak loan demand) ensure the actual money creation is less. On the AP exam, unless the problem explicitly states otherwise, apply the simple multiplier to calculate the maximum possible change in the money supply.

Connection to Monetary Policy Tools

The money multiplier does not operate in a vacuum—it is the mechanism through which the Federal Reserve's policy actions propagate into the broader economy. Understanding how each of the Fed's three traditional tools affects reserves and the multiplier is crucial for linking the financial sector to aggregate demand.

The Fed's monetary policy tools and their connections to money supply expansion
Fed ToolHow It WorksEffect on Money Supply
Open-market operations (OMO)Fed buys (expansionary) or sells (contractionary) government bonds. Buying injects reserves; selling drains them.Most frequently used tool. ΔMS = (1/rr) × ΔExcess reserves created by the bond transaction.
Discount rateThe interest rate the Fed charges banks for short-term borrowing from the discount window. Lowering it encourages borrowing of reserves.Indirectly increases reserves available for lending, but banks use the discount window sparingly due to stigma.
Reserve requirementsThe Fed sets the minimum fraction of deposits banks must hold. Lowering rr increases both excess reserves and the multiplier itself.A double effect: more excess reserves AND a larger multiplier. Rarely changed because the impact is so powerful.
Interest on reserves (IOR)Since 2008, the Fed pays interest on reserves held at Federal Reserve Banks. Raising IOR incentivizes banks to hold reserves rather than lend.Acts as a floor on interest rates and can effectively reduce the money multiplier even when reserves are abundant.

For the AP exam, the chain of causation runs as follows: the Fed changes reserves or the reserve ratio → bank excess reserves change → lending changes → the money supply changes through the multiplier → interest rates change (via the money market) → investment and consumption change → aggregate demand shifts → real GDP and/or the price level change. Mastering the money multiplier is therefore not an isolated skill; it is the bridge between Fed policy and the AD/AS model that dominates the macroeconomics curriculum.

Practice Problems

1
If the required reserve ratio is 25%, what is the maximum amount the money supply can increase from a $1,000 increase in excess reserves?
2
The Federal Reserve purchases $50,000 in government bonds from a commercial bank. If the required reserve ratio is 10%, what is the maximum increase in checkable deposits throughout the banking system?
3
A customer deposits $2,000 in cash into Bank X. The required reserve ratio is 20%. Bank X currently has no excess reserves. What is the maximum amount that Bank X alone (not the entire banking system) can lend as a result of this deposit?
PROBLEM 4APPLIED
Assume the economy is in a recession with high unemployment. The required reserve ratio is 10%, and the Federal Reserve decides to purchase $20,000 in government bonds from commercial banks. (a) Calculate the simple money multiplier. (1 point) (b) Calculate the maximum change in the money supply resulting from this open-market purchase. Show your work. (1 point) (c) Using a correctly labeled graph of the money market, show the effect of this increase in the money supply on the nominal interest rate. (1 point) (d) Explain how the change in the interest rate from part (c) will affect aggregate demand. (1 point) (e) Identify one reason why the actual change in the money supply might be less than the maximum you calculated in part (b). (1 point)
PROBLEM 5CRITICAL THINKING
In March 2020, the Federal Reserve reduced the required reserve ratio to 0% for all depository institutions. (a) According to the simple money multiplier formula, what would the money multiplier be if rr = 0? Explain why this result is not economically meaningful. (1 point) (b) Explain how the Federal Reserve can still control the money supply when the required reserve ratio is 0%. Identify one specific tool the Fed uses. (1 point) (c) Explain why banks would still choose to hold reserves even without a legal requirement to do so. (1 point)

Summary — Banking and the Expansion of Money Supply

The fractional-reserve banking system allows banks to lend out a portion of deposits, creating new money in the process. The required reserve ratio (rr) determines the fraction of each deposit that must be held in reserve, while excess reserves represent a bank's lending capacity. The simple money multiplier (1/rr) gives the maximum factor by which the money supply can expand from an initial change in excess reserves. A single bank can lend only its excess reserves, but the entire banking system expands deposits through successive rounds of lending until no excess reserves remain.

The Federal Reserve influences this process through open-market operations (buying or selling bonds to inject or drain reserves), changes to the discount rate, and adjustments to reserve requirements or interest on reserves. In practice, cash drains, voluntary excess reserves, and weak loan demand mean the actual expansion is typically less than the theoretical maximum. For the AP exam, use T-accounts to trace individual bank balance sheet changes, and apply the formula ΔMS = (1/rr) × ΔExcess Reserves to calculate the system-wide maximum change in the money supply. Remember: a single bank lends its excess reserves; the banking system multiplies them.

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