## Learning Outcomes

- Understand how the **money multiplier** determines the maximum expansion of the money supply
- Identify the difference between **required reserves**, **excess reserves**, and new bank reserves
- Calculate the maximum change in the money supply from a reserve change or an initial deposit
- Explain how repeated lending and redepositing create **multiple deposit expansion**
- Distinguish between the textbook maximum result and the smaller real-world outcome when banks hold extra reserves or people hold cash
- Apply the multiplier to **open-market purchases** and **open-market sales**

## AP Macroeconomics Syllabus

For the AP Macroeconomics, you are expected to understand how the banking system expands the money supply through fractional-reserve banking, with a focus on the following syllabus points:

- Know that the **money multiplier** in the AP model equals **1 / required reserve ratio**
- Identify how banks use **excess reserves** to make loans or buy assets
- Explain how one reserve injection can lead to repeated rounds of lending and redepositing
- Calculate the **maximum change in the money supply** from a given change in reserves
- Distinguish between a question that gives an **initial deposit** and one that gives a **change in reserves directly**
- Understand how **open-market purchases** raise reserves and expand the money supply, while **open-market sales** reduce reserves and contract it
- Recognize that the multiplier gives a **maximum possible** result only under simplifying assumptions

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. If the required reserve ratio is 10%, what is the money multiplier?
2. Why does a bank loan create more money in the banking system than existed as cash in one vault?
3. If bank reserves increase by $4 million and the reserve requirement is 5%, what is the maximum change in the money supply?
4. Why is the maximum expansion smaller if banks hold extra reserves or borrowers keep some cash?
5. What is the difference between being given a new deposit and being given new reserves directly?

## Introduction

This subtopic is one of the most tested parts of AP Macroeconomics Unit 4 because it combines banking logic, formulas, and policy application. You are not just expected to memorize **1 / reserve ratio**. You need to explain why the formula works, when to use it, and when a question is asking about the whole banking system rather than one bank.

At the center of this topic is a simple AP classroom model: when banks receive new reserves, they keep only a fraction and lend the rest. That loan becomes someone else’s deposit, which becomes reserves for another bank, which then lends again. The multiplier tells you the largest possible size of that chain.

> **Key Term: money multiplier**
> The number that shows the maximum possible expansion of the money supply from a given increase in bank reserves in the AP model. It equals 1 divided by the required reserve ratio.

### How fractional-reserve banking creates multiple expansion

Banks do not keep every deposited dollar sitting idle. In a **fractional-reserve banking** system, they keep only a fraction as reserves and use the rest to make loans or buy assets. That is why the banking system can expand the money supply.

> **Key Term: fractional-reserve banking**
> A banking system in which banks keep only part of deposits as reserves and lend out the remainder.

Suppose the required reserve ratio is 10%. A customer deposits **$1,000** in Bank A.

Bank A must hold:

- **Required reserves** = 10% of $1,000 = **$100**

That leaves:

- **Excess reserves** = $1,000 - $100 = **$900**
  > **Key Term: required reserve ratio**
  > The fraction of deposits that banks must keep as reserves rather than lend out.
  >
  > **Key Term: excess reserves**
  > Reserves held by a bank above the amount required. In the AP model, these are the funds available for new lending.

If Bank A lends the $900, the borrower spends it, and the receiver deposits that $900 in Bank B. Now Bank B has a new deposit of $900. It must keep 10% of that, or **$90**, and can lend **$810**. Then that $810 is deposited in Bank C, which keeps **$81** and lends **$729**.

The pattern is:

- First deposit: $1,000
- Second deposit: $900
- Third deposit: $810
- Fourth deposit: $729

Each round is smaller because 10% is held back each time.

Why does this expand the money supply? Because in AP Macro, **checkable deposits count as money**. When loans are made and spent, they usually become new deposits elsewhere in the banking system. Those new deposits are part of the money supply.

Students often miss one key point: the banking system is creating money through **new deposits**, not by creating new paper currency. Vault cash is not the same as money held by the public in M1. The expansion happens because lending creates additional deposit money.

> **Test Tip:** If a question asks why the money supply rises when banks lend, say that the loan funds are spent and redeposited, creating new demand deposits that count as money.

### How to calculate the maximum change in the money supply

For AP exam purposes, you need two formulas:

$$
\text{Money Multiplier} = \frac{1}{\text{Required Reserve Ratio}}
$$

$$
\Delta M = \Delta R \times \text{Money Multiplier}
$$

where:

- $\Delta M$ = change in money supply
- $\Delta R$ = change in bank reserves

This works because each bank keeps only the required fraction and relends the rest. Across the whole system, the repeated rounds add up to a multiple of the original reserve injection.

#### Worked example 1: change in reserves given directly

A central bank buys **$10,000** of government securities, and the required reserve ratio is **10%**.

Step 1: Calculate the multiplier

$$
\text{Money Multiplier} = \frac{1}{0.10} = 10
$$

Step 2: Multiply by the reserve increase

$$
\Delta M = \$10{,}000 \times 10 = \$100{,}000
$$

So the **maximum increase in the money supply** is:

$$
\$100{,}000
$$

This is the easiest type of AP question because the reserve change is given directly.

#### Worked example 2: reserve ratio of 5%

If reserves rise by **$4 million** and the required reserve ratio is **5%**:

Step 1: Multiplier

$$
\text{Money Multiplier} = \frac{1}{0.05} = 20
$$

Step 2: Change in money supply

$$
\Delta M = \$4 \text{ million} \times 20 = \$80 \text{ million}
$$

So the maximum increase is **$80 million**.

> **Key Term: maximum change in the money supply**
> The largest possible increase or decrease in the money supply from a given reserve change, assuming all excess reserves are lent and all loan proceeds are redeposited.

Now the subtle part: sometimes the question starts with a **new deposit**, not with a reserve increase.

If a bank receives a **new deposit of $1,000** and the reserve requirement is 10%, the bank can lend only its excess reserves:

- Required reserves = $100
- Excess reserves = $900

If the question asks for the **maximum increase in the money supply beyond the initial deposit**, use the lendable amount:

$$
\$900 \times 10 = \$9{,}000
$$

But if the question treats the $1,000 as **new reserves added to the banking system from outside**, the total maximum change is:

$$
\$1{,}000 \times 10 = \$10{,}000
$$

That distinction causes a lot of mistakes.

> **Test Tip:** Ask yourself: “Is this number an initial deposit already inside the first bank, or is it new reserves injected into the banking system from outside?” That decides whether you multiply the full amount or first subtract required reserves.

Common student errors:

- Using **10** instead of **0.10** in the formula
- Forgetting that 5% = **0.05**, not 5
- Multiplying a deposit by the multiplier when the question really wants lending from **excess reserves**
- Giving the change in loans at one bank instead of the **maximum system-wide** change

### Open-market operations and why the multiplier matters

The multiplier matters because monetary policy works through reserves. In the AP model, the central bank changes bank reserves, and the banking system expands or contracts the money supply by a multiple of that initial change.

> **Key Term: open-market operations**
> Central bank purchases or sales of government securities that change bank reserves and the money supply.

When the central bank **buys** government securities, it pays the sellers. Those payments enter bank accounts, so bank reserves rise. With more reserves, banks can make more loans. The money supply then rises by a multiple of the reserve increase.

When the central bank **sells** government securities, buyers pay with funds from their bank accounts. Those reserves leave the banking system. Banks now have fewer reserves and must reduce lending capacity. The money supply falls by a multiple of the reserve decrease.

#### Worked example 3: open-market sale

Reserve requirement = **10%**

Central bank sells **$29 million** in government securities.

Step 1: Multiplier

$$
\text{Money Multiplier} = \frac{1}{0.10} = 10
$$

Step 2: Reserve change

An open-market sale removes reserves, so:

$$
\Delta R = -\$29 \text{ million}
$$

Step 3: Change in money supply

$$
\Delta M = 10 \times (-\$29 \text{ million}) = -\$290 \text{ million}
$$

The **maximum change in the money supply** is a **$290 million decrease**.

This cause-and-effect chain is important for FRQs:

policy action -> bank reserves change -> lending ability changes -> money supply changes

That same chain can then connect to interest rates and aggregate demand elsewhere in the course.

### Why the multiplier gives a maximum, not a guaranteed outcome

The AP formula is a classroom model, not a promise about exact real-world results. It gives the **maximum possible** expansion only if several conditions hold:

- banks lend all excess reserves
- borrowers spend the funds
- recipients redeposit the funds in banks
- no one holds extra cash outside banks

If any part of that chain breaks, the actual expansion is smaller.

> **Key Term: cash drain**
> The reduction in deposit expansion that occurs when people hold part of loaned funds as cash instead of redepositing them.

There are two main leakages.

First, **banks may hold extra reserves**. If they are cautious, they may keep reserves above the required amount rather than lending them all. That shrinks the multiplier effect.

Second, households or firms may keep some of the funds as currency. That is cash drain. If money is kept in wallets instead of redeposited, later banks do not receive those funds as reserves, so the chain stops earlier.

Example: if the required reserve ratio is 10%, but banks also choose to hold another 10% idle, then effectively 20% is not being lent onward. In a simplified AP-style treatment, the multiplier becomes smaller:

$$
\frac{1}{0.10 + 0.10} = \frac{1}{0.20} = 5
$$

So a $10,000 reserve increase would now support only:

$$
\$10{,}000 \times 5 = \$50{,}000
$$

not $100,000.

That is exactly why FRQs sometimes ask why the actual change might be less than the maximum.

One final distinction matters for strong exam answers. The AP course still uses the simple reserve-based multiplier model for calculations, even though modern U.S. banking is more complicated and reserve requirements were reduced to **0% on March 26, 2020**. For AP exam purposes, you should still use the textbook multiplier model when the question provides a reserve ratio.

> **Test Tip:** If an FRQ asks for the “maximum possible” increase, use the textbook multiplier cleanly. If it asks why the actual increase may be smaller, discuss excess reserves and cash drain.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- The AP money multiplier formula is **1 / required reserve ratio**
- The multiplier shows the **maximum possible** change in the money supply
- In fractional-reserve banking, banks keep required reserves and lend excess reserves
- Loans create new deposits, and those deposits count as money
- A reserve increase leads to repeated rounds of lending and redepositing
- If reserves rise by a given amount, multiply that amount by **1 / RRR** to find the maximum money supply change
- If a question begins with a new deposit, first check whether you need to calculate **excess reserves**
- Open-market purchases increase bank reserves and expand the money supply
- Open-market sales reduce bank reserves and contract the money supply
- The maximum result assumes all excess reserves are lent and all funds are redeposited
- Holding extra reserves or cash drain reduces the actual size of money expansion
- AP Macro uses the simple multiplier model even though modern banking is more complex

## Key Terms and Concepts

- money multiplier
- fractional-reserve banking
- required reserve ratio
- excess reserves
- maximum change in the money supply
- open-market operations
- cash drain


Banking and the Expansion of the Money Supply - Multiplier determines money expansion size