Central Bank and the Money Supply — AP Macroeconomics Study Guide

For: AP Macroeconomics candidates sitting AP Macroeconomics.

Covers: Functions of the central bank, monetary base, fractional reserve banking, the money multiplier formula, required reserve ratio, and core monetary policy tools (open market operations, discount rate, interest on reserves) that change the money supply.

You should already know: Definitions of M1/M2 money supply; Basics of fractional reserve banking; Basic balance sheet assets and liabilities for commercial banks.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Macroeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Central Bank and the Money Supply?

A central bank is the official monetary authority of a sovereign nation, tasked with controlling the money supply, regulating commercial banks, stabilizing the financial system, and acting as a lender of last resort during banking panics. The money supply is the total stock of money circulating in an economy at a given time, most commonly measured in AP Macro as M1 (currency in circulation + demand deposits/checking accounts) or M2 (M1 + savings deposits, money market funds, and other near monies). Per the AP Macroeconomics Course and Exam Description (CED), this topic falls within Unit 4 (Financial Sector), which accounts for 15-20% of total exam score weight, and questions on central bank actions and money supply appear in both multiple-choice (MCQ) and free-response (FRQ) sections. Unlike direct control of total money, the central bank primarily adjusts the monetary base (the sum of bank reserves and currency held by the public) and relies on the fractional reserve system of commercial banking to expand or contract the total money supply through bank lending. Understanding how central bank tools translate to changes in the money supply is the foundational prerequisite for all subsequent study of monetary policy.

2. The Monetary Base and the Money Multiplier

The monetary base (denoted $MB$, also called high-powered money) is the portion of the money supply directly controlled by the central bank. It is defined as: $$MB=C+R$$ where $C$ = currency in circulation held by the public, and $R$ = total reserves held by commercial banks at the central bank.

Total reserves are split into required reserves ($RR$) and excess reserves ($ER$): $R=RR+ER$. Required reserves are the portion of deposits commercial banks are legally required to hold, set by the central bank as the required reserve ratio ($rr$), where $rr=\frac{RR}{D}$ and $D$ is total demand deposits. Excess reserves are any reserves held beyond the required amount.

In a fractional reserve banking system, banks lend out excess reserves, which creates new demand deposits and expands the total money supply. The simple money multiplier (the maximum possible change in the money supply from a change in the monetary base, assuming no excess reserves and no public currency holding) is given by: $$m=\frac{1}{rr}$$ The maximum change in total money supply $\Delta MS$ is then: $$\Delta MS=m\times \Delta MB=\frac{1}{rr}\times \Delta MB$$

The intuition here is that every dollar of new reserves added to the system gets lent out, redeposited, and partially re-lent again, leading to a multiplied total change.

Worked Example

Problem: The central bank adds $200 million in new reserves to the banking system. The required reserve ratio is 10%, banks hold no excess reserves, and the public holds no additional currency. What is the maximum total change in the money supply?

1. Identify given values: $\Delta MB=+\$200$ million (new reserves added), $rr=0.10$, no excess reserves or currency drain, so the simple multiplier applies.
2. Calculate the simple money multiplier: $m=\frac{1}{rr}=\frac{1}{0.10}=10$.
3. Calculate the maximum change in the money supply: $\Delta MS=m\times \Delta MB=10\times 200=\$2000$ million.
4. Confirm direction: Adding new reserves expands the money supply, so the total change is a +$2 billion ($\$2000$ million) increase.

Exam tip: If the AP exam does not mention excess reserves or currency drain, always use the simple $\frac{1}{rr}$ money multiplier. Only adjust the multiplier for these factors if the problem explicitly gives their values.

3. Open Market Operations

Open market operations (OMO) are the most frequently used monetary policy tool of the central bank, involving the purchase or sale of government securities (usually Treasury bonds) to commercial banks or the public to change the monetary base and thus the total money supply.

When the central bank buys government bonds, it pays for the bonds by adding new reserves to the banking system, which increases the monetary base, leading to a multiplied expansion of the money supply. This is expansionary monetary policy, used to fight recessions. When the central bank sells government bonds, it receives payment from commercial banks by withdrawing reserves from the system, decreasing the monetary base and leading to a multiplied contraction of the money supply, which is contractionary monetary policy used to fight inflation.

OMO directly change the monetary base, so the money multiplier can be used to calculate the total change in the money supply from any OMO action.

Worked Example

Problem: The central bank sells $50 million in government bonds to commercial banks. The required reserve ratio is 20%, banks hold no excess reserves, and the public holds no additional currency. What is the total change in the money supply?

1. Identify the change in the monetary base: Selling bonds removes $50millioninreservesfromthesystem,so$\Delta MB = -$50$ million.
2. Calculate the simple money multiplier: $m=\frac{1}{0.20}=5$.
3. Calculate the total change in the money supply: $\Delta MS=5\times (-50)=-\$250$ million.
4. Confirm direction: Selling bonds is contractionary, so the money supply decreases by $\$250$ million.

Exam tip: Memorize the direction rule once and for all: central bank Buys bonds = Increase money supply, central bank Sells bonds = Decrease money supply. Direction is tested far more often than calculation in MCQs.

4. Other Central Bank Monetary Policy Tools

In addition to open market operations, central banks use two other core tools to adjust the money supply: the discount rate and interest on reserves.

The discount rate is the interest rate commercial banks pay to borrow directly from the central bank to cover unexpected reserve shortfalls. If the central bank lowers the discount rate, borrowing reserves becomes cheaper, so commercial banks borrow more reserves, increasing the monetary base and expanding the money supply (expansionary policy). Raising the discount rate makes borrowing more expensive, reduces total borrowed reserves, and contracts the money supply (contractionary policy).

Interest on reserves (IOR) is the interest rate the central bank pays commercial banks on reserves held at the central bank. If the central bank lowers IOR, the opportunity cost of holding excess reserves increases, so banks lend out more excess reserves, which increases the effective money multiplier and expands the money supply. If the central bank raises IOR, the opportunity cost of lending falls, so banks hold more excess reserves, lend less, and the money supply contracts. Unlike OMO and the discount rate, IOR changes the money multiplier, not the monetary base, for a given level of reserves.

Worked Example

Problem: The monetary base is $\$200$ billion, no currency is held by the public, the required reserve ratio is 10%, and banks initially hold 0% excess reserves. After the central bank raises interest on reserves, banks choose to hold 5% of all deposits as excess reserves. Calculate the change in the total money supply.

1. Calculate initial money supply: With $rr=0.1$ and $er=0$, the initial money multiplier is $m_1=\frac{1}{rr+er}=\frac{1}{0.1}=10$. Initial $M{S}_1=m_1\times MB=10\times 200=\$2000$ billion.
2. Calculate new money multiplier: After the IOR increase, $er=0.05$, so $m_2=\frac{1}{0.1+0.05}=\frac{1}{0.15}\approx 6.67$.
3. Calculate new money supply: $M{S}_2=6.67\times 200\approx \$1334$ billion.
4. Calculate the change: $\Delta MS=1334-2000=-\$666$ billion. Raising IOR reduces the money supply by ~$\$666$ billion, holding the monetary base constant.

Exam tip: When the problem gives an excess reserve ratio, always add it to the required reserve ratio in the denominator of the money multiplier—do not just use $\frac{1}{rr}$. This is a common trick tested on AP FRQs.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Confusing the direction of open market operations, claiming selling government bonds increases the money supply. Why: Students mix up who is transacting; when the central bank sells, banks pay the central bank, removing reserves from circulation. Correct move: Use the mnemonic "BITE: Buy = Increase, Sell = Decrease" to confirm direction every time.
• Wrong move: Using $\frac{1}{rr}$ as the money multiplier when the problem explicitly states banks hold excess reserves. Why: The simple multiplier assumes no excess reserves, which only applies when this is stated or implied. Correct move: Scan the problem first for excess reserve or currency drain values; add them to $rr$ in the denominator if given.
• Wrong move: Claiming raising the discount rate increases the money supply. Why: Students confuse the discount rate with market interest rates and assume higher rates encourage lending. Correct move: Remember the discount rate is what banks pay to borrow; higher = more expensive = fewer reserves = lower money supply.
• Wrong move: Calculating $\Delta MS$ as $\Delta MB\times rr$ instead of $\Delta MB\times \frac{1}{rr}$. Why: Students invert the multiplier because they confuse the required reserve ratio with the multiplier itself. Correct move: Always write the full formula down before plugging in numbers.
• Wrong move: Assuming changing the required reserve ratio changes the monetary base. Why: Students mix up how different tools affect the monetary base vs. the money multiplier. Correct move: Changing the required reserve ratio changes the money multiplier, not the monetary base; lower $rr$ = higher multiplier = higher money supply for a fixed MB.
• Wrong move: Claiming raising interest on reserves increases the money supply. Why: Students assume higher interest rates mean more lending, but IOR is paid to banks for holding reserves, not for lending. Correct move: Higher IOR = more incentive to hold reserves = less lending = lower money supply.

6. Practice Questions (AP Macroeconomics Style)

Question 1 (Multiple Choice)

Which of the following actions by the central bank will lead to an increase in the money supply, all else equal? A) The central bank sells $100 million in government Treasury securities B) The central bank raises the required reserve ratio from 10% to 15% C) The central bank lowers the interest rate it pays on reserves D) The central bank raises the discount rate

Worked Solution: Evaluate each option systematically. Option A: Selling bonds removes reserves from the banking system, decreasing the money supply, so A is incorrect. Option B: Raising the required reserve ratio increases the denominator of the money multiplier, reducing the multiplier and the total money supply, so B is incorrect. Option C: Lowering interest on reserves reduces the incentive for banks to hold excess reserves, so banks lend more, increasing the effective money multiplier and the total money supply, so this is correct. Option D: Raising the discount rate makes it more expensive for banks to borrow reserves, reducing total reserves and the money supply, so D is incorrect. Correct answer: C.

Question 2 (Free Response)

Assume the banking system has no initial excess reserves, no currency is held by the public, and the required reserve ratio is 20%. The central bank undertakes an open market purchase of $40 million in government bonds. (a) Calculate the maximum possible change in the total money supply. Show your work. (b) If banks instead decide to hold 10% of all deposits as excess reserves, recalculate the total change in the money supply and explain why it differs from your answer in (a). (c) What open market operation would the central bank need to undertake to return the money supply to its original level after the change in (b)? Explain the direction and size of the operation.

Worked Solution: (a) The open market purchase adds $\$40$ million to the monetary base, so $\Delta MB=+\$40$ million. With no excess reserves and no currency drain, the money multiplier is: $$m=\frac{1}{rr}=\frac{1}{0.20}=5$$ Total change in money supply: $\Delta MS=5\times 40=\boxed{+\$200\text{ million}}$. (b) With an excess reserve ratio $er=0.10$, the adjusted multiplier is: $$m=\frac{1}{rr+er}=\frac{1}{0.20+0.10}\approx 3.33$$ Total change in money supply: $\Delta MS=3.33\times 40=\boxed{+\$133.2\text{ million}}$. The change is smaller than (a) because banks hold more reserves instead of lending them out, so the multiplier effect of new reserves is weaker. (c) To offset the $\$133.2$ million increase, the central bank needs a total change of $\Delta MS=-\$133.2$ million. Solving for the required change in monetary base: $\Delta MB=\frac{\Delta MS}{m}=\frac{-133.2}{3.33}=-\$40$ million. A negative change in the monetary base requires an open market sale of $\$40$ million in government bonds, which removes $\$40$ million of reserves from the system and returns the money supply to its original level.

Question 3 (Application / Real-World Style)

In 2020, the central bank of Country X added $\$3$ trillion in new reserves to the banking system in response to an economic crisis. The required reserve ratio in Country X is 10%, but after the crisis, commercial banks chose to hold 14% of all deposits as excess reserves, and the public holds 1% of all new money as currency. Use the adjusted money multiplier formula $m=\frac{1+c}{rr+er+c}$ (where $c$ is the currency drain ratio) to calculate the total change in the money supply from the new reserve injection, and interpret your result.

Worked Solution: First, identify all values: $\Delta MB=\$3$ trillion, $rr=0.10$, $er=0.14$, $c=0.01$. Plug into the adjusted multiplier: $$m=\frac{1+0.01}{0.10+0.14+0.01}=\frac{1.01}{0.25}=4.04$$ Total change in money supply: $\Delta MS=4.04\times 3=\$12.12$ trillion. In context, the large amount of excess reserves held by banks after the crisis reduced the money multiplier far below the simple maximum of 10, leading to a much smaller expansion of the money supply than the $\$30$ trillion maximum possible increase under the simple multiplier assumption.

7. Quick Reference Cheatsheet

8. What's Next

This topic is the foundational prerequisite for the study of monetary policy, which comes immediately next in Unit 4, and links the structure of the financial sector to aggregate demand and macroeconomic stabilization. Without mastering how central bank tools change the money supply, you cannot correctly analyze the transmission of monetary policy to interest rates, real output, and inflation—one of the most heavily tested content areas on the AP Macroeconomics exam. This topic also feeds into the broader study of fiscal and monetary policy interactions and long-run adjustments to monetary changes across the rest of the course. The following topics build directly on the concepts mastered in this chapter:

• Money Market and Nominal Interest Rates
• Monetary Policy and Aggregate Demand
• Inflation and Unemployment Tradeoffs