Questions: The Money Multiplier and Money Supply Expansion

Question 1

The Fed injects $500 billion of base money into the banking system. A simple 1/r calculation suggests the money supply should expand by $5 trillion. Instead, the money supply barely moves. Which explanation is most consistent with the money multiplier framework?

• A. The Fed miscalculated the reserve ratio and used the wrong multiplier
• B. Inflation automatically offsets money supply expansion, neutralizing the effect
• C. Banks chose to hold the new reserves as excess reserves rather than lending them out, causing the effective reserve ratio to rise and the multiplier to collapse
• D. The money multiplier only functions when nominal interest rates exceed 3%

Answer: (C)

The money multiplier is not a mechanical guarantee — it is an equilibrium outcome. The formula m = 1/(r + c) assumes banks lend out excess reserves and the public redeposits them. If banks instead hold excess reserves (as they massively did after the 2008 financial crisis), the effective r rises toward 1, and the multiplier approaches 1 rather than 10. The Fed can inject base money but cannot force banks to lend it or the public to borrow it. This is precisely why the post-2008 quantitative easing produced far less broad money expansion than naive multiplier arithmetic predicted.

Question 2

If households increase their preference for holding cash rather than keeping money in bank deposits (the currency ratio c rises), what happens to the money multiplier?

• A. The multiplier increases — more cash in circulation means more money in the economy
• B. The multiplier stays the same — currency preference does not appear in the multiplier formula
• C. The multiplier decreases — cash held outside banks drains out of the deposit-lending cycle, reducing the number of lending rounds
• D. The multiplier doubles, compensating for the reduced deposit base

Answer: (C)

The full multiplier formula is m = 1/(r + c). Each lending-redepositing round generates new deposits only to the extent that borrowed funds are redeposited at banks. When people hold more cash, they redeposit less of each loan, truncating the cycle earlier. A higher c raises the denominator, reducing m. This is why the multiplier is not just a function of central bank policy (r) but also of public behavior — a shift in cash preference changes the amount of money the system creates from any given injection of base money.

Question 3

The money multiplier is a fixed constant determined largely by the required reserve ratio set by the central bank.

• T. True
• F. False

Answer: False

The money multiplier m = 1/(r + c) depends on two behavioral variables: r (the effective reserve ratio, which includes both required and excess reserves banks choose to hold) and c (the currency ratio, reflecting how much of their deposits the public prefers to hold as cash). The central bank sets the required reserve ratio but cannot control how many excess reserves banks decide to hold or how the public splits its money between deposits and cash. During the 2008 financial crisis, banks accumulated enormous excess reserves, causing the actual multiplier to collapse far below what the required reserve ratio alone would imply.

Question 4

The central bank directly controls the monetary base but can only indirectly influence the broader money supply through the banking system's willingness to lend and the public's deposit behavior.

• T. True
• F. False

Answer: True

This captures the essential architecture of monetary transmission. The central bank controls M0 (base money = currency + reserves) directly through open market operations. But M1, M2, and broader money measures — which include demand deposits and time deposits — are created through the banking system's lending activity. If banks hoard reserves or if the public withdraws funds from deposits, the chain from base money to broad money is broken. The multiplier relationship M = m × H holds in equilibrium, but m itself is endogenous — it responds to economic conditions and bank behavior, not just central bank policy.

Question 5

Why did the Fed's massive quantitative easing after 2008 produce far less money supply expansion than a simple 1/r calculation would predict?

Model answer: Because banks chose to hold the injected reserves as excess reserves rather than lending them out. The simple 1/r multiplier assumes banks lend out all excess reserves, triggering successive rounds of deposits. Post-2008, banks had strong reasons not to lend: loan demand was weak, creditworthy borrowers were scarce, and the Fed began paying interest on excess reserves, making holding them risk-free. The effective reserve ratio rose sharply, collapsing the actual multiplier toward 1 even as the monetary base expanded dramatically.

This episode is the clearest modern illustration that the money multiplier is a behavioral equilibrium, not a physical law. The formula m = 1/(r + c) is always true by definition, but r and c are not fixed parameters — they reflect choices made by banks and households in response to economic conditions. Central banks discovered that 'pushing on a string' (injecting base money into a banking system unwilling to lend) produces very different results from injecting base money into a normally functioning financial system. Understanding this distinction is essential for interpreting monetary policy during crises.