The Core Idea
Tracing the Chain Round by Round, Not Just the Final Formula
The Money Supply Creation lesson introduced the money multiplier formula (1 ÷ Reserve Ratio) and its overall logic. This companion lesson focuses specifically on tracing the actual ROUND-BY-ROUND banking chain in detail — calculating exactly how much each successive bank in the chain can lend, and confirming that summing up every round matches the formula's predicted total.
Working through the chain step by step (rather than jumping straight to the final formula) builds a much more solid, intuitive understanding of WHY the formula works, and makes it much easier to spot errors or reason through variations, like what happens if a bank chooses to hold MORE than the required minimum reserve.
💡 Memory Trick
Picture a line of dominoes, where each domino represents one bank in the lending chain, and each domino is slightly SHORTER than the one before it — representing the shrinking amount each successive bank can lend, since a fraction gets held back as required reserves at every single step. The dominoes get shorter and shorter, eventually shrinking toward (but never quite reaching) zero — and the TOTAL distance covered by all the dominoes combined, from the tallest first one to the vanishingly small last one, is exactly what the money multiplier formula calculates in one clean step.
Tracing the Chain Step by Step
A Worked Example With a 10% Reserve Requirement
1
Round 1
An initial $1,000 deposit arrives at Bank A. With a 10% reserve requirement, Bank A holds $100 in reserve and lends out the remaining $900.
2
Round 2
That $900 gets deposited into Bank B, which holds $90 (10%) in reserve and lends out the remaining $810.
3
Round 3 and Beyond
That $810 gets deposited into Bank C, which holds $81 in reserve and lends $729, and this process continues — each round's lendable amount is exactly 90% of the previous round's, shrinking toward zero but never quite reaching it.
4
Summing the Infinite Series Matches the Formula
Summing $1,000 + $900 + $810 + $729 + ... (an infinite geometric series) converges to exactly $10,000 — precisely matching the money multiplier formula's prediction of $1,000 × (1 ÷ 0.10) = $10,000, confirming the shortcut formula correctly captures the full round-by-round chain.
A Real-World Complication
Excess Reserves Reduce the Actual Multiplier Below Its Theoretical Maximum
The formula and chain above both assume every bank lends out 100% of whatever isn't legally required to be held in reserve. In practice, banks sometimes voluntarily hold EXCESS RESERVES — reserves beyond the legal minimum — particularly during periods of economic uncertainty when banks may be more cautious about extending new loans, even when they're legally permitted to lend more.
Whenever banks hold excess reserves, each round of the chain lends out LESS than the theoretical maximum, meaning the ACTUAL total money creation falls short of the formula's theoretical prediction — this is a genuine, frequently observed real-world limitation on the simple money multiplier calculation, and it's exactly why central banks sometimes find that injecting money into the banking system doesn't translate into as much new lending and money creation as the textbook formula alone would predict.
🖥️ Applied Scenario
During an economic downturn, a bank receiving a new $500 deposit, with a 10% reserve requirement, chooses to hold $150 in reserve (well above its $50 legal minimum) due to caution about the uncertain economic outlook.
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You calculate that the theoretical maximum lending from this $500 deposit (holding only the required $50 in reserve) would be $450, feeding fully into the next round of the money-creation chain.
2
You calculate that this specific bank, holding $150 in reserve instead of the required $50, actually lends out only $350 — $100 less than the theoretical maximum.
3
You explain that this shortfall reduces the total money creation from THIS round of the chain, and — since each subsequent round builds on the previous one — this reduction compounds through every later round as well, meaning the FINAL total money supply created falls meaningfully short of the theoretical formula-based prediction.
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Conclusion: this illustrates exactly why real-world money creation during periods of banking caution can fall well short of the money multiplier formula's theoretical maximum — banks voluntarily holding excess reserves is a genuine, observable limitation on the simple textbook calculation.
📌 Exam Application
Exam questions frequently ask you to trace a money-creation chain through several explicit rounds, calculating the reserve held and amount lent at each step, and to confirm the sum converges to the formula's predicted total. You may also be asked to explain how excess reserves held by banks reduce actual money creation below the theoretical maximum.
⚠️ Most Common Money Multiplier Mistakes
The most common mistake, when tracing the chain manually round by round, is forgetting that each successive round's STARTING amount is the PREVIOUS round's lent amount, not the original deposit — each round shrinks by the same 90% (or whatever 1 minus the reserve ratio equals) factor applied to the prior round's result, not to the original deposit each time. Another frequent error is treating the money multiplier formula as an exact real-world guarantee rather than a theoretical maximum — actual money creation can and often does fall short of this maximum whenever banks hold excess reserves beyond the legal minimum.
✓ Quick Self-Test
Given an initial deposit and reserve requirement, can you trace at least three explicit rounds of the money-creation chain, calculating the reserve held and amount lent at each step? Can you explain, using a specific example, how banks holding excess reserves reduces actual money creation below the formula's theoretical maximum?
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