Week 9 — Graph & Model Workshop · "How Banks Create Money"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 7 — money, banking & monetary policy · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 9
Format: enter the deposit-loan chain into a spreadsheet, round by round, then compare your total to the money-multiplier shortcut (1/RR), then catch the AI's mistakes.

This is the course's signature weekly component. Every instructional week has one workshop: you set up a model, solve it, and explain what it means. All tools are links to free external sites — nothing to buy or download.

Part 1 — The Big Picture

This week you learned that an ordinary bank, just by keeping a fraction of every deposit and lending out the rest, sets off a chain reaction: that loan becomes someone else's deposit, which triggers another (smaller) loan, and so on. Today you'll build that chain by hand, round by round, in a spreadsheet — and then confirm that the shortcut formula, the money multiplier (1/RR), gives you the exact same answer as summing the entire infinite chain. Seeing both routes arrive at the same number is what makes the formula trustworthy instead of just "something to memorize." (Next week you'll meet the institution that actually sets the reserve requirement and the other levers of monetary policy — the Federal Reserve.)

The tool: a spreadsheet (Google Sheets: https://sheets.google.com or Excel on your computer). You will enter the deposit-loan chain and let formulas trace each round.

Part 2 — The Guiding Question

If a bank keeps a fixed fraction of every deposit and lends out the rest, how much does a single new deposit end up expanding the money supply once the lending chain runs its full course — and does the quick 1/RR formula actually match that total?

The scenario. A new customer deposits $1,000 into First Meadowland Bank. The reserve requirement (RR) is 10%. The bank keeps the required reserves and lends out the rest; each loan becomes a new deposit at the next bank in the chain, which repeats the same process.

Part 3 — Set Up the Model (in a spreadsheet)

1. Open Google Sheets (https://sheets.google.com) or Excel.
2. Label columns: Round · New Deposit · Required Reserve (10%) · New Loan
3. Row 1 (Round 1): New Deposit = 1000. Enter formulas:
   - Required Reserve: =B2*0.10 (New Deposit × RR)
   - New Loan: =B2-C2 (New Deposit − Required Reserve)
4. Row 2 (Round 2): New Deposit = the New Loan from Round 1 — link the cell (e.g., =D2), then repeat the same two formulas.
5. Fill down through at least 6 rounds. Add a running-total column (=SUM($D$2:D2), filled down) to watch the total climb toward the geometric limit.

Part 4 — Solve (complete this scaffold)

Fill in the blanks from your spreadsheet. Show the arithmetic for at least the first two rounds.

Part 5 — Interpret in Words (this is the SLO-A skill)

In 2–3 sentences, explain what the money multiplier actually represents in plain English (not just "1 divided by RR") — connect it explicitly to the round-by-round chain you just built in the spreadsheet, and state why a lower reserve requirement produces a bigger multiplier. (Hint: what does a lower RR mean for how much of each round gets re-lent?)

Part 6 — Analysis Questions

1. Your spreadsheet shows the money supply expanding well beyond the original $1,000. In one sentence, explain where this "new money" is actually coming from — is a printing press involved, or is something else going on?
2. Suppose the reserve requirement were 20% instead of 10%, on the same $1,000 deposit. Without redoing the whole spreadsheet, predict: would the money multiplier be bigger or smaller than 10? Would each round's loan shrink faster or slower than in the 10%-RR case? Briefly explain both.
3. Connect to policy: the 1/RR model assumes every bank lends out 100% of its available excess reserves at every round. In reality, some banks choose to hold excess reserves beyond what's required (perhaps out of caution, or because loan demand is weak), and the modern Federal Reserve operates in an ample-reserves environment. In 2–3 sentences, explain what that means for how you should treat the 1/RR number your spreadsheet produces — is it a guaranteed outcome, or something else? (You are not being asked whether banks SHOULD hold more or fewer reserves — just to explain honestly what the model can and can't promise.)

Part 7 — AI-Critique Moment (required — the BYOAI step)

Bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the economist who checks its work.

1. Paste this to the chatbot: "A new $1,000 deposit arrives at a bank with a 10% reserve requirement. What is the money multiplier, what is the maximum possible increase in the money supply, and does the bank lend out the required reserves or the excess reserves?"
2. Audit every claim against your own work:
   - Did it get the money multiplier = 10 (using 1/RR = 1/0.10), or did it accidentally use a spending-multiplier-style formula like 1/(1−0.10) = 1.11 (wrong for this scenario)?
   - Did it correctly say the maximum expansion is $10,000 (1,000 × 10), matching what your spreadsheet's running total is approaching?
   - Did it correctly say the bank lends the excess reserves ($900 in Round 1), or did it say (backwards) that the bank lends the required reserves ($100)?
   - Did it mention the upper-bound caveat (excess reserves; the modern ample-reserves environment) on its own, or present 1/RR as a guaranteed result?
3. Write 2–3 sentences naming what the AI got right and at least one thing you had to correct or watch. (If it got everything right, explain how you verified each claim — that's the skill.)

The habit all term: the tool drafts, you judge. A chatbot will confidently swap the money multiplier for the spending multiplier, or say a bank lends its required reserves — catching it is the point.

Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with arithmetic for at least Rounds 1–2), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your spreadsheet is welcome but optional. Due Sun, Nov 1, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified in Python — see _build/logs/week-09-numbers.txt. RR = 10% throughout the main scenario.

Part 4 scaffold answers:

(Running total = sum of each round's New Deposit, i.e., $1,000 + $900 + $810 + $729 = $3,439.00 after 4 rounds; the sequence continues shrinking by ×0.90 each round and converges to $10,000.)

• (e) Money multiplier at RR = 10%: 1 ÷ 0.10 = 10. ✓
• (f) Maximum expansion = 1,000 × 10 = $10,000. ✓
• (g) Yes — after 4 rounds the running total ($3,439) is climbing steadily toward $10,000, and it would keep climbing (by smaller and smaller amounts) toward that exact ceiling as more rounds are added — a converging geometric series. ✓
• Part 5: the money multiplier (1/RR) is a shortcut for summing the ENTIRE infinite chain of loan rounds at once — instead of adding $1,000 + $900 + $810 + … by hand forever, you multiply the original deposit by 1/RR and get the same converged total. A lower RR means each bank keeps back a smaller fraction and re-lends a bigger fraction every round, so the chain runs further before it fizzles out — which is exactly why a lower RR produces a bigger multiplier (RR=5% → multiplier 20; RR=25% → multiplier only 4).
• Part 6: (1) No printing press — the "new money" is created through ordinary bank lending: each loan becomes a new checking-account deposit, and checking-account balances count as money (M1). The banking system as a whole expands the money supply through this repeated lending-and-redepositing process. (2) At RR = 20%, the multiplier would be smaller (1/0.20 = 5, versus 10 at RR = 10%) — a higher reserve requirement means banks keep back MORE of each deposit, so each round's loan would shrink faster (each round would be only 80% of the round before, instead of 90%), and the chain would run out of steam sooner. (3) The 1/RR figure is a maximum, upper-bound teaching model, not a guaranteed outcome — real banks may voluntarily hold excess reserves beyond the required minimum (slowing or halting the chain early), and the modern Fed operates in an ample-reserves environment where reserves already sit well above any required minimum, so the actual money-supply expansion is typically smaller than the textbook 1/RR ceiling.
• Part 7 — common AI errors to look for: (1) using the spending-multiplier formula 1/(1−RR) instead of the money multiplier 1/RR; (2) reversing which reserves get lent (claiming the bank lends the required reserves rather than the excess reserves); (3) presenting 1/RR as a guaranteed result rather than an upper bound, omitting the excess-reserves/ample-reserves caveat entirely.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — required reserves (100, 90, 81, 72.90), new loans (900, 810, 729, 656.10), running total after 4 rounds (3,439.00), multiplier (10), maximum expansion (10,000), all Python-re-verified ✓. Graph-logic/conceptual-canon check — banks lend the excess reserves (never required, never the full deposit) ✓; money multiplier (1/RR) is distinct from the spending multiplier (1/(1−MPC)) ✓; 1/RR correctly taught as an upper bound (excess reserves; ample-reserves note) ✓. Quantitative gate: PASS. Graph-logic check: PASS.