Week 9 Model Workshop: How Far Can One Deposit Go?

Part 1 — The Big Picture

This week you learned that a bank keeps its required reserves and lends the excess, that each loan comes back as someone else's deposit, and that the money multiplier, 1 divided by the required reserve ratio, adds the whole chain up to a ceiling. In this workshop you build that chain yourself for a small lakeside banking system, one bank at a time in a spreadsheet, and watch the running total of deposits climb toward its limit without ever passing it. Then you find the most money the system's monetary base can support, see what happens to that ceiling when banks hold extra reserves, sort four statements about bank rules into what the model can test and what rests on values, and check a chatbot's reading of the same chain.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: How far can one 5,000-dollar deposit stretch through the lakeside banking system, and what keeps the real expansion below that ceiling?

Workshop data: An illustrative lakeside banking system's deposit chain

Source: A deposit chain for an illustrative lakeside banking system, one 5,000-dollar deposit followed bank by bank under a required reserve ratio of 0.20, plus a monetary base of 400 dollars, constructed for this workshop and printed in full in Part 4; it is not real data and describes no real place, bank, or person.

• Rows: 1 banking system described by 1 deposit, 1 required reserve ratio, 1 monetary base, and 1 optional extra-reserve share; the chain table in Part 4 has 4 rows, the ceilings table has 5 rows, and the sorting table has 4 rows
• Deposit and ratio: a first deposit of 5,000 dollars and a required reserve ratio of 0.20 at every bank
• Base and extra reserves: a monetary base of 400 dollars, and an optional extra 0.05 of each deposit that banks may choose to keep

Part 3 — Materials & Procedure

Tools and materials

• Desmos (free) or Google Sheets (free)
• A document or notebook for your written answers

Ways of working

• read-and-compute-from-macro-data
• build-and-shift-the-ad-as-model
• separate-positive-from-normative-claims

Procedure

1. Open a blank sheet in Google Sheets, or the free Desmos graphing calculator if you prefer to check the chain there later. In Google Sheets, type 5000 in cell A1, type =A1*0.2 in B1 for the required reserves the first bank keeps, and type =A1-B1 in C1 for the loan it makes. Tool: Desmos (free) or Google Sheets (free). Check: B1 shows the reserves kept and C1 shows the loan; together they add back to the 5,000 in A1.
2. Type =C1 in A2, because the first loan is spent and deposited at the second bank. Copy B1 and C1 down to row 2, then copy A2 to C2 down to row 4 so each row is the next bank in the chain. Tool: Desmos (free) or Google Sheets (free). Check: Each new deposit in column A equals the loan in column C of the row above, and each row is smaller than the one before.
3. Record the four banks in the chain table in Part 4. Then copy row 4 down one more row and type =SUM(A1:A5) in E1 for the running total of the first five deposits, and =5000/0.2 in E2 for the whole-chain ceiling. Copy the rows further down if you like and watch the running total climb toward the ceiling without passing it. Tool: Desmos (free) or Google Sheets (free). Check: E1 shows the running total of five deposits and E2 shows the ceiling; the running total stays below the ceiling no matter how far you copy down.
4. Type =1/0.2 in E3 for the money multiplier and =E3*400 in E4 for the most money the 400-dollar base can support. Then type =1/(0.2+0.05) in E5 and =E5*400 in E6 for the ceiling when banks also keep an extra 0.05 of every deposit. In Desmos instead, type y=5000(1-0.8^x) and read the running total after x banks; it levels off as x grows. Tool: Desmos (free) or Google Sheets (free). Check: E3 to E6 hold the multiplier and the two ceilings; the ceiling with extra reserves is lower than the ceiling without them.
5. Record every result in the ceilings table in Part 4, with the formula you typed and one sentence in words for each. Tool: Desmos (free) or Google Sheets (free). Check: Every row of the ceilings table holds a formula, a result, and a plain-language sentence.
6. Read the four statements in the third table of Part 4. Label each one positive or normative, and write either the evidence or model result that could test it or the value it rests on. Tool: Desmos (free) or Google Sheets (free). Check: All four statements are labelled, each with a test or a value beside it.

Fallback route

When to use it: Use this route if neither Desmos nor Google Sheets will open, or a formula will not run.

Work every step by hand or with a basic calculator from the numbers printed in Part 4: multiply each deposit by 0.20 for the reserves kept, subtract to find the loan, carry the loan down as the next deposit, add the first five deposits, and divide 5,000 and the 400-dollar base by the share kept for each ceiling. Complete every table, analysis question, and the critique step, and submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Follow the deposit bank by bank, so you can see each bank keep its required slice and lend the rest.

Student scaffold table 1

Bank in the chain	New deposit (dollars)	Required reserves kept (dollars)	Loan made (dollars)
Bank 1	5,000
Bank 2
Bank 3
Bank 4

Add the chain up and find the ceilings, so you can see how far the deposit and the base can stretch at most.

Student scaffold table 2

Quantity	Formula you typed	Result	What it means in words
Running total of the first five deposits
Whole-chain ceiling on deposits
Money multiplier at a required ratio of 0.20
Most money the 400-dollar base can support
Ceiling when banks also keep an extra 0.05

Sort the statements so the testable claims are kept apart from the value judgments.

Student scaffold table 3

Statement	Positive or normative	Evidence or model result that could test it, or the value it rests on
With a required ratio of 0.20, each bank lends 0.80 of every new deposit.
If banks keep extra reserves, the most money a base of 400 can support falls.
Lakeside banks should be required to keep at least 0.20 of every deposit.
Letting banks choose their own reserves is fairer to small borrowers.

Part 5 — Analysis Questions

1. Write the steps that give the first bank's reserves and loan, the next three banks' loans, the whole-chain ceiling, and the most money the base can support, and say each result in a full sentence with its dollar amount.
2. Compare the running total of the first five deposits with the whole-chain ceiling. How close did five banks get, and what happens to the gap as you copy the chain further down?
3. Explain why the first bank lends the amount in your chain table rather than its required reserves, and why the money multiplier, not the spending multiplier, gives the ceiling.
4. Choose one: (a) a friend says a bank that lends money is giving away other people's savings; explain to the friend, using your chain table, what happens to the original deposit and where the new deposits come from; or (b) name the statement in the sorting table that was hardest to label, and explain what made it hard and how you decided.
5. Your ceiling assumes every bank lends every spare dollar and nobody keeps cash out of the bank. Name one way this classroom model could mislead you about a real banking system, and say what you would want to know before trusting its ceiling as a description of real lending.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 9 Model Workshop tables above. They describe an illustrative lakeside banking system constructed for a class activity, not real data. A hardware-store owner deposits 5,000 dollars at the first bank, every bank must keep a required reserve ratio of 0.20, and the system's monetary base is 400 dollars. Please do six things. First, say how much the first bank keeps and how much it lends. Second, follow the loan to a second and a third bank and give what each one lends. Third, give the largest total of deposits the 5,000-dollar deposit can support across the whole banking system, and name the multiplier you used. Fourth, give the largest money supply the 400-dollar base can support, and then the new ceiling if banks also keep an extra 0.05 of every deposit. Fifth, tell me whether the new deposits the chain creates mean the economy produced that much more output this year, and, as a stretch question for next week, whether a rise in the monetary base is a movement along a curve or a shift of one in the money market. Sixth, sort these four statements into positive and normative: (1) With a required ratio of 0.20, each bank lends 0.80 of every new deposit. (2) If banks keep extra reserves, the most money a base of 400 can support falls. (3) Lakeside banks should be required to keep at least 0.20 of every deposit. (4) Letting banks choose their own reserves is fairer to small borrowers.

Test the response for these likely failures:

• Chatbots often reach for the spending-multiplier shape and divide 1 by 1 minus the reserve ratio, getting 1 ÷ (1 − 0.20) = 1.25, or they say the bank lends its 1,000 dollars of required reserves.
• Chatbots often say the 20,000 dollars of new deposits means the economy produced 20,000 dollars more this year, treating new money as new real output.
• Asked about the money market, chatbots often call a rise in the monetary base a movement along a curve, or launch into an interest-rate answer the workshop's data cannot support.
• Chatbots often call statement 2 normative because it sounds like a policy argument, or call statement 4 positive because it sounds like a fact about borrowers.

Write 3–5 sentences naming one thing the chatbot got right and at least two places it went wrong or overreached, quoting its words and correcting each with evidence from your own tables or this week's chapter.

Equivalent route (no AI required)

No AI account is required for this workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "The first bank keeps 4,000 dollars and lends its 1,000 dollars of required reserves. Because the ratio is 0.20, the multiplier is 1 divided by 1 minus 0.20, which is 1.25, so the 5,000-dollar deposit can grow to only 6,250 dollars. The new deposits the chain creates mean the economy produced that much more output this year. When the central bank raises the monetary base, the economy moves along the money-supply curve, so the interest rate falls to exactly 4 percent. Statement 2 is normative, because it is about bank rules." Mark it up: quote each flawed sentence, name what is wrong (lending the required reserves, the spending-multiplier shape used on a banking question, new money read as new real output, an interest-rate claim this week's data cannot support and a money-supply change described as a movement along a curve, or a positive statement labelled normative), cite the evidence from your tables or the chapter, and write a corrected sentence beneath it; for the money-market claim, say that the money market is next week's tool and that no interest-rate figure can come from these data. This route assesses the same objectives (Objective 6 and Objective 7) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All three completed scaffold tables
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Model Workshop report on an illustrative lakeside banking system: three completed tables (the four banks in the deposit chain, the running total and the ceilings, and the sorted statements), written answers to five analysis questions, and a critique of a chatbot's analysis of the same chain, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Building the deposit chain	All four banks show the required reserves kept and the loan made, each loan is carried down as the next deposit, and the running total of five deposits is computed and said in a full sentence.	The chain is attempted, but one value is wrong, a loan is not carried down, or the running total is missing.	No chain is built, or values are invented rather than computed.
Finding the ceilings with the money multiplier	The whole-chain ceiling, the money multiplier, the most money the base can support, and the ceiling with extra reserves are all correct, each built from the money multiplier and said in words.	Most ceilings are correct, but one is wrong, the extra reserves are ignored, or one ceiling uses the spending-multiplier shape.	No ceiling is found, or every ceiling uses the wrong multiplier.
Explaining the chain and its limit	The response explains why each bank lends the excess rather than its required reserves, compares the running total with the ceiling, and describes the ceiling as a limit rather than a forecast.	Two of the three parts are explained, or the ceiling is called a prediction.	No explanation is given, or required reserves are said to be lent.
Sorting positive and normative statements	All four statements are labelled correctly, each with a fitting test or value, and the chosen reflection option is answered with the model's prediction kept apart from any value judgment.	Most statements are labelled correctly, but one is wrong, a test or value is missing, or the reflection blurs the two kinds of claim.	The statements are not sorted, or positive is treated as meaning good and normative as meaning bad throughout.
Critiquing the AI analysis or the printed flawed analysis	The chatbot's analysis, or on the equivalent route the printed flawed analysis, is quoted and at least two errors are corrected with evidence from the tables or the chapter, including any output or interest-rate claim flagged as outside these data.	The critique names errors but corrects only one, or corrects without evidence, on either route.	No critique is submitted on either route, or the AI output or flawed analysis is accepted without checking.
Naming the limitation of the model	The response names a specific way the classroom multiplier could mislead about real lending and says what further information would be needed.	A limitation is named but not connected to what would be needed to trust the ceiling.	No limitation is named.

Quality Gate

• Every reserve, loan, total, and ceiling comes from your own formula, calculator, or hand work, never from memory or a chatbot.
• Each bank keeps its required reserves and lends the rest, and each loan is carried down as the next bank's deposit.
• The running total is compared with the ceiling, and the ceiling is described as a limit, not a forecast.
• The money multiplier, not the spending multiplier, is used for every ceiling.
• All four statements carry a label and either a test or a value.
• No statistic, reserve ratio, money-supply figure, multiplier, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence from your tables or the chapter.