Week 10 Model Workshop: Where Does the Interest Rate Land?

Part 1 — The Big Picture

This week you learned that the Federal Reserve runs monetary policy, that the dual mandate is read with the unemployment rate and the inflation rate, that buying bonds adds reserves and raises the money supply while selling bonds drains them, and that the money market sets the equilibrium interest rate where a downward-sloping money demand line meets a vertical money supply line. In this Model Workshop you build that money market yourself from an illustrative survey, find where the interest rate lands, shift the money supply with a bond purchase and a bond sale, shift money demand when incomes rise, read the two dual-mandate measures, sort positive claims from normative ones, and then check a chatbot's account of the same economy.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: In this illustrative economy, where does the equilibrium interest rate land, how far does it move when the central bank buys or sells bonds, what happens instead when incomes rise, and which claims about what the central bank should do are positive rather than normative?

Workshop data: Money-demand survey, central-bank balance, and labor-market tally for one illustrative economy

Source: A workshop-only data set constructed for this course, not real data: a five-row survey of how much money people in an illustrative economy want to hold at five interest rates, the economy's monetary base and required reserve ratio, and a small labor-market and price-index tally, all printed in full in the scaffold tables.

• Rows: 5 survey rows, one for each interest rate from 2 to 6 percent; the first scaffold table shows exactly those 5 rows
• Columns: interest rate (percent), money people want to hold (billions of dollars), and a blank change-from-the-row-above cell
• Central bank: a monetary base of 40 billion dollars and a required reserve ratio of 0.05; a bond purchase raises the base to 42 and a bond sale lowers it to 38
• Labor market and prices: 3,000 unemployed people in a labor force of 60,000, and a price index of 150 last year and 159 this year

Part 3 — Materials & Procedure

Tools and materials

• Desmos (free) or Google Sheets (free)

Ways of working

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

Procedure

1. Open Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. If you use Google Sheets, type the five survey rows from the first scaffold table into columns A and B, with the interest rate in column A and the money people want to hold in column B, starting in row 2. Tool: Desmos (free) or Google Sheets (free). Check: Five rows of survey data, interest rates 2 to 6 in column A.
2. Find how much money demand changes from one survey row to the next as the interest rate rises. In Google Sheets, type =B2-B3 in C3 and copy it down to C6; in Desmos, subtract one row from the next by hand. Use that change to write money demand as a line, M_d = 1,000 − 40r, and check one row: 1,000 − 40 × 2 should give the first survey value. Tool: Desmos (free) or Google Sheets (free). Check: The same change in every row, and a money demand line that reproduces all five survey values.
3. Find the money supply. Compute the money multiplier as 1 ÷ 0.05 and multiply it by the monetary base of 40. In Desmos, type y=(1000-x)/40 for money demand, with x the quantity of money and y the interest rate, then type x=20b and accept the slider for b; set b to 40 and click the crossing. In Google Sheets, type =(1000-800)/40 to solve for the rate. Tool: Desmos (free) or Google Sheets (free). Check: A money supply in billions of dollars and one crossing that gives the equilibrium interest rate.
4. Run a bond purchase and a bond sale. Drag the Desmos slider b to 42, then to 38, and record each new money supply and crossing in the second scaffold table. In Google Sheets, multiply each new base by the money multiplier and solve the rate the same way as in step 3. Tool: Desmos (free) or Google Sheets (free). Check: A lower interest rate after the purchase and a higher one after the sale, with money demand unchanged.
5. Shift money demand. Set b back to 40, then type y=(1080-x)/40 on a new line for money demand after incomes rise. Click where it crosses the money supply line and record it in the third scaffold table. In Google Sheets, type =(1080-800)/40. Tool: Desmos (free) or Google Sheets (free). Check: A second, higher crossing on the same vertical money supply line.
6. Read the two dual-mandate measures from the fourth scaffold table. In Google Sheets, type =3000/60000*100 for the unemployment rate and =(159-150)/150*100 for the inflation rate; in Desmos, type the same arithmetic on two new lines. Name the goal each rate tracks. Tool: Desmos (free) or Google Sheets (free). Check: Two rates in percent, each matched to maximum employment or stable prices.
7. Sort the four claims in analysis question 4 into positive and normative, then paste the Part 6 prompt into one approved chatbot, or use the equivalent route instead, and compare its answers with your tables on all four checks. Tool: Desmos (free) or Google Sheets (free). Check: Two claims labelled positive with a number or a test beside each, and a short critique that corrects at least two errors.

Fallback route

When to use it: Use this route if neither Desmos nor Google Sheets is available, or if you cannot get online.

Do every calculation by hand or with any calculator, writing each step on its own line, and sketch money demand and each vertical money supply line on graph paper, marking every crossing. Complete all four scaffold tables, every analysis question, and the critique step from your hand work; submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

The money-demand survey: fill in how much money demand changes from one row to the next; the steady change gives the slope of the money demand line.

Student scaffold table 1

Interest rate r (percent)	Money people want to hold (billions of dollars)	Change from the row above
2	920	—
3	880
4	840
5	800
6	760

The money supply and the interest rate: multiply each monetary base by the money multiplier, then read the equilibrium rate where money demand crosses that supply.

Student scaffold table 2

Situation	Monetary base (billions of dollars)	Money multiplier	Money supply M_s (billions of dollars)	Equilibrium r (percent)
Starting point	40
After a bond purchase	42
After a bond sale	38

Shifting money demand: incomes rise, so people want 80 billion dollars more money at every rate; record the new crossing with the money supply held at its starting level.

Student scaffold table 3

Situation	Money demand line	Money supply (billions of dollars)	Equilibrium r (percent)
Before incomes rise	M_d = 1,000 − 40r
After incomes rise	M_d = 1,080 − 40r

The dual-mandate readings: compute each rate and name the goal it tracks.

Student scaffold table 4

Measure	Data	Your calculation (percent)	Goal it tracks
Unemployment rate	3,000 unemployed in a labor force of 60,000
Inflation rate	Price index 150 last year and 159 this year

Part 5 — Analysis Questions

1. Show the slope of money demand from the survey, the money multiplier, the money supply, and the equilibrium interest rate, every step on its own line. Then say what the rate means in a plain sentence, and explain why money demand slopes down.
2. Use your second table to explain the bond purchase and the bond sale: name the line that shifts, its direction, and the new interest rate each time, and explain why the change in the rate is a movement along money demand rather than a shift of it.
3. Compare the rise in the rate after incomes rise with the rise after the bond sale. Name the line that moved in each case and explain how you can tell the two causes apart even though the rate went up both times.
4. Report the unemployment rate and the inflation rate from your fourth table and the dual-mandate goal each tracks. Then sort these four claims as positive or normative, and for each positive claim name the number in your tables that tests it or the evidence that would: (1) In this model, buying bonds lowers the equilibrium interest rate. (2) The central bank ought to care more about the 6 percent inflation reading than about jobs. (3) A higher interest rate will lead people to hold less money. (4) It is unfair for an unelected board to set interest rates.
5. Choose one and answer it in 3–4 sentences. (a) Your money supply used the classroom money multiplier 1 ÷ RR. Explain why that number is a ceiling rather than a forecast, and why it says little about a system where required reserve ratios are zero. (b) Your money demand line came from five survey rows. Explain why real money demand could shift from month to month, and what that means for reading one crossing as the answer.

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 am studying an illustrative economy. Its central bank reports a monetary base of 40 billion dollars, and banks must hold 0.05 of every deposit as reserves. A survey of how much money people want to hold found 920 billion dollars at a 2 percent interest rate, 880 at 3 percent, 840 at 4 percent, 800 at 5 percent, and 760 at 6 percent. What is the money supply, and what is the equilibrium interest rate? If the central bank buys bonds and the monetary base rises to 42 billion dollars, what are the new money supply and interest rate, and which curve shifted? If instead incomes rise so that people want 80 billion dollars more money at every interest rate, what happens to the interest rate? Does the bigger money supply mean the economy is producing more? Finally, should the central bank buy the bonds?

Test the response for these likely failures:

• Chatbots sometimes reach for a spending multiplier such as 1 ÷ (1 − 0.8) = 5, or multiply the base by the reserve ratio, instead of using the money multiplier on new reserves.
• Chatbots often say the fall in the interest rate after the bond purchase shifted money demand, or treat the rise in incomes as a slide along the same money demand line.
• Chatbots sometimes read the rise in the money supply from 800 to 840 billion dollars as the economy producing 5 percent more goods and services.
• Chatbots often answer whether the central bank should buy the bonds as if the money-market arithmetic settled it, presenting a value judgment as a fact.

In 3–5 sentences, quote the chatbot's answer on each of the four checks, say what it got right, and correct at least two errors using your own tables and the course rule, labelling which of its statements were positive and which were normative.

Equivalent route (no AI required)

No AI account is required for this Model Workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "With a base of 40 billion dollars and a spending multiplier of 5, the money supply is 200 billion dollars. When the central bank buys bonds, the lower interest rate shifts money demand to the left, so money demand is now smaller. When incomes rise, people slide along the same money demand line, so the rate does not change. The money supply grew from 800 to 840, so the economy produced 5 percent more goods. The numbers prove the central bank should buy the bonds." Mark it up: quote each flawed sentence, name what is wrong (a spending multiplier used where the money multiplier belongs, a movement along money demand called a shift, a shift of money demand called a movement along it, a stock of money read as real output, and a normative judgment presented as a fact), cite the evidence from your tables or the course rule, and write a corrected sentence beneath it. This route assesses the same objectives (Objective 3 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 marked-up analysis is the submission artifact that replaces the chatbot report and share link.

Part 7 — What to Submit

• All four completed scaffold tables
• A screenshot of your Desmos graph showing money demand and the money supply lines, or a labelled hand sketch of the lines and every crossing
• 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 money market: four completed tables (the money-demand survey, the money supply and the rate before and after a bond purchase and a bond sale, the money demand shift, and the dual-mandate readings), a screenshot or sketch of the money market, written answers to five analysis questions including the positive-or-normative sort, and a critique of a chatbot's account of the same economy, 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 money market from the data	The slope of money demand, the money multiplier, the money supply, and the equilibrium interest rate are computed from the printed survey and base with every step shown, and the rate is explained in a plain sentence.	Most figures are right, but one uses the wrong multiplier, misreads the slope, or skips its steps.	No money supply or interest rate is computed, or the numbers are not drawn from the printed tables.
Shifting money supply and money demand	The bond purchase and the bond sale are shown as shifts of the vertical money supply line with the correct new rates, the rate changes are described as movements along money demand, and the rise in incomes is shown as a shift of money demand with the correct new rate.	The shifts are attempted, but a direction is reversed, a crossing is misread, or a rate change is called a shift of money demand.	No shift of either line is submitted.
Reading the dual-mandate measures	The unemployment rate and the inflation rate are computed from the tally with steps shown and each is matched to the goal it tracks.	One rate is computed or matched correctly, or an index level is read as a rate.	No dual-mandate measure is computed.
Positive versus normative	All four claims are sorted correctly, and each positive claim is tied to a number in the tables or to the evidence that would test it.	Some claims are sorted correctly, or a positive claim has no number or test beside it.	No claims are sorted.
Critique of the chatbot or the printed analysis	On either route, the chatbot critique or the equivalent route's marked-up analysis quotes the text it checks, corrects at least two errors with evidence from the tables or the course rule, and labels its positive and normative statements; both routes earn the same credit.	On either route, the critique names an error but does not correct it with evidence, or corrects only one.	On either route, no critique is submitted, or pasted output appears without any checking.

Quality Gate

• Every money supply, slope, and interest rate comes from your own calculation on the printed tables, never from memory or a chatbot.
• The money multiplier 1 ÷ RR is used for the money supply, and no spending multiplier appears in the money-market calculations.
• Each bond purchase or sale is shown as a shift of the vertical money supply line, and each change in the rate it causes is described as a movement along money demand.
• The rise in incomes is shown as a shift of money demand, not as a movement along it.
• The money supply is described as a stock of money, never as real output.
• Each of the four claims is labelled positive or normative, with a number or a test beside each positive claim.
• No number, rule, 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 or the course rule.