Week 11 · Model Workshop

Week 11 Model Workshop: Follow One Bond Trade to Output

Principles of Macroeconomics Free sample edition

Part 1 — The Big Picture

This week you learned the transmission mechanism: a bond trade moves the money supply, the money supply moves the interest rate, the rate moves investment and other interest-sensitive spending, the spending multiplier scales that change, and aggregate demand shifts, so the price level and real output move together. In this Model Workshop you solve a fresh illustrative money market, add up five sectors' investment responses, size the shift with the spending multiplier while keeping the money multiplier in its own link, shift aggregate demand in Desmos and read where the price level and real output land, run the bond sale with every arrow reversed, 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: When the central bank of this illustrative economy buys bonds and the money supply rises from 1,200 to 1,320 dollars, how far does the interest rate fall, how much do the five sectors add to investment, how far does aggregate demand shift, where do the price level and real output land, what does a bond sale do instead, and which claims about the move are positive rather than normative?

Workshop data: Five-sector investment survey and money-market chain (illustrative)

Source: A workshop-only table constructed for this course, not real data: an illustrative economy's money demand and money supply, five sectors' reported investment response to a one-point fall in the interest rate, and a linear AD–AS pair, all printed in full in the scaffold tables.

Rows: 5 sectors, each with one investment response per one-point fall in the rate; the second scaffold table shows those 5 rows plus a totals row, 6 rows, and the first scaffold table, the money market, has 3 rows
Columns: sector, investment response per one-point fall (billions of dollars), and a blank change-in-investment cell
Money market: money demand 1,600 − 40r with r in percent, a starting money supply of 1,200 dollars, 1,320 after a bond purchase, and 1,080 after a bond sale
AD–AS pair: aggregate demand P = 20 − Y⁄108 and short-run aggregate supply P = 4 + Y⁄108, with Y in billions of dollars and P an index

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

Open Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. Solve the money market before and after the bond purchase: in Desmos, type (1600-1200)/40 on one line and (1600-1320)/40 on the next; in Google Sheets, type =(1600-1200)/40 in cell B2 and =(1600-1320)/40 in cell B3. Record both rates and the size of the fall in the first scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: Two interest rates, the second lower than the first, and a fall measured in whole percentage points.
Type the five sectors from the second scaffold table into Google Sheets, sector names in column D and responses in column E starting in row 2, and add them with =SUM(E2:E6); in Desmos, type 5+4+3+4+2. Multiply each sector's response by the size of the fall from step 1 to fill the change-in-investment column, and fill the totals row. Tool: Desmos (free) or Google Sheets (free). Check: A total investment response per point, and a total change in investment equal to that response times the fall in the rate.
Compute the spending multiplier from the marginal propensity to consume of 0.75: in Google Sheets type =1/(1-0.75) in a free cell, or in Desmos type 1/(1-0.75). Multiply it by the total change in investment and record the shift of aggregate demand in the third scaffold table. Beside it, record what the money multiplier, 1/0.10 in your tool, would wrongly give if used on the same change. Tool: Desmos (free) or Google Sheets (free). Check: A spending multiplier between 1 and 10 and a shift of aggregate demand several times the change in investment, next to a much larger wrong-multiplier figure.
In Desmos, type y=20-x/108 for aggregate demand and y=4+x/108 for short-run aggregate supply, letting x stand for real output Y and y for the price level P. Click the crossing to read it. Then type y=22-x/108 for aggregate demand after the bond purchase and click the new crossing. Record both crossings in the fourth scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: The second aggregate demand line sits to the right of the first, and its crossing with the unchanged supply line is higher and further right.
Run the bond sale: solve (1600-1080)/40 for the new rate, find the change in investment and the change in output with the same steps as before, and in Desmos type y=18-x/108 for aggregate demand after the sale and read its crossing. Record every link's direction in the fifth scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: A higher rate, a negative change in investment, a negative change in output, and a crossing lower and further left than the starting one.
Answer the five analysis questions, then paste the prompt from the critique step into one approved chatbot, or complete the equivalent route below, and write your critique. Check: Written answers and a critique that quotes the text it checks and 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 the three aggregate demand lines and the short-run aggregate supply line on graph paper, marking every crossing. Complete all five 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 market: solve for the interest rate before and after the bond purchase, and record the size of the fall in percentage points.

Student scaffold table 1
Situation	Money supply (dollars)	Interest rate r (percent)
Before the bond purchase	1,200
After the bond purchase	1,320
Fall in the rate (points)

The five sectors: multiply each response by the fall in the rate to find each sector's change in investment, then fill the totals row.

Student scaffold table 2
Sector	Response per one-point fall (billions of dollars)	Change in investment (billions of dollars)
Equipment	5
Home building	4
Cars bought on credit	3
Office buildings	4
Farm machinery	2
All five sectors

Sizing the shift: use the spending multiplier on the change in investment, and record the money multiplier's figure only to show why it does not belong here.

Student scaffold table 3
Multiplier	Formula	Value	Times the change in investment (billions of dollars)
Spending multiplier	1 ÷ (1 − 0.75)
Money multiplier, wrong link	1 ÷ 0.10

Shifting aggregate demand: record each crossing as real output and the price level, before and after the bond purchase.

Student scaffold table 4
Situation	Aggregate demand line	Real output Y (billions of dollars)	Price level P
Before the bond purchase	P = 20 − Y⁄108
After the bond purchase	P = 22 − Y⁄108

The bond sale: write the new value or the direction for every link of the contractionary chain.

Student scaffold table 5
Link	After the bond sale
Money supply (dollars)	1,080
Interest rate r (percent)
Change in investment (billions of dollars)
Change in output at the old price level (billions of dollars)
Aggregate demand line and its crossing (Y, P)	P = 18 − Y⁄108; crossing:

Part 5 — Analysis Questions

Show the two interest rates, the total investment response, the change in investment, the spending multiplier, and the shift of aggregate demand, every step on its own line. Then say each figure in a plain sentence, including why the money multiplier's figure in your third table does not answer this question.
Name the curve the bond purchase shifts and its direction, give the crossing before and after, and explain why the price level and real output move together. Then compute real output growth from your fourth table and explain why the change in nominal spending, the price level times real output, is not the same as the change in output.
Use your fifth table to trace the bond sale link by link. Explain why every arrow reverses rather than only the last one, and what the bond sale does to the price level and real output.
Positive or normative? Sort these four claims about the illustrative economy, and for each positive claim name the number in your tables that tests it or the evidence that would: (1) In this model, the bond purchase lowers the interest rate from 10 to 7 percent. (2) The central bank ought to make the purchase, because lower unemployment matters more than a higher price level. (3) In this economy the effect on investment will take more than a year to appear. (4) A central bank should follow a fixed rule instead of reacting to each new report.
Choose one and answer it in 3–4 sentences. (a) The five sectors' responses are fixed numbers. Explain how firms' expectations about future sales could make the real investment response smaller than your table shows, and what that means for the shift you computed. (b) Your chain happens all at once on paper. Explain how the inside lag and the outside lag would change when the price level and real output actually move, and why that matters for a central bank deciding when to act.

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 money demand is 1,600 minus 40 times the interest rate r, in percent, and its money supply is 1,200 dollars. The central bank buys bonds and the money supply rises to 1,320 dollars. Five sectors report how much more they would invest, in billions of dollars, for each one-point fall in the interest rate: equipment 5, home building 4, cars bought on credit 3, office buildings 4, and farm machinery 2. The marginal propensity to consume is 0.75 and the required reserve ratio is 0.10. Aggregate demand is P = 20 − Y⁄108 and short-run aggregate supply is P = 4 + Y⁄108, with Y in billions of dollars. What is the new interest rate, how much does investment change, and which multiplier sizes the change in output? If the bond purchase shifts aggregate demand to P = 22 − Y⁄108, what are the new price level and real output, and by what percent did output grow? What happens if the central bank sells bonds instead and the money supply falls to 1,080? Finally, should the central bank make this bond purchase?

Test the response for these likely failures:

Chatbots often multiply the change in investment by the money multiplier, 1 ÷ 0.10 = 10, and report 10 × 54 = 540 billion dollars, because the question also mentions a reserve ratio.
Chatbots sometimes describe the lower interest rate as a movement along aggregate demand, borrowing the interest-rate effect, or say the higher price level then shifts aggregate demand back to the left.
Chatbots often report the rise in nominal spending, from 12 × 864 = 10,368 to 13 × 972 = 12,636, as if it were the growth of output, mixing the higher price level with more production.
Chatbots often answer whether the central bank should make the purchase as if the chain's arithmetic settled it, presenting a value judgment about jobs and inflation 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: "The bond purchase lowers the rate from 10 to 7 percent, so investment rises 3 × 18 = 54. With a reserve ratio of 0.10 the multiplier is 10, so output rises 540 billion. The lower interest rate is a movement along aggregate demand, not a shift. Spending in the economy rose from 10,368 to 12,636, so output grew about 22 percent. If the central bank sells bonds instead, the rate rises, investment still rises, and aggregate demand shifts left. The numbers prove the central bank should make the purchase." Mark it up: quote each flawed sentence, name what is wrong (the money multiplier used on a spending change, a shift of aggregate demand called a movement along it, nominal spending read as real output, only the last arrow reversed in the bond sale, 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 5 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 five completed scaffold tables
A screenshot of your Desmos graph with aggregate demand before and after the bond purchase, or a labelled hand sketch of the lines and their crossings
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 bond purchase: five completed tables (the money market, the five sectors' investment, the multiplier comparison, the aggregate demand shift, and the bond-sale chain), a screenshot or sketch of aggregate demand before and after the purchase, 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
Computing the chain from the data	Both interest rates, the total investment response, the change in investment, and the shift of aggregate demand are computed from the printed tables with the spending multiplier on the output link and every step shown.	Most figures are right, but one uses the money multiplier on spending, skips the investment step, or skips its steps.	No chain figures are computed, or the numbers are not drawn from the printed tables.
Shifting aggregate demand in the AD–AS model	Aggregate demand is shifted right, both crossings are read correctly, the price level and real output are shown rising together along the unchanged supply line, and real output growth is kept apart from nominal spending.	The shift is drawn, but a crossing is misread, the direction is reversed, or real and nominal are mixed.	No aggregate demand shift is submitted.
The bond sale: every arrow reversed	Every link of the bond sale is traced with its new value or direction, ending with aggregate demand shifting left and the price level and real output falling.	The sale is traced, but one link keeps the expansionary direction or a value is missing.	No bond-sale work appears.
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.	Two or three claims are sorted correctly, or the positive claims are not tied to evidence.	The sort is missing or fewer than two claims are sorted correctly.
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 interest rate, investment change, and output change comes from your own calculation on the printed tables, never from memory or a chatbot.
The spending multiplier sizes the output link, and the money multiplier is recorded only as the wrong-link comparison.
The aggregate demand shift is named with its direction, and the price level and real output are read from both crossings.
Real output growth is kept apart from the change in nominal spending.
Every link of the bond-sale chain reverses, with each new value or direction recorded.
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.

Built with The Course Maker · samples.thecoursemaker.com