Week 15 Model Workshop: One Island, Two Advisers

Part 1 — The Big Picture

This week you put the Keynesian tradition and the classical and monetarist tradition side by side, stated the agreed ground plainly, and computed the deficit-to-GDP and debt-to-GDP ratios that both schools share. In this Model Workshop you take one fresh illustrative island economy and do the whole job yourself: measure its recessionary gap, size the Keynesian lever with the spending multiplier while keeping the money multiplier out of it, compute the budget ratios, shift aggregate demand in Desmos and read where real output and the price level land, see what a rising price index does to the debt ratio, and then sort claims about the island into positive and normative before you check a chatbot's account of the same economy.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: For this illustrative island economy, how big is the recessionary gap, how much new spending closes it in the simple model, what are the deficit and debt ratios, where do real output and the price level land when aggregate demand shifts, what does a rising price index do to the debt ratio, and which claims about borrowing to close the gap are positive and which are normative?

Workshop data: Island economy gap, budget, and price-index table (illustrative)

Source: A workshop-only set of figures constructed for this course, not real data: an illustrative island economy's potential and actual output, its spending propensity, one year's budget and debt, next year's price index and nominal GDP, and a linear AD–AS pair, all printed in full in the scaffold tables.

• Rows: one island economy observed over two years; the budget scaffold table has 5 rows, the gap table 3 rows, the AD–AS table 2 rows, the price-index table 3 rows, and the claims table 5 rows
• Output and spending: potential output 1,600 and actual output 1,520, in billions of dollars, with a marginal propensity to consume of 0.6 and a required reserve ratio of 0.10
• Budget: revenue 342, spending 380, a starting debt of 760, and GDP of 1,520, in billions of dollars
• Next year: a price index rising from 100 to 105 and nominal GDP of 1,596, with the debt held at its end-of-year level
• AD–AS pair: aggregate demand P = 40 − Y⁄80 and short-run aggregate supply P = 2 + Y⁄80, 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

1. Open Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. Measure the gap: in Desmos type 1600-1520 and 80/1600*100; in Google Sheets type =1600-1520 in cell B2 and =B2/1600*100 in cell B3. Then find the spending multiplier with 1/(1-0.6) and divide the gap by it. Record every figure in the first scaffold table, and beside it what 1/0.10 would wrongly give. Tool: Desmos (free) or Google Sheets (free). Check: A gap in billions of dollars and as a percent of potential, a spending multiplier between 1 and 10, and a new-spending figure smaller than the gap.
2. Compute the budget figures: in Google Sheets type 342 in D2, 380 in D3, 760 in D4, and 1520 in D5, then =D3-D2 in D6 for the deficit, =D6/D5*100 in D7, =D4/D5*100 in D8, and =(D4+D6)/D5*100 in D9; in Desmos type the same expressions with the numbers. Record each result in the second scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: A deficit, a small deficit ratio, and a debt ratio that is higher at the end of the year than at the start.
3. In Desmos, type y=40-x/80 for aggregate demand and y=2+x/80 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=41-x/80 for aggregate demand after the new spending and click the new crossing. In Google Sheets, solve each crossing with =(40-2)*80/2 and =(41-2)*80/2. Record both crossings in the third 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.
4. Run next year's price change: compute nominal growth with (1596-1520)/1520*100, real GDP with 1596/1.05, and the new debt ratio with 798/1596*100. Record each result in the fourth scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: A positive nominal growth rate, a real GDP equal to this year's, and a debt ratio lower than the end-of-year ratio from step 2.
5. Sort the five claims in the fifth scaffold table as positive or normative and name the column each one leans toward, using your own tables as evidence for every positive claim. Keep the two tools open so you can recheck a figure as you sort. Tool: Desmos (free) or Google Sheets (free). Check: Each claim carries a label, a column, and, for every positive claim, a figure or a test that could check it.
6. 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, rechecking any disputed figure in your tool. Tool: Desmos (free) or Google Sheets (free). 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 two aggregate demand lines and the short-run aggregate supply line on graph paper, marking both crossings. 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 gap and the lever: measure the gap, find the spending multiplier, and size the new spending, then record the money multiplier's figure only to show why it does not belong here.

Student scaffold table 1

Quantity	Formula	Value (billions of dollars unless noted)
Recessionary gap	1,600 − 1,520
Gap as a percent of potential	gap ÷ 1,600 × 100
Spending multiplier	1 ÷ (1 − 0.6)
New spending that closes the gap (simple model)	gap ÷ spending multiplier
Money multiplier, wrong tool	gap ÷ (1 ÷ 0.10)

The budget: compute the deficit and the two ratios both schools share, keeping the year's flow apart from the total owed.

Student scaffold table 2

Quantity	Formula	Value
Deficit (billions of dollars)	380 − 342
Deficit-to-GDP ratio (percent)	deficit ÷ 1,520 × 100
Debt-to-GDP ratio at the start (percent)	760 ÷ 1,520 × 100
Debt at the end (billions of dollars)	760 + deficit
Debt-to-GDP ratio at the end (percent)	end debt ÷ 1,520 × 100

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

Student scaffold table 3

Situation	Aggregate demand line	Real output Y (billions of dollars)	Price level P
Before the new spending	P = 40 − Y⁄80
After the new spending	P = 41 − Y⁄80

Next year: separate the rise in prices from any rise in production, and see what the price change does to the debt ratio.

Student scaffold table 4

Quantity	Formula	Value
Nominal GDP growth (percent)	(1,596 − 1,520) ÷ 1,520 × 100
Real GDP (billions of dollars)	1,596 ÷ 1.05
Debt-to-GDP ratio next year (percent)	798 ÷ 1,596 × 100

The claims: label each one positive or normative, name the column it leans toward, and give the figure or test that could check each positive claim.

Student scaffold table 5

Claim	Positive or normative	Column it leans toward	Figure or test
In the simple model, 32 billion dollars of new spending closes this island's gap.
The island ought to borrow, because idle workers matter more than a higher debt ratio.
Prices on the island adjust slowly enough that the gap would last for years.
Borrowing would push up interest rates and crowd out private building.
The island should keep its debt ratio low even if the recovery is slower.

Part 5 — Analysis Questions

1. Show the gap in billions of dollars and as a percent of potential, the spending multiplier, the new spending that closes the gap in the simple model, the deficit, and the deficit and debt ratios, every step on its own line. Then say each figure in a plain sentence, including why the money multiplier's figure in your first table does not answer this question.
2. Name the curve the new spending shifts and its direction, give the crossing before and after, and explain why the rise in the price level is a movement along the lines rather than a new shift. Then explain why real output rose by less than the 80 the simple model promised, and what that means for each school's reading of the lever.
3. Use your fourth table to explain why the debt ratio fell next year even though real GDP did not grow, and why a chatbot that calls the 5 percent rise in nominal GDP economic growth has mixed up real and nominal.
4. Use your fifth table: for each claim, say whether it is positive or normative, name the column it leans toward, and for each positive claim name the figure in your tables or the evidence that would test it. Then state one result from this week's agreed ground that you would state plainly, with no both-sides framing.
5. Choose one and answer it in 3–4 sentences. (a) The island's spending multiplier is a classroom model. Explain how taxes, imports, or crowding out could make the real effect of 32 billion dollars of spending smaller than your tables show, and which column would stress that. (b) Your lever lands all at once on paper. Explain how lags could change when the spending reaches the island's economy, and why that matters for whether borrowing helps or arrives after the gap has closed.

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 island economy. Potential output is 1,600 and actual output is 1,520, both in billions of dollars. The marginal propensity to consume is 0.6 and the required reserve ratio is 0.10. The government collects revenue of 342, spends 380, and starts the year owing a debt of 760, with GDP of 1,520. Aggregate demand is P = 40 − Y⁄80 and short-run aggregate supply is P = 2 + Y⁄80, with Y in billions of dollars. How big is the recessionary gap, how much new government spending closes it in the simple model, and what are the deficit-to-GDP ratio and the debt-to-GDP ratio at the start and the end of the year? If the new spending shifts aggregate demand to P = 41 − Y⁄80, where do real output and the price level land, and does the higher price level then push aggregate demand back to the left? Next year the price index rises from 100 to 105 and nominal GDP rises to 1,596 while the debt stays at 798: how fast did the economy grow, and what happens to the debt ratio? Finally, should the island's government borrow to close the gap?

Test the response for these likely failures:

• Chatbots often see the reserve ratio in the question and divide the gap by the money multiplier, 1 ÷ 0.10 = 10, reporting that 80 ÷ 10 = 8 billion dollars of spending closes the gap.
• Chatbots sometimes say the higher price level after the spending then shifts aggregate demand back to the left, treating a change in the price level as a shift of the curve.
• Chatbots often report next year's rise in nominal GDP, from 1,520 to 1,596, as 5 percent economic growth, mixing a higher price level with more production.
• Chatbots often answer whether the government should borrow as if the arithmetic settled it, or crown one school of thought, presenting a value judgment as a finding.

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 island's gap is 1,600 − 1,520 = 80. With a reserve ratio of 0.10 the multiplier is 10, so only 80 ÷ 10 = 8 billion dollars of spending closes it. The deficit ratio is 760 ÷ 1,520 × 100 = 50 percent. After the spending, the higher price level shifts aggregate demand back to the left, so output does not change. Next year nominal GDP rises 5 percent, so the economy grew 5 percent and the debt ratio fell because of growth. The numbers prove the Keynesian school is right, so the island should borrow." Mark it up: quote each flawed sentence, name what is wrong (the money multiplier used on a spending decision, the debt put on top of the deficit ratio, a price-level change called a shift of aggregate demand, nominal growth read as real growth, and a normative verdict 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 6 and Objective 8) 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 new spending, 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 island economy: five completed tables (the gap and the lever, the budget ratios, the aggregate demand shift, next year's price change, and the claims sort), a screenshot or sketch of aggregate demand before and after the new spending, written answers to five analysis questions, 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 gap, the lever, and the ratios	The gap in units and as a percent of potential, the spending multiplier, the new spending, the deficit, and all three ratios are computed from the printed tables with the flow and the stock kept apart and every step shown.	Most figures are right, but one uses the money multiplier, puts the debt on top of the deficit ratio, multiplies the gap instead of dividing, or skips its steps.	No 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 rise is described as a movement along the lines, and the smaller rise in real output is explained.	The shift is drawn, but a crossing is misread, the direction is reversed, or the price-level rise is called a new shift.	No aggregate demand shift is submitted.
Real versus nominal	Nominal growth, real GDP, and next year's debt ratio are computed, and the fall in the ratio is traced to the price index rather than to real growth.	The figures are computed, but the fall in the ratio is credited to economic growth, or one figure is missing.	No next-year work appears.
Positive versus normative	All five claims are labelled correctly with a column each, every positive claim is tied to a figure or a test, one agreed-ground result is stated plainly, and no school is declared the winner.	Three or four claims are labelled correctly, or the positive claims are not tied to evidence, or one school is declared the winner.	The sort is missing or fewer than three claims are labelled 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 gap, multiplier, spending, ratio, and price-index figure comes from your own calculation on the printed tables, never from memory or a chatbot.
• The spending multiplier sizes the lever, and the money multiplier is recorded only as the wrong-tool comparison.
• The deficit, a flow, and the debt, a stock, each sit on top of their own ratio.
• The aggregate demand shift is named with its direction, and real output and the price level are read from both crossings.
• Next year's nominal growth is kept apart from real growth.
• Each of the five claims is labelled positive or normative, with a figure or a test beside each positive claim, and no school is declared the winner.
• 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.