Week 6 Model Workshop: Two Gaps, Two Ways Home

Part 1 — The Big Picture

This week you learned that potential output is the vertical long-run aggregate supply line, that the crossing of aggregate demand and short-run aggregate supply is actual output, and that the distance between them is a recessionary or an inflationary gap, reported in billions of dollars and as a percentage of potential. You also saw that expected inflation shifts short-run aggregate supply, which is how an economy can close a gap on its own. In this Model Workshop you build two illustrative economies in a free tool, find where each one sits, measure each gap both ways, and then move the short-run aggregate supply line yourself to watch each economy return to potential. You finish by sorting positive claims from normative ones and checking a chatbot's account of the same two economies.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Economy A and Economy B each sit 25 billion dollars away from potential output, but on opposite sides: how big is each gap as a share of potential, which curve shifts as each economy corrects itself, and where do the price level and real output land?

Workshop data: Two-economy AD–AS lines with potential output (illustrative)

Source: A workshop-only pair of linear aggregate-demand and short-run aggregate-supply lines, with a potential output for each, constructed for this course and not real data; every value is printed in full in the first scaffold table.

• Rows: 2 illustrative economies, one row each in the first scaffold table
• Columns: aggregate demand line, short-run aggregate supply line, potential output, and blank cells for the crossing, the gap in billions of dollars, the gap as a percentage of potential output, and the gap's type
• Economy A: aggregate demand P = 30 − Y⁄50; short-run aggregate supply P = 6 + Y⁄50; potential output 625 billion dollars; nominal output at current prices 660 billion dollars
• Economy B: aggregate demand P = 35 − Y⁄50; short-run aggregate supply P = 14 + Y⁄50; potential output 500 billion dollars

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. In Desmos, type y=30-x/50 and y=6+x/50 on two lines for Economy A, then type x=625 on a third line for its vertical long-run aggregate supply line. In Google Sheets, type the aggregate demand intercept 30 in B2, the short-run aggregate supply intercept 6 in B3, and potential output 625 in B4. Tool: Desmos (free) or Google Sheets (free). Check: Two crossing lines and one vertical line in Desmos, or three filled cells in Google Sheets.
2. Find Economy A's crossing. In Desmos, click where the two sloped lines meet and read x and y. In Google Sheets, type =(B2-B3)*25 in B5 for real output, because setting the two lines equal gives Y = 25 × (30 − 6), and =B2-B5/50 in B6 for the price level. Write the crossing in the first scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: One crossing point, with real output and a price level, written as (Y, P).
3. Measure Economy A's gap. Decide which side of the vertical line the crossing sits on, then subtract in the direction that keeps the gap positive. In Google Sheets, type =B4-B5 in B7 and =B7/B4*100 in B8. Record the gap in billions of dollars, as a percentage of potential output, and by name. Tool: Desmos (free) or Google Sheets (free). Check: A gap in billions of dollars, a percentage of potential output, and the gap's type.
4. Repeat steps 1 to 3 for Economy B: in Desmos type y=35-x/50, y=14+x/50, and x=500; in Google Sheets put 35, 14, and 500 in C2, C3, and C4 and copy the formulas from column B into column C. Subtract so the gap comes out positive for Economy B too. Tool: Desmos (free) or Google Sheets (free). Check: A second crossing, gap, percentage, and gap type in the first scaffold table.
5. Watch self-correction. In Desmos, replace y=6+x/50 with y=c+x/50 and accept the slider for c. Drag c slowly and stop when the crossing lands on x=625; record the new c, the new price level, and the new real output. Do the same for Economy B, starting from c=14 with x=500. In Google Sheets, try values in B3 and C3 until the crossing in row 5 equals potential output in row 4. Tool: Desmos (free) or Google Sheets (free). Check: For each economy, the short-run aggregate supply line ends at a new intercept where the crossing sits on the vertical line.
6. Sort the four claims in analysis question 4 into positive and normative, and for each positive claim note the number in your tables that tests it. Tool: Desmos (free) or Google Sheets (free). Check: Each claim labelled positive or normative, with a number from the tables beside each positive claim.
7. 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: A short critique that quotes the chatbot or the printed analysis 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: set the two lines equal to find each crossing, subtract to find each gap, and divide by potential output. Sketch both economies on graph paper with the two sloped lines, the vertical line at potential, and the shifted short-run aggregate supply line. Complete both 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

Where each economy sits: fill in the crossing, then the gap in billions of dollars, as a percentage of potential output, and by name.

Student scaffold table 1

Economy	Aggregate demand	Short-run aggregate supply	Potential output (billions of dollars)	Crossing (Y, P)	Gap (billions of dollars)	Gap as a percentage of potential	Gap type
Economy A	P = 30 − Y⁄50	P = 6 + Y⁄50	625
Economy B	P = 35 − Y⁄50	P = 14 + Y⁄50	500

How each economy returns to potential with no new policy: name the curve that shifts, its direction, and where the price level and real output land.

Student scaffold table 2

Economy	Curve that shifts	Direction	New intercept c	New price level	New real output (billions of dollars)
Economy A
Economy B

Part 5 — Analysis Questions

1. Show how you found each economy's crossing and each gap, every step on its own line: the crossing, the gap in billions of dollars, and the gap as a percentage of potential output. Then say each gap in a plain sentence.
2. Both economies sit 25 billion dollars from potential output. Explain why their gaps are different shares of potential, which economy has positive cyclical unemployment and why, and why Economy A's nominal output of 660 billion dollars cannot tell you which side of potential it is on.
3. Describe what happened in Desmos or your spreadsheet as you moved c for each economy. Name the curve that shifted, its direction, and the new price level and real output, and explain how expected inflation and wage demands drive that shift. Then explain why the price level change itself is a movement along aggregate demand, not a shift of it.
4. Positive or normative? Sort these four claims about the two illustrative economies, and for each positive claim name the number in your tables that tests it: (1) Economy A's actual output is below its potential output. (2) Economy A's government ought to act now instead of waiting. (3) With no new policy, Economy B's price level ends higher once its gap closes. (4) A long recessionary gap is a worse problem than a short burst of inflation.
5. Choose one and answer it in 3–4 sentences. (a) Potential output is estimated, not observed. Explain how your conclusions about Economy A would change if its true potential output were 600 billion dollars instead of 625, and what evidence you would want before trusting either figure. (b) The slider moved short-run aggregate supply in a second, but real wages and expectations adjust slowly. Explain why self-correction might take many months, and what that means for the wait-or-act debate.

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 two illustrative economies, each drawn as an AD–AS model with real output Y in billions of dollars and the price level P. Economy A: aggregate demand is P = 30 − Y⁄50, short-run aggregate supply is P = 6 + Y⁄50, potential output is 625 billion dollars, and its nominal output at current prices is 660 billion dollars. Economy B: aggregate demand is P = 35 − Y⁄50, short-run aggregate supply is P = 14 + Y⁄50, and potential output is 500 billion dollars. For each economy, find where the curves cross, say whether it has a recessionary or an inflationary gap, and give the gap in billions of dollars and as a percentage of potential output. If no new policy is used, which curve shifts as each economy returns to potential, and in which direction? What multiplier would tell us how big a spending increase would close Economy A's gap? Finally, should Economy A's government act now rather than wait?

Test the response for these likely failures:

• Chatbots often compare Economy A's nominal output of 660 billion dollars with its potential of 625 and call the gap inflationary, mixing higher prices with more output.
• Chatbots often say aggregate demand shifts back to close the gap on its own, or describe the fall in the price level as a shift of aggregate demand.
• Chatbots often reach for a multiplier, such as the money multiplier 1 ÷ RR, to size a policy that closes the gap, mixing a banking tool into a question about output.
• Chatbots often answer whether Economy A's government should act as if the gap 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: "Economy A's nominal output of 660 billion dollars is above its potential of 625, so it has an inflationary gap of 35 billion dollars. Economy B's curves cross at 525, so its gap is 500 − 525 = −25. To return to potential, Economy A's aggregate demand will shift back on its own. Using the money multiplier, a small injection of reserves would close Economy A's gap. The numbers prove that Economy A's government should act at once." Mark it up: quote each flawed sentence, name what is wrong (nominal output used in place of real output, a gap left as a bare negative number, aggregate demand named where short-run aggregate supply shifts, a banking multiplier brought into a question about 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 5) 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

• Both completed scaffold tables
• A screenshot of your Desmos graphs before and after you moved c for each economy, or a labelled hand sketch of both economies with the shifted short-run aggregate supply line
• 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 two illustrative economies: two completed tables (each economy's crossing, gap in billions of dollars, gap as a percentage of potential output, and gap type, then the curve, direction, new intercept, price level, and real output after self-correction), a screenshot or sketch of both economies before and after the shift, written answers to five analysis questions including the positive-or-normative sort, and a critique of a chatbot's account of the same economies, 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
Finding the crossings and measuring the gaps	Both crossings are found from the printed lines, and both gaps are subtracted so they are positive, divided by potential output, named, and shown step by step.	Most figures are right, but one gap flips its sign, divides by actual output, uses nominal output, or skips its steps.	No crossings or gaps are computed, or the numbers are not drawn from the printed lines.
Reading the gaps and cyclical unemployment	The answer explains why equal gaps in billions of dollars are different shares of potential, identifies the economy with positive cyclical unemployment and why, and explains why nominal output cannot locate the gap.	One or two of the three explanations are present, or one is reversed.	No explanation of the gaps appears.
Shifting the model through self-correction	Short-run aggregate supply is shifted in the right direction for each economy, the new intercept, price level, and real output are recorded, expected inflation is named as the driver, and the price-level change is described as a movement along aggregate demand.	The shift is shown for one economy only, the direction is reversed for one, or aggregate demand is named as the curve that moves.	No self-correction work is submitted.
Positive versus normative	All four claims are sorted correctly, and each positive claim is tied to a number in the tables that tests 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 crossing and gap in the tables comes from your own calculation on the printed lines, never from memory or a chatbot.
• Every gap is measured in real output, subtracted so it is a positive distance, divided by potential output for its percentage, and named recessionary or inflationary.
• The self-correction answer names short-run aggregate supply as the curve that shifts, gives its direction for each economy, and reads the new price level and real output.
• Each of the four claims is labelled positive or normative, with a number from the tables 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.