Week 6 — Graph & Model Workshop · "Diagnose the Gap"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 5 — the AD–AS model & the business cycle; output gaps · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 6
Format: given three P/Y readings against potential output, diagnose the gap (type, size, and % of potential), place each on the AD–AS picture, and reason through the self-correction-vs-policy question — then catch the AI's mistakes.

This is the course's signature weekly component. Every instructional week has one workshop: you set up a model, solve it, and explain what it means. All tools are links to free external sites — nothing to buy or download.

Part 1 — The Big Picture

Last week you learned to shift the right curve in the AD–AS model and read off the new price level and output. This week you use that same model to answer a different, very practical question: given a report on where an economy's output actually stands, how do you diagnose it — is it running hot, cold, or right at its sustainable potential? You'll practice the exact skill economists (and financial journalists, and policymakers) use every time a new GDP report comes out: compare actual output to potential output, name the gap, and place it on the diagram. Then you'll turn to the deeper question this diagnosis raises — does the gap fix itself, or is waiting for that too costly? — reasoning through it evenhandedly, the way a professional would.

The tool: 🔗 Desmos Graphing Calculator (optional) — https://www.desmos.com/calculator (free, instant, no login) — useful if you want to sketch the vertical LRAS line against each scenario's AD–AS crossing.

Part 2 — The Guiding Question

Given only a report of actual output vs. potential output, how do you determine whether an economy has a recessionary gap, an inflationary gap, or no gap at all — and what does each diagnosis imply?

The scenario. A fictional economy has potential output Y* = 1,000 (the same sustainable-capacity anchor from this week's lecture). You receive three separate quarterly reports, each with a different actual-output reading. Your job: diagnose each one.

• Scenario A: actual output Y = 970.
• Scenario B: actual output Y = 1,020.
• Scenario C: actual output Y = 1,000.

Part 3 — Set Up the Model

1. Potential output is fixed at Y* = 1,000 for all three scenarios — this is your benchmark, drawn as a vertical LRAS line on the AD–AS diagram (real output Y on the horizontal axis, the price level P on the vertical axis).
2. For each scenario, compare the reported actual output to 1,000. If actual < 1,000, the AD/SRAS crossing sits to the LEFT of the LRAS line. If actual > 1,000, it sits to the RIGHT. If actual = 1,000, the crossing sits exactly on the LRAS line.
3. (Optional Desmos step: sketch a vertical line at x = 1,000 to represent LRAS, then mark each scenario's actual-Y value as a point on the horizontal axis relative to that line.)

Part 4 — Solve (complete this scaffold)

Fill in the blanks. Show the arithmetic for every gap size and percentage.

Part 5 — Interpret in Words (this is the SLO-A skill)

In 2–3 sentences, explain what your Scenario A diagnosis means for the whole economy — not just "output is below potential," but what that typically implies about unemployment relative to its natural rate and what the phrase "recessionary gap" is actually describing (a measured shortfall, not a moral judgment or an "impossible" situation).

Part 6 — Analysis Questions

1. Scenario B is an inflationary gap — the economy is producing MORE than its sustainable potential. Explain in 1–2 sentences why this is treated as a gap (something to be concerned about) rather than simply "good news, because output is higher."
2. A classmate says, "If potential output is 1,000, then any actual output above 1,000 is impossible — you can't produce more than 'the max.'" Use this week's model to explain why that claim about potential output is incorrect.
3. Connect to policy: Scenario A (the recessionary gap) raises the term's central policy debate. In 2–3 sentences, explain both (a) how a believer in classical self-correction would expect this gap to close on its own, and (b) how a Keynesian-leaning policymaker might instead want to act on it faster. (You are not being asked which view is "right" — just to explain each fairly.)

Part 7 — AI-Critique Moment (required — the BYOAI step)

Bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the economist who checks its work.

1. Paste this to the chatbot: "An economy has potential output of 1,000. In one quarter, actual output is 970. What type of output gap is this, what is its size, and what percentage of potential is that? Also, is 'two consecutive quarters of negative GDP growth' the official U.S. government definition of a recession?"
2. Audit every claim against your own work:
   - Did it correctly identify a recessionary gap of 30 (3% of potential) — 1,000 − 970 = 30, 30 ÷ 1,000 × 100 = 3%? Chatbots sometimes subtract in the wrong direction, report a bare negative number without naming the gap type, or divide by the wrong base (using actual output instead of potential as the denominator).
   - Did it correctly say NO — "two consecutive quarters of negative GDP growth" is a popular rule of thumb, not the NBER's official method (a committee judging multiple indicators together)? Chatbots very often state the two-negative-quarters rule as if it were the official definition, with high confidence — this is one of the single most common macro factoids gotten wrong.
   - Did it correctly avoid calling potential output "the absolute maximum" the economy can produce?
3. Write 2–3 sentences naming what the AI got right and at least one thing you had to correct or watch. (If it got everything right, explain how you verified each claim — that's the skill.)

The habit all term: the tool drafts, you judge. A chatbot will confidently state the two-negative-quarters "rule" as official U.S. policy — catching that is exactly the point of this exercise.

Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with the arithmetic), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. An optional Desmos screenshot is welcome. Due Sun, Oct 11, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see _build/logs/week-06-numbers.txt). Potential output Y* = 1,000 for all three scenarios.

• (a) Scenario A: 1,000 − 970 = 30. ✓
• (b) Scenario A: 30 ÷ 1,000 × 100 = 3% of potential. ✓
• (c) Scenario A: actual output (970) is BELOW potential (1,000) → recessionary gap, sitting to the LEFT of the vertical LRAS line. ✓
• (d) Scenario B: 1,020 − 1,000 = 20. ✓
• (e) Scenario B: 20 ÷ 1,000 × 100 = 2% of potential. ✓
• (f) Scenario B: actual output (1,020) is ABOVE potential (1,000) → inflationary gap, sitting to the RIGHT of the vertical LRAS line. ✓
• (g) Scenario C: 1,000 − 1,000 = 0. ✓
• (h) Scenario C: actual output EQUALS potential output — no gap; the AD/SRAS crossing sits exactly on the LRAS line, and the economy is producing at its sustainable, full-employment level (unemployment at its natural rate). ✓
• Part 5: Scenario A's recessionary gap of 30 (3% of potential) means the economy is producing 3% less than it sustainably could. This typically corresponds to unemployment ABOVE its natural rate — some workers who would normally be employed are not — but the resources to close the gap already exist; nothing is "impossible" about producing more, it's simply not currently happening.
• Part 6: (1) An inflationary gap is treated as a concern rather than pure good news because running above sustainable capacity typically brings rising inflation pressure — the "extra" output isn't free, it shows up as upward pressure on prices as the economy strains past its normal capacity. (2) The claim is incorrect because potential output is a sustainable, full-employment benchmark, not a hard physical ceiling — an economy can temporarily push output above potential (overtime, unemployment below the natural rate, capacity utilization above normal), it just isn't sustainable and tends to generate rising inflation pressure rather than being literally impossible. (3) Classical self-correction: unemployment above the natural rate (from Scenario A's recessionary gap) puts downward pressure on wages; falling wages lower firms' costs, shifting SRAS right until output returns to potential on its own — no policy action required, in this view. Keynesian-leaning view: wages are "sticky" in the short run (long contracts, resistance to nominal cuts), so this self-correction can take a long time, during which real hardship (unemployment, lost income) accumulates; active fiscal or monetary stabilization could close the gap faster. Full credit for any answer presenting both views fairly without declaring one "right" (evenhandedness).
• Part 7: full credit for a specific catch — most commonly the AI subtracting in the wrong direction or misreporting the percentage, or asserting "two negative quarters" as the official NBER definition (it is a rule of thumb, not the official method — the NBER committee judges multiple indicators together).

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — gap sizes (30, 20, 0), percentages (3%, 2%, 0%), all three point classifications (recessionary/left, inflationary/right, no gap/on the line) all Python-re-verified ✓. Graph-logic check — recessionary = left of vertical LRAS with unemployment above the natural rate; inflationary = right of vertical LRAS with unemployment below the natural rate; LRAS itself never shifts, all correct ✓. Quantitative gate: PASS. Graph-logic check: PASS.