Week 5 — Graph & Model Workshop · "Shift the Right Curve"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 5 — the AD–AS model & short-run fluctuations · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 5
Format: solve the AD–AS anchor in Desmos (free, no account), then read two qualitative shift scenarios off the same diagram, 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.

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Part 1 — The Big Picture

This week you met the model that anchors most of the rest of the course — aggregate demand and aggregate supply (AD–AS). Today you'll do three things with it: (1) solve the anchor system for its exact equilibrium and shift AD right, with every digit computed; (2) read, qualitatively, what happens when an oil shock hits (SRAS shifts left); and (3) read, qualitatively, what happens when consumer confidence drops (AD shifts left). By the end, "which curve, which direction, what happens to P and Y" should be a reflex you can run on almost any economic-news headline.

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login).

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Part 2 — The Guiding Question

When something shifts either side of the AD–AS diagram — total spending, or firms' costs and capacity — which curve actually moves, which direction does it move, and what happens to the price level and real output as a result?

The scenario. In the fictional economy of Meadowland, this period's aggregate demand (AD) is P = 20 − Y/100 and short-run aggregate supply (SRAS) is P = 4 + Y/100 (Y in billions of dollars of real output; P is a price-level index). Government spending then rises, shifting AD to P = 22 − Y/100 (SRAS unchanged). After the numeric part, you'll set the algebra aside and read two more scenarios qualitatively on the same kind of diagram: an oil shock, and a confidence drop.

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Part 3 — Set Up the Model (in Desmos)

1. Open Desmos. Type the two starting curves (x = Y, y = P):
   y = 20 - x/100 (AD) and y = 4 + x/100 (SRAS).
2. Desmos will show the two lines crossing. Zoom/pan if needed to see the crossing point clearly (it's out around x = 800).
3. Now type a third line: y = 22 - x/100 (the new AD after government spending rises). Leave the original AD line on the graph too, so you can see it move.
4. Find where the NEW AD line crosses the SAME (unchanged) SRAS line — that's your new equilibrium.

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Part 4 — Solve (complete this scaffold)

Fill in the blanks with your algebra and Desmos check. Show the steps.

Section A — Baseline equilibrium

Question	Your answer
(a) Set AD equal to SRAS: 20 − Y/100 = 4 + Y/100. Solve for Y. Show the step where you combine the Y terms.	______
(b) Plug your Y back into the AD equation to find P.	______
(c) Check: does the SAME Y and P also satisfy the SRAS equation? (Plug Y into P = 4 + Y/100.)	______

Section B — Government spending rises (AD shifts right)

Question	Your answer
(d) The new AD equation is P = 22 − Y/100. Set it equal to the SAME (unchanged) SRAS equation and solve for the new Y.	______
(e) Plug the new Y back into the new AD equation to find the new P.	______
(f) Compared to Section A: did P go up, down, or stay the same? Did Y go up, down, or stay the same?	______
(g) In ONE sentence, name the shifter, which curve moved, which direction, and the P/Y result.	______

Section C — Qualitative scenario 1: an oil shock (read the diagram, no new algebra)

Question	Your answer
(h) An oil-price shock raises the cost of a key input for firms across the economy. Which curve does this shift — AD, SRAS, or LRAS?	______
(i) Which direction does it shift?	______
(j) Walking the OTHER (unchanged) curve to the new crossing point: does P rise or fall? Does Y rise or fall?	______
(k) What is the name for this specific combination of a rising price level and falling output happening together?	______

Section D — Qualitative scenario 2: a confidence drop (read the diagram, no new algebra)

Question	Your answer
(l) Consumer and business confidence drops sharply, and households/firms plan to spend less at every price level. Which curve does this shift?	______
(m) Which direction does it shift?	______
(n) Walking the OTHER (unchanged) curve to the new crossing point: does P rise or fall? Does Y rise or fall?	______
(o) Compare Section C and Section D: in ONE sentence, what is the key DIFFERENCE in how P and Y move together in each case?	______

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

In 2–3 sentences, explain why an oil shock (Section C) and a confidence drop (Section D) can both make an economy look "worse" in the news, even though they move the price level in opposite directions relative to output. (Hint: think about which curve moved in each case, and what that means for whether P and Y move the same way or opposite ways.)

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Part 6 — Analysis Questions

1. Suppose a policymaker sees real output falling and immediately proposes "boost government spending to fix it," without first checking whether the cause was a demand shock or a supply shock. Using this week's model, explain one risk of applying that fix if the true cause was actually Section C's oil shock rather than Section D's confidence drop.
2. Meadowland's AD is P = 20 − Y/100 and its SRAS is P = 4 + Y/100 (the Section A baseline). If a favorable productivity improvement shifted SRAS to P = 2 + Y/100 instead of the Section C oil shock, would that make output higher or lower than the Section A baseline — and would prices be higher or lower? (You don't need to re-solve algebraically — reason from the direction logic.)
3. Connect to policy: two different real economic slowdowns can look similar in a single headline ("growth slowed this quarter") but have opposite root causes. In 2–3 sentences, explain why a citizen reading the news should ask "which curve moved?" before accepting a claim about what caused a slowdown — without taking a position on which specific real-world event (if any) was which type.

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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: "Aggregate demand is P = 20 − Y/100 and short-run aggregate supply is P = 4 + Y/100. Government spending rises, shifting AD to P = 22 − Y/100. What is the new equilibrium price level and real output? Separately, if an oil-price shock instead shifted short-run aggregate supply left, what would happen to the price level and real output?"
2. Audit every claim against your own work:
   - Did it get the AD-shift result right: Y = 900, P = 13 (both UP)? Chatbots sometimes shift the wrong curve (moving SRAS instead of AD when the shifter is clearly a demand-side change like government spending).
   - Did it correctly describe the oil-shock case as P rising WHILE Y falls (stagflation — opposite directions), rather than saying both move the same direction (the classic AD-shift pattern, misapplied here)?
   - Did it ever describe a plain change in the price level itself as a "shift," instead of correctly calling it a movement along the curve?
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 shift the wrong curve or report P and Y moving the same direction for a supply shock — catching it is the point.

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Part 8 — What to Submit

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

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Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see _build/logs/week-05-numbers.txt). AD: y = 20 - x/100; SRAS: y = 4 + x/100.

Section A — baseline

• (a) 20 − Y/100 = 4 + Y/100 → 20 − 4 = Y/100 + Y/100 → 16 = 2Y/100 → Y = 16 ÷ (2/100) = 800. ✓
• (b) P = 20 − 800/100 = 20 − 8 = 12. ✓
• (c) Check: P = 4 + 800/100 = 4 + 8 = 12 — matches. ✓ Equilibrium: Y* = 800, P* = 12.

Section B — AD shifts right (government spending rises)

• (d) 22 − Y/100 = 4 + Y/100 → 18 = 2Y/100 → Y = 900. ✓
• (e) P = 22 − 900/100 = 22 − 9 = 13. ✓ (Check: 4 + 900/100 = 13 — matches.)
• (f) P went UP (12 → 13). Y went UP (800 → 900). ✓
• (g) "Government spending rises → AD shifts RIGHT → we walk UP the unchanged SRAS curve → P rises from 12 to 13, and Y rises from 800 to 900." ✓

Section C — oil shock (qualitative)

• (h) SRAS shifts (input costs are a supply-side factor). ✓
• (i) SRAS shifts LEFT (higher costs mean firms supply LESS at every price level). ✓
• (j) Walking the unchanged AD curve to the new (higher) SRAS line: P rises, Y falls. ✓
• (k) Stagflation. ✓

Section D — confidence drop (qualitative)

• (l) AD shifts (planned spending is a demand-side factor). ✓
• (m) AD shifts LEFT (less spending at every price level). ✓
• (n) Walking the unchanged SRAS curve to the new (lower) AD line: P falls, Y falls — together. ✓
• (o) The key difference: in Section C, P and Y move in OPPOSITE directions (P up, Y down — stagflation); in Section D, P and Y move in the SAME direction (both down). ✓

Part 5 (model interpretation)

Both events shrink real output (Y falls in both cases), which is why both look "bad" in a headline — but they pull the price level in opposite directions: the oil shock (a supply-side shock) makes the price level RISE as output falls (stagflation, driven by rising costs), while the confidence drop (a demand-side shock) makes the price level FALL as output falls (a garden-variety demand-side slump). Same "output is falling" headline, opposite price-level signature — which is exactly the diagnostic clue that tells the two apart.

Part 6 (model answers)

1. If the true cause was the Section C oil shock (a supply shock) but the policymaker applies a demand-side fix (more government spending, which shifts AD right), that fix would raise Y back up somewhat — but it would push the price level even HIGHER on top of an already-elevated price level, worsening the inflation side of the stagflation problem. The mismatch between the diagnosis and the tool is the risk.
2. A favorable productivity shift to SRAS: P = 2 + Y/100 shifts SRAS RIGHT relative to the Section A baseline (P = 4 + Y/100 → P = 2 + Y/100 supplies MORE at every price level). Walking the unchanged AD curve to this new, more-generous SRAS line gives higher output than the Section A baseline (Y > 800) and a lower price level than the Section A baseline (P < 12) — the mirror image of the oil shock.
3. Any reasonable answer earns credit that (a) notes a single headline like "growth slowed" is consistent with EITHER a demand-side or a supply-side cause, (b) notes the price-level DIRECTION relative to output is the tell (same direction = demand-side; opposite directions = supply-side), and (c) does not assert which real cause was actually at work in any specific real-world case (evenhandedness — this course reasons with the fictional Meadowland numbers, not a real dated episode).

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold (Part 4) — Sections A & B arithmetic fully correct; Sections C & D qualitative directions all correct (20)	20	10–16	0–8
Interpretation (Part 5) — correctly explains the opposite P-direction signature between a supply shock and a demand shock, in words (10)	10	5–8	0–4
Analysis (Part 6) — policy-mismatch risk; SRAS-right mirror case; the "ask which curve moved" reasoning presented fairly (12)	12	6–10	0–5
AI-critique (Part 7) — names a specific thing checked/corrected in the AI's answer (8)	8	4–6	0–3

Quality gate (self-checked): quantitative gate — baseline (Y=800,P=12), AD-right shift (Y=900,P=13) all Python-re-verified ✓. Graph-logic check — AD-right moves P&Y the SAME direction (up/up); SRAS-left (oil shock) moves P&Y OPPOSITE directions (stagflation: P up, Y down); AD-left (confidence drop) moves P&Y the SAME direction (down/down); SRAS-right (productivity) is the favorable mirror of the oil shock (P down, Y up); a plain price-level change is never treated as a shift — all correct ✓. Quantitative gate: PASS. Graph-logic check: PASS.