Week 3 — Graph & Model Workshop · "Plot a Demand Curve, Shift It, and Catch the AI's Mistake"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 2 — demand and comparative statics · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 3
Format: plot a demand curve in Desmos (free, no account), read quantities at several prices, apply a determinant shock (demand shift), interpret the result in words, then catch the AI's mistakes.

This is the course's signature weekly component — the economics analog of a lab. Every instructional week has one workshop: you set up a model, solve it, and explain what it means in plain English. 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 built the demand curve: a model that shows the entire price-quantity relationship for a market. The curve slopes downward (law of demand), and its position depends on determinants — income, prices of related goods, tastes, expectations, and the number of buyers. Today you'll plot the week's model, read it, then shock it with a determinant change and trace through what happens.

The central trap we're watching for: when a good's own price changes, you move along the demand curve. When a determinant changes, the whole curve shifts. Chatbots mix these up constantly — your job in Part 7 is to catch it.

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

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Part 2 — The Guiding Question

If demand for a good is described by Qd = 120 − 10P, exactly how much do buyers want at different prices — and what happens to that whole relationship if something other than the price changes?

The scenario. The local market for craft coffee has a demand described by:

Qd = 120 − 10P

where P is the price per cup in dollars and Qd is the number of cups demanded per week.

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Part 3 — Set Up the Model (in Desmos)

1. Open Desmos. The demand curve in inverse form (P on the y-axis, Q on the x-axis) is:
   P = 12 − 0.1Q
   Type this into Desmos as: y = 12 - 0.1x (where y = Price, x = Quantity)
2. You'll see a downward-sloping line — the law of demand made visible.
3. Check the intercepts: at x = 0 (Q = 0), y should be 12. At y = 0 (P = 0), x should be 120.

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Part 4 — Solve (complete this scaffold)

Fill in the blanks from your Desmos graph and the equation Qd = 120 − 10P. Show every step.

Question	Your answer
(a) At P = $2, what is Qd? (Qd = 120 − 10 × 2 = ?)	______
(b) At P = $4, what is Qd?	______
(c) At P = $6, what is Qd?	______
(d) At P = $8, what is Qd?	______
(e) Does quantity demanded rise or fall as price increases? Is this the law of demand?	______
(f) If the price rises from $4 to $6, what is this change called — a movement along or a shift of the demand curve? Why?	______

The demand shock. Suppose buyers' incomes rise and craft coffee is a normal good.

Question	Your answer
(g) Is this change in income a movement along the demand curve or a shift of the curve? Why?	______
(h) Does demand increase or decrease? Does the curve shift right or left?	______
(i) At the same price of $4, would buyers now want more or fewer cups per week than the original 80?	______

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

In 2–3 sentences, explain in plain English:
- What the downward slope of the demand curve means for buyers of craft coffee.
- What it means — in words, not just "shifts right" — when the demand curve shifts right because of a rise in income.

(Hint: the goal is to be able to explain this to someone who has never taken economics.)

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Part 6 — Analysis Questions

1. The local craft coffee shop lowers its prices from $6 to $4 per cup. A classmate says, "This will increase demand for craft coffee." Using the movement-vs-shift distinction, explain precisely why this statement is not quite right — and what the correct statement is.
2. Name one additional event (other than rising income) that would shift the demand for craft coffee to the left. Identify which of the six determinants it belongs to.
3. Connect it: if a competing coffee chain opens nearby and sells comparable coffee at a lower price, what happens to the demand for the original craft coffee? Name the determinant and the shift direction.

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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: "The demand for craft coffee is Qd = 120 − 10P. The price rises from $4 to $6. Does demand for craft coffee shift left?"
2. Audit the answer against your own work:
   - Did the chatbot correctly say No — this is a movement along the demand curve, not a shift? Chatbots frequently say "yes, demand shifts left" or "demand for coffee decreases" when they mean "quantity demanded decreases."
   - If the chatbot said "demand shifts left," write out the error precisely: the curve does not shift when the good's own price changes.
   - Did it correctly compute Qd at P=$4 as 80 and Qd at P=$6 as 60?
3. Then ask the chatbot: "If buyers' incomes rise and coffee is a normal good, does the demand curve shift right or left?" The correct answer is right. Did the chatbot get it?
4. 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.)

The habit all term: the tool drafts, you judge. A chatbot will confidently confuse "quantity demanded fell" with "demand shifted left" — catching it is the point.

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Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with all calculations), 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, Sep 20, 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 against Qd = 120 − 10P. Graph-shift directions verified below.

Part 4 scaffold:
- (a) Qd = 120 − 10(2) = 100. ✓
- (b) Qd = 120 − 10(4) = 80. ✓
- (c) Qd = 120 − 10(6) = 60. ✓
- (d) Qd = 120 − 10(8) = 40. ✓
- (e) Quantity demanded falls as price increases. Yes, this is the law of demand. ✓
- (f) A movement along the demand curve. Reason: only the good's own price changed; the demand curve itself does not shift. ✓
- (g) A shift of the demand curve. Reason: income is a determinant (not the good's own price); a determinant change shifts the whole curve. ✓
- (h) Demand increases; the curve shifts right. Reason: income↑ + normal good → buyers want more at every price. ✓
- (i) Buyers would want more cups at P=$4 than the original 80 — the curve has shifted right, so the new Qd at any given price is higher. ✓

Part 5:
- Downward slope: at higher prices, buyers of craft coffee choose to buy fewer cups — they switch to other drinks, make coffee at home, or cut back. At lower prices, they buy more.
- Right shift: the whole demand relationship has improved. At every price, buyers now want more craft coffee than before. This is not a price effect — it is because their budgets are larger and they can afford more of a good they enjoy.

Part 6:
1. Correct statement: when the price falls from $6 to $4, the quantity demanded of craft coffee increases — a movement along the existing demand curve. The demand curve (the whole relationship) does not change just because the price changes. "Demand increases" would mean the whole curve shifted.
2. Any valid left-shift event, e.g.: (a) the price of a complement (e.g., pastries to pair with coffee) rises → left shift (determinant: price of a complement); (b) health reports warn against caffeine → left shift (determinant: tastes); (c) the number of buyers in the neighborhood falls (migration out) → left shift (determinant: number of buyers).
3. A competing chain is a substitute. Its lower price makes buyers switch away from the original craft coffee → demand for the original shifts left. Determinant: price of a substitute (lower price of substitute → left shift for our good).

Part 7 (AI-critique):
- The correct answer to "did demand shift left when price rose from $4 to $6?" is No — it was a movement along the demand curve. The most common AI error: saying "demand fell" or "demand shifted left." The precise statement is: "quantity demanded fell from 80 to 60 — a movement along the demand curve."
- Qd at P=$4: 120−40=80 ✓; Qd at P=$6: 120−60=60 ✓.
- Income rises + normal good → right shift ✓. Full credit for noting a specific thing verified or corrected.

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold (Part 4) — all four Qd values correct with arithmetic; movement vs. shift correctly identified in (f) and (g); shift direction correct in (h) and (i) (22)	22	11–18	0–10
Interpretation (Part 5) — slope explained in plain English; right-shift interpreted in words (not just "curve moves right") (10)	10	5–8	0–4
Analysis (Part 6) — movement/shift distinction applied correctly; a valid left-shift determinant named; competing chain correctly identified as substitute → left shift (10)	10	5–8	0–4
AI-critique (Part 7) — names a specific claim the chatbot made; verifies or corrects it with reasoning; cites the movement-vs-shift trap (8)	8	4–6	0–3

Quality gate (self-checked): quantitative gate — all four Qd values (100, 80, 60, 40) Python-re-verified against Qd=120−10P ✓. Graph-logic check — own-price change = movement along (not a shift) ✓; income↑ + normal good = right shift ✓; substitute lower price = left shift for our good ✓; complement price↑ = left shift ✓. Central trap correctly identified and featured in Part 7 ✓.