Week 4 — Graph & Model Workshop · "Solve a Market, Shift the Supply Curve, and Catch the AI's Error"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 2 — supply, equilibrium & comparative statics · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 4
Format: solve and plot a supply-and-demand equilibrium in Desmos, trace a supply shift to a new equilibrium, interpret the results in words, then catch the AI's economics errors.

This is the course's signature weekly component — the economics analog of a lab. Every instructional week has one workshop: you set up the 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

This week you built the full supply-and-demand model and learned how to find the equilibrium price and quantity where the two curves cross. The model doesn't just show where the market settles — it predicts how it moves when something in the economy changes. Today you'll solve the week's verified market algebraically, plot both curves in Desmos to see the visual intersection, then apply a supply shock and find the new equilibrium — the complete comparative-statics workflow.

The tools:
- 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login)
- 🔗 OpenStax, Principles of Microeconomics 3e, Ch. 3 — https://openstax.org/details/books/principles-microeconomics-3e (reference)

---

Part 2 — The Guiding Question

If a fall in production costs increases supply, what exactly happens to the market price and quantity — and by how much?

The scenario. A market for an everyday consumer good has the following demand and supply equations:

• Demand: Qd = 100 − 2P
• Supply (original): Qs = −20 + 4P

Then a fall in input prices increases supply by 30 units at every price, shifting supply to:

• Supply (new): Qs_new = 10 + 4P

---

Part 3 — Set Up the Model (in Desmos)

1. Open Desmos. You'll plot demand and both supply curves as P on the y-axis, Q on the x-axis — the economist's convention. To do that, solve each equation for P:
   - Demand: Qd = 100 − 2P → P = (100 − x)/2 (type this as y = (100 - x)/2 in Desmos)
   - Original supply: Qs = −20 + 4P → P = (x + 20)/4 (type y = (x + 20)/4)
   - New supply: Qs_new = 10 + 4P → P = (x − 10)/4 (type y = (x - 10)/4)
2. You'll see two upward-sloping supply curves and one downward-sloping demand curve. The first intersection (demand with original supply) is the original equilibrium; the second intersection (demand with new supply) is the new equilibrium.
3. Use Desmos's intersection feature (click a point where curves cross) to read off the coordinates — they should match your algebra below.

---

Part 4 — Solve (complete this scaffold)

Work through the algebra. Show every step.

Part A — Original equilibrium (Qd = 100 − 2P, Qs = −20 + 4P):

Step	Your work
Set Qd = Qs:	100 − 2P = −20 + 4P
Solve for P*:	______
Find Q*: plug P* into Qd = 100 − 2P	______
Verify: plug P* into Qs = −20 + 4P	______
Original equilibrium:	P* = __, Q* = ____

Part B — The supply shift:

Question	Your answer
Input prices fall → what happens to supply (increase or decrease)?	______
Which direction does the supply curve shift (left or right)?	______
Why? (one sentence)	______

Part C — New equilibrium (Qd = 100 − 2P, Qs_new = 10 + 4P):

Step	Your work
Set Qd = Qs_new:	100 − 2P = 10 + 4P
Solve for new P:	______
Find new Q: plug new P into Qd = 100 − 2P	______
Verify: plug new P into Qs_new = 10 + 4P	______
New equilibrium:	New P = __, New Q = ____

Part D — Change summary:

Variable	Original	New	Direction (rose or fell)
Price (P)
Quantity (Q)

---

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

In 3–4 sentences, explain what your numbers mean for buyers and sellers in this market:
- What happened to the price buyers pay, and why?
- What happened to the quantity traded, and why?
- Is this result consistent with the direction rule you learned this week (↑ Supply → P↓, Q↑)?

---

Part 6 — Analysis Questions

1. The self-correcting mechanism. Before the supply increase, the market was at P* = $20, Q* = 60. Suppose a price control froze the price at $25 (above the new equilibrium of $15). Using the new supply equation Qs_new = 10 + 4P and the demand Qd = 100 − 2P, compute the quantity demanded and quantity supplied at P = $25. Is there a surplus or shortage, and by how much?
2. The both-shift trap. Suppose, at the same time supply increased, a wave of new buyers entered the market (demand also increased). Would you still be able to say confidently that the new price is lower than the original $20? Explain what you can say about P and what you cannot, and why.
3. Connect to the real world. Name one real market where input costs have fallen in recent years (e.g., solar panels, batteries, streaming services). What does the supply model predict happened to the market price and quantity? Is that roughly what you observe?

---

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: "In a market with Qd = 100 − 2P and Qs = −20 + 4P, what is the equilibrium price and quantity? Then if supply increases by 30 (new Qs = 10 + 4P), what is the new equilibrium, and which direction do price and quantity move?"
2. Audit every claim against your own work:
   - Did it get P* = $20, Q* = 60? (Chatbots sometimes make arithmetic errors on this step.)
   - Did it correctly say the supply curve shifts RIGHT when supply increases? (Chatbots sometimes say "left" or skip naming the direction.)
   - Did it get new P = $15, new Q = 70? (The two most common errors: price rises instead of falls, or the chatbot just states the original equilibrium twice.)
   - Did it keep the direction rule straight — ↑ Supply → P↓, Q↑? (Chatbots frequently say "price rises" when supply increases, which is the wrong direction.)
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. The most common chatbot error on supply-and-demand is shifting the wrong curve or stating the wrong direction for price after a supply change. Catching those errors is the point.

---

Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with the algebra), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your Desmos curves with both intersections marked is welcome but optional. Due Sun, Sep 27, 11:59 p.m. (50 points).

---

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified in Python. Check the Week-4 verified-numbers block in the BUILD_BRIEF.

Part A — Original equilibrium:
- 100 − 2P = −20 + 4P → 120 = 6P → P* = 20. ✓
- Q* = 100 − 2·20 = 100 − 40 = 60. ✓
- Verify: Qs = −20 + 4·20 = −20 + 80 = 60. ✓ Match.

Part B — Supply shift:
- Input prices fall → supply increases. ✓
- Supply curve shifts RIGHT (more units supplied at every price). ✓
- Reason: lower production costs make it profitable to produce more, so sellers supply more at each price.

Part C — New equilibrium:
- 100 − 2P = 10 + 4P → 90 = 6P → New P = 15. ✓
- New Q = 100 − 2·15 = 100 − 30 = 70. ✓
- Verify: Qs_new = 10 + 4·15 = 10 + 60 = 70. ✓ Match.

Part D — Directions: P fell from $20 to $15 (FELL ✓). Q rose from 60 to 70 (ROSE ✓). Confirms ↑ Supply → P↓, Q↑. ✓

Part 6 — Analysis:
1. At P = $25 with new supply: Qd = 100 − 50 = 50; Qs_new = 10 + 100 = 110. Qs > Qd → SURPLUS of 110 − 50 = 60 units. ✓ (The price control freezes the price above the new (lower) equilibrium, creating a large surplus.)
2. With both curves shifting right: Q rises unambiguously (both shifts push Q up). But P is INDETERMINATE — supply increase pushes P down, demand increase pushes P up, and without knowing the magnitudes you can't say which wins. Full-credit answer explicitly names the opposing forces.
3. Any reasonable real-world example earns credit; the model predicts lower price and higher quantity when supply rises due to lower input costs — solar panels and batteries are well-documented examples.

Part 7 — AI-Critique: full credit for a specific catch. Most common chatbot errors: (a) saying P rises when supply increases (wrong direction), (b) shifting the demand curve instead of supply, (c) getting P* = 20 right but then saying "new P = 20" again without re-solving, (d) stating Q* = 60 but then saying new Q = 60 as well.

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold Part A — P*=20, Q*=60, algebra shown, check verified (12)	12	6–10	0–5
Scaffold Parts B–C — shift direction identified with reason; new P=15, Q=70 with algebra and check (12)	12	6–10	0–5
Interpretation Part 5 — price fell (and why), quantity rose (and why), direction rule confirmed (10)	10	5–8	0–4
Analysis Part 6 — surplus at P=25 computed correctly; both-shift indeterminacy explained; real-world connection (10)	10	5–8	0–4
AI-critique Part 7 — names a specific claim checked and at least one error caught or verified (6)	6	3–5	0–2

Quality gate (self-checked): quantitative gate — P*=20, Q*=60, new P=15, new Q=70, surplus at P=25 is 60 units — all Python-re-verified ✓. Graph-logic check — supply increase = rightward shift; P falls; Q rises; ↑ Supply → P↓, Q↑ confirmed; Part A check (same Q from both equations) verified ✓. Indeterminacy check (Part 6 #2) correct ✓.