Week 2 — Graph & Model Workshop · "Two Producers, Two Goods: Who Should Make What — and Why?"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 1 — economic modeling & quantitative/graphical analysis · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 2
Format: build a comparative-advantage table in a spreadsheet (Google Sheets, Excel, or any free tool) or on paper, compute the opportunity-cost ratios, identify comparative advantage, find a mutually beneficial terms of trade, show both producers gain, 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. All tools are links to free external sites — nothing to buy or download.

Part 1 — The Big Picture

Last week you learned opportunity cost. This week you applied it to two producers at once — and discovered that even when one producer is more efficient at everything, both still gain from specializing according to comparative advantage. Today you'll work through a full two-producer, two-good table from scratch: compute the ratios, identify who should specialize in what, find a terms of trade that benefits both, and show the gain with arithmetic.

The tool: any free spreadsheet — 🔗 Google Sheets (https://sheets.google.com) or 🔗 Microsoft Excel Online (https://office.com) or paper and a calculator. You can also use 🔗 Desmos (https://www.desmos.com/calculator) to plot each producer's PPF as a line for a visual.

Part 2 — The Guiding Question

When two producers have different opportunity costs, both can gain from specialization and trade — but only if the terms of trade fall inside the right range. How do you find that range, and how do you verify that both actually come out ahead?

The scenario. Country A and Country B each have 1 worker-day to allocate between wheat and cloth.

Part 3 — Set Up the Model (in a spreadsheet or on paper)

Create a small table with the following columns: Country | Wheat output | Cloth output | Opp cost of 1 cloth (in wheat) | Opp cost of 1 wheat (in cloth).

Leave the last two columns blank for now — you'll fill them in Part 4.

Part 4 — Solve (complete this scaffold)

Fill in every blank. Show the arithmetic for each step.

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

In 2–3 sentences, explain why both A and B benefit from this trade in plain English — not just the numbers, but the logic. Why does A want to buy cloth from B rather than make it at home? Why does B want to sell cloth to A?

Part 6 — Analysis Questions

1. Country A makes more wheat AND more cloth per worker-day than B. A friend says: "So A should just make everything and skip trade." Use the opportunity-cost ratios to explain why that reasoning is wrong.
2. Suppose the terms of trade were offered at 0.8 wheat per cloth. Would B agree to that? Why or why not?
3. Suppose the terms of trade were offered at 2.5 wheat per cloth. Would A agree to that? Why or why not?
4. Connect it: name a real-world example (a person, a firm, or a country) where you think comparative advantage explains a pattern of specialization. In one sentence, what is the opportunity cost that drives it?

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: "Country A produces 10 wheat or 5 cloth per worker-day; Country B produces 6 wheat or 6 cloth per worker-day. Who has comparative advantage in each good? What is the mutually beneficial range of terms of trade for cloth in wheat? If trade happens at 1.5 wheat per cloth, does A gain?"
2. Audit every claim against your own verified work:
   - Did it correctly compute A's opportunity cost of 1 cloth = 2 wheat (not ½, not 1)?
   - Did it say B has comparative advantage in cloth (cost = 1 wheat < A's 2 wheat)?
   - Did it give the terms-of-trade range as strictly between 1 and 2 wheat per cloth?
   - Did it correctly show A gains (pays 1.5 vs. domestic cost 2 → saves ½ wheat per cloth)?
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 is the skill.)

The most common chatbot error here: confusing absolute with comparative advantage (declaring A has CA in both goods because A makes more of both), or inverting the opportunity-cost ratio (saying A's cloth costs ½ wheat instead of 2 wheat). Catch it and correct it. The tool drafts; you judge.

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. A screenshot of your spreadsheet is welcome but optional. Due Sun, Sep 13, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (Python check confirms all ratios and gains).

• (a) A's opp cost of 1 cloth = 10 ÷ 5 = 2 wheat. ✓
• (b) B's opp cost of 1 cloth = 6 ÷ 6 = 1 wheat. ✓
• (c) A's opp cost of 1 wheat = 5 ÷ 10 = ½ cloth. ✓
• (d) B's opp cost of 1 wheat = 6 ÷ 6 = 1 cloth. ✓
• (e) Comparative advantage in cloth → Country B (B's cost 1 wheat < A's cost 2 wheat). ✓
• (f) Comparative advantage in wheat → Country A (A's cost ½ cloth < B's cost 1 cloth). ✓
• (g) Mutually beneficial ToT for cloth: between 1 and 2 wheat per cloth. ✓ (B's floor = 1; A's ceiling = 2.)
• (h) A makes 10 wheat, pays 1.5 for 1 cloth → keeps 8.5 wheat (+ 1 cloth). ✓
• (i) A paid 1.5 wheat; A's domestic cost = 2 wheat → A saves 0.5 wheat per cloth. ✓
• (j) B sells 1 cloth → earns 1.5 wheat. ✓
• (k) B earned 1.5; B's domestic cost of 1 cloth = 1 wheat → B gains 0.5 wheat per cloth. ✓
• Part 5: The logic is: A's cloth is expensive (costs A 2 wheat to make), so A would rather pay 1.5 wheat to B for it. B's cloth is cheap (costs B only 1 wheat), so B is happy to sell at 1.5 wheat — it profits. Both producers reach a combination they couldn't achieve on their own.
• Part 6: (1) A's cloth costs A 2 wheat but costs B only 1 wheat — B is the cheaper cloth-maker in opportunity-cost terms, regardless of A's absolute advantage. (2) At ToT = 0.8 wheat per cloth, B earns only 0.8 wheat for 1 cloth, but B's domestic cost is 1 wheat — B would lose. B would not agree. (3) At ToT = 2.5 wheat per cloth, A would pay 2.5 wheat for 1 cloth, but A can make it at home for only 2 wheat — A would not agree. (4) Any real-world example with a plausible opportunity cost stated earns credit.
• Part 7: Full credit for a specific catch. Most common AI errors: absolute-vs-comparative confusion; inverting the ratio (saying A's cloth costs ½ wheat); citing the wrong ToT range boundary.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — all 11 scaffold answers Python-verified ✓ (a: 2; b: 1; c: ½; d: 1; e: B; f: A; g: 1 to 2; h: 8.5; i: 0.5; j: 1.5; k: 0.5). Graph-logic check — comparative advantage assignments (A in wheat, B in cloth) verified by opportunity-cost comparison ✓; ToT range (1 < ToT < 2) verified ✓; both gains-from-trade computations checked ✓.