Week 13 — Graph & Model Workshop · "Comparative Advantage & the Terms of Trade"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 8 — the Phillips curve & the quantity theory; trade, exchange rates & the open economy (this week: trade) · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 13
Format: build an opportunity-cost table for two fictional countries in a spreadsheet (free), assign comparative advantage, test a terms of trade, and prove both countries gain, 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 learned macro's most surprising result: comparative advantage — not absolute advantage — is what should drive specialization and trade, and it makes both trading partners better off, even when one country is more productive at everything. Today you'll build the opportunity-cost table yourself for two fictional countries, assign each one its comparative advantage, test whether a proposed terms of trade actually benefits both sides, and prove it with a concrete production/consumption table. (Next week you'll add currencies to the picture — exchange rates and how they ripple through to net exports.)

The tool: a spreadsheet — Google Sheets (🔗 https://sheets.google.com, free with a Google account) or Microsoft Excel. A spreadsheet is the natural home for a table with division in every cell.

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Part 2 — The Guiding Question

If one country gives up less of one good and another country gives up less of the other good, exactly how much should each specialize, at what trade ratio do both come out ahead — and can you prove it with numbers, not just intuition?

The scenario (verified; use these numbers exactly).

Two fictional countries, one worker-day each, two goods:

Country	Wheat (per worker-day)	Cloth (per worker-day)
Northland	4	2
Southport	6	2

Each country has 12 worker-days available this period.

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

1. Open a spreadsheet. Create a small table with Country, Wheat/worker-day, Cloth/worker-day, OC of 1 cloth (wheat given up ÷ cloth gained), and OC of 1 wheat (cloth given up ÷ wheat gained).
2. Enter Northland and Southport's per-worker-day numbers from the table above.
3. In the OC of cloth column, write a formula dividing the wheat column by the cloth column for each row (e.g., = B2 / C2); in the OC of wheat column, write the inverse (= C2 / B2). Copy both down.
4. You now have all four opportunity costs — the numbers that determine comparative advantage.

🔗 Google Sheets: https://sheets.google.com
🔗 Desmos (optional — for plotting each country's PPF as a check): https://www.desmos.com/calculator

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Part 4 — Solve (complete this scaffold)

Step A — opportunity costs and comparative advantage. Fill in the blanks. Show the arithmetic.

Question	Your answer
(a) Northland's opportunity cost of 1 cloth, in wheat (4 ÷ 2)	______
(b) Southport's opportunity cost of 1 cloth, in wheat (6 ÷ 2)	______
(c) Which country has the comparative advantage in cloth? (compare a & b — lower wins)	______
(d) Northland's opportunity cost of 1 wheat, in cloth (2 ÷ 4)	______
(e) Southport's opportunity cost of 1 wheat, in cloth (2 ÷ 6)	______
(f) Which country has the comparative advantage in wheat? (compare d & e — lower wins)	______
(g) Does Southport have the absolute advantage in anything? Does that change your answers to (c) or (f)?	______

Step B — test a terms of trade. Northland's own cost of 1 cloth is your answer to (a); Southport's own cost of 1 cloth is your answer to (b).

Question	Your answer
(h) What is the mutually beneficial range of terms of trade (wheat per cloth), using your answers to (a) and (b)?	______
(i) Is a terms of trade of 2.5 wheat per cloth inside that range?	______

Step C — prove both countries gain. Before trade, Northland makes 32 wheat and 8 cloth (8 worker-days on wheat, 4 on cloth); Southport makes 36 wheat and 12 cloth (6 worker-days on wheat, 6 on cloth). Each country then fully specializes in its comparative-advantage good (all 12 worker-days), and Northland trades 14 units of cloth to Southport at the 2.5-wheat-per-cloth rate.

Question	Your answer
(j) After full specialization, how much cloth does Northland produce (12 × 2)? How much wheat does Southport produce (12 × 6)?	______
(k) How much wheat does Northland receive for 14 units of cloth, at 2.5 wheat per cloth?	______
(l) Northland's post-trade totals: cloth kept (from j minus 14) + wheat received (from k)	______
(m) Southport's post-trade totals: wheat kept (from j minus the amount from k) + cloth received (14)	______
(n) Compare Northland's post-trade totals (l) to its BEFORE-trade totals (32 wheat, 8 cloth) — did it gain on both goods?	______
(o) Compare Southport's post-trade totals (m) to its BEFORE-trade totals (36 wheat, 12 cloth) — did it gain on both goods?	______

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

In 3–4 sentences, explain in plain English:
- why Northland can have the comparative advantage in cloth even though Southport ties or beats it on raw output (what's the difference between "producing more" and "giving up less"?);
- what it means, in economic terms, that the total amount of wheat and cloth available to both countries combined went up purely from re-allocating the same 24 worker-days;
- why the specific terms of trade (2.5, versus some other number inside the 2–3 range) still matters even once you know both countries could gain.

(Hint: think about what would happen to the split of gains if the terms of trade moved closer to 2 versus closer to 3 — who would capture more of the extra output?)

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Part 6 — Analysis Questions

1. Suppose a third country, Eastvale, could produce 10 wheat or 5 cloth per worker-day — MORE of both goods than either Northland or Southport. Does Eastvale have the absolute advantage in both goods? Compute Eastvale's opportunity cost of 1 cloth (10 ÷ 5) and explain whether Eastvale could still have a comparative advantage relative to Northland or Southport in something.
2. A classmate says, "If the terms of trade is exactly 2 wheat per cloth (Northland's own opportunity cost), would Northland want to trade at all?" Use the model to answer — what happens to Northland's incentive to trade as the terms of trade approaches its own opportunity cost?
3. Connect to policy: name one real-world industry where you think a country's comparative advantage (not absolute advantage) plausibly explains why it specializes in that industry rather than trying to produce everything domestically. In 2–3 sentences, explain the opportunity-cost logic as you understand it — you are not being asked to declare whether more or less specialization is "right," just to explain the reasoning fairly.

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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: "Northland produces 4 wheat or 2 cloth per worker-day. Southport produces 6 wheat or 2 cloth per worker-day. Which country has the comparative advantage in cloth, and which in wheat? If they trade at 2.5 wheat per cloth, can both countries end up better off than before trade?"
2. Audit every claim against your own spreadsheet:
   - Did it correctly say Northland has the comparative advantage in cloth (opportunity cost 2 wheat, lower than Southport's 3 wheat) and Southport in wheat (opportunity cost ⅓ cloth, lower than Northland's ½ cloth)? Chatbots routinely flip the ratio (stating a country's cost of cloth in cloth instead of wheat) or divide in the wrong direction.
   - Did it correctly conclude that YES, both countries can gain at 2.5 wheat per cloth (since 2 < 2.5 < 3, inside the mutually beneficial range) — or did it wrongly assume the more-productive country (Southport, which has the absolute advantage in wheat) automatically "wins" and shouldn't need to trade?
   - Did it keep comparative advantage (opportunity cost) and absolute advantage (raw output) straight, rather than treating them as the same thing?
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 flip an opportunity-cost ratio or assume the "better at everything" country needs no trading partner — 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 the arithmetic for all 15 blanks), 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, Nov 29, 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.

Step A:
- (a) Northland's OC of 1 cloth = 4 ÷ 2 = 2 wheat. ✓
- (b) Southport's OC of 1 cloth = 6 ÷ 2 = 3 wheat. ✓
- (c) 2 < 3 → Northland has the comparative advantage in cloth. ✓
- (d) Northland's OC of 1 wheat = 2 ÷ 4 = ½ cloth. ✓
- (e) Southport's OC of 1 wheat = 2 ÷ 6 = ⅓ cloth. ✓
- (f) ⅓ < ½ → Southport has the comparative advantage in wheat. ✓
- (g) Yes — Southport has the absolute advantage in wheat (6 > 4 per worker-day) and the two tie in cloth (2 = 2). This does NOT change (c) or (f): Northland still holds the comparative advantage in cloth (lower opportunity cost), even though Southport has the absolute advantage in wheat. Comparative advantage ≠ absolute advantage — the week's central lesson. ✓

Step B:
- (h) The mutually beneficial range is between 2 and 3 wheat per cloth (Northland's own cost of 2, up to Southport's own cost of 3). ✓
- (i) Yes — 2 < 2.5 < 3, so 2.5 wheat per cloth is inside the mutually beneficial range. ✓

Step C:
- (j) After full specialization: Northland produces 12 × 2 = 24 cloth (0 wheat); Southport produces 12 × 6 = 72 wheat (0 cloth). ✓
- (k) 14 cloth × 2.5 wheat/cloth = 35 wheat. ✓
- (l) Northland post-trade: cloth = 24 − 14 = 10 cloth; wheat = 0 + 35 = 35 wheat. ✓
- (m) Southport post-trade: wheat = 72 − 35 = 37 wheat; cloth = 0 + 14 = 14 cloth. ✓
- (n) Compare to BEFORE trade (32 wheat, 8 cloth): Northland now has 35 wheat (up from 32) AND 10 cloth (up from 8) — gained on BOTH goods. ✓
- (o) Compare to BEFORE trade (36 wheat, 12 cloth): Southport now has 37 wheat (up from 36) AND 14 cloth (up from 12) — gained on BOTH goods too. ✓

Part 5 (model interpretation): "Producing more" (absolute advantage) and "giving up less" (comparative advantage) are different comparisons — Southport produces more wheat per worker-day, but Northland gives up LESS wheat for each unit of cloth it makes (2 vs. Southport's 3), so Northland is the relatively cheaper cloth producer even though it's not the most productive country overall. The total wheat and cloth available to both countries combined rose (wheat 68→72, cloth 20→24) purely from re-allocating the SAME 24 worker-days toward each country's comparative-advantage good — specialization made the whole economic pie bigger before a single unit was traded. The specific terms of trade matters because it determines how that extra output is SPLIT between the two countries: a rate closer to 2 (Northland's own cost) favors Southport, capturing more of the gain for Southport, while a rate closer to 3 (Southport's own cost) favors Northland — 2.5 splits the gain roughly in the middle.

Part 6:
1. Yes, Eastvale (10 wheat or 5 cloth per worker-day) has the absolute advantage in BOTH goods over Northland and Southport (10>4, 10>6; 5>2, 5>2). Eastvale's opportunity cost of 1 cloth = 10 ÷ 5 = 2 wheat — exactly tied with Northland's own cost, and lower than Southport's 3 wheat. So Eastvale would have the SAME comparative-advantage standing as Northland in cloth relative to Southport (both give up 2 wheat per cloth, both cheaper than Southport's 3), even though Eastvale is absolutely more productive at everything. This confirms: absolute advantage in everything does not eliminate the logic of comparative advantage relative to a specific partner. ✓
2. If the terms of trade sits exactly AT Northland's own opportunity cost (2 wheat per cloth), Northland gains NOTHING from trading — it could get exactly the same 2 wheat per cloth by producing wheat itself instead of trading. Northland's incentive to trade shrinks toward zero as the terms of trade approaches its own opportunity cost; the closer the rate gets to 2, the smaller Northland's share of the gains from trade becomes (and the more of the gain flows to Southport instead). ✓
3. Any reasonable industry with a named opportunity-cost-style chain earns credit — examples: a country with abundant arable land and low relative labor costs specializing in grain exports because its opportunity cost of producing grain (in terms of manufactured goods forgone) is lower than a densely populated, capital-intensive economy's; a country with strong semiconductor fabrication capacity specializing there because its opportunity cost of diverting those specialized engineers/plants to, say, textile production is very high relative to a country where labor is more plentiful and less specialized.

Part 7 (AI-critique): full credit for a specific catch — most commonly: the bot states an opportunity-cost ratio in the wrong good (e.g., "Northland's cost of cloth is ½ wheat" instead of 2 wheat), or assumes Southport (the absolute-advantage country in wheat) has no reason to trade, or conflates "Southport produces more" with "Southport should do everything."

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold (Part 4) — all opportunity costs, both comparative-advantage assignments, the mutually beneficial range, and the full production/consumption table correct with arithmetic shown (20)	20	10–16	0–8
Interpretation (Part 5) — absolute vs. comparative distinguished, total-output gain explained, terms-of-trade split explained, in words (10)	10	5–8	0–4
Analysis (Part 6) — absolute advantage in everything ≠ no comparative advantage; incentive-to-trade reasoning; a fairly explained real-world connection (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 — OC ratios (2, 3, ½, ⅓ wheat/cloth), mutually beneficial range (2 to 3), specialization outputs (24 cloth, 72 wheat), trade quantities (14 cloth for 35 wheat), and both countries' before/after comparisons (Northland 32→35 wheat & 8→10 cloth; Southport 36→37 wheat & 12→14 cloth) all Python-re-verified ✓. Graph-logic check — comparative advantage (opportunity cost) correctly distinguished from absolute advantage (raw output) throughout; the mutually-beneficial-range logic applied correctly; both countries shown gaining on both goods with whole-number arithmetic ✓. Quantitative gate: PASS. Graph-logic check: PASS.