Model Workshop: Who Should Make What? Two Countries, Rice, and Cloth

Part 1 — The Big Picture

This week you learned that the producer who is faster at everything still gains by trading, because what matters is what each producer gives up. In this workshop you build an opportunity-cost table for two illustrative countries yourself, in a spreadsheet or a graphing calculator, and use it to decide who should make what. You find the range of trade rates that helps both countries, test a proposed rate, prove the gains with a before-and-after table, label a pair of statements positive or normative, and then catch the slips a chatbot makes on the same questions. The two countries are a classroom model, like the food stand in the chapter, so every number lands cleanly and you can check each step by hand.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: North Valley can produce more rice and more cloth than South Coast in a worker-day; which country should specialize in which good, and can both end up with more of both goods by trading?

Workshop data: Two illustrative countries producing rice and cloth

Source: Output per worker-day of rice and cloth in two illustrative countries, North Valley and South Coast, constructed for this workshop and printed in full in Part 4; it is not real data and describes no real country, business, or person.

• Rows: 2 countries (North Valley and South Coast), each with its rice and cloth output per worker-day; the data table in Part 4 has 2 rows
• Columns: country, bushels of rice per worker-day, bolts of cloth per worker-day, and worker-days available
• Worker-days: each country has 10 worker-days to divide between rice and cloth

Part 3 — Materials & Procedure

Tools and materials

• Desmos (free) or Google Sheets (free)
• A document or notebook for your written answers

Ways of working

• build-the-supply-and-demand-schedule
• shift-vs-move-along-the-curve
• compute-elasticity-by-the-midpoint-formula

Procedure

1. Open a blank Google Sheet. In row 1 type the headers Country, Rice per day, Cloth per day, Worker-days. In row 2 type North Valley, 12, 3, 10, and in row 3 type South Coast, 4, 2, 10. If you prefer Desmos, open a new graph, add a table, and type the same numbers into four columns. Tool: Desmos (free) or Google Sheets (free). Check: Two rows of numbers sit under four headers, and North Valley's rice and cloth numbers are both larger than South Coast's.
2. Build the opportunity cost of one bolt of cloth. In cell E1 type Cost of 1 cloth (rice), in cell E2 type =B2/C2, and copy it to E3. In Desmos, type 12/3 and 4/2 on two lines instead. Tool: Desmos (free) or Google Sheets (free). Check: North Valley's cost of a bolt of cloth is larger than South Coast's, and each result is a number of bushels of rice.
3. Build the opportunity cost of one bushel of rice. In cell F1 type Cost of 1 rice (cloth), in cell F2 type =C2/B2, and copy it to F3. In Desmos, type 3/12 and 2/4. Check that each country's two costs are reciprocals by typing =E2*F2 in G2 and copying it to G3. Tool: Desmos (free) or Google Sheets (free). Check: Both cells in column G show 1, because each country's two costs are flips of each other.
4. Find the range of trade rates. Write down the two costs of a bolt of cloth from column E; any rate between them, in bushels of rice per bolt, helps both countries. Test the proposed rate of 3 bushels per bolt against both ends. Check: The proposed rate of 3 falls between the two costs of a bolt of cloth.
5. Build the before-and-after table in rows 5 to 9 of your sheet. Before trade, each country splits its 10 worker-days evenly, 5 and 5. After specializing, South Coast puts all 10 days into cloth, and North Valley puts 7 days into rice and 3 into cloth. Then South Coast trades 7 bolts of cloth to North Valley for 21 bushels of rice. Use formulas such as =5*B2 for output and =B7-21 for what a country keeps after giving rice away, and fill in the second scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: Each country ends with at least as much of each good as before trade, and the combined totals rise.
6. Paste your completed tables into an approved chatbot, then paste the prompt from Part 6 below them, and save the conversation's share link. If you take the equivalent route instead, open the printed flawed analysis in Part 6. Check: You have the chatbot's reply, or the printed analysis, ready to check against your own tables.

Fallback route

When to use it: Use this route if no spreadsheet or graphing calculator is available or a formula will not work.

Work every step by hand or with any calculator from the data table in Part 4. Divide to build each opportunity cost, write each country's output at every stage, and add the combined totals, writing each step on its own line. Complete both scaffold tables and answer every analysis question and the critique step; submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

This is the two countries' data; copy it into your sheet exactly, because every later number is built from it, and fill in the two cost columns from your formulas.

Student scaffold table 1

Country	Rice per worker-day (bushels)	Cloth per worker-day (bolts)	Cost of 1 bolt of cloth (bushels of rice)	Cost of 1 bushel of rice (bolts of cloth)
North Valley	12	3
South Coast	4	2

This table proves or disproves the gains from trade; fill in each country's bundle at each stage, writing rice first, then cloth.

Student scaffold table 2

Stage	North Valley (rice, cloth)	South Coast (rice, cloth)	Combined (rice, cloth)
Before trade: 5 days on each good
After specializing: South Coast all cloth; North Valley 7 days rice, 3 days cloth
After South Coast trades 7 bolts of cloth for 21 bushels of rice

Part 5 — Analysis Questions

1. Using your first table, show the division behind each of the four opportunity costs, with its units, and say which country has the absolute advantage in each good.
2. Name the country with the comparative advantage in cloth and the country with the comparative advantage in rice, and explain in one sentence why the answer differs from your absolute-advantage answer.
3. State the range of trade rates, in bushels of rice per bolt of cloth, that helps both countries, and show why 3 bushels per bolt works for each country by comparing it with that country's own cost.
4. Using your second table, explain to someone who has never studied economics how both countries can end up with more of both goods without working any more days, and say where the extra output came from.
5. Choose one and answer it in 3–4 sentences. (a) This model assumes each country's cost stays the same for every worker-day; explain how the result might change if the tenth day spent on cloth cost more rice than the first. (b) Name one group inside South Coast that might be worse off after it specializes in cloth, call that loss an adjustment cost, and say whether that is a positive or a normative point.
6. Label each statement positive or normative and give the reason: (i) if the two countries specialize by comparative advantage, their combined output of rice and cloth rises; (ii) South Coast should protect its rice farmers with a tariff on imported rice. For the positive statement, name the row of your second table that checks it.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 2 Model Workshop tables above. They describe two illustrative countries, North Valley and South Coast. In one worker-day, North Valley can produce 12 bushels of rice or 3 bolts of cloth, and South Coast can produce 4 bushels of rice or 2 bolts of cloth; each country has 10 worker-days. Please do four things. First, say which country has the comparative advantage in cloth and which in rice, and show the opportunity-cost arithmetic. Second, find the range of trade rates, in bushels of rice per bolt of cloth, that would leave both countries better off, and say whether 3 bushels per bolt is inside it. Third, label each statement positive or normative and say why: (i) if the two countries specialize by comparative advantage, their combined output of rice and cloth rises; (ii) South Coast should protect its rice farmers with a tariff on imported rice. Fourth, say whether each of these ten statements is accurate, in one sentence each: (a) a fall in the price of cloth shifts the demand for cloth to the right; (b) a rise in incomes raises the quantity demanded of a normal good; (c) the demand curve Qd = 200 − 20P has the same elasticity at every price because its slope is constant; (d) demand on that curve is elastic between 2 and 4 dollars; (e) a legal maximum price set below the equilibrium price is a price floor that creates a surplus; (f) sellers who send a per-unit tax to the government bear all of it; (g) the cost of one more chair equals the average total cost; (h) accounting profit subtracts the wages an owner gives up; (i) a monopolist sets its price equal to its marginal cost; (j) a market that ignores a cost it imposes on neighbors still produces the efficient quantity.

Test the response for these likely failures:

• Chatbots often give the cloth to North Valley because it makes more cloth per worker-day (3 bolts against 2), reading comparative advantage off the output numbers.
• Chatbots sometimes call statement (i) normative because it sounds like praise for trade, or call statement (ii) positive because a tariff can be measured.
• Chatbots often say a fall in the price of cloth shifts the demand for cloth to the right.
• Chatbots sometimes say a rise in buyers' incomes raises the quantity demanded of a normal good, as if it were a movement along the curve.
• Chatbots often say the demand curve Qd = 200 − 20P has the same elasticity everywhere because its slope is a constant −20.
• Chatbots sometimes call demand elastic between 2 and 4 dollars on that same line.
• Chatbots sometimes call a legal maximum price set below the equilibrium price a price floor and say it creates a surplus.
• Chatbots often say that because sellers send a per-unit tax to the government, sellers bear all of it.
• Chatbots sometimes report the cost of one more chair as the average total cost.
• Chatbots sometimes say accounting profit already subtracts the wages an owner gives up by running the business.
• Chatbots often say a monopolist sets its price equal to marginal cost.
• Chatbots sometimes call a market's own output efficient even when each unit imposes a cost on neighbors.

Write 3–5 sentences naming one thing the chatbot got right and at least two places it went wrong or overreached, quoting its words and correcting each with evidence from your own tables or the course's definitions; for the ten preview statements, say which ones the course will check later and flag any the chatbot got wrong.

Equivalent route (no AI required)

No AI account is required for this workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "North Valley makes more cloth per worker-day, 3 bolts against 2, so North Valley has the comparative advantage in cloth. A bushel of rice costs North Valley 12 ÷ 3 = 4 bolts of cloth. Any trade the two countries agree on helps both, so 5 bushels of rice per bolt is fine. Statement (i), that specializing raises combined output, is normative because it praises trade, and statement (ii), that South Coast should add a tariff, is positive because a tariff can be measured. Looking ahead: a fall in the price of cloth shifts the demand for cloth to the right; a rise in incomes raises the quantity demanded of a normal good; Qd = 200 − 20P has the same elasticity everywhere because its slope is constant; demand on that line is elastic between 2 and 4 dollars; a legal maximum price below equilibrium is a price floor that creates a surplus; sellers who send in a per-unit tax bear all of it; the cost of one more chair equals the average total cost; accounting profit subtracts the owner's forgone wages; a monopolist sets its price equal to marginal cost; and a market that ignores the cost it imposes on neighbors still produces the efficient quantity." Mark it up: quote each flawed sentence, name what is wrong (comparative advantage read off output, an inverted ratio, a rate outside the range accepted, a positive statement called normative or the reverse), cite the evidence from your tables or the course's definitions, and write a corrected sentence beneath it; for the looking-ahead sentences, flag each one and say which later week of the course will check it. This route assesses the same objective (Objective 1 — use the tools of economic modeling — scarcity, opportunity cost, the production possibilities frontier, comparative advantage, and the gains from trade — and distinguish positive statements (what is) from normative statements (what ought to be)) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• Both completed scaffold tables, with the formulas or hand steps you used
• Written answers to all six analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Model Workshop report on the two illustrative countries: two completed tables (the opportunity costs and the before-and-after bundles), written answers to six analysis questions, and a critique of a chatbot's answer to the same questions, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Opportunity-cost table built from the data	All four opportunity costs are correct, carry their units, and are built by visible formulas or hand steps; each country's two costs are shown to be reciprocals.	Most costs are correct, but one is inverted, missing its units, or has no visible step.	The cost table is missing, or most costs are inverted or unsupported.
Comparative advantage and terms of trade	Comparative advantage in each good is named by the lower cost and kept apart from absolute advantage, and the proposed rate is tested against both countries' costs.	Comparative advantage is named correctly but the rate test is incomplete, or the rate is tested but one advantage is assigned by output.	Comparative advantage is assigned by output alone, or no rate test appears.
Gains from trade shown and explained in words	The before-and-after table is complete and correct, and the explanation says in plain words how both countries gain without working more days.	The table is mostly correct or the explanation is present but thin.	No table or explanation of the gains is submitted.
AI slip caught and corrected (either route)	At least two errors in the chatbot's reply, or in the printed flawed analysis on the equivalent route, are quoted and corrected with evidence from the tables or the course's definitions, and the later-week statements are flagged.	One error is caught and corrected, or errors are named without evidence; either route earns this band equally.	No critique is submitted on either route, or chatbot output is pasted without any checking.
Reflection and the positive or normative labels	The chosen reflection option is answered in 3–4 sentences tied to the model's assumptions or to an adjustment cost, and both statements in question 6 are labelled with reasons.	The reflection is answered but stays general, or one statement is mislabelled.	No reflection and no labels are submitted.

Quality Gate

• Every value in the tables comes from your own formulas or hand steps on the Part 4 data, never from memory or a chatbot.
• Every opportunity cost carries its units, and no ratio is turned upside down.
• Comparative advantage is named by the lower opportunity cost, never by the larger output.
• The proposed rate is tested against both countries' costs, and the before-and-after totals are added correctly.
• Each statement in question 6 is labelled positive or normative with a reason.
• No statistic, figure, or source is invented anywhere in the submission, and the two countries are described as illustrative.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence.