Week 13 Model Workshop: Who Makes the Bicycles?

Part 1 — The Big Picture

This week you learned that comparative advantage, the lower opportunity cost, decides who should make what, that terms of trade between the two costs let both countries gain, and that the trade balance is exports minus imports, read neutrally. In this Model Workshop you build an opportunity-cost table for two fresh illustrative economies, Cedaria and Pellona, check whether a trade leaves both with more of both goods, turn Cedaria's trade account from nominal into real terms, size how far its rise in net exports shifts aggregate demand with the spending multiplier, read the new price level and real output in Desmos, sort positive claims from normative ones about a tariff, and then check a chatbot's account of the same economies.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Which of the two illustrative economies should make the bicycles, does the trade at 3.5 bushels of rice per bicycle leave both with more of both goods, how much did Cedaria's real net exports change, how far does that shift aggregate demand and where do the price level and real output land, and which claims about a tariff are positive rather than normative?

Workshop data: Cedaria and Pellona trade tables (illustrative)

Source: A workshop-only set of tables constructed for this course, not real data: two illustrative economies' output of rice and bicycles per worker-day, their worker-day allocations before and after trade, Cedaria's trade account in two years with a price index, and a linear AD–AS pair, all printed in full in the scaffold tables.

• Rows: 2 countries in the output table; the before-and-after table has 6 rows (rice and bicycles for each country and for the world); the trade-account table has 3 rows; the multiplier table has 2 rows; the AD–AS table has 2 rows
• Output per worker-day: Cedaria 15 bushels of rice or 5 bicycles; Pellona 8 bushels of rice or 2 bicycles; 20 worker-days each
• Trade: 22 bicycles traded at 3.5 bushels of rice per bicycle
• Cedaria's trade account: exports 50 and imports 80 in year 1; exports 66 and imports 88 in year 2, in billions of dollars, with a price index of 100 in year 1 and 110 in year 2
• AD–AS pair: aggregate demand P = 30 − Y⁄40 and short-run aggregate supply P = 10 + Y⁄40, with Y in billions of dollars and P an index

Part 3 — Materials & Procedure

Tools and materials

• Desmos (free) or Google Sheets (free)

Ways of working

• read-and-compute-from-macro-data
• build-and-shift-the-ad-as-model
• separate-positive-from-normative-claims

Procedure

1. Open Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. Fill the first scaffold table: for each country, the cost of one bicycle is the rice given up divided by the bicycles gained, and the cost of one bushel of rice is the bicycles given up divided by the rice gained. In Desmos, type 15/5 and 8/2 on separate lines; in Google Sheets, put the rice figures in column B and the bicycle figures in column C and type =B2/C2 and =C2/B2, then fill them down one row. Tool: Desmos (free) or Google Sheets (free). Check: Four costs, with each country's two costs flips of each other, and one country's bicycle cost lower than the other's.
2. Fill the second scaffold table. Multiply worker-days by output per worker-day for each country before trade (10 days on each good) and after trade opens (Cedaria 5 days on rice and 15 on bicycles; Pellona 20 days on rice). Then apply the trade: Cedaria sends 22 bicycles and receives 22 times 3.5 bushels of rice. In Google Sheets, type =22*3.5 in a free cell, or type 22*3.5 in Desmos. Tool: Desmos (free) or Google Sheets (free). Check: A before column, a produced-after column, and an after-trade column for both goods in both countries, with world totals in the last two rows.
3. Fill the third scaffold table. Turn each year-2 dollar figure into year-1 prices by dividing by the price index as a decimal, 110 ÷ 100 = 1.10: in Google Sheets type =66/1.10 and =88/1.10, or type 66/1.10 and 88/1.10 in Desmos. Then compute net exports, exports minus imports, in both years, and the change in real net exports. Tool: Desmos (free) or Google Sheets (free). Check: Real year-2 exports and imports smaller than their dollar figures, and a change in real net exports that is positive.
4. Fill the fourth scaffold table. Compute the spending multiplier from the marginal propensity to consume of 0.75, 1/(1-0.75) in Desmos or =1/(1-0.75) in Google Sheets, and multiply it by the change in real net exports. Beside it, record what the money multiplier, 1/0.10 in your tool, would wrongly give if used on the same change. Tool: Desmos (free) or Google Sheets (free). Check: A spending multiplier between 1 and 10 and a shift of aggregate demand several times the change in net exports, next to a much larger wrong-multiplier figure.
5. In Desmos, type y=30-x/40 for aggregate demand and y=10+x/40 for short-run aggregate supply, letting x stand for real output Y and y for the price level P. Click the crossing to read it. Then type y=31-x/40 for aggregate demand after the rise in net exports and click the new crossing. Record both crossings in the fifth scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: The second aggregate demand line sits to the right of the first, and its crossing with the unchanged supply line is higher and further right.
6. Answer the five analysis questions in your own words, using the numbers in your tables, then paste the prompt from the critique step into one approved chatbot, or complete the equivalent route, and write your critique. Keep your tool open to recheck any figure the chatbot reports. Tool: Desmos (free) or Google Sheets (free). Check: Written answers and a critique that quotes the text it checks and corrects at least two errors.

Fallback route

When to use it: Use this route if neither Desmos nor Google Sheets is available, or if you cannot get online.

Do every calculation by hand or with any calculator, writing each step on its own line, and sketch the two aggregate demand lines and the short-run aggregate supply line on graph paper, marking both crossings. Complete all five scaffold tables, every analysis question, and the critique step from your hand work; submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Output and opportunity cost: write each cost as the good given up divided by the good gained, with its units.

Student scaffold table 1

Country	Rice per worker-day (bushels)	Bicycles per worker-day	Cost of one bicycle (bushels of rice)	Cost of one bushel of rice (bicycles)
Cedaria	15	5
Pellona	8	2

Before and after trade: use the worker-day allocations in the procedure, then apply the trade of 22 bicycles at 3.5 bushels of rice per bicycle.

Student scaffold table 2

Good and country	Before trade	Produced after trade opens	After the trade	Change
Cedaria rice (bushels)
Cedaria bicycles
Pellona rice (bushels)
Pellona bicycles
World rice (bushels)
World bicycles

Cedaria's trade account: convert year 2 into year-1 prices before you compare the years.

Student scaffold table 3

Item (billions of dollars)	Year 1 (price index 100)	Year 2 in dollars (price index 110)	Year 2 in year-1 prices
Exports X	50	66
Imports IM	80	88
Net exports NX = X − IM

Sizing the shift: use the spending multiplier on the change in real net exports, and record the money multiplier's figure only to show why it does not belong here.

Student scaffold table 4

Multiplier	Formula	Value	Times the change in real net exports (billions of dollars)
Spending multiplier	1 ÷ (1 − 0.75)
Money multiplier, wrong link	1 ÷ 0.10

Shifting aggregate demand: record each crossing as real output and the price level, before and after the rise in net exports.

Student scaffold table 5

Situation	Aggregate demand line	Real output Y (billions of dollars)	Price level P
Before the rise in net exports	P = 30 − Y⁄40
After the rise in net exports	P = 31 − Y⁄40

Part 5 — Analysis Questions

1. Show the four opportunity costs, every step on its own line, and name which country has the comparative advantage in bicycles and which in rice. Then state the range of terms of trade, in bushels of rice per bicycle, that benefits both countries, and say whether 3.5 sits inside it and why, even though Cedaria makes more of both goods per worker-day.
2. Use your second table to say, for each country and good, whether the after-trade amount is larger than the before-trade amount, and by how much. Then say how world output of each good changed and where that extra output came from.
3. Using your third, fourth, and fifth tables, explain why Cedaria's real exports grew by less than its dollar exports, give the change in real net exports, size the shift of aggregate demand with the spending multiplier, and explain why the money multiplier's figure does not answer this question. Then name the curve that shifts and its direction, and give the crossing before and after.
4. Positive or normative? Sort these four claims, and for each positive claim name the number in your tables that tests it or the evidence that would: (1) In this model, specializing raises world output of both rice and bicycles. (2) Pellona ought to put a tariff on bicycles to protect its bicycle makers, even if bicycles cost more there. (3) A tariff on bicycles would raise the price of bicycles in Pellona. (4) Cedaria should cut its imports until its trade balance reaches zero.
5. Choose one and answer it in 3–4 sentences. (a) The model lets Pellona's bicycle workers switch to rice overnight at no cost. Explain who would bear an adjustment cost in a real economy and why that matters for the gains you computed. (b) Your shift of aggregate demand uses the spending multiplier 1 ÷ (1 − 0.75). Explain why taxes and spending on imports would make the real shift smaller than your table shows.

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 am studying two illustrative economies. In one worker-day, Cedaria makes 15 bushels of rice or 5 bicycles, and Pellona makes 8 bushels of rice or 2 bicycles. Each has 20 worker-days. Before trade, each puts 10 worker-days on each good. After trade opens, Cedaria puts 5 worker-days on rice and 15 on bicycles, Pellona puts all 20 on rice, and Cedaria trades 22 bicycles to Pellona at 3.5 bushels of rice per bicycle. Which country has the comparative advantage in each good, and do both countries end with more of both goods? Cedaria's exports rose from 50 to 66 and its imports from 80 to 88, in billions of dollars, while the prices of both rose 10 percent, from an index of 100 to 110. By what percent did Cedaria's exports grow, and how much did its net exports change? With a marginal propensity to consume of 0.75 and a required reserve ratio of 0.10, how far does aggregate demand shift? If aggregate demand is P = 30 − Y⁄40 and short-run aggregate supply is P = 10 + Y⁄40, with Y in billions of dollars, and the rise in net exports moves aggregate demand to P = 31 − Y⁄40, where do the price level and real output land? Finally, should Pellona put a tariff on bicycles?

Test the response for these likely failures:

• Chatbots often report that Cedaria's exports grew (66 − 50) ÷ 50 × 100 = 32 percent, reading the rise in dollar value as more goods sold even though export prices rose 10 percent.
• Chatbots often multiply the rise in net exports by the money multiplier, 1 ÷ 0.10 = 10, and report 10 × 10 = 100 billion dollars, because the question also mentions a reserve ratio.
• Chatbots sometimes call the rise in exports a movement along aggregate demand, borrowing the exchange-rate effect, instead of a shift of the whole curve.
• Chatbots often answer whether Pellona should put a tariff on bicycles as if the trade table settled it, presenting a value judgment about who bears the cost as a fact.

In 3–5 sentences, quote the chatbot's answer on each of the four checks, say what it got right, and correct at least two errors using your own tables and the course rule, labelling which of its statements were positive and which were normative.

Equivalent route (no AI required)

No AI account is required for this Model Workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "Cedaria makes more rice and more bicycles per worker-day, so it has the comparative advantage in both goods and gains nothing from trade. Pellona's bicycle costs 2 ÷ 8 = 0.25 bushels of rice. Cedaria's exports grew from 50 to 66, which is 32 percent more goods sold. With a reserve ratio of 0.10 the multiplier is 10, so aggregate demand shifts by 100 billion dollars. The rise in exports is a movement along aggregate demand, not a shift. The trade table proves Pellona should put a tariff on bicycles." Mark it up: quote each flawed sentence, name what is wrong (comparative advantage assigned by output, an inverted ratio, nominal export growth read as real, the money multiplier used on a spending change, a shift of aggregate demand called a movement along it, and a normative judgment presented as a fact), cite the evidence from your tables or the course rule, and write a corrected sentence beneath it. This route assesses the same objectives (Objective 1 and Objective 8) 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 marked-up analysis is the submission artifact that replaces the chatbot report and share link.

Part 7 — What to Submit

• All five completed scaffold tables
• A screenshot of your Desmos graph with aggregate demand before and after the rise in net exports, or a labelled hand sketch of the lines and their crossings
• Written answers to all five 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 two illustrative trading economies: five completed tables (output and opportunity costs, before and after trade, Cedaria's trade account in real terms, the multiplier comparison, and the aggregate demand shift), a screenshot or sketch of aggregate demand before and after the rise in net exports, written answers to five analysis questions including the positive-or-normative sort, and a critique of a chatbot's account of the same economies, 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
Computing opportunity costs and the gains from trade	All four opportunity costs are written with the good given up on top, the comparative advantage is assigned to the lower cost, the range of terms is stated, and the before-and-after table is complete for both goods, both countries, and the world, with every step shown.	Most figures are right, but one ratio is inverted, the comparative advantage follows the larger output, or a row of the before-and-after table is missing or unsupported.	No opportunity costs or trade figures are computed, or the numbers are not drawn from the printed tables.
Real versus nominal trade figures	Year-2 exports and imports are converted to year-1 prices, real export growth is kept apart from the growth of dollar exports, and the change in real net exports is reported with its sign.	The conversion is done for one figure only, or real and nominal growth are mixed in one statement.	No conversion to real terms appears.
Shifting aggregate demand in the AD–AS model	The change in real net exports is scaled by the spending multiplier, aggregate demand is shifted right, both crossings are read correctly, and the price level and real output are shown rising together along the unchanged supply line.	The shift is drawn, but the money multiplier is used, a crossing is misread, or the rise in exports is described as a movement along the curve.	No aggregate demand shift is submitted.
Positive versus normative	All four claims are sorted correctly, and each positive claim is tied to a number in the tables or to the evidence that would test it.	Two or three claims are sorted correctly, or the positive claims are not tied to evidence.	The sort is missing or fewer than two claims are sorted correctly.
Critique of the chatbot or the printed analysis	On either route, the chatbot critique or the equivalent route's marked-up analysis quotes the text it checks, corrects at least two errors with evidence from the tables or the course rule, and labels its positive and normative statements; both routes earn the same credit.	On either route, the critique names an error but does not correct it with evidence, or corrects only one.	On either route, no critique is submitted, or pasted output appears without any checking.

Quality Gate

• Every opportunity cost, trade amount, and gain comes from your own calculation on the printed tables, never from memory or a chatbot.
• Each opportunity cost is written with the good given up on top, and the comparative advantage goes to the lower cost.
• Cedaria's year-2 trade figures are converted to year-1 prices before any growth rate or change is reported.
• The spending multiplier sizes the shift of aggregate demand, and the money multiplier is recorded only as the wrong-link comparison.
• The aggregate demand shift is named with its direction, and the price level and real output are read from both crossings.
• Each of the four claims is labelled positive or normative, with a number or a test beside each positive claim.
• No number, rule, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence or the course rule.