Week 1 Model Workshop: An Island's Frontier and the Council's Memo

Part 1 — The Big Picture

Every economy, large or small, faces the trade-off you priced this week: more of one good means less of another. In this workshop you build the frontier for a small island that can catch fish or build boats, test three combinations against it, watch the frontier shift when the island gains worker-days, and then sort the island council's memo into what the model can test and what rests on values. Finally, you check a chatbot's reading of the same island.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Which combinations of fish and boats can the island reach with 600 worker-days, what does one boat cost in fish, and which sentences in the council's memo could evidence settle?

Workshop data: An illustrative island's season of worker-days

Source: A season's worker-days and the worker-days each good takes on an illustrative island economy, constructed for this workshop and printed in full in Part 4; it is not real data and describes no real place or person.

• Rows: 1 island economy with 3 inputs: 600 worker-days in a season, 5 worker-days per crate of fish, and 20 worker-days per boat; the combination table in Part 4 has 3 rows
• Goods: crates of fish (a consumer good, on the horizontal axis) and boats (a capital good, on the vertical axis)
• Memo: 6 numbered sentences from the island council's memo, printed in Part 4

Part 3 — Materials & Procedure

Tools and materials

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

Ways of working

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

Procedure

1. Open the free Desmos graphing calculator in a browser, or a blank sheet in Google Sheets. In Desmos, type 5x+20y=600 on the first line; x counts crates of fish and y counts boats. Tool: Desmos (free) or Google Sheets (free). Check: Desmos draws a straight line that meets the horizontal axis at (120, 0) and the vertical axis at (0, 30); click each end to see its label.
2. Record both ends of the frontier in the first table in Part 4, and divide the crates at one end by the boats at the other to find what one boat costs in crates of fish. Tool: Desmos (free) or Google Sheets (free). Check: The first table holds two endpoints and one opportunity cost, each with its division written out.
3. In Desmos, type (40,20), (60,10), and (80,15) on three new lines. In Google Sheets, type Fish crates, Boats, and Worker-days needed in cells A1, B1, and C1, enter the three combinations in rows 2 to 4, and type =5*A2+20*B2 in C2, then copy it down to C4. Tool: Desmos (free) or Google Sheets (free). Check: Each combination appears as a dot on, below-left of, or above-right of the line, or as a worker-day total in column C that you can compare with 600.
4. Complete the second table in Part 4: for each combination, write the worker-days it needs, whether it lies on, inside, or outside the frontier, and how many worker-days sit idle or are missing. Tool: Desmos (free) or Google Sheets (free). Check: Every row of the second table holds a worker-day total, a position, and an idle or missing count.
5. In Desmos, change the first line to 5x+20y=w and choose add slider for w. Set the slider to run from 600 to 700 and drag it slowly. In Google Sheets, type 700 in a spare cell and divide it by 5 and by 20 to find the new ends. Tool: Desmos (free) or Google Sheets (free). Check: The whole line moves outward, parallel to itself, and at 700 its ends sit at (140, 0) and (0, 35); one of the three test combinations now sits on the line.
6. Read the council memo in the third table of Part 4. Label each sentence positive or normative, and write either the evidence that could test it or the value it rests on. Tool: Desmos (free) or Google Sheets (free). Check: All six memo rows are labelled, each with a test or a value beside it.

Fallback route

When to use it: Use this route if neither Desmos nor Google Sheets will open, or a formula will not run.

Work every step by hand from the numbers printed in Part 4: divide 600 by the worker-days each good takes to find the ends, multiply and add to find each combination's worker-days, and sketch the frontier on paper with the axes labelled in words. Complete every table, analysis question, and the critique step, and submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Start with the frontier itself: its two ends and the price of one boat paid in fish.

Student scaffold table 1

Quantity	Your arithmetic	Your result
All 600 worker-days on fish (crates)
All 600 worker-days on boats (boats)
Opportunity cost of one boat (crates of fish)

Test each combination by adding up the worker-days it needs and comparing the total with the 600 the island has.

Student scaffold table 2

Combination (crates, boats)	Worker-days needed	On, inside, or outside	Worker-days idle or missing
(40, 20)
(60, 10)
(80, 15)

Sort the council's memo so the testable claims are kept apart from the value judgments.

Student scaffold table 3

Memo sentence	Positive or normative	Evidence that could test it, or the value it rests on
Last season the island used 500 of its 600 worker-days.
Building one more boat means catching 4 fewer crates of fish this season.
The council should put the idle worker-days into building boats.
More boats would let the island catch more fish in future seasons.
It is unfair to ask families to eat less fish now so that the island can have more boats later.
If the island gains 100 more worker-days, it could produce 80 crates of fish and 15 boats.

Part 5 — Analysis Questions

1. Write the divisions that give both ends of the frontier and the opportunity cost of one boat, and say the cost of one boat in a full sentence.
2. Which combination lies inside the frontier, and what is the macro reading of the worker-days it leaves idle?
3. When the slider moved from 600 to 700 worker-days, did the island move along its frontier or did the frontier shift? Explain the difference, and name the test combination that became attainable.
4. Choose one: (a) write a two-sentence case for the council's sentence 3 and a two-sentence case against it, labelling the positive and normative parts of each; or (b) name the memo sentence that was hardest to sort, and explain what made it hard and how you decided.
5. The island's frontier is a straight line. Name one way a straight-line frontier misstates a real economy, and say how the shape of a real frontier would change the cost of each extra boat.

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 1 Model Workshop tables above. They describe an illustrative island economy constructed for a class activity, not real data: the island has 600 worker-days in a season, a crate of fish takes 5 worker-days, and a boat takes 20 worker-days. Please do five things. First, find both ends of the island's production possibilities frontier and the opportunity cost of one boat in crates of fish. Second, say whether the combination of 60 crates and 10 boats is attainable, and why. Third, if the island gains 100 more worker-days, say whether that is a movement along the frontier or a shift of the frontier. Fourth, sort these six memo sentences into positive and normative statements: (1) Last season the island used 500 of its 600 worker-days. (2) Building one more boat means catching 4 fewer crates of fish this season. (3) The council should put the idle worker-days into building boats. (4) More boats would let the island catch more fish in future seasons. (5) It is unfair to ask families to eat less fish now so that the island can have more boats later. (6) If the island gains 100 more worker-days, it could produce 80 crates of fish and 15 boats. Fifth, as a stretch question for later in the course, tell me the island's GDP in dollars this season and how much a boat-building program would multiply into extra output.

Test the response for these likely failures:

• Chatbots often label a statement normative because it sounds like advocacy, for example calling sentence 4 normative, or call a value judgment positive because it sounds reasonable.
• Chatbots often call a change in total worker-days a movement along the frontier, or say that moving from 60 crates and 10 boats to 40 crates and 20 boats shifts the frontier.
• Asked for GDP in dollars, chatbots often invent fish and boat prices and report a dollar total, mixing a count of goods with a dollar value.
• Asked how far boat building multiplies, chatbots often apply a multiplier formula, sometimes a banking formula such as 1 divided by a reserve ratio, to the island's spending.

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 this week's chapter.

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: "The island can make 120 crates of fish or 30 boats, so one boat costs 0.25 crates of fish. The combination of 60 crates and 10 boats is unattainable, because it is not on the line. If the island gains 100 worker-days, it moves along its frontier. Sentences 3 and 4 of the memo are normative, because both are about what the island wants. At ten dollars a crate, the island's GDP this season is 1,200 dollars, and with a multiplier of 10, a boat-building program would add ten times its cost to output." Mark it up: quote each flawed sentence, name what is wrong (a flipped opportunity-cost ratio, an inside combination read as unattainable, a shift read as a movement along the frontier, a positive statement labelled normative, or an invented dollar or multiplier figure), cite the evidence from your tables or the chapter, and write a corrected sentence beneath it; for the dollar and multiplier claims, say which later week of the course takes them up and that no such figure can come from these data. This route assesses the same objective (Objective 1 — apply the tools of macroeconomic modeling — scarcity, opportunity cost, the production possibilities frontier, and the circular-flow model — 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

• All three completed scaffold tables
• Written answers to all five analysis questions
• A labelled sketch or screenshot description of the frontier before and after the shift, in words
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Model Workshop report on an illustrative island economy: three completed tables (the frontier's ends and the cost of a boat, the three combinations tested against the frontier, and the sorted council memo), a sketch or word description of the frontier before and after the shift, written answers to five analysis questions, and a critique of a chatbot's analysis of the same island, 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
Building the frontier	Both ends of the frontier and the cost of one boat are correct, each with its division visible and the cost said in a full sentence.	The ends or the cost are attempted, but one value is wrong, a division is missing, or the cost is given with the ratio flipped.	No ends or cost are recorded, or the values are invented rather than computed.
Testing combinations against the frontier	All three combinations show correct worker-day totals, the right position on, inside, or outside, the idle or missing worker-days, and the macro reading of idle time.	The combinations are tested, but one total or position is wrong, or the macro reading of the idle worker-days is missing.	No combination is tested, or positions are asserted without worker-day totals.
Shift versus movement along the frontier	The response says the whole frontier shifts outward, gives the new ends, names the combination that becomes attainable, and contrasts this with a movement along a fixed frontier.	The shift is described, but the new ends, the newly attainable combination, or the contrast with a movement along the frontier is missing.	The change is called a movement along the frontier, or the question is not answered.
Sorting positive and normative statements	All six memo sentences are labelled correctly, each with a fitting test or value, and the chosen reflection option is answered with the positive and normative parts kept apart.	Most sentences are labelled correctly, but one or two labels are wrong, a test or value is missing, or the reflection blurs the two kinds of claim.	The sentences are not sorted, or positive is treated as meaning good and normative as meaning bad throughout.
Critiquing the AI analysis or the printed flawed analysis	The chatbot's analysis, or on the equivalent route the printed flawed analysis, is quoted and at least two errors are corrected with evidence from the tables or the chapter, including any out-of-scope claim flagged as coming later.	The critique names errors but corrects only one, or corrects without evidence, on either route.	No critique is submitted on either route, or the AI output or flawed analysis is accepted without checking.
Naming the limitation of the model	The response names a specific way the straight-line frontier misstates a real economy and explains how a bowed frontier changes the cost of each extra boat.	A limitation is named but not connected to the changing cost of extra boats.	No limitation is named.

Quality Gate

• Every endpoint, cost, and worker-day total comes from your own division, formula, or hand work, never from memory or a chatbot.
• Each combination's worker-days equal 5 times its crates plus 20 times its boats, and each is compared with 600.
• The shift question names the whole frontier moving, not a movement along it.
• All six memo sentences carry a label and either a test or a value.
• No statistic, price, dollar figure, 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 from your tables or the chapter.