Week 1 · Model Workshop

Week 1 Model Workshop: A River Town's Frontier and the Council's Memo

Principles of Microeconomics Free sample edition

Part 1 — The Big Picture

Every economy, from one household to a whole town, 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 river town that can gather firewood or berries, read the rising cost of each extra bundle of firewood, test three combinations against the frontier, decide whether a better basket shifts the frontier or moves the town along it, and sort the town council's memo into what evidence could test and what rests on values. Finally, you check a chatbot's reading of the same town.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: What does each extra bundle of firewood cost the river town in berries, which combinations can the town reach, and which sentences in the council's memo could evidence settle?

Workshop data: An illustrative river town's day of firewood and berries

Source: A day's possible combinations of firewood and berries for an illustrative river town, constructed for this workshop and printed in full in Part 3; it is not real data and describes no real place or person.

Rows: 6 frontier combinations, from 0 to 25 bundles of firewood in steps of 5; the first scaffold table summarizes them as 5 steps
Goods: bundles of firewood (on the horizontal axis) and baskets of berries (on the vertical axis), gathered per day
Memo: 6 numbered sentences from the town 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

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

Procedure

Open a blank sheet in Google Sheets, or a new graph in the free Desmos graphing calculator. In Sheets, type Firewood in cell A1 and Berries in cell B1, then type the firewood values 0, 5, 10, 15, 20, 25 in cells A2 to A7 and the berry values 30, 28, 24, 18, 10, 0 in cells B2 to B7. In Desmos, click the plus sign, choose table, and type the same two columns. Tool: Desmos (free) or Google Sheets (free). Check: Six rows of data, one for each frontier combination, with firewood rising and berries falling down the columns.
In Sheets, type =B2-B3 in cell C3 and fill it down to cell C7. Each cell shows the baskets of berries the town gives up for that step of 5 more bundles. Copy the five results into the first scaffold table, with the subtraction written out. Tool: Desmos (free) or Google Sheets (free). Check: Five numbers appear in column C, and each one is larger than the one above it.
In Sheets, type =C3/5 in cell D3 and fill it down to cell D7 to find the berries given up per bundle of firewood in each step. Copy those results into the first scaffold table too. Tool: Desmos (free) or Google Sheets (free). Check: Five per-bundle costs appear in column D, each larger than the one above it.
Select cells A1 to B7 and choose Insert, then Chart, then set the chart type to Scatter chart (in Desmos the table already plots). Describe the shape in words: where the curve starts, where it ends, and whether it bulges away from the corner where the axes meet. Tool: Desmos (free) or Google Sheets (free). Check: Six plotted combinations that trace a curve from the vertical axis down to the horizontal axis.
Test the three combinations in the second scaffold table. For each one, find the frontier's berry count at the same firewood level in column B, compare it with the combination's berries, and write the difference with its subtraction. Check: Each combination has a frontier berry count, a label of on, inside, or outside, and a difference written out.
Read memo sentence 5 about a better basket. In Sheets, type =B2+6 in cell E2 and fill it down to cell E6 to see the berry counts the better basket would allow from 0 to 20 bundles. Use column E to decide whether the third test combination becomes attainable, and whether the change is a shift of the frontier or a movement along it. Tool: Desmos (free) or Google Sheets (free). Check: Column E shows a second set of berry counts, each 6 baskets above the matching count in column B.
Sort the six memo sentences in the third scaffold table. For each, write positive or normative, then the evidence that could test it or the value it rests on. Check: All six sentences carry a label and either a test or a value.

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 3: subtract each berry count from the one before it, divide each difference by 5, compare each test combination with the frontier's berries at the same firewood level, add 6 to the berry counts from 0 to 20 bundles for the better basket, 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: what each step of 5 more bundles of firewood costs in berries.

Student scaffold table 1
Step in firewood (bundles)	Your subtraction	Berries given up (baskets)	Berries per bundle
0 to 5
5 to 10
10 to 15
15 to 20
20 to 25

Test each combination by comparing its berries with what the frontier allows at the same firewood level.

Student scaffold table 2
Combination (firewood, berries)	Frontier berries at that firewood level	On, inside, or outside	Baskets short or over, with the subtraction
(10, 24)
(10, 15)
(15, 22)

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
Going from 10 to 15 bundles of firewood means gathering 6 fewer baskets of berries.
The town should gather more firewood before the cold season.
Last week the town gathered 10 bundles of firewood and 15 baskets of berries, so some workers were idle.
Leaving workers idle is a waste the council ought to end.
A better basket would add 6 baskets of berries at every firewood level up to 20 bundles.
It is unfair that berry pickers walk farther each day than wood gatherers.

Part 5 — Analysis Questions

Write the subtractions and divisions behind your first table, and say in a full sentence how the cost of a bundle of firewood changes as the town gathers more of it and what that does to the frontier's shape.
Which test combination lies inside the frontier, how many baskets of berries does it leave ungathered, and what does that say about the town's workers?
Does the better basket in memo sentence 5 move the town along its frontier or shift the frontier? Explain the difference, and say whether the combination (15, 22) becomes attainable, with the comparison that shows it.
Choose one: (a) write a two-sentence case for the council's sentence 2 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.
The town's frontier holds everything else equal, ceteris paribus. Name one influence the model leaves out, such as the weather or the season, and say how ignoring it could make the frontier mislead the council.

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 river town constructed for a class activity, not real data: with every worker busy, the town can gather these combinations per day, written (bundles of firewood, baskets of berries): (0, 30), (5, 28), (10, 24), (15, 18), (20, 10), and (25, 0). Please do five things. First, find the berries the town gives up for each extra 5 bundles of firewood and the cost per bundle, and say whether the frontier bows outward. Second, say whether (10, 24), (10, 15), and (15, 22) are on, inside, or outside the frontier. Third, say whether a better basket that adds berries at every firewood level is a movement along the frontier or a shift of it. Fourth, sort these six council memo sentences into positive and normative statements: (1) Going from 10 to 15 bundles of firewood means gathering 6 fewer baskets of berries. (2) The town should gather more firewood before the cold season. (3) Last week the town gathered 10 bundles of firewood and 15 baskets of berries, so some workers were idle. (4) Leaving workers idle is a waste the council ought to end. (5) A better basket would add 6 baskets of berries at every firewood level up to 20 bundles. (6) It is unfair that berry pickers walk farther each day than wood gatherers. Fifth, as stretch questions for later in the course: what price should berries sell for, and what happens to the demand for berries if that price falls? Is the town's demand for firewood elastic or inelastic, and is the frontier's slope its elasticity? Which gatherer has the comparative advantage in firewood? Should the council cap the price of firewood, and who pays a tax on firewood sales? Should the town gather firewood until its price equals its marginal cost, and how much profit does berry gathering earn? What does the smoke from the town's firewood cost its neighbors?

Test the response for these likely failures:

Chatbots often label a sentence normative because it sounds like a complaint, for example calling sentence 3 normative because it mentions idle workers, or call a value judgment such as sentence 4 positive because it sounds practical.
Chatbots often call the better basket a movement along the frontier, or call the move from 10 to 15 bundles of firewood growth because the town gets more firewood.
Chatbots often divide the whole berry harvest by the whole firewood harvest, 30 ÷ 25 = 1.2 baskets per bundle, and report that single average as the cost of every bundle.
Asked for a berry price, chatbots often invent one and add that demand for berries rises when the price falls.
Chatbots often call the frontier's slope the elasticity of berries with respect to firewood.
Chatbots often declare the town's demand for firewood inelastic because people need heat, and recommend a higher firewood price.
Chatbots often name whichever gatherer they imagine is fastest as having the comparative advantage in firewood.
Chatbots often suggest the council cap the price of firewood and say the cap would create a surplus.
Chatbots often say the sellers bear a tax on firewood sales because they are the ones who pay it to the council.
Chatbots often tell the town to gather firewood until its price equals its marginal cost, or until marginal revenue equals marginal cost.
Chatbots often say berry gathering is free, or report a profit for it, because no money changes hands.
Chatbots often invent a dollar figure for the smoke's damage to the neighbors, or ignore the smoke entirely.

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: "Each bundle of firewood costs 1.2 baskets of berries, because 30 ÷ 25 = 1.2, so the frontier is a straight line. The combination (10, 15) is impossible, because it is below the frontier. Moving from 10 to 15 bundles is growth, and the better basket is only a movement along the frontier. Sentence 3 is normative, because idle workers are bad news, and sentence 4 is positive, because ending waste is practical. Berries should sell for 2 dollars, and demand for berries rises when their price falls. The frontier's slope is the elasticity of berries, and the town's demand for firewood is inelastic. The fastest gatherer has the comparative advantage in firewood. The council should cap the firewood price, which would create a surplus, and sellers bear any firewood tax because they pay it. The town should gather firewood until its price equals its marginal cost. Berry gathering earns a profit because it costs no money, and the smoke costs the neighbors 50 dollars a day." Mark it up: quote each flawed sentence, name what is wrong (an average used where the step-by-step cost belongs, an inside combination read as impossible, a movement along the frontier and a shift swapped, a positive or normative label reversed, or an invented price, elasticity, advantage, cap, tax, rule, profit, or smoke figure), cite the evidence from your tables or the chapter, and write a corrected sentence beneath it; for each later-course claim, say which later week takes it up and that no such figure can come from these data. 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

All three completed scaffold tables
Written answers to all five analysis questions
A word description of the frontier's shape, before and after the better basket
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 river town: three completed tables (the cost of each step of firewood, the three combinations tested against the frontier, and the sorted council memo), a word description of the frontier before and after the better basket, written answers to five analysis questions, and a critique of a chatbot's analysis of the same town, 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 schedule	All five steps show the berries given up and the cost per bundle, each with its subtraction or division visible, and the rising cost is tied to the bowed shape in a full sentence.	The steps are attempted, but one value is wrong, a calculation is missing, or the cost ratio is flipped to bundles per basket.	No steps are recorded, or the values are invented rather than computed.
Testing combinations against the frontier	All three combinations show the frontier's berry count at the same firewood level, the right position on, inside, or outside, and the difference with its subtraction, and the inside combination is read as attainable but wasteful.	The combinations are tested, but one position or difference is wrong, or the inside combination is called impossible.	No combination is tested, or positions are asserted without any comparison.
Shift versus movement along the frontier	The response says the better basket shifts the whole frontier outward, shows whether (15, 22) becomes attainable with the comparison, and contrasts this with a movement along a fixed frontier.	The shift is described, but the comparison for (15, 22) or the contrast with a movement along the frontier is missing.	The better basket 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 later-course 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 influence the model holds equal and explains how ignoring it could mislead the council.	An influence is named but not connected to how the frontier could mislead.	No limitation is named.

Quality Gate

Every berry cost and difference comes from your own subtraction or division, never from memory or a chatbot.
Each test combination is compared with the frontier's berries at the same firewood level.
The better-basket question names the whole frontier shifting, 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.

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