Week 1 — Graph & Model Workshop · "Build a PPF, Read the Opportunity Cost"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 1 — economic modeling & quantitative/graphical analysis · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 1
Format: build and read a production possibilities frontier in Desmos (free, no account), complete a short scaffold, interpret the result in words, then catch the AI's mistakes.

This is the course's signature weekly component — the economics analog of a lab. 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.

Part 1 — The Big Picture

This week you learned the field's first model — the production possibilities frontier (PPF) — which shows, on one graph, scarcity, trade-offs, opportunity cost, and efficiency at once. The PPF's slope literally is the opportunity cost. Today you'll build one, drag points around, and read the trade-off straight off the line. (Next week you'll use the same skill to explain why two countries that trade both come out ahead.)

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login).

Part 2 — The Guiding Question

If your time is scarce, exactly how many of one thing must you give up to get one more of another — and what does the graph of that trade-off look like?

The scenario. Sam has 12 hours this week to make two things for a club fundraiser: pizzas (each takes 2 hours) or tutoring sessions (each takes 4 hours). Sam can split the time any way.

Part 3 — Set Up the Model (in Desmos)

1. Open Desmos. The PPF is every combination that uses all 12 hours:
   2·(pizzas) + 4·(tutoring) = 12.
2. Let x = pizzas and y = tutoring sessions. Type into Desmos: 2x + 4y = 12
3. You'll see a straight line. Find where it hits each axis (the intercepts) — those are the "all of one good" points.

Part 4 — Solve (complete this scaffold)

Fill in the blanks from your Desmos graph and a little arithmetic. Show the steps.

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

In 2–3 sentences, explain what the slope of this PPF means in plain English (not just the number), and what a point inside the frontier would mean for Sam's time. (Hint: "inside" = some hours are…?)

Part 6 — Analysis Questions

1. Sam's PPF is a straight line, so the opportunity cost is constant. Real economies' PPFs bow outward. In one sentence, why — what's different about a whole economy's resources?
2. A friend says, "Sam should just make 6 pizzas and 3 tutoring sessions — maximize both!" Use the model to explain why that's unattainable with 12 hours.
3. Connect it: name one real choice in your week that's a trade-off between two uses of a scarce resource (time, money, energy). What's the opportunity cost of leaning one way?

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: "On a PPF where 12 hours make pizzas (2 hrs each) or tutoring sessions (4 hrs each), what is the opportunity cost of one tutoring session, and one pizza? Is the point (6 pizzas, 2 sessions) attainable?"
2. Audit every claim against your own work:
   - Did it get the opportunity cost of 1 tutoring session = 2 pizzas (not ½)? Chatbots routinely flip the ratio or state it in the wrong good.
   - Did it correctly say (6, 2) is unattainable (needs 20 hours), or did it wave it through?
   - Did it keep "inside = inefficient" vs. "outside = unattainable" straight?
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 — catching it is the point.

Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with the arithmetic), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your Desmos line is welcome but optional. Due Sun, Sep 6, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see the Week-1 verified-numbers check). The frontier is 2x + 4y = 12.

• (a) 12 ÷ 2 = 6 pizzas (x-intercept (6, 0)). ✓
• (b) 12 ÷ 4 = 3 tutoring sessions (y-intercept (0, 3)). ✓
• (c) Opportunity cost of 1 tutoring session = 6 pizzas ÷ 3 sessions = 2 pizzas. ✓
• (d) Opportunity cost of 1 pizza = 3 sessions ÷ 6 pizzas = ½ tutoring session. ✓
• (e) 2·2 + 4·1 = 8 < 12 → inside the frontier → inefficient (4 idle hours). ✓
• (f) 2·6 + 4·2 = 20 > 12 → outside → unattainable (would need 20 hours). ✓
• Part 5: the slope's magnitude (2 pizzas per session) is the opportunity cost — each tutoring session costs Sam 2 pizzas; a point inside means some of the 12 hours are idle (wasted), so Sam could make more of both without working more.
• Part 6: (1) a whole economy's resources are specialized (not equally good at both goods), so pushing all-in on one raises its opportunity cost → the curve bows outward. (2) (6, 3) needs 2·6 + 4·3 = 24 hours > 12 → unattainable; scarcity binds. (3) any reasonable personal trade-off with a named opportunity cost earns credit.
• Part 7: full credit for a specific catch — most commonly the AI flipping the ratio (saying ½ a pizza), mislabeling (6, 2) as attainable, or confusing inefficient with unattainable.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — intercepts (6, 3), ratios (2 pizzas; ½ session), point tests (8<12 inside; 20>12 outside) all Python-re-verified ✓. Graph-logic check — interior point = inefficient, exterior = unattainable, slope = opportunity cost: all correct ✓.