Week 9 — Graph & Model Workshop · "Build the Cost Curves — and Catch the AI's Arithmetic"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 5 — production & cost relationships · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 9
Format: enter a cost schedule into a spreadsheet (Google Sheets or Excel, free), compute the four per-unit cost curves, find the minimums, and then catch the AI's errors in its own cost-table output.

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

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Part 1 — The Big Picture

This week you crossed from the market level (Weeks 1–8) to the firm level. The cost curves you build today — AFC, AVC, ATC, and MC — are the mechanical heart of everything in Weeks 10–12: where a perfectly competitive firm produces, whether a firm shuts down, and how a monopolist chooses its output. Get the curves right now; everything else clicks.

The tools: a spreadsheet (Google Sheets: https://sheets.google.com or Excel on your computer). You will enter a cost schedule and let formulas do the work.

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Part 2 — The Guiding Question

How does a firm's per-unit cost change as it produces more — and why does the marginal cost curve cut through both the AVC and ATC curves at their lowest points?

The scenario. A firm has fixed cost FC = $60. Its variable costs follow this schedule:

Q	VC
1	40
2	70
3	90
4	120
5	160
6	210

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Part 3 — Set Up the Model (in a spreadsheet)

1. Open Google Sheets (https://sheets.google.com) or Excel.
2. Label columns: Q · VC · TC · AFC · AVC · ATC · MC
3. Enter Q = 0 through 6 in column A, and the VC values above (with Q=0 having VC=0) in column B.
4. Enter formulas — for a row where Q > 0 (let's say row 3 = Q=1):
   - TC: =B3+60 (VC + FC)
   - AFC: =60/A3
   - AVC: =B3/A3
   - ATC: =C3/A3 (or =E3+D3, which must give the same result)
   - MC: =C3-C2 (change in TC; for Q=1, TC(1)−TC(0) = TC(1)−60)
5. Fill formulas down through Q=6. Your completed table should match the verified numbers below (check it before moving on).

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Part 4 — Solve (complete this scaffold)

Once your spreadsheet is built, verify it matches the verified cost schedule and fill in the blanks:

Q	VC	TC	AFC	AVC	ATC	MC
0	0	60	—	—	—	—
1	40	100	60	40	100	40
2	70	130	30	35	65	30
3	90	150	20	30	50	20
4	120	180	15	30	45	30
5	160	220	12	32	44	40
6	210	270	10	35	45	50

Using the table, answer these questions. Show the arithmetic.

Question	Your answer
(a) What is TC at Q = 5? (Show: FC + VC = ?)	______
(b) What is ATC at Q = 5? (Show: TC ÷ Q = ?)	______
(c) At what quantity is ATC minimized? What is that minimum ATC?	______
(d) At what quantity is AVC minimized? What is that minimum AVC?	______
(e) At Q = 5: MC = 40 and ATC = 44. Is ATC rising, falling, or at its minimum? Why?	______
(f) At Q = 6: MC = 50 and ATC = 45. Is ATC rising, falling, or at its minimum? Why?	______
(g) Verify: ATC = AVC + AFC at Q = 5. Show the addition.	______

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

In 3–4 sentences, explain in plain English:
- Why does AFC always fall as output increases? (Hint: the numerator and denominator — what stays constant, what grows?)
- Why do AVC and ATC both turn upward at higher output levels? (Hint: think about what happens to MC — and then apply the grade-average logic.)
- In your own words, what does it mean that MC cuts ATC at the ATC minimum? Why doesn't MC cut ATC somewhere else?

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Part 6 — Analysis Questions

1. The AVC minimum is at Q = 3 (AVC = 30) and the ATC minimum is at Q = 5 (ATC = 44). The ATC minimum occurs at a higher Q than the AVC minimum. In one sentence, explain why — what is pulling ATC down even after AVC starts rising?

2. Suppose the firm's fixed cost doubled to FC = $120 (but VC stays the same). Without recomputing the whole table, predict: would the AVC curve change? Would the ATC curve change? Would the ATC minimum move to a different Q? Briefly explain each.

3. Connect it: a city has a fixed cost of $5 million per year for its bus fleet (loan payments, insurance) and a variable cost per bus-route of $200,000/year. Explain which category of cost maps to FC and which to VC — and what the AFC implication is for running more routes.

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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:
   "A firm has FC=60 and VC: Q=1→40, Q=2→70, Q=3→90, Q=4→120, Q=5→160, Q=6→210. Compute TC, AFC, AVC, ATC, and MC for Q=1 through 6. At what Q is ATC minimized? At what Q is AVC minimized?"

2. Audit every claim against your verified table:
   - Did it compute TC = FC + VC (with FC=60 at every row), or did it forget to add FC and just report VC as TC?
   - Did it get ATC minimum at Q = 5 (ATC = 44), or did it misidentify Q = 3 (the AVC minimum) as the ATC minimum?
   - Did it get AVC minimum at Q = 3 (AVC = 30)?
   - Did it compute MC = ΔTC correctly? (Common error: computing MC as AVC or as VC/Q.)
   - Did it recognize that ATC = AVC + AFC at every Q?

3. Write 2–3 sentences naming what the AI got right and at least one specific thing you caught or had to verify. (If it got everything right, describe step-by-step how you confirmed each claim — that verification is the skill.)

The habit all term: the tool drafts, you judge. Cost-table errors are among the most common chatbot mistakes in economics — confusing ATC with AVC, forgetting FC, or identifying the wrong minimum.

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Part 8 — What to Submit

One document (or text entry) with: your Part 4 scaffold (with arithmetic), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your spreadsheet is welcome but optional. Due Sun, Nov 1, 11:59 p.m. (50 points).

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Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified in Python. FC = 60 throughout.

Part 4 scaffold answers:
- (a) TC at Q=5: FC + VC = 60 + 160 = $220. ✓
- (b) ATC at Q=5: 220 ÷ 5 = $44. ✓
- (c) ATC minimized at Q = 5; min ATC = $44. ✓
- (d) AVC minimized at Q = 3 (and ties Q=4); min AVC = $30. ✓
- (e) At Q=5: MC = 40 < ATC = 44 → MC is below ATC → ATC is still falling (the next unit is cheaper than the current average, pulling the average down). ✓
- (f) At Q=6: MC = 50 > ATC = 45 → MC is above ATC → ATC is rising (the next unit is more expensive than the current average, pulling it up). ✓
- (g) AVC + AFC at Q=5 = 32 + 12 = 44 = ATC. ✓

Part 6 analysis:
1. AFC keeps falling (60/5=12, 60/6=10, etc.) and is added to AVC to get ATC. After Q=3, AVC starts rising — but AFC is still falling fast enough to offset it, pulling ATC down through Q=4 (ATC=45→44) until Q=5. After Q=5, the rising AVC dominates the falling AFC, and ATC turns up.
2. Doubling FC to $120 does NOT change AVC (VC stays the same). It DOES change ATC (ATC = AVC + AFC, and AFC doubles). The ATC curve shifts upward everywhere. Whether the minimum Q changes: with the same VC schedule, AVC min is still at Q=3. ATC min will still occur at a higher Q (the exact Q where MC first equals ATC — may be the same Q=5 or could shift by one unit depending on the new numbers). The qualitative answer (ATC min at a higher Q than AVC min) does not change.
3. FC = the $5 million loan/insurance (fixed regardless of routes). VC = the $200,000 per route. AFC = $5M ÷ (number of routes) — it falls as more routes are added, meaning the per-route fixed cost shrinks with more routes, a scale-economy argument for operating more bus lines.

Part 7 — common AI errors to look for: (1) computing ATC = VC/Q (forgetting to add FC before dividing); (2) reporting ATC min at Q=3 (confusing AVC min with ATC min); (3) MC errors (computing MC as TC/Q instead of ΔTC); (4) AVC min identified at the wrong Q.

Quantitative gate verification (Python):
- TC(1..6) = 100,130,150,180,220,270 ✓
- AFC(1..6) = 60,30,20,15,12,10 ✓ (always falls)
- AVC(1..6) = 40,35,30,30,32,35 ✓ (min at Q=3,4 = 30)
- ATC(1..6) = 100,65,50,45,44,45 ✓ (min at Q=5 = 44)
- MC(1..6) = 40,30,20,30,40,50 ✓
- ATC = AVC+AFC: Q=5: 32+12=44 ✓; Q=3: 30+20=50 ✓; all rows verified

Graph-logic check:
- AFC always falls: ✓ (60,30,20,15,12,10 — strictly decreasing)
- AVC U-shaped, min at Q=3/4 (=30): ✓ (MC crosses AVC at the flat bottom — MC(3)=20ATC(6)=45 rising) - MC cuts AVC at AVC min (Q=3–4 transition) and ATC at ATC min (Q=5–6 transition): ✓ - ATC > AVC at every Q (because AFC>0): ✓

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold (Part 4) — 7 questions answered with arithmetic; TC, ATC, mins, MC-vs-ATC comparisons, ATC=AVC+AFC (20)	20	10–16	0–8
Interpretation (Part 5) — AFC always falls (fixed/growing); U-shape (diminishing returns/MC); MC-cuts-at-minimum explained in words (12)	12	6–10	0–5
Analysis (Part 6) — AFC pull-down explanation; doubled-FC prediction; city bus application (10)	10	5–8	0–4
AI-critique (Part 7) — names at least one specific thing checked or caught in the AI's cost-table output (8)	8	4–6	0–3