Week 10 — Graph & Model Workshop · "The Price-Taking Firm: Profit, Loss & the Shutdown Decision"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 6 — perfect competition, P = MC, shutdown rule · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 10
Format: use a spreadsheet (Google Sheets, Excel, LibreOffice, or Numbers — free) and the verified cost schedule to find the profit-maximizing output, compute profit or loss, apply the shutdown rule, and then catch the AI's mistakes.

This is the course's signature weekly component — the economics analog of a lab. This week you apply the P = MC rule and the shutdown decision to a real cost schedule, end-to-end, then verify your answers against a chatbot's attempt.

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Part 1 — The Big Picture

This week's lecture gave you two tools that work together: (1) the P = MC output rule (find the Q where price equals marginal cost on the rising arm of the curve), and (2) the shutdown rule (operate if P ≥ min AVC; shut down if P < min AVC). Today you apply both tools to the same cost schedule you built last week, first with a spreadsheet and then with an AI-critique check.

The tool: a free spreadsheet — Google Sheets (https://sheets.google.com), LibreOffice Calc (https://www.libreoffice.org), or any spreadsheet you already have. No special software needed.

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Part 2 — The Guiding Question

At a given market price, exactly how much should a competitive firm produce — and when should it produce nothing at all?

The cost schedule. A competitive firm has the following data (FC = $60):

Q	VC	TC	AVC	ATC	MC
1	40	100	40.00	100.00	40
2	70	130	35.00	65.00	30
3	90	150	30.00	50.00	20
4	120	180	30.00	45.00	30
5	160	220	32.00	44.00	40
6	210	270	35.00	45.00	50

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

1. Open a blank spreadsheet. Create columns: Q, VC, TC, AVC, ATC, MC (you can copy the table above).
2. Add two more columns: TR (= market price × Q — you'll fill this in for each price scenario) and Profit (= TR − TC).
3. Identify: (a) Min AVC (the lowest value in the AVC column) and the Q at which it occurs; (b) Min ATC and the Q at which it occurs. These are the two critical thresholds for this week.

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Part 4 — Solve (complete this scaffold)

Scenario A — Market price P = $40. Fill in the spreadsheet for each Q.

Question	Your answer
(a) What is the MC value at Q=5? Is it on the falling arm or the rising arm of MC?	______
(b) Profit-maximizing Q (where P = MC on the rising arm)	______
(c) TR at that Q (= P × Q)	______
(d) TC at that Q (from the table)	______
(e) Profit or loss = TR − TC	______
(f) Verify using (P − ATC) × Q	______
(g) Is P ($40) ≥ min AVC ($30)? → Operate or shut down?	______
(h) What is the loss if the firm shuts down instead? (Hint: what costs remain?)	______

Scenario B — Market price P = $50. (Use the same spreadsheet column for TR at P=50.)

Question	Your answer
(i) Profit-maximizing Q (where P = MC on the rising arm)	______
(j) TR, TC, and profit at that Q	______
(k) Operate or shut down? Justify using the shutdown rule.	______

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

In 3–4 sentences, explain why the firm in Scenario A keeps producing even though it is losing money. Use the words "fixed costs," "variable costs," and "operating loss" in your explanation. Then explain what would have to happen to the market price to make the firm want to shut down.

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Part 6 — Analysis Questions

1. The rising-arm trap. In Scenario A, the MC column shows MC = 40 at both Q = 1 (falling arm) and Q = 5 (rising arm). Why is Q = 5 the right answer and not Q = 1? What goes wrong economically if a firm stops at Q = 1?

2. Long-run thinking. At P = $50, the firm earns a profit of $30. In plain English, describe what happens in this industry over the long run — who does what, and where does the price end up? (Hint: use "entry," "supply," and "min ATC.")

3. Connect it to the model benchmark. A classmate says, "The perfectly competitive market is just a textbook fantasy — no real market works like that." Without taking a side on the normative question, give one positive economic reason the model is still analytically useful even if real markets don't match it perfectly.

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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 competitive firm has FC=$60 and this cost schedule: Q=1 MC=40, Q=2 MC=30, Q=3 MC=20, Q=4 MC=30, Q=5 MC=40, Q=6 MC=50. Min AVC=$30 at Q=3. At market price P=$40, what is the profit-maximizing output, and should the firm operate or shut down? Show the profit calculation."
2. Audit every claim against your own work:
   - Did it pick Q=5 (rising arm) or Q=1 (falling-arm trap)?
   - Did it compare P to min AVC ($30) for the shutdown decision, or did it mistakenly compare P to min ATC ($44)?
   - Did it compute profit correctly as TR − TC = $200 − $220 = −$20?
   - Did it interpret the result correctly (operate since loss = $20 < FC = $60)?
3. Write 2–3 sentences naming what the AI got right and at least one error or ambiguity you had to catch or verify. (If it got everything right, explain exactly how you verified each claim — that verification is the skill.)

The habit all term: the tool drafts, you judge. Chatbots commonly pick the falling-arm Q, apply the shutdown rule against ATC instead of AVC, or drop the fixed-cost comparison in the shutdown logic.

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Part 8 — What to Submit

One document (or text entry) with: your Part 3 threshold identification, your Part 4 scaffold (both scenarios, 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 8, 11:59 p.m. (50 points).

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Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently Python-verified (FC=60, VC table as above).

Thresholds (Part 3):
- Min AVC = $30 at Q=3. ✓
- Min ATC = $44 at Q=5. ✓

Scenario A (P=$40):
- (a) MC at Q=5 = 40. It is on the rising arm (MC fell from Q1=40 to Q3=20, then rose back through Q4=30, Q5=40, Q6=50). ✓
- (b) Profit-maximizing Q = 5 (P=MC=40 on the rising arm). NOT Q=1 (falling arm). ✓
- (c) TR = 40 × 5 = $200. ✓
- (d) TC = $220 (from table: VC=160 + FC=60). ✓
- (e) Profit = 200 − 220 = −$20 (a loss of $20). ✓
- (f) Verification: (P − ATC) × Q = (40 − 44) × 5 = −4 × 5 = −20. ✓
- (g) P=$40 ≥ min AVC=$30 → OPERATE. ✓
- (h) If firm shuts down: loss = FC = $60 (all variable costs go away; fixed costs remain). Operating saves $40 vs. shutting down. ✓

Scenario B (P=$50):
- (i) P=MC=50 on the rising arm at Q=6. ✓
- (j) TR = 50 × 6 = $300. TC = $270. Profit = 300 − 270 = +$30. Verify: (50−45)×6 = 5×6 = +30. ✓
- (k) P=$50 > min AVC=$30 → OPERATE. Positive profit — easy call. ✓

Part 5 (interpretation key): The firm loses $20 because its ATC ($44) exceeds the price ($40). But fixed costs ($60) must be paid whether it produces or not. By operating, the firm earns TR=$200, covers all VC=$160, and contributes $40 toward the $60 in fixed costs — leaving a net loss of only $20. Shutting down leaves the full $60 loss. The firm would shut down if price fell below min AVC = $30 — at that point, even variable costs are not fully covered, and every unit produced adds to the loss.

Part 6 answers:
1. At Q=1, MC is on the FALLING arm (MC is heading downward toward the minimum). Producing more (Q=2, 3…) would continue to lower the cost of the next unit while still adding P=$40 in revenue — so profit keeps rising. Q=1 is not the maximum; it's just the first crossing. Q=5 is where MC has turned upward and equals P from below — the true maximum.
2. At P=$50, positive profit attracts new firms (free entry). Industry supply increases (shifts right). Market price falls. This continues until P = min ATC = $44, at which point economic profit = 0 and entry stops.
3. Even if no market is perfectly competitive, the model provides a benchmark for allocative efficiency: economists can compare the actual outcome (higher price, lower quantity) to the competitive ideal and compute the deadweight loss from market power. Without the benchmark, there is no analytical baseline for antitrust or regulatory analysis.

Part 7 common AI errors: (1) picking Q=1 instead of Q=5 (falling-arm trap); (2) checking P against ATC ($44) instead of AVC ($30) for the shutdown rule; (3) computing profit as TR − VC instead of TR − TC; (4) omitting the FC comparison in the operate-vs-shut-down reasoning.

Grading rubric — 50 points

Criterion	Full	Partial	None
Scaffold Part 4, Scenario A — correct Q=5, TR=$200, TC=$220, profit=−$20, (P−ATC)×Q verified, operate decision with AVC comparison (20)	20	10–16	0–8
Scaffold Part 4, Scenario B — correct Q=6, profit=+$30, operate (8)	8	4–6	0–3
Interpretation Part 5 — fixed costs sunk, operating vs. shutdown comparison, shutdown price stated (10)	10	5–8	0–4
Analysis Part 6 — rising-arm logic; long-run entry/supply/price; model as benchmark (4)	4	2–3	0–1
AI-critique Part 7 — specific error caught or each claim verified (8)	8	4–6	0–3

Quality gate (self-checked): quantitative gate — all numbers Python re-verified: A min AVC=30 Q=3, min ATC=44 Q=5; Q=5 at P=40 (rising arm ✓); TR=200, TC=220, profit=−20, (40−44)×5=−20 ✓; Q=6 at P=50; TR=300, TC=270, profit=+30, (50−45)×6=+30 ✓; shutdown loss=FC=60>20 operating loss ✓. Graph-logic check — rising-arm P=MC identified correctly; shutdown comparison P vs min AVC (not ATC) ✓; long-run P=min ATC=44, economic profit=0 ✓.