Stage 3 — Report the Findings

Objective

Stage 2 produced an answer: 10 / 20 / 30, $42,762. This stage is where the work becomes worth something — explain why that is the answer, in economics, using your own model's evidence, and then compress it into a recommendation somebody can act on.

An optimizer output you can't account for is a coincidence you happen to have committed.

Learn — the four things your model is trying to tell you

Every one of these is visible in your own workbook. None of them can be answered from a textbook, and an answer that reads like a textbook is the tell that the model wasn't consulted.

1. Why tomatoes stop at ~10 beds when they're the money crop

Tomatoes earn $8,800 a bed — four times what carrots do — and the optimizer still plants half the allowed amount. Because revenue per bed is not the decision variable; marginal cost at the margin is. MC hits $8,249 at bed 10 and $9,391 at bed 11, and the price line sits between them. Being the highest-revenue crop earns you nothing at the point where the next unit stops paying for itself. This is P = MC doing the only thing it does.

2. Which constraints bind — and what relaxing one is worth

Carrots and mesclun both stop at their bed caps with marginal cost still below price. That is a different situation entirely: the economics hasn't ended production, a fence has. One more carrot bed would add roughly $352 of profit; one more mesclun bed about $246. Those numbers are shadow prices — what the constraint costs you — and they are directly actionable: they say which ground is worth money to acquire, and how much. Note the slack constraints too: 64 total beds and 4 temp workers never bind, so neither is worth spending a dollar on.

3. The tomato MC dip at ~6 beds

Marginal cost falls, then resumes climbing. Diminishing returns never paused — hours per bed kept rising the whole way. What changed is the price of the marginal hour: the farmer's own 720 field hours ($34.72/hr) run out around there, cheaper temp labor ($17.36/hr) takes over, and for a few beds that wage drop outweighs the extra hours. Then diminishing returns win again and MC climbs through the price line.

The general lesson is worth more than the example: marginal cost reflects input prices as much as physical returns. Any real cost curve with a step change in an input price will do this. An analysis that ignores the dip has ignored the most interesting thing in the model.

4. Why grow crops that lose money on their own

Run any single crop by itself and it loses money at every quantity — the $20,000 of fixed cost swamps it. Yet the optimum plants all 20 carrot beds and all 30 mesclun. The resolution is MC vs AVC: fixed costs are paid whether or not you plant, so they have no business in the planting decision. Price exceeds average variable cost everywhere, so every bed contributes something toward the fixed costs the farm owes anyway. Standalone crops "lose money" only because each is being asked to carry the whole $20,000 alone. This is the short-run shutdown rule wearing farm clothes, and it is the single most transferable idea in the engagement — it is the same reasoning that keeps an airline flying a half-empty route.

Do — write the analysis

One to two pages in analysis/perfect-competition-analysis.md, plus at least two figures exported or screenshotted from your workbook into analysis/figures/. MC-vs-price charts are the obvious pair. Every figure has to be referenced in the text — a chart nobody points at is decoration, and decoration earns nothing.

Cover all four questions above, and cite your cells. "MC rises due to diminishing returns" is a lecture note. "Carrot MC reaches $1,742 at bed 20, still $352 under price — the cap binds" is analysis. The difference is visible from across the room.

Close with one honest paragraph against your Stage 1 hypothesis: what you predicted, what the model found, and what your prior got wrong. Being wrong and precise about why is exactly what this paragraph is for; being vague about having been right defeats it.

Do — write the memo

The memo template — recommendation, why, the judgment call, what would change your answer — is on Deliverable templates.

Half a page in docs/decisions/perfect-competition-memo.md, written to whoever has to sign off on the plan — a partner, a lender, or you next February. Briefs ask; memos answer. You wrote the question in Stage 1; this is where you close it.

If the memo takes more than twenty minutes, the analysis hasn't finished its job. A memo that is hard to write is a diagnosis, not a writing problem.

Do — update the prompt log

Add a dated section for this engagement to the prompt-log.md at your repo root — it accretes across every engagement rather than starting fresh each time. Log the sessions that mattered: where AI explained something that finally landed, where it caught an error, where it introduced one. Per session: date, tool, what you asked, what you got, what you did with it. A curated record, not a transcript dump.

Then a reflection of 300 words or fewer. Where AI helped, where it was wrong, and — the part that matters most — how you verified. "It seemed right" is not verification. "I checked its MC formula against the labor function at q = 1 and it had dropped the exponent" is. If nothing it told you turned out wrong, document the checks that convinced you of that; "the AI was flawless" with no evidence of checking reads as "I didn't look."

After any session where you helped with graded work, append an entry to
prompt-log.md: the date, the tool, what I asked for, and what you
produced. Facts only. Never write the reflection, never fill in what you
got wrong, and never assess how I verified your output — those are mine.

AI boundary for this stage: asking AI to critique your draft explanation of the MC dip is in bounds and worth logging. Pasting the case in and asking for an analysis is out of bounds — and it is obvious, because AI-written analysis explains the textbook rather than your workbook's numbers.

Deliverable

• P = MC evidence shown per crop, from your model's own numbers
• Binding caps identified, with shadow-price reasoning (~$352 carrots, ~$246 mesclun)
• Slack constraints named — 64 beds and 4 temp workers
• The tomato MC dip explained by mechanism, not merely observed
• The "grow at a loss?" paradox resolved with MC vs AVC
• At least two figures in analysis/figures/, each referenced in the text
• Figures render on the GitHub page, not just in your editor
• Honest paragraph comparing the result against your Stage 1 hypothesis
• Memo written: the plan, the judgment call, and what would change your answer
• Prompt log updated with curated sessions + a reflection of ≤300 words
• Reflection names something concrete you verified, and how
• Skill README.md "exercised in:" line updated
• At least two descriptive commits for this stage

Check yourself