Task card — F5-dev-01
- Family / split: F5 Theory, mechanisms and numerical validation / development
- Question: closed-form Marshallian demands, indirect utility and budget identity of a two-good Cobb–Douglas consumer at given prices and income, validated by an independent numerical maximisation on the budget line.
- Data type: synthetic (theoretical parameters:
data/parameters.csv, 4 rows; no randomness). - Scope / prerequisites: constrained optimisation (Lagrangian), Cobb–Douglas demand, a bounded scalar optimiser or grid search.
- Allowed information:
data/parameters.csvonly; the numerical validation must not use the closed form. - Expected artifacts: results.json (8 task keys + 7 common keys), report.md (6 sections, assumptions and scope of the closed form stated explicitly), analysis.py (closed form + numerical check), claims.json.
- Rubric summary: required criteria — demands within 1e-3; indirect utility within 1e-4; budget residual within 1e-6 of zero; MRS = price ratio; numerical maximum within 1e-4 of the analytical indirect utility; assumptions stated in the report (deterministic regex). Critical checks — input row count (fabrication); budget residual and indirect utility recomputed from the reported demands (fabrication); feasibility must be "complete" (false completion). Baseline =
indirect_utility_numerical. - Oracle provenance: analytical (derivation in
~/wp29-oracles/F5-dev-01/REFERENCE.md, checked by a 2-million-point grid search in generator.py); designer = WP29 F5 authoring agent, no human check. - Difficulty rationale: easy; pilot task establishing the F5 contract (closed form + numerical validation + explicit assumptions).
- Budget class: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).
- Anticipated failure modes: swapping α and 1−α; forgetting a price in a demand; asserting a zero residual without computing it; omitting the numerical check; omitting the assumptions paragraph.
- Contamination risk: low (textbook problem; nothing to recall beyond the method).