# F5-conf-01 — Competitive equilibrium of a two-agent, two-good exchange economy

# Scientific question

Two agents A and B trade two goods in a pure exchange economy. Agent i has Cobb–Douglas preferences u_i(x1, x2) = α_i ln x1 + (1 − α_i) ln x2 and an endowment (e1_i, e2_i). Good 2 is the numeraire (p2 = 1). The estimands are the competitive (Walrasian) equilibrium relative price p = p1/p2, the equilibrium allocation (x1_A, x2_A, x1_B, x2_B), the aggregate excess demand for good 1 at the equilibrium price (which must be zero), and the Walras' law residual p·z1 + z2 (value of aggregate excess demand, which must be identically zero). Derive the closed-form equilibrium, verify market clearing and Walras' law numerically, and validate the closed-form price by an independent numerical root-finding of the excess-demand function.

# Inputs

data/endowments.csv — columns agent (A or B), good1, good2: individual endowments in units of each good. One row per agent. These are the primary data of the exercise (theoretical parameters, not observed data).
data/parameters.csv — columns parameter, value, description: the preference parameters alpha_A, alpha_B and the aggregate endowments of each good as recorded in the summary sheet that accompanied the exercise (aggregate_endowment_good1, aggregate_endowment_good2).

# Information-availability rules

Use only the two files under data/.
The numerical validation must solve the market-clearing condition directly (root of the aggregate excess demand of good 1 in p), not evaluate the closed-form expression.
Report in data_issues every problem you detect in the inputs and how you handled it.

# Required outputs

out/results.json with the keys:

key	type	unit	meaning
`task_id`	string	—	"F5-conf-01"
`price_ratio_p1_over_p2`	number	—	closed-form equilibrium relative price p1/p2
`x1_A`, `x2_A`, `x1_B`, `x2_B`	number	units of goods	equilibrium consumption of each good by each agent
`excess_demand_good1`	number	units of good 1	aggregate excess demand for good 1 at the reported price (demand minus aggregate endowment)
`walras_law_residual`	number	units of numeraire	p·z1 + z2 at the reported price, where z_g is the aggregate excess demand for good g
`aggregate_endowment_good1`	number	units of good 1	aggregate endowment of good 1 used in the market-clearing condition
`aggregate_endowment_good2`	number	units of good 2	aggregate endowment of good 2 used in the market-clearing condition
`price_ratio_numerical`	number	—	equilibrium price found by the independent numerical root-finding (the baseline check)
`feasibility`	string	—	"complete", "partial" or "infeasible"
`feasibility_reason`	string or null	—	explanation if not complete
`data_issues`	array of {"issue","handling"}	—	data problems detected and how handled (empty list if none)
`n_input_rows`	object	—	{"endowments.csv": rows read, "parameters.csv": rows read}
`n_analysed`	integer or null	—	number of agents in the equilibrium computation
`random_seed`	integer or null	—	seed used, if any

out/report.md with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. State explicitly the assumptions behind the closed form (interior solution, strictly positive endowments, price normalisation) and the scope of the numerical validation.
out/analysis.py — running ~/wp29/venv/bin/python out/analysis.py from the workspace root must regenerate out/results.json from data/ only, deterministically.
out/claims.json — a list of the central claims of the report: [{"id": "C1", "text": "...", "results_keys": ["..."], "status": "supported"|"unsupported"|"not_evaluated", "caveat": "..."}].

# Constraints

No network access. Python: ~/wp29/venv/bin/python (numpy, pandas, scipy, statsmodels available). Do not modify data/.
This task is designed to be completed in well under 20 minutes of work.

spb/wp29_uqo