# Contract (P0)

Question. Find the Walrasian equilibrium of a 2-agent, 2-good pure exchange economy with Cobb–Douglas preferences u_i = α_i ln x1 + (1-α_i) ln x2, endowments (e1_i, e2_i), numeraire p2 = 1.

Estimands. p = p1/p2 (closed form); allocation x1_A, x2_A, x1_B, x2_B; aggregate excess demand of good 1 at p (should be 0); Walras residual p·z1 + z2 (should be 0 identically); numerical p from root-finding z1(p)=0 (not evaluating the closed form). Assumptions: α_i in (0,1), strictly positive endowments/wealth → interior demands x1_i = α_i w_i / p, x2_i = (1-α_i) w_i, w_i = p e1_i + e2_i; p2 = 1 normalisation; z1 is strictly decreasing in p so the root is unique.

Outputs. out/results.json with keys task_id, price_ratio_p1_over_p2, x1_A, x2_A, x1_B, x2_B, excess_demand_good1, walras_law_residual, aggregate_endowment_good1, aggregate_endowment_good2, price_ratio_numerical, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed; out/report.md (6 sections); out/analysis.py; out/claims.json.

Information rules. Only data/endowments.csv and data/parameters.csv; numerical check must be a root-finder on z1(p); every input problem must be listed in data_issues with handling.

Invalidity. α outside (0,1), non-positive endowments (corner solutions), inconsistent aggregate endowments that make market clearing infeasible, missing agents.