# Contract (P0)

Question: Walrasian equilibrium of a 2-agent, 2-good Cobb-Douglas exchange economy; good 2 numeraire (p2=1). Estimands: equilibrium 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 (identically 0); independent numerical root of z1(p). Assumptions: Cobb-Douglas with 0<alpha_i<1 (interior demands), strictly positive endowments (positive income at any p>0), normalisation p2=1, price-taking agents. Closed form: p = sum_i alpha_i e2_i / sum_i (1-alpha_i) e1_i. Outputs: out/results.json (task_id, price_ratio_p1_over_p2, x1_A, x2_A, x1_B, x2_B, excess_demand_good1, walras_law_residual, aggregate_endowment_good1/2, 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; plus protocol state files. Information rules: only data/ files; numerical validation must root-find z1(p)=0 directly, not evaluate the closed form; report all input problems in data_issues. Invalidity: nonpositive endowments, alpha outside (0,1), missing agent, or inconsistent aggregates used in market clearing (budgets and clearing must use same endowments, otherwise Walras' law fails).