# Contract (P0)

Question. Deterministic optimal growth, log utility, y' = (y-c)^alpha (Cobb–Douglas, full depreciation, TFP=1). Compare the closed-form optimal consumption policy and value function with those produced by value-function iteration (VFI) on a prescribed log-spaced grid. Estimands. Closed-form c(y) at y=0.5,1,2; VFI c(y) at the same points (interpolated if off-grid); max abs policy discrepancy over the 3 points; closed-form and VFI V(1); closed-form savings rate (y-c)/y; sup-norm contraction modulus of the Bellman operator. Meaningful under: log utility, Cobb-Douglas, full depreciation, interior solution, 0<alpha<1, 0<beta<1. Outputs. out/results.json (keys per TASK.md table: task_id, c_closed_y05/y1/y2, c_num_y05/y1/y2, max_abs_error_policy, value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations, final_sup_change, 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 files. Information rules. Use only data/model.csv; prescribed grid and parameters; deviations recorded in data_issues; numerical policy from VFI only; closed form derived and stated. Invalidity. Missing parameters; grid that cannot contain the optimal choices (bound binding); VFI not converging; using closed form to produce the numerical policy.