# Contract (P0)

Question. Deterministic optimal growth, log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the closed-form policy/value with value-function iteration (VFI) on a prescribed log-spaced grid.

Estimands. Closed-form c(y) at y=0.5,1,2; VFI policy at the same points (interpolated); max abs gap; closed-form and VFI V(1); closed-form savings rate (y-c)/y; sup-norm contraction modulus of the Bellman operator; plus diagnostics (grid points, iterations, final sup change). Assumptions: log utility, Cobb-Douglas technology, full depreciation, interior solution, 0<alpha<1, 0<beta<1. Contraction via Blackwell's conditions (monotonicity, discounting) on bounded functions -> modulus beta; log utility is unbounded on (0,inf) but bounded on the compact grid [y_min,y_max] with feasible choices bounded away from c=0.

Outputs. out/results.json with keys 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. Also out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json.

Information rules. Use only data/model.csv; prescribed grid & parameters; deviations go in data_issues. Numerical policy must come from VFI, not the closed form; closed form derived by guess-and-verify and stated in report.

Invalidity. Grid not containing optimal choices (truncation binding), VFI not converging, using closed form inside VFI, missing parameters.