1[2{"id":"C1","text":"The closed-form policy is c(y)=(1-alpha*beta)y, giving 0.329, 0.658, 1.316 at y=0.5,1,2, with a savings rate of alpha*beta=0.342.","results_keys":["c_closed_y05","c_closed_y1","c_closed_y2","savings_rate_closed_form"],"status":"supported","caveat":"Requires log utility, Cobb-Douglas technology, full depreciation and an interior solution."},3{"id":"C2","text":"Discrete-choice VFI on the prescribed 400-point log grid reproduces the closed-form policy at the three evaluation points within 0.0064 (about 0.5% of consumption).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Error is mostly discretisation plus log-linear interpolation; it holds for this grid and parameter point only."},4{"id":"C3","text":"The VFI value at y=1 matches the closed-form V(1)=-19.5244 to within about 3.4e-4 utils.","results_keys":["value_closed_y1","value_num_y1","diag_value_error_y1"],"status":"supported","caveat":"Interpolated in ln y; y=1 is not a grid node."},5{"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95, and VFI met the 1e-8 stopping rule in 361 iterations, so the iteration error is bounded by about 1.9e-7 utils.","results_keys":["contraction_modulus","n_iterations","final_sup_change","diag_vfi_error_bound_beta_over_1mbeta_times_final_change"],"status":"supported","caveat":"The contraction argument uses bounded utility on the compact grid; on the full domain, log utility needs a weighted norm."},6{"id":"C5","text":"Discretisation, not iteration, dominates the numerical error: the maximum policy error over all grid nodes is 0.025 and grows with y.","results_keys":["diag_max_abs_policy_error_on_grid","diag_grid_log_step","final_sup_change"],"status":"supported","caveat":"The claim that the error grows with y comes from the step-function structure; only the maximum is stored in the results."}7]8