1[2{"id":"C1","text":"The closed-form policy is c(y)=(1-alpha*beta)y, giving c=0.329, 0.658, 1.316 at y=0.5,1,2 and savings rate 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, full depreciation, interior solution; verified by zero Bellman residual."},3{"id":"C2","text":"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points with max absolute error 0.0064 (at y=2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Discrete-choice discretisation error; single grid and parameter point."},4{"id":"C3","text":"VFI value at y=1 (-19.52476) matches closed-form V(1) (-19.52441) to about 3.4e-4.","results_keys":["value_num_y1","value_closed_y1","diag_closed_form_A"],"status":"supported","caveat":"Gap is discretisation error, far above the iteration error bound."},5{"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95; VFI met the 1e-8 stopping rule after 361 iterations.","results_keys":["contraction_modulus","n_iterations","final_sup_change","diag_vfi_error_bound_tol"],"status":"supported","caveat":"Blackwell argument applies to bounded returns on the compact grid, not to unbounded log utility on (0,inf)."},6{"id":"C5","text":"The grid bounds do not truncate the optimal policy and the numerical error is dominated by grid discretisation, not iteration.","results_keys":["diag_policy_hits_grid_boundary","diag_policy_index_range","diag_max_abs_value_error_grid","diag_vfi_error_bound_tol","diag_log_grid_step"],"status":"supported","caveat":"Grid-refinement study not performed."}7]8