1[2 {"id":"C1","text":"Guess-and-verify gives the closed-form policy c(y) = (1 - alpha*beta) y, i.e. 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":"Valid under log utility, Cobb-Douglas technology with unit productivity, full depreciation, interior solution."},3 {"id":"C2","text":"The closed-form value at y = 1 is V(1) = A = -19.5244 utils.","results_keys":["value_closed_y1"],"status":"supported","caveat":"Closed form also verified numerically as a Bellman fixed point at three points (checks.md)."},4 {"id":"C3","text":"VFI on the prescribed 400-point log grid converged in 361 iterations with final sup-norm change below 1e-8.","results_keys":["n_iterations","final_sup_change","grid_points_used"],"status":"supported","caveat":"Starting value V0 = 0."},5 {"id":"C4","text":"The VFI policy matches the closed form to within 0.0064 units of output (at most 0.49% relative) at the three evaluation points.","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","diag_policy_max_rel_error_eval"],"status":"supported","caveat":"Discrepancy is discretisation error of the discrete-choice grid plus linear interpolation; specific to this grid and parameter point."},6 {"id":"C5","text":"The VFI value at y = 1 is -19.5248, within 3.4e-4 utils of the closed form.","results_keys":["value_num_y1","value_closed_y1","diag_value_abs_error_y1"],"status":"supported","caveat":"Interpolated linearly in ln y; y = 1 is not a grid node."},7 {"id":"C6","text":"The Bellman operator (on the bounded discretised problem) is a sup-norm contraction with modulus beta = 0.95, so the stopping-rule error is at most about 1.9e-7 utils, and discretisation dominates the numerical error.","results_keys":["contraction_modulus","diag_vfi_tolerance_error_bound","diag_value_abs_error_y1"],"status":"supported","caveat":"Blackwell conditions on the bounded discretised problem; unbounded log-utility case needs a weighted-norm argument not developed here."},8 {"id":"C7","text":"The grid truncation is not binding: under the closed-form policy next-period output stays in [0.231, 1.213] and the VFI policy never selects a grid edge.","results_keys":["diag_closed_yprime_min","diag_closed_yprime_max","diag_policy_edge_hits"],"status":"supported","caveat":""}9]10