1[2 {"id":"C1","text":"The closed-form optimal policy is c(y) = (1 - alpha*beta) y, giving c = 0.329, 0.658, 1.316 at y = 0.5, 1, 2 and a 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 technology, full depreciation, interior solution."},3 {"id":"C2","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","feasibility"],"status":"supported","caveat":"Starting value V0 = 0; iteration count depends on starting value."},4 {"id":"C3","text":"The VFI policy matches the closed form to within 0.0064 units of output at the three evaluation points (max at y = 2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy"],"status":"supported","caveat":"Error is driven by restricting next-period output to grid nodes and by interpolation in ln y; single grid and parameter point."},5 {"id":"C4","text":"The numerical value at y = 1 (-19.52476) agrees with the closed-form value (-19.52441) to about 3.4e-4 utils.","results_keys":["value_closed_y1","value_num_y1"],"status":"supported","caveat":"Value function interpolated linearly in ln y."},6 {"id":"C5","text":"The Bellman operator on the compact grid is a sup-norm contraction with modulus beta = 0.95 (Blackwell conditions).","results_keys":["contraction_modulus"],"status":"supported","caveat":"On the unbounded state space log utility is unbounded; a weighted-norm argument is needed there."}7]8