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 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 reproduces the closed-form policy at the three evaluation points with maximum absolute error 0.0064 (largest at y=2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Discretisation error from the discrete choice grid; not monotone in grid size; valid only for this grid and parameter point."},4 {"id":"C3","text":"The VFI value at y=1 (-19.524756) matches the closed-form V(1) (-19.524412) to about 3.4e-4 utils.","results_keys":["value_num_y1","value_closed_y1"],"status":"supported","caveat":"V_num interpolated linearly in ln y; the closed form is exactly linear in ln y."},5 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta = 0.95; VFI converged in 361 iterations with final sup change below the 1e-8 tolerance.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"Blackwell argument applied to the bounded discretised problem; log utility is unbounded on the continuous domain."}6]7